Patent Publication Number: US-6668230-B2

Title: Computer readable medium for performing sensor array based materials characterization

Description:
This application is a continuation of application Ser. No. 09/458,398 filed Dec. 10, 1999 now U.S. Pat. No. 6,535,824 which is a continuation-in-part of the following applications: application Ser. No. 09/210,086 filed on Dec. 11, 1998, which issued Aug. 20, 2002 as U.S. Pat. No. 6,438,497; application Ser. No. 09/210,428 filed on Dec. 11, 1998, which issued Nov. 5, 2002 as U.S. Pat. No. 6,477,479; and application Ser. No. 09/210,485 filed on Dec. 11, 1998; and the present application claims the benefit of the filing date of all these applications. 
     RELATED CASES 
     The present application is a continuation-in-part of co-pending U.S. patent application Ser. Nos. 09/210,086; 09/210,428 and 09/210,485, all filed on Dec. 11, 1998, and are incorporated herein by reference. The present application is also related to a PCT application (Ser. No. PCT/US99/3008) having the same title and filed concurrently herewith on Dec. 10, 1999. 
    
    
     TECHNICAL FIELD 
     The present invention is directed to a computer controlled apparatus for characterizing a plurality of organic or inorganic materials, and more particularly to a characterization apparatus that uses an electrically-driven sensor array to characterize a plurality of materials simultaneously and rapidly. 
     BACKGROUND 
     Companies are turning to combinatorial materials science techniques for developing new compounds or materials (including formulations, materials having different processing histories, or mixtures of compounds) having novel physical and chemical properties. Combinatorial materials science refers generally to methods and apparatuses for creating a collection of chemically diverse compounds or materials and to methods and apparatuses for rapidly testing or screening such compounds or materials for desired performance characteristics and/or properties. The collections of chemical compounds or materials are commonly called “libraries”. See U.S. Pat. No. 5,776,359, herein incorporated by reference, for a general discussion of combinatorial methodologies. 
     A virtually infinite number of useful materials or compounds can be prepared by combining different elements of the Periodic Table of Elements in varying ratios, by creating compounds with different arrangements of elements, and by creating materials comprising mixtures of compounds or formulations with differing processing histories. Discovery of useful materials for a particular application may require preparation or characterization of many candidate materials or compounds. Preparing and screening a large number of candidates increases the probability of useful discoveries. Thus, any system that can analyze and characterize the properties of combinatorially prepared library members quickly and accurately is highly desirable. 
     Many conventional measurement systems comprise a distinct specialized machine for characterizing a particular material property, so that testing of a candidate material can use many machines and can be cumbersome and time-consuming. Also, most known materials characterization devices measure only one material sample at a time, severely limiting the number of samples that can be characterized per unit time. 
     Optical screening methods and devices have been preferred for many combinatorial chemistry and combinatorial materials science applications because they are non-contact and non-destructive. See for example WO 98/15805, incorporated herein by reference. For example, luminescence may be screened optically. When monitoring chemical reactions, for example, thermal imaging with an infrared camera can detect heat released during relatively fast exothermic reactions. See WO 98/15813, incorporated herein by reference. Although optical methods are particularly useful for characterizing materials or properties in certain circumstances, many materials characterization techniques are difficult or impossible to perform using optical methods. Therefore, there is still a need for a more direct materials characterization method that involves more intimate contact between the material samples and the sensing apparatus. 
     Conventional sensors that generate electrical data corresponding to material properties are typically designed as individual, discrete units, each sensor having its own packaging and wiring connections. Many materials characterization sensors are designed to be used individually in or with a machine that characterizes one sample at a time. Linking a plurality of these individual sensors in an array format, assuming that it is physically possible, would be expensive and often creates overly complicated wiring schemes with minimal gains in operating efficiency for the overall sensing system. 
     One structure using multiple material samples is a microfabricated array containing “microhotplates”. The microhotplates act as miniature heating plates for supporting and selectively heating material samples placed thereon. U.S. Pat. No. 5,356,756 to Cavicchi et al and U.S. Pat. No. 5,345,213 to Semancik et al. as well the article entitled “Kinetically Controlled Chemical Sensing Using Micromachined Structures,” by Semancik and Cavicchi, ( Accounts of Chemical Research,  Vol. 31, No. 5, 1998), all illustrate the microhotplate concept and are incorporated herein by reference. Although arrays containing microhotplates are known, they have been used primarily to create varied processing conditions for preparing materials. A need still exists for an array-based sensor system that can actually characterize material properties. 
     It is therefore an object of the invention to provide a materials characterization system that can measure properties of many material samples quickly, and in some embodiments simultaneously. 
     It is also an object of the invention to construct a materials characterization system having a modular structure that can be connected to a flexible electronic platform to allow many different material properties to be measured with minimal modification of the apparatus. 
     SUMMARY OF THE INVENTION 
     This invention provides an apparatus (or system) and method for testing materials in an array format using sensors that contact the materials being tested. Accordingly, the present invention is directed to an electronically-driven sensor array system for rapid characterization of multiple materials. A plurality of sensors are disposed on a substrate to form a sensor array. Properties that can be measured include thermal, electrical and mechanical properties of samples. Regardless of the property being measured or the specific apparatus, the materials characterization system of the invention includes multiple sensors carrying multiple samples, means for routing signals to and from the sensors, electronic test circuitry, and a computer or processor to receive and interpret data from the sensors. In a preferred embodiment, a modular system is constructed including a single sensor array format, and signal routing equipment compatible with this format which can be used with multiple sensor types and multiple electronic test equipment types, permitting maximum flexibility of the system while preserving the general advantages of sensor array-based characterization. Alternatively, some or all of the different parts of the system may be integrated together into a single physical component of the system. 
     The sensors can be operated in serial or parallel fashion. A wide range of electronically driven sensors may be employed, which those of skill in the art will appreciate provide the opportunity to design an apparatus or method for specific applications or property measurements. The environment in which the measurement is made by the sensor can be controlled. 
     This invention allows for rapid screening of combinatorial libraries or large numbers of samples prepared by other means. This invention allows for property measurements that cannot be done optically. However, optical measurements may be made in conjunction with the sensor based electronic measurements of this invention. One potentially important feature is the speed of the property measurements made with this invention. Two independent reasons for this speed are that one can measure samples in parallel or with smaller sample sizes than with conventional measurement techniques. Moreover, automated sample handling, array preparation and/or sensor operation allows for a completely automated rapid property measurement system in accord with this invention. 
     The materials characterization system of the present invention computer controlled. The control program includes a series of program instructions that implement and execute data gathering from the sensors, processing the data and making control decisions based on the data, supplying test equipment operational control instructions, performing signal processing operations on signals (data) gathered from the sensors, and calculating an arithmetic value for selected material properties based on the gathered and processed data from the sensors. 
     Further preferred embodiments are defined by the dependent claims 2 to 46. 
     Preferably, a microthin film membrane forming said sensors is a silicon nitride membrane, and said substrate supporting said silicon nitride membranes in said sensor array is a silicon wafer. 
     Preferably, at least one sensor in said sensor array comprises: a microthin film membrane supported by said substrate such that said sensor array is an array of microthin film windows; a first wire disposed on said microthin film membrane, said first wire acting as a heater and a first thermometer; and a second wire spaced apart from said first wire and disposed on said substrate, said second wire acting as a second thermometer. 
     Preferably, said microthin film membrane forming said sensors is a silicon nitride membrane, and said substrate supporting said silicon nitride membranes in said sensor array is a silicon wafer. 
     Preferably, said substrate is made of a polymer sheet, and said sensor array includes a plurality of heater/thermometers disposed on said polymer sheet. 
     Preferably, said polymer sheet is a polyimide. 
     Preferably, said heater/thermometer is printed on said polymer sheet via lithography. 
     Preferably, said substrate is made of a poor thermal conducting material that is at least 100 microns thick, and wherein said sensor array includes a plurality of heater/thermometers disposed on said material. 
     Preferably, said heater/thermometer is printed on a glass plate via lithography. 
     Preferably, said sensor array includes a plurality of thermometers disposed on a top surface of said substrate, and said substrate includes a large area heater disposed on a bottom surface of said substrate. 
     Preferably, said substrate is made of a polymer sheet. 
     Preferably, said substrate is made from a material having poor thermal conductivity and is placed on a heater block, and wherein said sensor array includes a plurality of temperature sensors disposed on the substrate such that a temperature difference between a first portion and a second portion of the substrate can be determined. 
     Preferably, said substrate is a glass plate. 
     Preferably, at least one sensor in said sensor array comprises: a sample support with a thermal measurement pattern disposed thereon; a gap between said sample support and said substrate for thermally isolating said sample support from said substrate; and a plurality of bridges connecting said sample support to said substrate over said gap. 
     Preferably, said leads are deposited on said substrate, and wherein said material samples in said materials library are deposited on top of said leads. 
     Preferably, said material samples in the materials library are deposited on said substrate, and said leads are deposited on top of said samples. 
     Preferably, a generating means comprises a magnet that generates a magnetic field over the entire sensor array. 
     Preferably, said generating means comprises a magnet array having a plurality of magnets arranged in the same format as said sensors in said sensor array, wherein each magnet in said magnet array corresponds with a sensor in said sensor array to generate a magnetic field over the corresponding sensor. 
     Preferably, said sensors in said sensor array further measure temperature, and said apparatus further comprises a plurality of temperature controlled elements to impose a temperature gradient across at least one sample in said sensor array. 
     Preferably, at least one sensor in said sensor array comprises interdigitated electrodes disposed on said substrate. 
     Preferably, at least one sensor in said sensor array comprises: a mechanical resonator formed on said substrate; and a piezoelectric material deposited on top of said sensor to form an acoustic wave sensing electrode. 
     Preferably, said acoustic wave sensing electrode is operable in at least one of a surface acoustic wave resonance mode, a thickness shear mode, and a flexural plate wave resonance mode. 
     Preferably, said acoustic wave sensing electrode acts as both a mechanical resonator and a materials characterization device. 
     Preferably, at least one sensor in said sensor array comprises interdigitated electrodes disposed on said substrate. 
     Preferably, at least one sensor in said sensor array comprises: a mechanical resonator formed on said substrate; and a piezoelectric material deposited on top of said sensor to form an acoustic wave sensing electrode. 
     Preferably, said acoustic wave sensing electrode is operable in at least one of a surface acoustic wave resonance mode, a thickness shear mode, and a flexural plate wave resonance mode. 
     Preferably, said acoustic wave sensing electrode acts as both a mechanical resonator and a materials characterization device. 
     Preferably, the cantilever sensor is attached to a piezoresistor such that a deflection amount of said cantilever sensor is detected by a change in a resistance value of the piezoresistor. 
     Preferably said sensors in said sensor array are arranged in a format compatible with combinatorial chemistry instrumentation. 
     Preferably, said sensor array is an 8×8 array with a 0.25 mm pitch. 
     Preferably, said sensor array is an 8×12 array with a 9 mm pitch. 
     Preferably, said sensor array is a 16×24 array. 
     Preferably, said sensors in said sensor array are disposed on said substrate in a planar arrangement. 
     Preferably, said sensors in said sensor array are attached to said substrate via a plurality of sensor plates disposed in an array format and extending generally perpendicularly from said substrate. 
     Preferably, said plurality of sensors in said sensor array are arranged in a geometric shape. 
     Preferably, said geometric shape is a closed shape having straight sides. 
     Preferably, said geometric shape is a closed shape having curved sides. 
     Preferably, said geometric shape is a closed shape having both straight and curved sides. 
     Preferably, said geometric shape is an open shape having straight sides. 
     Preferably, said geometric shape is an open shape having curved sides. 
     Preferably, said geometric shape is an open shape having both straight and curved sides. 
     Preferably, said sensor array contains at least 48 sensors. 
     Preferably, said sensor array contains at least 96 sensors. 
     Preferably, said sensor array contains at least 128 sensors. 
     Preferably, said sensor array contains between 5 and 400 sensors. 
     Preferably, said circuit board in said standardized interconnection device and said sensor array are coupled together via a connector, said connector being one selected from the group consisting of conducting elastomeric connectors, conducting adhesives, cantilever probes, stick probes, wafer-to-board bonding, solder bump bonding, wire bonding, spring loaded contacts, soldering, and direct pressure connection between contact pads. 
     Preferably, said circuit board and said sensor array are coupled through one selected from the group consisting conducting elastomeric connectors, conducting adhesives, cantilever probes, stick probes, wafer-to-board bonding, solder bump bonding, wire bonding, spring loaded contacts, soldering, and direct pressure connection between contact pads. 
     Preferably, said link is a multi-wire cable. 
     Preferably, said link is a wireless connection. 
     Preferably, said interconnection device comprises a signal routing means for selectively coupling a sensor or a group of sensors in said sensor array to said electronic platform such that said electronic platform sends signals to and receives signals from said sensor array via said signal routing means. 
     Preferably, said link is a multi-wire cable. 
     Preferably, said link is a wireless connection. 
     Preferably, said interconnection device comprises a signal routing means for selectively coupling a sensor or a group of sensors in said sensor array to said electronic platform such that said electronic platform sends signals to and receives signals from said sensor array via said signal routing means. 
     Preferably, the computer is managed by software that controls data collection, data viewing, and user interface. 
     Preferably, said signal routing means selects a group of two or more sensors at a time for simultaneous analysis, and the apparatus further comprises two or more electronic channels connecting each of said group of sensors to said electronic test circuitry, the number of electronic channels being equal to the number of sensors in said group by said signal routing means. 
     Preferably, said automated material dispensing device are arranged in a format compatible with combinatorial chemistry instrumentation. 
     Preferably, said automated material deposition device employs a method selected from the group consisting of sputtering, electron beam evaporation, thermal evaporation, laser ablation and chemical vapor deposition. 
     Regarding the method of the present invention, further preferred embodiments are defined in the dependent claims 48 to 69. 
     Preferably the depositing step includes placing at least one material on each sensor by vapor deposition to create the samples. 
     Preferably, the vapor deposition method is a combinatorial vapor deposition method that deposits two or more materials in varying proportions on different sensors in the sensor array. 
     Preferably, the depositing step further includes the step of heating the samples on the sensor array after they are placed on the sensors by vapor deposition. 
     Preferably, the environment that is changed is at least one selected from the group consisting of humidity, temperature, pressure, illumination, irradiation, magnetic field and atmospheric composition. 
     Preferably, the input signal transmitted in the transmitting step is a combination of a linear ramp signal and a modulated AC signal superimposed on the linear ramp signal, and wherein the monitoring step monitors a modulation amplitude in the output signal and an average value of the output signal. 
     Preferably, at least one sensor in the sensor array has a heater portion and a thermometer portion, the combined linear ramp signal and modulated AC signal is transmitted through the heater portion, a DC signal is transmitted through the thermometer portion, and wherein the modulation amplitude in the output signal corresponds with a heat capacity of the sample and the average value of the output signal corresponds with an average temperature of the sample. 
     Preferably, the transmitting step transmits a linear ramp signal and an AC sinusoidal signal, and wherein the monitoring step monitors an output signal. 
     Preferably, at least one sensor in the sensor array has a heater portion and a thermometer portion, the linear ramp signal is transmitted through the heater portion and the AC signal is transmitted through the thermometer portion. 
     Preferably, a first frequency component of the output signal corresponds with the average temperature of the sample and wherein a second frequency component of the output signal corresponds with the heat capacity of the sample. 
     Preferably, the loss of mass in the sample is due to at least one selected from the group consisting of decomposition, burning, and outgassing of reaction products. 
     Preferably, the measuring step measures a difference between the sample on the top surface of the substrate and a bottom surface of the substrate, wherein the temperature difference corresponds to the heat capacity of the sample. 
     Preferably, the heating step comprises the step of increasing the temperature applied to the bottom surface of the substrate at a measured rate, and wherein the measuring step comprises the step of comparing the rate at which the sample temperature increases and the measured rate at the bottom surface of the substrate. 
     Preferably, the measuring step measures a difference between the first portion of the substrate and a second portion of the substrate, wherein the temperature difference corresponds to the heat capacity of the sample. 
     Preferably, the heating step comprises the step of increasing the temperature applied to the first portion of the substrate at a measured rate, and wherein the measuring step comprises the step of comparing the rate at which the sample temperature increases and the measured rate at the first portion of the substrate. 
     Preferably, the method further comprises the step of measuring a temperature of the sample. 
     Preferably, the temperature and the complex impedance of the sensor are measured simultaneously. 
     Preferably, at least one sensor in the sensor array is a mechanical resonator, wherein the depositing step includes depositing a sample material on the mechanical resonator and wherein measuring step includes the step of transmitting an input signal to said at least one sensor to operate the sensor in a resonance mode, and wherein the monitoring step includes the step of measuring a resonator response. 
     Preferably, at least one sensor in the sensor array is a mechanical resonator, wherein the depositing step includes depositing a sample material on the mechanical resonator, and wherein the measuring step includes the steps of: placing the sensor array in a magnetic field; and 
     generating a resonance signal in the mechanical resonator; measuring an amount of damping in the resonance signal, wherein the damping amount corresponds with the sample material&#39;s response to the magnetic field. 
     Preferably, at least one sensor in the sensor array is a mechanical actuator, wherein the depositing step includes depositing a sample material on the mechanical actuator and wherein the monitoring step includes the step of measuring an actuator response. 
     Preferably, at least one sensor in the sensor array is a mechanical actuator, wherein the depositing step includes depositing a sample material on the mechanical actuator, and wherein the measuring step includes the steps of: placing the sensor array in a magnetic field; measuring an amount of displacement in the mechanical actuator, wherein the displacement amount corresponds with the sample material&#39;s response to the magnetic field. 
     Preferably, the measuring step includes the steps of: passing current through at least one sample; and measuring a voltage across the sample to obtain the resistance of the sample. 
     Preferably, the measuring step includes the steps of: placing the sensor array in a magnetic field; passing current through at least one sample; and measuring one or more voltages across the sample to obtain either a Hall resistance, a magnetoresistance of the sample or both. 
     Preferably, the measuring step includes the steps of: heating or cooling one portion of at least one sample; measuring a first temperature at the first portion of the sample and a second temperature at a second portion of the sample; and calculating a temperature difference between the first temperature and the second temperature, wherein the temperature difference corresponds with a thermal conductivity of the sample. 
     Preferably, the heating step includes placing a heater or cooler at one portion of the sensor array such that the sensor array has a heated or cooled portion and a non-heated or non-cooled portion. 
     Preferably, the heating or cooling step includes placing a heater or cooler at each sensor such that each sensor has a heated or cooled portion and a non-heated or non-cooled portion. 
     Preferably, the method further comprises the step of placing the sensor array in a vacuum. 
     Preferably, the method further comprises heating or cooling one portion of at least one sample; 
     determining a first temperature at the first portion of the sample and a second temperature at a second portion of the sample; and measuring a voltage difference across the sample, wherein the voltage difference and the temperature difference corresponds with a thermopower of the sample. 
     Preferably, at least one sensor in the sensor array is a Hall effect sensor, and wherein the measuring step comprises the steps of: placing the sensor array in a magnetic field; 
     measuring a response of at least one Hall effect sensor; and comparing the response of said at least one Hall effect sensor containing a sample with a reference Hall effect sensor that does not contain a sample deposited thereon. 
     Preferably, at least one sensor in the sensor array is a cantilever sensor, and wherein the measuring step comprises the steps of: placing the sensor array in a magnetic field; and measuring an electrical signal corresponding to said at least one cantilever sensor, wherein the electrical signal corresponds to a deflection amount of the cantilever sensor and the magnetic property of the sample material disposed on the cantilever sensor. 
     Preferably, the transmitted signal comprises a step or pulse and the measurement step comprises monitoring the temperature change of the sample in response to the stepper pulse, and determining a thermal time constant. 
     Preferably, a single wire acts as both the thermometer and heater. 
     Preferably, the transmitting step transmits a linear ramp signal and an AC sinusoidal signal, and wherein the monitoring step monitors an output signal. 
     Preferably, a first frequency component of the output signal corresponds with the average temperature of the sample and wherein a second frequency component of the output signal corresponds with the heat capacity of the sample. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1A through 1E are diagrams illustrating the overall system of the present invention; 
     FIGS. 2A through 2D are diagrams illustrating examples of sensor array and contact configurations in the present invention; 
     FIGS. 3A and 3B are examples of a printed circuit board in the invention; 
     FIG. 4 is one embodiment of a sensor array/circuit board assembly in the invention; 
     FIG. 5 is a representative diagram of a matrix switch in the invention; 
     FIGS. 6A and 6B are representative diagrams illustrating two contemplated sensor addressing schemes in the invention; 
     FIG. 7 illustrates one alternative contact structure for the sensor array; 
     FIG. 8 illustrates another embodiment of the invention; 
     FIGS. 9A through 9C are examples of a sensor structure for thermal analysis in the present invention; 
     FIG. 10 illustrates an alternative thermal analysis sensor substrate structure; 
     FIGS. 11A through 11F are sample traces of thermal analysis scans conducted according to the present invention; 
     FIGS. 12A through 12I illustrate one system for conducting thermal analysis according to the present invention; 
     FIGS. 13A through 13G illustrate another system for conducting thermal analysis according to the present invention; 
     FIG. 14 illustrates a thermal decomposition measurement according to the invention; 
     FIGS. 15A and 15B illustrate dynamic thermal analysis conducted according to the present invention; 
     FIGS. 16A through 16E illustrate dielectric spectroscopy conducted according to the present invention; 
     FIGS. 17A and 17B show an example of a mechanical resonator structure that can be used in the invention; 
     FIGS. 18A through 18C illustrate electrical transport characterization conducted according to the present invention; 
     FIGS. 19A through 19C illustrate thermoelectric property characterization conducted according to the present invention; 
     FIGS. 20A and 20B illustrate thermal conductivity characterization conducted according to the present invention; and 
     FIGS. 21A and 21B illustrate magnetic property characterization conducted according to the present invention. 
     FIG. 22 illustrates a thermopower property characterization conducted according to the present invention. 
     FIG. 23 illustrates the electrical circuitry used in the thermopower characterization example of FIG.  22 . 
     FIGS. 24A-C graphically represent the data points generated or measured during the thermopower property characterization of FIG.  22 . 
     FIG. 25 graphically illustrates an atomic composition versus thermopower curve showing a comparison of the results of the present invention with results from the Neisecke &amp; Schneider study, 1971. 
     FIG. 26 illustrates a thermal conductivity property characterization conducted according to the present invention. 
     FIGS. 27A-D represent the electrical circuitry and a plot of the data points for the thermal conductivity example illustrated in FIG.  26 . 
     FIG. 28 illustrates a graphical representation of aluminum (“Al”) film thickness versus thermal conductance for the example illustrated in FIG.  26 . 
    
    
     The abbreviation “abb.” as used in the drawings means arbitrary. An arbitrary scale is most typically used in identifying prominent features in the heat capacity curve that are associated with phase transitions or other significant thermal events, and not the precise absolute value of the heat capacity. 
     DETAILED DESCRIPTION 
     Description of Apparatus 
     FIG. 1A illustrates the generic apparatus or system concept of the materials characterization system of the present invention, and FIGS. 1B through 1E illustrates possible variations of the system. Regardless of the property being measured or the specific hardware in the apparatus, the materials characterization system of the invention includes multiple sensors in contact with multiple samples, means for routing signals to and from the sensors, electronic test circuitry, and a computer or processor to receive and interpret data from the sensors or the electronic test circuitry. FIG. 1B is a representative diagram of an apparatus where each component is separate and interchangeable, allowing maximum flexibility and interchangeability of parts. FIGS. 1C through 1E illustrate variations where portions of the apparatus, such as the sensor array and electronic test circuitry, are integrated into one part, allowing for a more compact design, but with a greater degree of customization of the apparatus for a particular application or property measurement. Regardless of the degree to which components in the apparatus are integrated into one unit, the overall operation of the sensor-array based apparatus remains the same, as will be explained in further detail below. 
     In one embodiment that those of skill in the art will appreciate provides a great deal of flexibility, each sensor has adjacent to it a plurality of associated sensor contact pads. Alternatively, the contact pads can be arranged near the edges of the sensor array, with leads on the substrate connecting the sensors to the contact pads, to prevent the contact pads from being contaminated with the materials being tested. The system in this embodiment also includes a printed circuit board having a plurality of board contact pads arranged in the same configuration as the sensor contact pads in the sensor array. Connectors, such as conducting elastomers, stick probes, cantilever probes, conducting adhesives, wafer-to-board bonding techniques, or other contact devices, couple the sensor array with the printed circuit board by creating contacts between the sensor contact pads and the board contact pads, preferably the contacts are reversible and non-permanent. Thus, sensor arrays incorporating different sensor functionalities can be created using the same array and contact pad format and contacted using the same circuit board and connections. 
     The printed circuit board in the inventive system also includes traces that connect the individual contact pads to standard multi-pin connectors placed near the edges of the board. This construction allows easy connection between the printed circuit board assembly and the rest of the system using standard multi-wire ribbon cable assemblies compatible with the chosen multi-pin connectors. In the system according to a preferred embodiment, the multiwire cables and connectors couple the printed circuit board assembly to a multiplexer or other signal routing means for selecting one or more sensors to be activated, depending on the specific software instructions to the signal routing means. 
     The multiplexer or signal routing means is, in turn, coupled to a flexible electronic platform, which can include electronic test and measurement circuitry, a computer, or both. The electronic platform can also include a switch matrix, preferably under control of the computer, for connecting the multiplexer outputs to a variety of different electronics test instruments without manually reconnecting cables. Thus, when a sensor array incorporating a different sensor functionality is needed, to test for a different material property, only minimal reconfiguration of the electronic platform is needed. In this manner, the same system can be used to test for a wide variety of material properties. 
     In other cases, it may be desirable to collect information from many sensors simultaneously, rather than in a rapid serial fashion. In the preferred embodiment of the invention for such cases, the multi-wire cables and connectors themselves serve as the signal routing means and are directly attached to an electronics module having a multiplicity of independent electronics channels for driving and reading the sensors. The outputs of these independent channels are then collected by the computer. 
     The sensor array itself may contain different types of sensors designed to measure different material properties in the different operation modes as well. Further, standardizing the sensor array configuration, the contact format, and the connections from the board to the multiplexer and/or the electronic platform allows easy “plug-and-play” interconnection as well as simplification of the sensor structures themselves. In one embodiment of the invention, no active circuitry is included in the sensor array, reducing the manufacturing cost of the sensor array enough to make the sensor array disposable, if desired. 
     The sensor array generally includes a plurality of sensors for measuring preselected material properties or other properties that may be used in calculating an arithmetic value corresponding to a material property. The sensors are supported by a support member such as a metal or plastic substrate. In one embodiment, a contact pad is positioned adjacent the substrate. Alternatively, as discussed above, the contact pad may be positioned at or near the edges of the substrate. 
     In a preferred embodiment, the sensor array has the same format as a standardized format used in combinatorial chemistry applications (e.g., an 8×12 grid with 9 mm spacing in between each sensor). By using a standardized format, substances to be tested by the sensors in combinatorial applications can be placed on multiple sensors simultaneously rather than one sensor at a time, e.g., via simultaneous transfer from a standard microtiter plate, further increasing testing and processing speed in the apparatus. 
     The sensors in a single array can be constructed so that they all measure the same material property, or alternatively a single array can contain several different types of sensors that measure different material properties. The modular format of the sensor array, the standardized interconnection means, and the flexible electronic platform allows a great deal of flexibility in determining what types of sensors to include in the array since the same general electronic platform (e.g. electronic test circuitry and computer) and array format is used, regardless of the specific property being measured. 
     Alternatively, the sensors can be suspended at the end of an array of rods or plates that hang vertically from a common supporting plate, preferably in a standard combinatorial chemistry format, to form a “dipstick” array structure. The sensors can then be dipped simultaneously into wells containing solutions of materials to be characterized, wherein the materials to be analyzed are mixed with a solvent. After removing the dipsticks from the solutions and allowing the solvent to evaporate, the sensors remain coated with a film of the material to be characterized. 
     The material can then be tested in the same manner as the sensors in the flat sensor array. The materials or liquids can also be tested while in the wells. Other embodiments of the invention include integrating the printed circuit board with the signal routing parts and/or the electronic test circuitry to construct a more customized characterization device or placing all components and electronic circuitry on the same substrate as the sensors. 
     FIGS. 2A,  2 B and  2 D illustrate one example of a sensor array and contact pad layout pattern using an 8×8 square array with a 0.25 inch pitch (spacing between the centers of adjacent sensors in the array). This particular two-inch square sensor array is compatible with vapor deposition chamber equipment that is often used in combinatorial chemistry and combinatorial materials science applications. 
     Another widely used combinatorial configuration is an 8×12 rectangular array with a 9 mm pitch, shown in FIG.  2 C. The specific sensor array configuration is selected to be compatible with, for example, the automated deposition equipment being used and/or the physical configuration of the material libraries being tested. A standardized sensor array configuration allows material deposition apparatus to deposit entire rows, columns or an entire library of samples on all of the sensors in the array simultaneously, which is generally more efficient than depositing materials one sensor at a time. The specific material deposition method used depends on the material properties being measured and the physical characteristics of the material itself. For example, in some thermal analyses, it is desirable to dissolve the material to be characterized in a solvent, deposit solution onto the sensor, and let the solvent evaporate to leave a film of material on the sensor&#39;s surface. 
     In some embodiments, it is possible to modify silicon-nitride membrane using a silanization process to improve confinement of the solution to the well. Silanization involves applying a surface coating that will either attract or repel the deposited solution. A typical material is a perchloro-silane compound that when applied to the surface of the sensor array, bonds to the surface and modifies the surface&#39;s wettability. Application is made by immersing the sensor array into a solution of a solvent and the perchloro-silane compound. In the case of silicon nitride membranes on a silicon substrate, the higher affinity of the compound to bond to the silicon than the nitride changes the wettability of the edge of the well. This has the effect of confining the droplet in the well as it is repelled from the edges of the well. This can be used to confine the liquid droplet inside a well and allow much larger volumes of liquid than the well can hold normally. This technique may be also applied to other substrates such as metals, glasses or polymers such as Kapton®. By selectively treating the surface of a material such as Kapton® and leaving untreated dots in the area of the sensor, liquid confinement can be implemented without physical wells. 
     For other materials, it may be more appropriate to place material that is in the form of a slurry or powder directly on the sensor. Sample thickness on the sensor may depend on the testing method, the sample itself or the method of sample deposition. Throughout this specification, the terms “thin” and “thick” may be used when referring to films, however, those terms are not meant to be limiting. 
     Referring to FIGS. 2A and 2B, the sensor array  10  includes a plurality of sensors  12  and a plurality of sensor contact pads  14  corresponding to the sensors  12 . The specific micro-structure of the sensor  12  depends on the material property or properties that the sensor  12  is designed to measure. Sensors  12  that are designed to measure different properties have different micro-structures. More detailed descriptions of the actual sensor  12  structure are provided below in the Experimental Example sections with respect to sensors that measure specific material properties. To the naked eye, however, the sensors  12  may look like small pads or tiny wells, depending on the specific material characterization application, that are arranged on a planar substrate  16 ; the functional differences are within each individual sensor  12  at the microscopic level. More importantly, different sensor arrays  10 , incorporating different sensors  12 , will share a common array  10  and contact pad  14  format. 
     The electronic wiring and interconnection devices for sending sensor data to and from the sensor array  10  are arranged into a configuration that is compatible with the sensor array  10  format. As a result, different sensor arrays  10  for use in the same materials characterization apparatus will have the same sensor locations and the same overall wiring patterns for electrical connections; different arrays  10  will look identical at a superficial level, even if they measure different properties. This sensor array  10  standardization allows arrays  10  that measure completely different material properties to be electrically contacted using a single interconnection device, which is in turn attached to a flexible electronic platform. 
     As illustrated in FIG. 2B, the contact pads  14  are located immediately adjacent the sensors  12 , and the sensors  12  and the contact pads  14  are arranged in electrical communication. The sensors  12  and sensor contact pads  14  are formed on the substrate  16  in any selected array format that is desired. For example, they may be compatible with the material deposition machine being used. Any desired geometry can be achieved, such as lines, squares, rectangles, circles, triangles, spirals, abstract shapes, etc. Such geometric shapes can be considered to have either an open or closed shape with either straight or curved sides or both. Any number of sensors  12  can be used, including 5 sensors, 48, 96 or 128 sensors, and preferably from 5 to 400 sensors may be in one array  10 . 
     The material selected for the substrate  16  can vary depending on the application in which the sensor array  10  will be used, as will be explained by examples below. Possible substrate materials include, but are not limited to, silicon, silicon nitride, glass, amorphous carbon, quartz, sapphire, silicon oxide or a polymer sheet. For example, the polymer substrate may be a polyimide such as Kapton® from DuPont. Other polymer substrates may be used, including those selected from the group consisting of aramids (such as Kevlar®), polyester (such as poly(ethyleneterephthalate), oriented films such as Mylar®, or poly(ethylenenaphthalate)), epoxy resins, phenol-formaldehyde resins, polytetrafluoroethylene (such as Teflon®), polyacetal (such as Delrin®), polyamide (such as Nylon®), polycarbonates, polyolefins, polyurethanes, silicones, polysiloxanes and the like. Other materials can also be used for the substrate  16 . 
     Substrates  16  used for thermal characterization and other tests requiring thermal isolation of small amounts of sample material should have the ability to be formed into a thin film or sheet that can withstand the temperatures at which the materials will be tested. In a thermal analysis application in which the sample material is a thin film, for example, the portion of the substrate  16  that supports the sample material is ideally between 0.1 and 25 micrometers thick or the same order of magnitude as the thickness of a material sample, to minimize the effects of the heat capacity and thermal conductivity of the substrate  16  in the test results without making the substrate  16  too fragile to work with easily. In short, the optimum dimensions of the substrate  16  will depend on the characteristics of the specific material chosen for the substrate  16  and the specific property or properties to be characterized by the sensor array  10 . 
     The sensors  12  and sensor contact pads  14  are preferably formed on the substrate  16  via lithography. The specific number and design of the lithographic layers will depend on the characteristics to be measured and the particular sensor application. If possible, the number of layers is preferably as few as possible, for example less than four or five layers, to minimize the number of fabrication steps and reduce the overall cost of the sensor array. The number of lithographic layers can be kept to a minimum by creating sensors  12  that characterize only one or two material properties and also by eliminating on-board control circuitry within the sensor  12  itself, if desired. More specific sensor structures are explained in further detail below with respect to the experimental examples. 
     Keeping the sensor array  10  manufacturing cost low makes disposability of the array  10  possible, if desired or necessary (e.g. after testing inorganic materials that may not be easily removed from the sensors). Further, if there is no on-board control circuitry that could be harmed under extreme conditions on the sensor array  10 , the sensor array  10  can be cleaned after use by dipping the entire array structure into a solvent or acid or heating the sensor array  10  at a very high temperature to remove sample material residue. The cleaned sensor array  10  can then be reused. Of course, placing on-board electronics on the sensor array  10  or integrating the array with a circuit board having electronic components is also an option, if deemed appropriate for the application in which the array  10  will be used. 
     In one embodiment, eight sensor contact pads  14  are provided for each sensor, as shown in FIGS. 2A,  2 B and  2 D. For identification purposes, the eight pads can be divided into four pairs labeled A through D, with each pair having a H (high) contact pad and a L (low) contact pad as best seen in FIG.  2 D. Using this labeling scheme, each sensor contact pad in the sensor array can be identified by an array position, a letter, and a H or L designation (e.g., (1,1)AH). Of course, other sensor  12  and sensor contact pad  14  configurations are possible as well as alternative sensor contact pad identification systems. Also, in this example, the sensor contact pads  14  are preferably spaced at a {fraction (1/16)} inch pitch with a 1 mm spacing in between adjacent columns of pads  14 . This physical arrangement is particularly suited for coupling the sensor contact pads  14  to a printed circuit board  30  via elastomeric connectors, which will be explained in greater detail below. Other sensor contact pad  14  arrangements can also be used, depending on the specific manner in which the sensor array  10  will be electrically contacted and the specific application in which the sensor array  10  will be used, without departing from the scope of the invention. 
     FIGS. 3A and 3B are top views of a specific embodiment of a printed circuit board  30  to be coupled with the sensor array  10  shown in FIGS. 2A and 2B, and FIG. 4 shows an exploded view of one portion of an apparatus that connects the sensor array to the circuit board  30  in the inventive materials characterization device. 
     The circuit board  30  used in the examples (except for the dielectric example) measures 11 inches in diameter and includes 8 layers of metallization. Gold was used for the top layer of metallization to obtain good electrical contact with elastomeric connectors. All eight layers are super-imposed in FIG.  3 B. Of course, this specific design can be modified by those of skill in the art without departing from the invention. 
     Generally, the printed circuit board  30  preferably includes a plurality of board contact pads  32  having an arrangement which is a mirror image of the arrangement of the sensor array contact pads  14 , such that when the sensor array  10  is connected to the printed circuit board  30 , there is a one-to-one correspondence between the board contact pads  32  and the sensor contact pads  14 . Tolerances in the positioning of the pads and trails of 0.001-inches can be easily attained with modern manufacturing techniques, permitting precise matching of the sensor and board contact pad patterns. The sensor contact pads  14  and the board contact pads  32 , via leads  33  and connectors  34  that are disposed on the board  30 , are the primary contact points through which the sensor array  10  connects with a flexible electronic platform, such as a computer and/or electronic test circuitry. 
     To connect the sensor array  10  to the printed circuit board contact pads  32 , a plurality of Z-axis connectors  40  can be used, as shown in FIG.  4 . The Z-axis connectors  40  create the electrical connection between the sensor contact pads  14  and the board contact pads  32 . In the embodiment shown in FIG. 4, the Z-axis connectors are formed from rubber or other elastomeric strips containing conductive metal particles or wires for carrying current. These elastomeric conductors are preferably designed to conduct electricity in only one direction to prevent cross-talk between closely spaced contacts. Other possible connectors that can be used to couple the sensor contact pads  14  with the board contact pads  32  include cantilever or stick probes or other types of spring-loaded contacts, conducting adhesives, glues or epoxies, wire bonding, soldering, or direct contact between the sensor array and board contact pads  14 ,  32 . Regardless of the specific type of structure, the Z-axis connectors  40  must create a reliable connection between the sensor contact pads  14  and the board contact pads  32 , even when very closely spaced together, to ensure reliable coupling between the sensor array electronic platform without cross-talk between adjacent contact pads. 
     The Z-axis connectors  20  can be placed in a frame or positioning fixture  42  that may be attached to the circuit board  30 , as shown in FIG.  4 . This allows the sensor and board contact pads  14 ,  32  to be lined up with each other precisely and coupled through the Z-axis connectors  40  in a one-to-one relationship. In an alternative embodiment, the positioning fixture  44  may be modified with one or more cavities for receiving a fluid for either heating or cooling the entire array. For instance, a cryogenic fluid may be circulated through or applied to the fixture resulting in a cooling of the array to subzero temperatures. Alternatively, the fixture  42  can be heated by circulating a heating fluid, such as a glycol, through the cavities or by applying a resistive heating element to the fixture. In a preferred embodiment, temperatures ranging between −195° C. and 200° C. have been achieved. One of skill in the art will appreciate that fluids and heating elements capable of obtaining temperatures outside the stated range may be used without departing from the scope of the invention. 
     The positioning fixture used with elastomeric connectors in the example experiments discussed below had a square cavity, 2.002-inch+/−0.001″ tolerance, for precisely positioning of the sensor array  10 , slots  41  to hold the connectors  40 , and holes  43  for optical/atmospheric access. The connectors  40  in the example experiments discussed below were elastomeric connectors, such as Fujipoly “Zebra Silver” connectors, having dimensions of 1 mm wide, 2″ long, and 5 mm high. 
     A compression plate  44  can be used to provide additional security in the connection between the sensor and board contact pads  14 , 32 , especially if the sensor array  10  and the printed circuit board  30  are not bonded together. The compression plate  44  is simply placed on top of the sensor array  10 , secured in place with screws or other fasteners  46  and tightened until the sensor array  10 , the Z-axis connectors  40  and the printed circuit board  30  are pressed firmly together. The compression plate  44  may have a plurality of holes  48  having the same configuration as the sensors  12  in the sensor array  10  to allow optical testing of the sensor array  10 , either alone or in conjunction with the electrical characterization according to the present invention, if desired, and permit gas exchange or evacuation. Holes  49  may also be provided in the printed circuit board  30  for the same purposes. 
     The printed circuit board  30  may provide the primary electronic link between the sensors  12  and any peripheral devices used to control and monitor the sensor array  10 , such as the components in the flexible electronic platform. The printed circuit board  30  also can, in many cases, be considered part of the signal routing equipment (as opposed to being considered a part of the sensor array  10 ). In the embodiment shown in FIGS. 3A and 3B, as noted above, the printed circuit board  30  has a plurality of connectors  34  arranged around the board&#39;s  30  periphery, leaving enough space in the center area of the printed circuit board  30  for positioning the sensor array  10 . The connectors  34  on the printed circuit board  30  are preferably standard multiple-pin connectors so that a commercially available ribbon cable wire assembly can route signals to and from the sensor array  10  or couple the printed circuit board  30  with peripheral devices, such as a multiplexer and flexible electronic platform. The illustrated structure, which was used in the examples discussed below, is a Robinson-Nugent P50E-100STG 100-pin connector that is compatible with the inputs of the multiplexer, but any other multiple-pin connector can be used without departing from the spirit and scope of the invention. 
     Each board contact pad  32  has an associated lead  33  that extends from the board contact pad  32  to a pin on the connector  34 . It should be noted that the connection between the printed circuit board  30  and the electronic platform need not be a physical connection, such as a ribbon cable, but can also be any type of wireless connection as long as signals can be transmitted between the sensor array  10  and the electronic platform. 
     A multiplexer as illustrated in FIGS. 12D and 15B may be included in the apparatus as signal routing equipment linking the sensor array  10  and the electric platform or test equipment being used, which is schematically represented in FIG.  6 A. The multiplexer used in the experimental examples discussed below was an Ascor model 4005 VXI multiplexer module, containing four custom Ascor switch modules (model 4517). Each switch module contains 64 2-wire relays, in eight groups of eight relays per group, for a total of 128 input connections per module (512 connections total, corresponding to the number of contact pads on the sensor array). This design was chosen because it was easy to integrate with the embodiment having an 8×8 array with 8 contact pads per sensor. Thus, it will be apparent to one skilled in the art that different designs may be used without departing from the invention. Each switch module also has four output connections, which can be connected to different input connections by closing selected relays under computer control. The signal routing equipment shown in FIG. 6A emphasizes simultaneous contact and connection of all of the sensors  12  to multiplexer inputs, with sensor selection being conducted by closing selected switches in the multiplexer. 
     A preferred embodiment facilitates attachment of standard electronic test and measurement equipment to the outputs of the signal routing equipment. For the experimental examples discussed below, there were eight terminals, one for each contact pad  14  on the sensor  12 . The outputs were routed to a panel containing standard panel-mounted BNC coaxial connectors. However, again this design can be modified by those of skill in the art without departing from the invention. Generally, a given pair of signals (e.g. AH and AL) can either be connected to a center conductor and shield a single BNC terminal, which is electrically isolated from the mounting panel, or be connected to the center conductors of two separate BNC terminals whose outer shields are connected to the system ground. This permits either single-ended or true differential connections to the sensors, with the connection mode chosen manually for each pair of leads (e.g. A, B, C, and D) by means of a toggle switch. Thus, when a single sensor  12  is selected, the eight contact pads  14  of the selected sensor  12  can be easily accessed from the panel of BNC connectors, using virtually any desired piece of electronic test and measurement equipment. Other types of terminals can of course be used. 
     For the apparatus used in the examples, thirty-two analog backplane connections were provided between multiple 4517 switch modules in the common 4005 multiplexer module, permitting highly flexible configuration of the multiplexer. In addition to permitting selection of one sensor at a time, the backplane connections permit selection of one sensor from each row at a time, with the outputs being made available on one or more 32-terminal output modules, which are also housed in the 4005 multiplexer module and are connected to the analog backplane. The flexible multiplexer design also permits the multiplexer to be used with arrays larger than 8×8 by permitting additional switch modules to be inserted into the housing and connected to the common backplane. 
     Again for the example experiments, the Ascor 4005 multiplexer module was housed in a Hewlett-Packard model HP E8400A 13-slot VXI mainframe. Communication with a computer was through a National Instruments GPIB-VXI/C interface module, which allows control of the VXI system via the computer&#39;s GPIB interface. The multiplexer was controlled from the computer by sending appropriate commands to the GPIB-VXI/C interface module. The software for controlling the multiplexer preferably permits operation in two different modes. In both cases, a graphic representation of the sensor array  10  was shown on the computer screen in the form of an array of “buttons.” In manual operation mode, the user selects one or more sensors by clicking on the corresponding buttons and then instructing the computer to close the appropriate switches. All eight connections to the selected sensor or sensors  12  are then closed, while any previously closed connections on non-selected sensors  12  are opened. 
     In automatic or scan operation mode, using the control software the user again selects a group of sensors by clicking on the corresponding buttons. The computer then closes the switches to the first sensor, performs a measurement procedure, and opens the switches to the first sensor. The procedure is repeated for all of the sensors selected by the user, scanning across each row from left to right and moving from the top row to the bottom. Relays are not closed and measurements are not performed on unselected sensors. This software can be changed to accommodate preferred modes of operation, including running in parallel. 
     Once a sensor  12  is routed to the multiplexer output, many different commercially available electronics components may be connected to the sensor array  10  to input and output signals to and from the sensor  12 . For example, if the sensor array is designed to measure resistance, a resistance meter that has one input is connected to the multiplexer output and can measure the resistance of any of the sensors  12  that are connected to the multiplexer inputs. The multiplexer allows a user to select any one of the sensors  12  on the array  10  and output data related to the resistance properties of the sample material containing the selected sensor  12 . 
     Alternative signal routing equipment is illustrated in FIG. 6B. A probe assembly  61  having probes  63  disposed thereon in an arrangement that matches the sensor contact pad arrangement  14  on one or more sensors  12  is position over a selected sensor  12  via a three-axis translation stage. The three axis translation stage is preferably controlled by motors under computer control. The probe assembly  61  itself may be moved, or the substrate  16  may be moved to position the assembly  61  and the substrate  16  relative to each other. To select a sensor  12 , the probe assembly  61  is positioned over the selected sensor  12  and moved toward the substrate  16  to make electrical contact with the selected sensor&#39;s  12  contact pads. Wiring from the probe assembly connects the selected sensor or sensors to the electronic platform. The specific technology used for positioning the probe assembly  61  can be any positioning mechanism known in the art. The advantage of the sensor selection and signal routing system shown in FIG. 6B is that it largely reduces or eliminates the need for a circuit board, multiwire cables, and multiplexer. 
     FIG. 5 illustrates one possible configuration for a generic flexible electronic platform that can be used in conjunction with the sensor array  10  of the present invention. In this example, the outputs from the signal routing means  129 , such as the multiplexer  126 , are connected to a matrix switch  50  that is controlled by a computer  52 . Thus, it will be appreciated that the computer  52  controls both The matrix switch  50  has a plurality of electronic test measurement instruments  54  that can be coupled to any or all of the multiplexer outputs. A user can select which instruments to connect to particular sensors  12  in the sensor array  10  by either inputting instructions into the computer  52  to open and/or close the matrix switch  50  connections by opening and closing the connections manually, including manually rerouting cables that attach outputs to electronic inputs. Thus, this particular type of flexible electronic platform can output and read many different signals required for measuring many different material properties with different sensors, simply by changing the connections within the matrix switch  50 . 
     Because the sensors  12  can be accessed using off-board circuitry, the inventive structure allows great flexibility in the manner in which the sensors  12  are addressed. If a multiplexer is not used to control sensor  12  addressing, and if a separate electronics channel is provided for each sensor  12  as the signal routing means  129 , then all of the sensors  12  in the array  10  can be monitored simultaneously, allowing rapid parallel characterization of entire material libraries. If a multiplexer is used, any channel from any sensor  12  can be made available for input or output via its corresponding multiplexer terminal, and simultaneous but separate of addressing individual sensors in different rows in the array  10  is also possible. Alternatively, the computer  52  can also be programmed to conduct rapid serial measurement (addressing one sensor  12  at a time), addressing all sensors  12  in a selected group simultaneously (such as heating each row to a different temperature to study thermal processing conditions), and simultaneously addressing one sensor  12  from each row (combined serial/parallel sensor measurement) as shown by the structure illustrated in FIG.  6 A. All of these sensor accessing schemes can be implemented electronically, through software instructions to the multiplexer, without physically reconfiguring or rewiring any part of the apparatus because of the apparatus&#39; modular construction, the interconnection structure, and the flexible electronic platform. Of course, if desired, any or all of the components (e.g., the multiplexer, the printed circuit board  30 , the sensor array  10 , and the electronic test circuitry from the electronic platform) can also be integrated in various ways to construct a more customized materials characterization unit. 
     An alternative structure for the sensor array  10  is shown in FIGS. 2C and 7. In certain applications, such as characterization of liquid materials, it is not desirable to have the contacts between the sensor array  10  and the printed circuit board  30  located in the same vicinity as the sensors  12  themselves. The liquid materials would tend to contaminate the contact pads  14 ,  32 , reducing the integrity of the interconnection between the sensor array  10  and the printed circuit board  30  and preventing reuse of the interconnection hardware, such as the Z-axis connectors  40 . To overcome this problem, the sensor array  10  shown in FIGS. 2C and 7 directs the leads from all of the sensors  12  to the edge of the substrate  16 , away from the actual sensor sites. Contact between the sensor array  10  and the printed circuit board  30  is made at the edge of the substrate  16 , either with Z-axis connectors  40  as in the sensor array described above or with probe cards or probe arrays  70  (traces and connectors not shown), as shown in FIG.  7 . Cantilever probes  72  on the probe array  70  provide the electrical link between the sensor array  10  and, for example, the multiplexer  126 , the flexible electronic platform, or some other peripheral device. 
     Because the sensors  12  in the sensor arrays  10  shown in FIGS. 2C and 7 are relatively flat and have their top surfaces physically exposed, a rubber gasket (not shown) containing holes in the same locations as the sensors can be placed on top of the sensor array  10  to hold liquids in place over the sensors  10 . The gasket can be pressed or bonded to the plate while the traces connecting the sensor array  10  to the printed circuit board  30  can still be run along the substrate  16  to its edge. Further, because there is a clear optical path to the sensors  12  from an overhead vantage point, the sensor array  10  can be used in conjunction with a camera or other optical sensing device, allowing even more material properties to be measured simultaneously. For example, if the sensors  12  in the array  10  are designed to measure the progress of a curing process via measurement of material dielectric constants, using a camera in conjunction with the materials characterization device of this invention allows detection and measurement of exothermic properties and/or temperature changes at the same time as measurement of the dielectric constant, further increasing the number of characteristics that can be measured at one time. See WO 98/15805, incorporated herein by reference, for a discussion of optical screening techniques. 
     An alternative structure for the present invention is shown in FIG.  8 . In this embodiment, substrate  16  is coupled to a mounting plate  17 , which incorporates wiring for communication and multiplexing. The individual sensors  12  are cut apart and mounted onto individual sensor plates  80  to form “dipsticks”  82  that preferably extend vertically from the substrate  16 . The spacing and format of the dipsticks  82  may follow a conventional combinatorial chemistry format, such as an 8×12 array with 9 mm spacing, so that all of the dipsticks  82  in the array  10  can be dipped into standard combinatorial chemistry wells  84  simultaneously, as shown in FIG.  8 . 
     In a preferred embodiment, the wells  84  contain solutions comprising the materials to be characterized dissolved in a solvent. It will be appreciated that each vessel  84  may contain the same or different solutions for testing. Once the dipsticks  82  are dipped into the wells  84  and removed, the solvent is allowed to evaporate and the sensors  12  are left coated with the sample material. Input and output signals are then sent to and from the sensors  12  in the same way as described above to characterize the material properties. The liquids in the wells  84  can also be directly characterized as the while the sensors are immersed in the wells  84 . 
     Because the materials characterization system of the present invention has a modular, flexible structure, many different material properties can be monitored simply by changing the sensor structures in the sensor array  10  and attaching different electronic components to the array outputs or signal router outputs as needed, depending on the specific material property to be measured. Thus, the same interconnection method and signal routing equipment may be used for all types of measurements, where the only components that need to be changed are the sensor array  10  itself (“plug-and-play” operation) and possibly some specific electronic test circuitry in the electronic platform. This is much less expensive than purchasing a separate machine for measuring each property. Also, as can be seen below, the sensor arrays  10  themselves may be reusable in certain applications, reducing expenditures for testing even further. The measurements obtained from the sensors  12  in the sensor array  10  of the present invention can be directly correlated to known testing results. In other words, the results obtained from the sensor arrays  10  correlate with results obtained from conventional materials characterization methods. This advantage of the present invention will be highlighted in greater detail with respect to the experimental examples described below. 
     Thermal Analysis Background 
     Thermal analysis is one of the most generally useful techniques of materials analysis, particularly measurements of heat capacity. In many cases for thermal analysis, it is important that the sample being analyzed is thermally isolated from its environment to a large degree. Thermal isolation insures that heat flows into and out of the sample and the associated changes in the sample temperature may be accurately determined and are not masked by much larger heat flows associated with other objects, such as the sample holder or substrate, heater and thermometer, etc. Samples produced in combinatorial materials synthesis may consist of films, created by physical vapor deposition techniques (evaporation, sputtering, etc.) or by deposition of a liquid solution or suspension and subsequent evaporation of the solvent. The samples preferably have small lateral dimensions (e.g. 1 mm or less), to allow more samples to be deposited on a given area. A sensor designed for thermal analysis of combinatorial libraries must therefore allow accurate measurements to be made on very small samples that are packed closely together on a substrate. Although thermal isolation of minute samples initially poses a challenge, it also offers an advantage in that the thermal time constants for internal equilibration of the sample, heater, and thermometer are greatly reduced, permitting more rapid measurements to be made. 
     Thermal isolation of small-area thin film samples may be most easily achieved by using a thin film of low thermal conductivity material to support the sample, where the support&#39;s thickness is comparable to or less than that of the sample. The heat capacity and thermal conductance of the support are thus comparable to that of the sample film, can be independently measured, and can be subtracted from measurements made with a sample present. Further isolation during the measurement can be achieved by use of various modulated or pulsed heat capacity measurement methods, which will be discussed below. 
     Issues affecting the design of a thin film calorimeter are the materials used for fabricating the substrate and thin support membrane, the materials used for fabricating the heater and thermometer, the geometry of the heater and thermometer, membrane, sample, and substrate as they affect the temperature profile and transport of heat, and the way in which the sensors can be connected to an interface so that useful information can be obtained from the sensors. FIGS. 9A through 9C illustrate preferred sensor structures for use in thermal analysis applications with thin film samples. Although the figures illustrate the structure of one individual sensor, it is understood that all or part of the sensors in the sensor array can be manufactured on the substrate  16  simultaneously. 
     FIG. 9A is a preferred thin-film structure for conducting thermal analysis of a thin-film sample  90 . A micro-thin membrane  94 , which supports the sample material  90 , is preferably made of silicon nitride (Si 3 N 4 ) on a silicon wafer substrate  92 . The substrate  92  preferably has a plurality of membranes  94  that are formed thereon in the desired sensor array arrangement. To form the membranes  94 , a thin film of silicon nitride  95  is deposited on the top and the bottom surfaces of the silicon wafer  92 . The thickness of the silicon nitride film  95  is preferably between 500 angstroms and 2 microns, as this thickness can be easily produced by chemical vapor deposition and other techniques; it also corresponds to the typical thickness of the thin film samples  90  to be studied. Nitride membranes having a thickness of 2 microns are generally preferred. Nitride membranes having a thickness of this amount tend to have improved durability with a tradeoff as to sensitivity. An additional benefit is improved consistency of temperature measurement across the sensor array  10 . 
     The desired membrane pattern is then created on the bottom surface of the silicon wafer  92  to open up “windows” 96 in the silicon nitride film  95 , exposing the silicon  92  at selected locations. The entire wafer structure is dipped into an etching solution, such as potassium hydroxide, to erode or etch away the silicon  92  exposed through the windows and form the structure shown in FIG.  9 A. Regardless of the specific etchant used, it should etch silicon but not etch silicon nitride. Because of silicon&#39;s crystal structure, the etching process forms a well  97  with sloping walls through the silicon layer  92  and which stops at the top silicon nitride layer  95 . The resulting structure is a suspended, micro-thin silicon nitride membrane  94  supported by silicon  92 . The well  97  makes the sensor array structure particularly suited for depositing films from solids dissolved in a solvent, as a drop of the solvent can be held in the well  97  during drying. The well  97  can also contain liquids that are being tested. 
     FIGS. 9B and 9C illustrate one possible heater/thermometer pattern  100  that can be printed on the membrane  94  to form a complete thermal analysis sensor. As can be seen in the figure, the preferred heater/thermometer pattern  100  is designed so that the thermometer portion  102  is much smaller than the heater portion  104  and so that the thermometer  102  is located in the center of and surrounded by the heater  104 . The heater  104  is still sufficiently small so that the edges of the heater/thermometer pattern  100  are isolated from the edges of the membrane  94 . These design features give the sensor  12  several desirable properties that make it useful for conducting rapid heat capacity measurements on thin film samples. The time constant for equilibration of the heater  104  with the thick part of the substrate  92  (beyond the edge of the “window”) is much longer (slower) than the time constant for internal equilibration of the portion of sample  90  adjacent to the heater  104  and thermometer  102 , since the time constant is proportional to the square of the distance over which the heat must diffuse. The temperature profile across the heater  104  may to some extent have a non-uniform dome-shaped profile due to heat flow from the center of the heater  104  outwards; placing a small thermometer  102  in the center of the heater  104  allows measurement of the temperature in a region whose temperature is much more uniform than the temperature of the entire heater  104 . 
     The heater/thermometer  100  is preferably printed on the flat side of the membrane  94  via lithography so that the sample  90  can be deposited on the membrane  94  within the “well” portion  97  and be characterized without actually touching the heater/thermometer pattern  100 . The membrane  94  prevents direct physical contact between the heater/thermometer  100  and the sample, yet is still thin enough to create intimate thermal contact between the heater/thermometer  100  and the sample  90  and allow heat to conduct through the membrane  95  to warm the sample  90  and measure its thermal characteristics. This feature is particularly useful when characterizing metals, where direct physical contact between the heater/thermometer  100  and the sample  90  would create a short circuit in the heater  104 . Heater/thermometer leads  106  are connected to the sensor contact pads  14  or are otherwise configured for coupling with the flexible electrical platform so that the power input and the sample&#39;s temperature can be monitored and controlled electrically. Thus, it can be seen that in some embodiments, coatings may be used on the sensors to protect the sensors from the samples or vice versa. 
     The specific configuration for the micro-calorimeter array and the system architecture for coupling the sensors  12  in the array  10  to the electrical platform can be any structure desired by the user as long as electrical signals can be sent to and read from each individual sensor  12  in the array  10 . The micro-calorimeter used in the example experiments was custom manufactured so that the substrate  92  was a 0.5 mm silicon wafer, with 0.5 μm of low-stress LPCVD silicon nitride deposited on both sides. The silicon nitride membranes  94  were 2 mm squares and prepared by known procedures. To produce the metallization patterns, a liftoff procedure was used. Photoresist is spun on to the front side of the wafer, and is patterned by photolithography using a stepper. 50 Å of Ti was then deposited on the photoresist and the exposed portions of the substrate, followed by 2000 Å of Pt. The Ti layer was added for adhesion purposes. The photoresist was then dissolved, leaving metal in the desired pattern on the substrate. In the embodiment of the heat capacity sensor used in the examples, the heater  104  consists of a serpentine pattern, with 60 μm lines separated by 20 μm spaces. The thermometer  102  is a smaller area serpentine pattern, with 20 μm lines and 20 μm spaces. Following liftoff, the wafer was cut into the form of a square measuring 2.000″+/−0.001″ precision, using a dicing saw. Accurate dicing of the wafer is needed for accurate positioning of the wafer relative to the circuit board, using the positioning frame. A dimension of 2″ was chosen to allow the substrates to be inserted into combinatorial vapor deposition equipment. 
     An alternate material for the substrate  16  is a polymer sheet. A particularly suitable polymer is a material called Kapton®, which is manufactured by DuPont. Kapton® is thermally stable and can withstand temperatures up to 350-400 degrees C. without deterioration. Kapton® is often sold in sheets ranging from 6 microns thick to 100 microns thick, and the heater/thermometer design, such as that shown in FIGS. 9B and 9C, can be printed directly onto the film via lithography or other techniques. To suspend the Kapton® sheet when conducting thermal analysis, the contacts can be printed such that they are all at the edges of the sheet, as shown in FIGS. 2C and 7, and the sheet can be stretched and clamped at the edges to connect the contacts on the sheet with corresponding contacts associated with the flexible electronic platform. 
     Sensor arrays are fabricated on 12.5 and 25 micron Kapton® films using standard lithography techniques and metal films such as gold or platinum. Arrays are bonded to a rigid metal substrate with circular holes to produce a format compatible with substrates such as silicon. A substrate of metal such as aluminum or copper is used. For bonding, adhesives such as epoxies chosen for thermal and chemical compatibility with the materials to be tested are used. 
     The substrate is fabricated with openings on the same spacing as the Kapton® sensor array elements and bonded together. The resulting structure of the substrate and Kapton® film form a well or cavity into which samples may be deposited. In the case of thermal sensors, electrical connections are located on the opposite side of the array and thus electrically isolated from the samples. The Kapton® film serves both as the membrane for the sensor as well as electrical insulation of the traces from the substrate and sample while maintaining thermal contact essential for the measurement. The openings in the substrate may be fabricated as circular, square, rectangular or any convenient shape. Circular openings are optimal for liquid deposition due to the circular shape of liquid droplets. 
     If the samples are not electrically conducting, then the entire side of the sheet opposite the side containing the sensors can be covered with a layer of metal, which can be used as a blanket heater for heating all of the samples simultaneously, either via a DC signal or a modulated signal. As noted above, the inventive structure provides enough flexibility so that selected samples can be heated individually, simultaneously, or in any grouped combination simply by changing the electronic signals sent by the electronic platform. 
     In applications where larger amounts of material are available for analysis, e.g. samples which may be 10&#39;s to 100&#39;s of micrometers thick, it may be possible to use thicker substrates. In these cases, thermal isolation can be improved by using substrates with low thermal conductivity, such as glass, or by micromachining a gap or “moat”  110  around a sample support  112 , which is spanned only by microbridges  114  of material, as illustrated in FIG.  10 . The heater/thermometer pattern may be printed on the sample support  112 . The microbridges  114  hold the sample support  112  in place on the substrate while minimizing heat leakage, and also act as supports for wires which must pass into and out of the sensor for coupling with the electronic platform. 
     Experimental Example 
     Thermal Analysis of Polymers and Metal Alloys 
     The modular sensor array structure described above is particularly useful for rapidly measuring thermal properties of combinatorially synthesized libraries of polymers. The predominant use of heat capacity measurements with polymers is for the determination of the temperatures at which phase transitions occur and the identification of the types of phase transitions occurring (generally either glass transitions or melting points). This information can then be used in two general ways. 
     In some specific cases, it is desirable to have a phase transition occur at a particular temperature, and the goal of combinatorial synthesis might in part be to tune the polymer&#39;s physical properties until that value is achieved. For example, the glass transition temperature is an important parameter for the polymer particles used in latex paints, as it strongly affects how the latex particles will coalesce and form a film under given environmental conditions. A latex for a given coating application may have to fulfill many other conditions as well, related to properties such as adhesion and weatherability. 
     It is a common practice to try to achieve several desirable properties simultaneously by making random copolymers, containing an essentially random sequence made from two or more different monomers. The types and numbers of monomers used and their relative proportions can be varied in many different combinations, to attempt creating a polymer that simultaneously fulfills all of the desired criteria. However, adding a monomer that improves adhesion may reduce the glass transition to an unacceptable value, for example. Thus, being able to rapidly measure the glass transition temperature (in addition to other properties) for many hundreds of random copolymers allows the balancing of different physical properties to be done much more rapidly. 
     An example is shown in FIG. 11A, where the glass transitions have been determined for a series of styrene-co-butyl acrylate random copolymers with different styrene contents, using the specific details discussed above. The example shown in FIG. 11A illustrates temperature (T) vs. heat capacity signal (HCS) data for 100% styrene having an increasing butyl acrelate content as shown by line  19 . The random copolymers were synthesized by Atom Transfer Radical Polymerization (ATRP) at 140 C. for 15 hours, using CuCl with two equivalence of 4,4′-dinonyl-2,2′-bipyridine (dNbpy) as the control agent and (1-chloro)ethyl benzene (PhEtCl) as the initiator. The monomers styrene (S) and n-butyl acrylate (BA) were combined to make 11 solutions ranging from 100% S to 100% BA in steps of 10 volume %. A catalyst stock solution was made in toluene by combining 1 part PhEtCl with 1 part CuCl and 2 parts dNbpy. For each of the 11 monomer stock solutions were set up five polymerizations with varying ratios of monomer to initiator, by varying the amount of catalyst stock solution added. This led to a 55 element array of random co-polymerizations that varied in the x-axis by the composition of monomers, and in the y-axis by the theoretical molecular weight (ranging from 10,000 to 50,000). 
     The samples in the example were chosen from the styrene-rich portion of the library, in order to produce Tg&#39;s above room temperature. The example of the inventive apparatus and method described here does not contain a means for cooling samples below room temperature; however, as is obvious to anyone skilled in the art, this can be accomplished easily in many different ways. The molecular weight of the polymers used was approximately 30,000 gm/mol. The polymers were dissolved in toluene at room temperature to a concentration of approximately 2%. Small drops (approximately 5 μl) of the solutions were manually pipetted onto the sensors, and allowed to dry in air until a film was formed. The heat capacity data shown in FIG. 11A were obtained using the inventive apparatus and method, following the “3ω” measurement procedure, which is discussed below. 
     The glass transitions of the polymers can clearly be observed as a “step” in the heat capacity vs. temperature data. This is identical to the type of behavior observed using traditional differential scanning calorimetry to measure the heat capacity, and the data are of entirely comparable quality with respect to the sharp definition of the feature associated with the glass transition. The glass transition of polystyrene occurs near 100° C., in fair agreement with known results. It should be noted that these data were taken using an approximate calibration for the temperature sensor; improved calibration procedures will naturally yield more quantitatively precise values for Tg. 
     In addition, the glass transition temperature Tg can be seen to clearly decrease to lower temperatures with increasing butyl acrylate incorporation. This is entirely in accord with the known behavior of random copolymers, which typically show a glass transition temperature at a value intermediate between that of the pure component polymers (a 100% butyl acrylate polymer would have a glass transition temperature Tg of approximately −75° C.). However, the total time required to acquire this data using the inventive method is less than 2 minutes. Similar measurements using a conventional differential scanning calorimeter would take several hours or more. 
     Another example in which the precise value of a phase transition temperature is important is in the area of thermally responsive polymers, including polymers with crystalline side chains, liquid crystallinity, etc. Thermally responsive polymers are important to a wide variety of applications. Thermal measurements on polymers are also important in determination of a polymer&#39;s performance under different environments, including solvent, vapors, humidity, radiation, oxidation and the like. For example, the sample polymers may be tested after exposure to a certain environment or may be tested while being exposed to the environment. 
     Even more generally, however, information about phase transitions can give a great deal of insight into the chemical and physical structure of the polymer being studied, which in turn can be related either to the success or failure of a particular synthetic strategy, or to the suitability of the material for applications involving properties other than the melting or glass transition temperatures. Thus, thermal analysis is extremely useful within a combinatorial polymer synthesis program, as it allows a scientist to rapidly assess variations in polymer physical properties due to different catalysts, process conditions, etc, as well as to assess whether or not a polymer with a desired chemical composition or architecture has in fact been synthesized. The following examples will illustrate these points. 
     Even in the case of polymers made from a single monomer (e.g. ethylene), the physical properties of the polymer will vary tremendously depending on the architecture of the polymer, e.g. the molecular weight, and the degree and type of branching. For example, high density polyethylene (HDPE) and paraffin (wax) are chemically similar, but differ in their molecular weights and the amount of bridging between crystallites. The greater number of chain ends in paraffin severely disrupts the crystalline packing of the chains, in comparison to HDPE, leading to vastly inferior mechanical properties. The difference in physical properties is also directly manifested in a lower melting point for paraffin in comparison to HDPE. 
     Other factors which result in a reduced melting point are branching, and comonomer incorporation. Branching not only reduces the value of the melting point, but also reduces the total degree of crystallinity. Crystalline polymers in fact consist of both crystalline domains, or crystallites, and amorphous regions between the crystallites due to chain folding and chain ends. Generally, the greater degree of branching, the larger the amorphous fraction of the polymer. The amorphous regions display a glass transition, and by measuring the heat capacity signals associated with both the glass transition and the melting point, one can obtain information on the degree of crystallinity of the polymer, which in turn strongly affects the mechanical properties of the polymer. Similar considerations apply for polymers which incorporate comonomers. 
     Thus, in evaluating combinatorial libraries of ethylene catalysts, a rapid determination of the melting point and degree of crystallinity can give a good qualitative picture of what type of polyethylene is being produced by the catalyst. This adds a great deal of information to lower level screens such as the degree of catalyst activity and the polymer molecular weight, information which is more closely related to the end uses of the polymer produced by a given catalyst. 
     FIG. 11B shows heat capacity (HC) curves created with the apparatus of this invention for a series of ethylene-co-methyl acrylate random copolymers. The polyethylene-co-methyl acrylate copolymers used in the experiment were purchased from Aldrich, and the Aldrich catalog numbers, the percentages of methyl acylate incorporation, and melting points according to the manufacturer were: #43076-5, 9% MA, MP=93° C.; #43264-4, 16% MA, MP=85° C.; and #43075-7, 29% MA, MP=48° C. The ethylene co-polymers were dissolved at a concentration of approximately 5 wt % in trichlorobenzene, a high boiling point solvent, at 150 degrees C. Approximately 5 to 10 micro liters were dispensed onto each sensor  12  and were kept in place by the naturally occurring wells beneath the silicon nitride membranes  94 . The solvent was allowed to air dry, leaving a polymer film  90  deposited on each membrane  94 . 
     In the present example, the heat capacity data was obtained using the 2ω method, as described below. A broad peak in the heat capacity is observed, marking the melting point. This peak is due to the latent heat associated with melting of crystalline portions of the polymer and the data are comparable to the results that may be obtained by traditional DSC. The reduction of the value of the melting point and the degree of crystallinity with increasing methyl acrylate incorporation can be easily seen in FIG.  11 B. 
     Heat capacity measurements can also be used to gain information on the architecture and microstructure of glassy (entirely non-crystalline) polymers. For example, a “random” copolymer of a given composition may be either random or “blocky”, depending on whether or not the comonomers alternate in a random way or tend to occur in longer “runs” of a given monomer type. The degree of randomness or blockiness can affect the end properties of the material. The degree of blockiness can be assessed through heat capacity measurements: a random copolymer tends to have a single broad glass transition, at a temperature intermediate between the Tg&#39;s of the constituent monomers. If the random copolymer is actually blocky, however, two distinct Tg&#39;s may be observed, corresponding to domains which form almost entirely from long runs of one or the other monomer. 
     In a similar manner, heat capacity measurements can distinguish between immiscible and miscible polymer blends or between phase-separated or phase-mixed block copolymers. Phase-mixed systems show a single Tg, while phase separated systems show two distinct Tg&#39;s. Even in the case of a phase separated blend, small amounts of miscibility will occur, i.e., the two phases are not “pure”. This can also be assessed using Tg measurements, as the two Tg&#39;s will be somewhat shifted from the values for the pure polymers. 
     The above examples illustrate the many ways in which thermal analysis data can be used to gain important information on the structure and physical properties of polymers. This information can be used to evaluate the success or failure of a particular synthetic route in making a polymer with a given chemical composition and physical structure/architecture; or to judge the suitability of a particular polymer for a given application. Within the context of a combinatorial materials science approach to developing new polymer synthetic strategies or new polymeric materials, in which many catalysts, process conditions, chain compositions and architectures, etc, will be attempted, it is highly desirable to be able to obtain thermal analysis information in a rapid fashion. 
     The sensor array method and apparatus of the present invention has a significant advantage over other thermal analysis methods and apparatuses because it can characterize many different materials simultaneously and quickly. Instead of obtaining only one heat capacity scan per unit time, the inventive method and structure can obtain tens or even hundreds of heat capacity plots in the same amount of time. Further, the sensor for this particular application obtains data that can be readily correlated with known data, e.g., from a conventional differential scanning calorimeter (DSC), in that the heat capacity of the sample can be directly measured and plotted. Thus, the sensor output needs only minimal processing to generate data that can be easily interpreted. 
     Description of the Method for Using the Invention 
     The method for utilizing the present invention is also simple, and further facilitates the rapid analysis of numerous samples. Once a library of, for example, 100 polymers is created via combinatorial methods, each polymer may be deposited on the microcalorimeter sensor array of the present invention to measure each polymer&#39;s thermal properties. To form a sample  90 , a small amount of solution containing the polymer sample is placed on each sensor  12  and allowed to dry, leaving a film of the polymer behind. This can be done one sample at a time or multiple samples at a time manually or automatically, such as by using a liquid dispensing robot with a single or multiple syringe tip. In a preferred embodiment, the sensor array  10  has a standardized combinatorial chemistry format so that the polymers may be deposited simultaneously on multiple sensors  12  in the sensor array  10 , using known combinatorial tools such as multiple syringe/multiple tip pipettes, containing 4, 8, 12, or even 96 pipette tips possibly with the standard 9 mm spacing. 
     Once the solvent has evaporated, leaving a polymer film sample  90  on each sensor  12 , the sensor array  10  is simply connected to the electronic platform. This will be done, for example as shown in FIG. 4, by inserting the sensor array  10  in a positioning fixture  42  attached to the printed circuit board  30  and applying pressure to the sensor array substrate  16  by tightening screws  46  or other fasteners (such as clips or clamps) on a compression fixture  44 , insuring good contact between the sensor array  10  and the printed circuit board  30 . Preferably, the printed circuit board  30  is housed in a chamber that can be evacuated. This eliminates heat losses to the atmosphere, and noise in the temperature measurements due to convection. A heat capacity scan is then generated for each sensor  12  (typically in less than a minute), obtaining each material sample&#39;s crystallinity/amorphous properties, melting point, glass transition point, and other material characteristic information. The entire measurement procedure may be controlled and executed by a computer program in the electronic platform. Using the software, the user initially specifies which samples in the array  10  are to be analyzed and provides other measurement information, such as the temperature sweep rate and modulation frequency. 
     As a result, in this example, the heat capacity plots can be obtained for 100 samples in about 90 minutes or less, compared to around one or two samples in 90 minutes for known materials characterization devices, such as standard differential scanning calorimeters. By comparing and analyzing the heat capacity plots of each material in the library quickly, a user can select which polymers in the library have the most desirable physical properties for a selected application or determine whether or not a given synthetic strategy and set of starting ingredients has in fact produced a polymer of a desired architecture and associated-physical properties. 
     Of course, thermal analysis is not limited to polymers. The same type of analysis can also be used to characterize inorganic solid state materials, such as glasses, metal alloys, and compounds. 
     FIG. 11C shows an example using this invention of a glass transition (Tg) measurement in a thin film of low-Tg (400° C.) silica glass manufactured by Ferro Corporation, type 7578 crystallizing solder glass. Such “solder glasses” are widely used as sealing or fusing materials in a variety of specialized electronics and other applications, and the ability to rapidly measure Tg of different combinatorially synthesized silica glass formulations would be highly desirable in the development of new specialty glasses. The glass used in this example has a glass transition temperature at approximately 395° C. according to the manufacturer. The glass is normally obtained in powder form, and the powder was formed into a disk for this experiment by placing the powder in a mold and sintering at 450 degrees C. for four hours. A 1 μm thick film was then deposited onto the sensor array using laser ablation. The measurements were made using the 3ω method, described below. 
     The present invention is also useful in the context of a search for new bulk amorphous metallic alloys, metals which do not have a regular crystal structure, and which display a reversible glass transition much in the same manner as silica glasses. Such materials are highly desirable for their unique high strength and resiliency in comparison to conventional alloys. Amorphous alloys typically consist of three or more different metal atoms, and achieving desirable physical properties such as strong glass forming ability and a low Tg requires synthesizing many different alloys with slight variations in composition. Thermal analysis is a widely used technique for analyzing the glass transition and other phase transitions in candidate amorphous alloy materials. Thus, the combination of combinatorial synthesis and rapid thermal analysis is a powerful technique which can be used in the search for new amorphous alloys. 
     FIGS. 11D and 11F show examples of the determination of melting points of several pure metals, and FIG. 11E shows a thermal analysis scan for a compound using the apparatus and method of this invention. The aluminum and lead films, each about 0.5 μm thick, shown in FIGS. 11D and 11F, respectively, were deposited on the sensors by RF sputtering, using single element sputtering targets. The Al 3 Mg 2  film was deposited as a multilayer film, using a combinatorial sputtering chamber. The film as deposited contained alternating layers of 24 of AL and 26 of Mg. This layering was repeated 65 times, for a total film thickness of 3250. The layers mix to form the desired compound during the initial heating stage, which is below the melting point. The results shown in FIGS. 11D through 11F were obtained using the 3ω method, as described in this application. Thus, the present invention, when combined with combinatorial synthesis of thin solid films, can be used to map out the outlines of entire binary, ternary, and higher order phase diagrams. This can be extremely useful in the search for new solid state compounds, alloys, and other materials. 
     The method, which will be described in greater detail below, and the apparatus of the present invention, which has been described, can thus analyze libraries of metal alloys, glasses, and other solid state compounds and materials having varying compositions, to detect the occurrence of important phase transitions. Again, because of the sensor array  10  and library format used in the invention, a large number of materials can be generated and screened in a short period of time. In the preferred method of deposition, the library of thin film materials is directly produced on the sensor array substrate  16 , using combinatorial masking and deposition techniques. See, e.g., WO 98/47613, incorporated herein by reference. Solid state films can also be produced from liquid precursors by sol-gel processes. 
     In short, material samples  90  are placed in intimate thermal contact with the membrane  94  using vapor deposition techniques or by dissolving the sample in a solvent, depositing the solution on a sensor  12  and allowing the solvent to dry to form a thin sample material film on the membrane  94  of the sensor  12 . The thinness of the membrane  94  and the sample  90  allows the sample  90  to be heated through very quickly, making rapid scanning of the sample over a wide temperature range possible while still obtaining clear thermal characteristic plots showing phase transitions. This specific embodiment of the invention can scan over several hundred degrees and obtain heat capacity data for a given sample in 10 to 30 seconds, compared with 30 minutes to 2 hours for conventional calorimeters. This processing speed is further enhanced by the invention&#39;s array format, allowing parallel or rapid serial scanning of multiple samples which are deposited on a single substrate, and increasing the number of samples tested per unit time to as high as 64 or more samples in 15 minutes. 
     Experimental Example 
     Thermal Analysis with Temperature Modulation 
     FIGS. 12A through 12H and FIGS. 13A through 13F illustrate thermal analysis using temperature modulation. The preferred sensor structure for conducting this type of analysis is the structure described above and shown in FIGS. 9A through 9C, but other thermal sensor structures can be used without departing from the spirit of the invention. The following discussion of non-modulated calorimetry will provide an explanation of the theory behind heat capacity measurements and will illustrate why temperature-modulated calorimetry is the preferred method for making heat capacity measurements with the sensors  12 . 
     In an ideal or simplistic heat capacity measurement, all heat input into a sample is retained by the sample, resulting in increases in the temperature or change of the physical state of the sample. The heat capacity can then be determined as the ratio between the rate of heat input and the rate of temperature increase, C p =ΔQ/ΔT. In reality, some of the heat input to the sample is continuously lost to the environment through conduction, convection, radiation, etc. In order for the results of a heat capacity measurement to be meaningful, either some procedure must be implemented to measure or account for the heat energy lost to the environment, as is done in differential scanning calorimetry by means of an “empty cell” reference sample, or the rate at which heat is input to the sample must be much greater than the maximum rate at which heat is lost, so that losses may be neglected while maintaining a good approximation of the sample&#39;s heat capacity. 
     In the latter case, the entire measurement must be completed in a time shorter than the thermal relaxation time t1 of the sample, where t1 is the time that it takes for the sample to come to equilibrium at a new temperature when the heat input level is changed to a new value. If the heat input is set to zero, t1 is the time constant for the sample to return to the temperature of the environment. The relaxation time is given by t1=C p /k, where C p  is the heat capacity and k is the thermal loss constant to the environment. The reason for conducting a rapid (less than t1) measurement is easy to understand: if the power is suddenly turned up to a certain level, the temperature will initially increase rapidly and the losses to the environment will be negligible, since the sample is initially at nearly the same temperature as the environment. However, after a time of approximately a few times t1, the sample&#39;s temperature saturates or plateaus to a limiting value, as the heat input and losses to the environment become exactly equal. Thus, heat losses to the environment can be neglected only if the temperature increase is conducted over a time much shorter than t1. 
     For small, microthin samples, such as those tested in the invention, the time constant t1 can be quite short, typically 0.1 seconds, due to the sample&#39;s very low heat capacity. The high temperature ramp rates which must be used with such samples in a “continuous sweep” calorimetry experiment, e.g. 100&#39;s to 10,000&#39;s of degrees per second, make analysis of many phase transitions difficult or impossible, particularly in more complex materials. If a much slower ramp rate is used, then an equilibrium prevails between the heat input and the losses to the environment, and generally no information can be gained about the heat capacity. Increasingly complex materials may take increasingly long times to complete structural rearrangements that occur at a phase transition, which involve collective motions and rearrangements of many atoms or molecules. Therefore, it is desirable to use a measurement method in which the heat capacity can be measured while the average temperature is varying at an arbitrary rate. 
     AC calorimetry, when combined with the sensor design of the invention, is a preferred way to obtain a rapid determination of heat capacity versus temperature with a minimum of off-line data analysis, but without requiring prohibitively fast scanning of the average temperature. Although this discussion focuses on modulated calorimetry, other calorimetric methods may be used in conjunction with the sensors or system of this invention, including methods based on measurements of the thermal relaxation time or methods in which the entire measurement is performed in a time that is shorter than the thermal relaxation time, which are well known in the art. 
     The general concepts of AC calorimetry will now be explained in conjunction with FIGS. 12A and 12B, which are general to the concepts. In AC calorimetry, the power input to the sample consists of a slowly varying average value P(t), and a modulated part ΔP. The heater power (HP) modulation frequency 2ω (corresponding to modulation of the heater voltage V H (t) at a frequency ω, since P=V 2 /R) is chosen such that the period Δt=π/ω is much shorter than the time constant t1 for equilibration of the sample with the external environment, but much longer than the time constant t2 for internal equilibration between the sample, heater, and thermometer. 
     If the frequency ω is too low (ω&lt;&lt;π/t1), then the total power input is always equal to the losses to the environment; in this case, the temperature modulation is in phase with the power input modulation, contains information only about the thermal losses to the environment, and contains no information about the heat capacity. If the frequency is chosen so that ω&gt;&gt;π/t1, however, the sample temperature modulation lags behind the power input modulation by a phase angle of 90°, because there is insufficient time during a cycle for the sample to reach the temperatures corresponding to the maximum and minimum power inputs. The larger the heat capacity of the sample, the more slowly it responds to the power modulation, and the smaller the resulting temperature modulation will be. Under these conditions, the temperature modulation amplitude ΔT is given by ΔT=ΔP/2ωC p , where ΔP is the amplitude of the power modulation and C p  is the heat capacity. Thus, the heat capacity is inversely proportional to the temperature modulation amplitude, for a fixed ΔP. If the frequency is too high, however, i.e. ω&gt;&gt;π/t2, then the heater, thermometer, and sample are not in equilibrium with each other, and the thermometer thus does not give accurate information about the response of the sample temperature to the heater power input. 
     Thus, AC calorimetry generally involves measuring both the average temperature and the temperature modulation amplitude for a given sample, with an appropriately chosen frequency 2π/t1&lt;&lt;ω&lt;&lt;2π/t2, as the average temperature is varied. The heat capacity is given by Cp=ΔP/2ωΔT. 
     FIGS. 12C through 12H are explanatory diagrams of a particular embodiment of a heat capacity measurement system and measurement method, which uses the preferred sensor design discussed above and the AC calorimetry technique. This particular embodiment is referred to throughout this specification as the “2ω method”. FIGS. 12C and 12D are representative diagrams explaining the 2ω method, while FIGS. 12E through 12H show examples of input and output signals according to this method. 
     The voltage signal to the heater, V H (t), is the sum of a slowly varying average value V H,0 (t) and a modulation V H (t)=v H e iωt  at frequency ω, i.e., V H (t)=V H,0 (t)+v H e iωt . The input power is V H   2 (t)/R H =[V H,0   2 (t)+2V H,0 (t)v H e iωt +v 2   H e 2iωt ]/R H , and contains modulations at frequencies of both ω and 2ω. The temperature of the sample is monitored by measuring the resistance of the thermometer  102 , R TH (t). In the 2ω method, this is done by passing a small DC current I TH  through the thermometer  102  and measuring the voltage V TH (t). For many metals, the resistance varies linearly with temperature, and can be parameterized by the formula R(T)=R(T=T 0 )[1+α(T−T 0 )], where α is a constant characteristic of the metal, and T 0  is an arbitrary reference temperature. Thus, the temperature can be calculated directly from the thermometer voltage, using the formula T=T 0 +[(V TH /V TH (T 0 ))−1]/α, if α, T 0  and V TH (T 0 ) are known. 
     The average temperature and the temperature modulation at frequencies ω or 2ω can easily be determined over the course of an experiment by a number of means. The average temperature is most easily obtained by passing the thermometer voltage signal through a low pass filter  120  with a suitable cutoff frequency, which removes the modulation, measuring the filtered thermometer voltage with an analog-to-digital converter, and calculating the temperature using the formula given above. The modulation is most easily and accurately measured using a lockin amplifier  124 , with the reference frequency set at ω or 2ω depending on which frequency is being monitored. Other techniques can also be used, such as an AC voltmeter with a narrow band pass filter on the input, a spectrum analyzer, or direct recording of the waveform and subsequent off-line analysis by fast Fourier transform. 
     It is preferred to monitor and analyze the signal at frequency 2ω. The principal reason is that the power modulation ΔP(2ω), given by v 2   H /R H , varies relatively little during the experiment, varying only due to changes in the heater resistance R H  as the temperature is varied. In contrast, the power modulation ΔP(ω)=2V H (t)v H /R H  is zero when the average heater voltage is zero, and varies over a much wider range during the course of an experiment due to the linear dependence on V H (t). This leads to vanishing sensitivity near the base temperature, and a large variation in the signal-to-noise ratio over the course of an experiment. 
     The heat capacity is given by Cp=ΔP/2ωΔT, as described earlier. Because R H  increases with temperature, the input power modulation ΔP=v H   2 /R H  decreases with increasing temperature. This leads to a decrease in the temperature modulation amplitude, independent of any changes in the heat capacity. This must be accounted for in analyzing the data. Because ΔP is inversely proportional to R H , the heat capacity is proportional to 1/R H ΔT, since v H  and ω are constant during a given experiment. Although R H  can in principle be precisely determined by an additional measurement, e.g., by monitoring the DC current drawn by the heater in response to the DC voltage V H  and an absolute value of Cp determined, it is a reasonable approximation for many purposes to assume that the heater and thermometer are at the same temperature, and substitute R TH  (which is already being measured) for R H . 
     Thus, if one is only interested in identifying prominent features in the heat capacity curve that are associated with phase transitions or other significant thermal events, as is often the case, and is not interested in the precise absolute value of the heat capacity, then the heat capacity can be approximated (up to a multiplicative constant or scaling factor) by 1/[&lt;V TH &gt;ΔV TH (2ω)], where the denominator is the product of the DC and modulated values of the thermometer voltage. A plot of this quantity vs. the temperature (which is derived from V TH ) captures all of the essential information in the heat capacity curve. More precise analysis methods may be used to obtain an absolute value of the heat capacity, without departing from the scope and spirit of the invention. 
     It is now possible to explain more clearly why AC calorimetry, as embodied by the 2ω method, combined with the preferred sensor design, allows for such rapid measurements of heat capacity curves and determinations of phase transition points. A measurement of the heat capacity at a given temperature requires measuring the modulation amplitude at that temperature. An accurate measurement of the modulation amplitude typically requires averaging or Fourier transforming over at least several cycles. Five cycles, for example, is a reasonable minimum number. Thus, at a given temperature, an accurate determination of the heat capacity can be made in approximately 0.1 seconds for a typical temperature modulation frequency of 2ω=50 Hz. If it is desired to obtain one measurement per degree as the temperature is varied, for example, then the average temperature may be varied at a rate of approximately 10° C. per second, or 600° C. per minute, compared to typical sweep rates of 10° C. per minute for conventional DSC instruments. 
     In practice, the temperature is not stabilized at a set of discrete values while measurements are made at these values; rather, the temperature increases continuously, and the modulation data can be considered a “running average” of the modulation amplitude over a finite temperature range. This temperature range is typically several degrees, and is determined by the temperature sweep rate and the averaging time for the modulation amplitude measurement. 
     Referring to FIG. 12C, using the 2ω method in the sensor array structure according to the present invention does not require any modification of the sensor structure itself because of the modular sensor array structure, standardized interconnection method, and flexible electronic platform. As explained above, each sensor  12  in the sensor array  10  is connected to a multiplexer  126  or other signal routing means  129 , and both the multiplexer  126  and the electronic test circuitry  127  for driving the sensors  12  are controlled by a computer  52 . The electronic test circuitry  127  and the computer  52  together can be considered a flexible electronic platform. To characterize materials on the sensors  12  one at a time, the computer  52  controls the multiplexers  126  so that it connects a given sensor  12  the electronic test circuitry  127 . The electrical signals for a complete scan (as selected by the user) are sent to and read fiom the heater  104  and thermometer  102  on the selected sensor  12 , and then the multiplexer  126  switches the connection to link the electronics platform with the next sensor in the sequence. Thus, the invention allows for ultimate flexibility in sensor array testing. 
     Sample results from a test conducted according to the 2ω method are shown in FIGS. 12E through 12H for illustrative purposes only. More specific details on the preferred manner in which the tests are conducted are as follows: The heater ramp voltage is obtained from an auxiliary analog output of an Stanford Research Systems SRS 830 lockin amplifier. This voltage is set via instructions to the lockin amplifier from the computer, transmitted over a GPIB interface. For the specific heater  104  design in the preferred sensor embodiment, a voltage ramp from 0 to 1.5 volts is sufficient to raise the temperature of the sensor to approximately 150° C. (in vacuum). Higher maximum voltages result in higher maximum temperatures. The ramp voltage is incremented by a small amount (approximately ten times per second) and the size of the increment can be specified by the user before beginning a scanning operation. The size of the increment is typically in the range of from about 0.005 to 0.01 volts, so the total scan time is approximately 15 to 30 seconds. When the maximum voltage is reached, the ramp voltage is either ramped back down to zero at the same rate while taking data; or the ramp voltage is set to zero and the scan is completed. 
     The heater modulation voltage is generated by the same lockin amplifier&#39;s sine wave oscillator output. Fundamental frequencies of 10-40 Hz were generally used with the 2ω method, and a typical modulation amplitude is several tenths of a volt. The ramp and modulation signals are added by a summing amplifier from OpAmp Labs, which also buffers the signals and supplies adequate current to drive the heater, which has a 2-wire impedance of approximately 100 Ω. 
     The DC current for the thermometer  102  was generated by connecting a 9V battery in series with a 10 kΩ resistor and the thermometer  102 , producing a current of approximately 1 mA. The use of a battery-powered current source insures that the thermometer  102  circuit is isolated from ground and from the circuitry connected to the heater  104 . The thermometer  102  resistance is measured in a 4-wire configuration, and the 4-wire resistance at room temperature is typically 50 Ω. Thus, the initial thermometer voltage is approximately 50 mV. 
     The thermometer voltage is then analyzed to extract the average value, which gives information on the temperature, and the modulation amplitude, which gives information on the temperature oscillation amplitude and the heat capacity. To measure the average thermometer voltage, the thermometer voltage is connected to the differential inputs of an SRS 560 low-noise voltage preamplifier with variable gain and a programmable filter. The preamplifier is typically used with a voltage gain of approximately 10, and a low pass filter set at 1-3 Hz to remove the modulation. The preamplifier output is connected to an auxiliary analog-to-digital converter input of the lockin amplifier, and the voltage is read via instructions from the computer. 
     To measure the modulation voltage, the thermometer voltage is sent to the differential inputs of the SRS 830 lockin amplifier, which is set for signal detection at the second harmonic frequency of the sin wave being output from the oscillator. The second harmonic frequency is thus typically in the range 2f=20-80 Hz. The lockin input bandpass filter is set at 24 dB/octave, and a 0.3 second output time constant is typically used. Although phase-sensitive detection can easily be done, only the total magnitude of the modulation signal was recorded for simplicity. This is permissible if the frequency is properly chosen so that t1&gt;&gt;π/ω&gt;&gt;t2, where t1 and t2 are the external and internal thermal relaxation times discussed above. 
     The correct measuring frequency is chosen by measuring the modulation voltage V th (2ω) as a function of the drive frequency, and looking for a broad peak in a plot of ω*V th (2ω) versus f=ω/2π, as is well known to those skilled in the art of AC calorimetry. An example is shown in FIG. 12I, using the preferred sensors discussed above. At low frequencies ω&lt;&lt;π/t1, the temperature modulation amplitude ΔT and V th (2ω) are independent of frequency, since a balance always prevails between the modulated heat input and the losses to the environment. In this region, ω*V th (2ω) increases linearly with Ω. In the optimal frequency range for conducting calorimetry measurements, ΔT is proportional to 1/ω, as explained previously, so ω*V th (2ω) is approximately constant. At high frequencies ω&gt;&gt;π/t2, the thermometer temperature is out of equilibrium with the heater temperature, since there is insufficient time for heat to diffuse across the width of the thermometer during a single cycle. The temperature distribution over the thermometer takes the form of a damped travelling wave, with a wavelength shorter than the size of the thermometer, and the average temperature and voltage modulation decrease as the frequency is increased above π/t2. Thus a plot of ω*V th (2ω) has the form of a peak, with the broad maximum indicating the optimum frequency range for performing calorimetry measurements. Because of the breadth of the peak in this plot, it is not necessary to perform a frequency analysis for each sample. Once it has been done for a given type of sample (e.g. a class of materials with roughly similar film thickness and thermal conductivity), the same frequency can be used for all subsequent measurements on samples of that general type. In the example, 15 Hz is preferred, but anywhere in the range of from about 5 to about 30 Hz may be used. 
     Once the modulation frequency and amplitude have been set and all of the signals are properly routed, numerous measurements can be rapidly made using a simple procedure. In the preferred embodiment of the procedure, a group of sensors is first specified for measurement via manual input to the computer by the user. Once this has been done, the user instructs the computer to begin an automated measuring procedure. All operations described below are performed automatically by the computer, following parameters set by the user before the automated procedure is begun, such as setting the ramp rate, etc. 
     The computer closes selected switches in the multiplexer so that the first sensor in the specified set is connected to the electronics instruments (current source, lockin, oscillator, etc.). It is desirable to wait several seconds for the electronics to settle after closing the connections between a sensor and the electronic platform, to eliminate transient responses. 
     The heater ramp voltage is initially zero. Before beginning to increase the ramp voltage, the computer records the average thermometer voltage, which is defined as V(T 0 ). T 0  is the temperature of the sensor at the beginning of the scan. This will be somewhat higher than room temperature due to the power dissipated in the heater by the modulation voltage. In a preferred procedure, the modulation voltage is also set to zero before V(T 0 ) is recorded. It can then be assumed that T 0  is equal to the room temperature, provided that the heat dissipated in the thermometer  102  by the DC current causes only minimal self-heating. Various other procedures may be performed to determine more precisely the sensor temperature at the beginning of the scan. 
     The modulation voltage is then turned on again, and the following procedure is iterated or looped approximately ten times per second: (1) measure the average thermometer voltage &lt;V th &gt; and the modulation voltage V th (2ω); (2) calculate the temperature T using the formula T=[&lt;V th &gt;/V th (T 0 )−1]/α+T 0 , where the coefficient α is characteristic of the metal which the thermometer is made out of and can be determined separately by a variety of well known means. For Pt, typically α=0.0025-0.003; (3) calculate a quantity proportional to the heat capacity, referred to as the “heat capacity signal” C p , using the formula C p =[&lt;V th &gt;*V th (2ω)] −1 , as discussed above; (4) store the values of the time, the heater drive voltage V H , and the measured and derived quantities &lt;V th &gt;, V th (2ω), T, and C p  in computer memory; (5) increment V H  to a new value; and (6) repeat steps (1) through (5). When the scan is finished, V H  is set to zero and the data stored in memory are transferred to a file on a storage device. The next sensor is then selected by the computer and multiplexer, and the entire scan procedure is repeated. 
     An alternative AC calorimetry method that can be used in the invention is the “3ω” method. For measurements concerning the thermal response of polymers, the 3ω method is preferred. FIGS. 13A and 13B are representative diagrams explaining the preferred materials characterization apparatus configuration using the 3ω method, while FIGS. 13C through 13F show examples of input and output signals according to this method. In this method, the heater receives only a ramped DC voltage V H,0 (t), instead of a ramped voltage with a modulated AC voltage superimposed thereon. Also in the “3ω” method, an AC current in the form of a pure sine wave at frequency ω is sent through the thermometer instead of a DC current. The AC current through the thermometer preferably has a constant amplitude. Further, rather than measuring the 2ω modulation amplitude and the average value of the thermometer voltage to determine the sample material&#39;s heat capacity and temperature, respectively, the 3ω method measures the third harmonic in the thermometer voltage to determine the sample&#39;s heat capacity, as shown in FIG. 13E, and measures the first harmonic voltage to determine the temperature, as shown in FIG.  13 D and as explained below. 
     If the AC current amplitude is sufficiently small, or the sample&#39;s heat capacity is sufficiently large, then the temperature of the sample does not vary in response to the AC current. The thermometer resistance is constant, and the thermometer voltage is a pure sine wave, since V TH =IR TH  and I is a pure sine wave. In this case there are no higher harmonic signals. If the AC current is sufficiently large, however, the input power modulation at frequency 2ω will cause a temperature modulation, and therefore a resistance modulation, at frequency 2ω, i.e., R TH (t)=&lt;R TH &gt;+ΔRe 2iωt , where ΔR is proportional to ΔT. Since V TH =IR TH  and I is a pure sine wave, V TH =I 0 e iωt R TH (t)=I 0 &lt;R TH &gt;e iωt +I 0 ΔRe 3iωt . The first harmonic voltage is thus proportional to the thermometer resistance, and therefore to the temperature, while the third harmonic voltage is proportional to the temperature modulation, and therefore gives information about the heat capacity, as in the 2ω method. 
     Typically, the ω component of V TH  is between 100 and 1000 times larger than the 3ω component, depending on the sample&#39;s particular thermal characteristics, the AC signal amplitude, and the geometry of the heater/thermometer  100 . To analyze the voltage output from the heater/thermometer  100 , a component in the electronic platform that receives the voltage output can lock in at frequency ω to detect the basic sine waveform and at frequency 3ω to detect the third harmonic. As explained in FIGS. 13A and 13B, two separate lockin amplifiers  130 ,  132  or a single lockin amplifier that can switch between the two frequencies can be used. The advantage of using two separate lockin amplifiers tuned, respectively, to the ω and 3ω frequencies  130 ,  132  is that both the temperature and the heat capacity measurements can be conducted simultaneously in real time, greatly increasing measurement speed and eliminating the waiting period needed for a single lockin amplifier to settle after switching its frequency. A representative block diagram illustrating the components of a preferred sensor array and electronic platform for the 3ω method is shown in FIG.  13 B. 
     The 3ω method in its preferred embodiment requires additional signal processing equipment or methods in order to extract separately the modulation amplitudes at two separate frequencies. However, the 3ω method has a number of advantages over the 2ω method as well, and is the preferred embodiment. In the 2ω method, the power modulation is produced by the heater  104 , while the temperature modulation is sensed at the thermometer  102 . The time constant t2 is the thus time required for heat to diffuse laterally across the membrane  94  from the heater  104  to the thermometer  102 . While this time can be made fairly small, this still limits the frequency range to typically 5-50 Hz, and therefore places some limits on the measurement speed. 
     In the 3ω method, the temperature modulation is both produced and measured by the thermometer; in this case, t2 is the time required for heat to diffuse vertically across the thickness of the membrane  94  and into the thin film sample  90  rather than horizontally from the heater  104  to the thermometer  102 . Because the sample  90  and the sensor  12  taken together are typically only a few microns thick, this time is much shorter than the t2 associated with the 2ω method. This in turn permits the use of measuring frequencies in the kHz range, with a corresponding increase in the possible temperature ramp rate and measurement speed. In addition, because the modulated power does not have to diffuse any distance laterally across the membrane, there are no radiative losses as the power travels from the modulation source to the modulation sensor since they are one and the same. 
     Sample test results obtained using the 3ω method are shown in FIGS. 13C through 13F. The samples are a film of low Tg solder glass, form Ferro, as detailed above. The configuration of the electronics platform for the 3ω method is somewhat different than for the 2ω method, but once the configuration is completed, the measurement procedure is essentially the same as described above with respect to the 2ω method. The heater ramp voltage is generated in the same way as in the 2ω method, but instead of being summed with a modulation signal, it is simply buffered and sent to the heater  104 . The modulation signal contains a sinusoidal AC current and is sent to the thermometer  102  instead of the DC current used in the 2ω method. The AC current can be produced in many ways. For the example discussed here, the sinusoidal voltage output from a lockin amplifier&#39;s oscillator output is used as the input to a voltage-controlled current source, which is a simple op-amp circuit. The amplitude of the modulation current is typically several tens of mA in order to get an adequate third harmonic signal due to temperature modulation. 
     The thermometer  102  is connected in parallel to the differential inputs of two separate lockin amplifiers  130 ,  132 . A ω lockin amplifier  130  is set to detect signals at the same frequency as the oscillator driving the AC current source, while a 3ω lockin amplifier  132  is set to detect signals at the third harmonic of this frequency. The oscillator output from the lockin  130  used to drive the AC current source is also connected to the reference input of the second lockin  132 , insuring that both lockins  130 ,  132  are synchronized and tuned to the correct reference frequency and phase. As noted above, the signal at 3ω is typically 100-1000 times smaller than the signal at ω (e.g., 10 μV vs. 10 mV), so a much higher gain setting is used for the lockin which is monitoring the third harmonic. Because the 3ω lockin  132  must reject the much larger first harmonic signal, it must usually be used in “high dynamic reserve” mode, instead of “low noise” mode as is possible in the 2ω method, in order to avoid overloading the inputs. 
     Once the measurement has, been configured, the same measurement procedure used in the 2ω method can be used in the 3ω method. In this case, V th (ω) corresponds to the resistance of the thermometer  102  and the average temperature; and V th (3ω) corresponds to the temperature modulation and heat capacity, as explained earlier. The temperature is calculated from V th (ω) in the same way as described above for the 2ω method using &lt;V th &gt;. However, the heat capacity is approximated as Cp=V th (ω)/V th (3ω), which differs in form from the formula Cp=[&lt;V th &gt;*V th (2ω)] used with the 2ω method. 
     The reason is again related to the formula C p =ΔP/2ωΔT, discussed earlier. In the 3ω method as described here, the modulation is driven by a sinusoidal current of fixed magnitude I th , and the power modulation in the thermometer ΔP is given by I th   2 R th , which is proportional to R th  and therefore to V th (ω). In the embodiment of the 2ω method described earlier, the modulation power to the heater was due to a modulation voltage of fixed amplitude v H . The modulation power is then v H   2 /R H , and is inversely proportional to the heater resistance. 
     It should be noted that both AC and DC power can be coupled into the heater  104  and/or thermometer  102  in either the 2ω or 3ω methods, and the temperature and temperature modulation may be determined by monitoring either the voltages on the sensors caused by known currents, or the currents caused to flow by known voltages. It should also be noted that other implementations of AC calorimetry in a sensor array format are possible, without departing from the spirit of the invention. For example, two separate heaters and one thermometer can be used, wherein one heater provides a DC power input and the other heater provides an AC power input. Also, a single resistive element can be used as both a heater and thermometer if the 3ω method is used and the resistive element is properly designed so that the temperature is substantially uniform over the area of the thermometer. An example of such a sensor design is shown in FIG.  13 G. Although the sensor consists of a single wire, with uniform current passing along its entire length, the voltage is only measured from a portion of the wire, which is in the center of the area being heated. A combined DC and AC current is used, and the voltage may have frequency components at all harmonics up to the third. As in the previous description above, the temperature and heat capacity may be obtained from the first and third harmonics, respectively. This sensor design has the advantage that both AC and DC power are created uniformly across the entire sensor. 
     Further, the temperature of the sensor can be varied via an external heating method, such as contact with a heated block or illumination by infrared radiation, while the temperature and temperature modulation are measured electronically by the temperature sensor  102 . 
     Although the preferred substrate for thermal analysis is a film having a thickness comparable to the thickness of the sample, the use of modulation techniques, such as the 3ω method, also permits thermal analysis of films on substrates that are much thicker than the sample. In such a case, the modulation frequency must be sufficiently high so that the distance over which heat diffuses into the substrate during one modulation cycle is comparable to or less than the sample thickness. This distance defines the effective sampling depth of the modulated calorimetry measurement, and so the heat capacity contributions from the sample and substrate will be comparable, even though the total heat capacity of the substrate is much larger. The 3ω method is particularly useful in this case because it can access much higher measuring frequencies than the 2ω method. 
     Experimental Example 
     Thermal Stability Analysis 
     The thermal analysis array structure explained above can also be used to measure the thermal stability of a material. Thermal stability measurements indicate how hot a material can get before it decomposes or vaporizes and how quickly decomposition takes place as its temperature increases. Thermal stability is particularly important when determining whether a particular material can withstand high temperatures without breaking down or otherwise exhibiting volatile properties. 
     Thermal stability can be measured in several ways. FIG. 14 shows sample results of a glass transition and thermal decomposition of a polystyrene film using the sensor array of the present invention. The polystyrene was obtained from Aldrich and used as obtained, which was catalog no. 43,010-2 having a listed melt index of 8.5 and a molecular weight of 230,000. The polymer sample was dissolved in toluene to create a 3% solution, which was manually pipetted onto the sensor. The sample was allowed to air dry on the sensor and then placed in a chamber that was evacuated for a measurement using the 3ω method, described above. Thermal stability measurements can be conducted via any of the signal modulation methods described above. The measurement is conducted in an identical manner as the heat capacity measurement, but the temperature is increased until the material decomposes or otherwise gives up mass. When this occurs, the heat capacity drops sharply and the modulation amplitude increases sharply. This occurs because the same amount of modulated power is going into the heater/thermometer  100  and the membrane  94 , but the sample has partially or largely disappeared, so the modulation becomes larger. Further, because the change in the material is not reversible, the modulation will remain large even if the temperature is lowered because of the material&#39;s irreversibly changed state. 
     Heat capacity and thermal stability measurements conducted in this manner are most appropriate for materials that do not liquefy excessively when exposed to heat, such as high molecular weight polymers, because materials having extremely low molecular weights may not stay on the heater/thermometer  100  when heated and may tend to run to the edges of the sensor  12 , leaving the heater/thermometer  100  exposed. As a result, the exposed heater/thermometer  100  will give a false indication of decomposition (e.g. a large increase in modulation), because much of the material is no longer on the sensor  12 , when in reality the material has simply liquefied and flowed off the heater/thermometer  100 . Thus, the thermal capacity measurements described above are more suitable for materials that tend to hold their shape rather than low viscosity liquids. Thermal stability can also be measured with the present invention by heating the sample material on the heater/thermometer  100  in a chamber until it bums and decomposes, then measuring the amount of gaseous fragments in the air as well as the fragments&#39; mass and the air pressure within the chamber. 
     Dynamic Thermal Analysis 
     Dynamic thermal analysis may be a less quantitative technique for identifying phase transitions. A sample is typically placed in a cell in contact with a heater block. One thermometer monitors the temperature of the sample, while another thermometer measures the temperature in a reference cell or reference location. The difference in the temperatures of the two thermometers is measured as the temperature of the heater block is steadily raised. The sample temperature tends to lag behind the reference cell temperature, in proportion to the heat capacity of the sample. Thus, phase transitions, such as glass transitions or melting points, show up as kinks or bumps in the temperature vs. time curve. 
     A preferred structure for conducting dynamic thermal analysis in a sensor array according to the invention is shown in FIG.  15 A. The structure has a heater block  150  constructed from a block of material having good thermal conductivity, such as copper or another metal. The high thermal conductivity of the block material causes the heater block  102  to have and maintain a uniform temperature throughout even while the heater power and temperature are varied. 
     The preferred structure also includes a glass plate  152  that is placed on top of the metal block. Glass is the preferred material for thicker substrates because of its relatively low cost, rigidity, and low thermal conductivity. A plurality of temperature sensors  154 , are printed on the top surface of the glass plate  152  in any desired array configuration using any known method, such as lithography. Because glass has very poor thermal conductivity, there will be a relatively large difference between the top and the bottom surfaces of the glass plate  152 . 
     For clarity, the following discussion will describe characterization of a single material, but a library of materials can be simultaneously and/or selectively characterized on the sensor array. The main principle behind dynamic thermal analysis is that the temperature drop across the thickness of the glass plate or between two predetermined points on a surface of the glass plate is proportional to the heat flow through the glass into the sample. Although this ignores the heat flow that is absorbed by the glass to raise its temperature, this heat absorption is the same at all locations on the sensor array and can effectively be disregarded. For materials characterization, as illustrated in FIG. 15A, a sample material is placed on a sensor and the temperature of the heater block T0 is increased to supply heat through the glass plate  152  to a sample  156 . In this particular example, the temperature increase in the heater block  150  will create a temperature difference ΔTij across the thickness of the glass  152 , and the heat will eventually conduct through the glass to heat the sample up to a temperature Tij. Thus, the temperature difference across the glass plate ΔTij=Tij−T0. Alternatively, the temperature difference can be measured between a point on the glass plate  152  containing the sample and a reference point on the glass plate  152 , which reference point may contain a sample that is known to not have any phase transitions in the temperature range of interest. 
     The sensors  154  on the glass plate  152  measure the temperature and temperature increase rate of each sample. If the temperature of the sample  156  is rising at 1 degree per second, for example, there must be a certain amount of heat flowing through the glass  152  to the sample  156 . When the temperature of the heater block  150  is ramped upward, a certain amount of heat flow J is required to increase the sample&#39;s temperature at the same rate. If there is not enough heat supplied to the sample  156  to raise its temperature, the temperature of the sample  156  increases mores slowly than the heater block  150 , increasing the temperature difference ΔTij between the top and bottom surfaces of the glass  152 . As the temperature difference increases, more heat flows through the glass  152 . For each material, there is a specific value of ΔTij at which the heat flow through the glass  152  is the correct, steady state amount for raising the temperature of the material sample. Because each material has different thermal characteristics, the heater temperatures at which this steady state condition occurs, and thus the ΔTij value, will be different for different materials. 
     The temperature difference ΔTij corresponds qualitatively to the heat capacity of the sample  156  because some materials require a greater heat input to raise its temperature a certain amount and therefore causes a higher value for ΔTij. As a result, a large ΔTij corresponds qualitatively with a higher heat capacity material, while a lower ΔTij corresponds to a lower heat capacity material. More importantly, the large changes in the heat capacity, which occur at phase transitions, will show up as kinks or bumps in the temperature vs. time data for a given sensor. For example, the temperature difference ΔTij between the top and bottom surfaces of the glass plate  152  increases sharply at a melting point because large increases in the heat input result in little or no change in the sample material&#39;s temperature; the temperature increase in the sample material lags behind the temperature increase in the heater block  150  by a much larger amount than at a point away from the melting point of the sample  156 . After melting is complete, ΔTij may return to a lower value. 
     The structure for dynamic thermal analysis is particularly suitable for testing materials that cannot dissolve easily in a liquid and form a thin film on the sensor when the liquid evaporates, such as highly crystalline polyethylene samples. For dynamic thermal analysis, as explained above, the sample material can be simply dabbed onto each sensor without having to form a thin film, e.g., from a slurry, gel, or powder. Further, the thermal characteristics of the glass plate  152  in the present embodiment do not adversely affect the thermal characterization procedure if the dimensions of the material sample and the glass plate&#39;s thickness are on the same order of magnitude. 
     FIG. 15B is a representative block diagram of a materials characterization apparatus that is designed for dynamic thermal analysis. As explained above, an insulating substrate, such as a glass plate, has a plurality of thermometers  154  disposed on its surface and sits on top of a metal block heater. The temperature of the metal block heater is increased, and the electronic platform monitors the temperature of the block with one or more thermometers that are in contact with the block. 
     Because the entire sensor array structure is heated simultaneously in this particular example, all of the samples on the sensor array must be measured simultaneously or via rapid repeated scanning. Therefore, the preferred electronic link between the sensor array and the electronic platform will include multiple channels for monitoring the sensor operation, preferably one channel per sensor, for maximum speed. Alternatively, the electronic platform rapidly scans through all of the sensors via the multiplexer to measure each sample&#39;s temperature (by measuring the resistance in each thermometer). The temperature difference ΔTij can be calculated by the computer or processor, if desired, to generate the thermal characterization data and/or plot. The reference temperature can be the temperature of the heater block  102 , or the temperature of a sensor that does not carry a sample or that carries a sample having no phase transitions over the temperature range being studied. 
     Experimental Example 
     Dielectric Spectroscopy 
     The sensor array of the present invention is not limited only to conducting thermal analysis. As illustrated in FIGS. 16A through 16D, for example, the invention can also characterize electrical properties, including but not limited to the complex dielectric constants of materials. 
     The basic principles behind dielectric spectroscopy are now briefly discussed. To measure the dielectric constant of a material, the material is typically placed in between two metal plates that have an electric field in between them going from a positive charge to a negative charge. If the molecules of the material in between the two metal plates are more asymmetric, they usually have a greater tendency to polarize in response to the electric field, and the molecules will rotate so that they align with the electric field. The molecular realignment of the material creates its own electric field responsive to the electric field imposed on the material and tends to cancel out at least part of the imposed electric field. Materials having stronger dipole characteristics (and therefore a greater dielectric constant) will create a stronger responsive electric field and will therefore cancel out a greater portion of the imposed electric field. 
     The overall electric field reduction can be measured by monitoring the charge Q required to create a voltage V between the two metal plates. When the material to be tested is placed between the metal plates, an additional charge (ε−1)Q may flow onto the plates to maintain the voltage V, wherein ε is the dielectric constant of the material. As can be seen from the equation, a material with a larger dielectric constant will require more charge to achieve a given voltage drop across the metal plates. In short, the plates and the material together form a capacitor, and changes in the capacitance reflect changes in the dielectric constant. 
     The dielectric constant provides information about the physical characteristics of the material being tested at the microscopic level. Some molecules whose positive and negative charges are at the center of each atom in the molecule will exhibit dielectric properties when placed in the electric field because the electric field will slightly displace the nuclei of the atoms in the molecules, creating a positive charge at one end of molecule and a negative charge at the other end. Materials that exhibit greater dielectric properties, however, often have molecules that are asymmetrically charged to begin with. When the material is placed in the electric field, the molecules simply rotate and align themselves with the electric field. 
     Monitoring the dielectric properties of materials over time is an effective way to detect, for example, curing or cross-linking of glues, thermosets, epoxies, and similar adhesive materials. FIG. 16B illustrates an example where the dielectric properties of a 5-minute epoxy are monitored over time using the sensors described below. In a typical epoxy curing reaction, the molecules in the liquid resin initially move and rotate relatively freely, allowing them to orient in response to an imposed electric field. As the molecules begin to cross-link (e.g., thereby hardening the epoxy or glue), they are less able to align themselves in response to the electric field, decreasing the dielectric constant of the material and thereby decreasing the sensor&#39;s capacitance. After the epoxy is completely cured, the molecules are not able to realign themselves, dropping the dielectric constant of the material, and therefore the capacitance of the sensor down even further. Thus, monitoring changes in the dielectric constant of a material over time can provide valuable information about the speed and nature of chemical reactions, such as the epoxy curing reaction described above. 
     FIGS. 16A,  16 C,  16 D and  16 E explain the preferred sensor geometry and apparatus structure that can be used for dielectric spectroscopy in the sensor array of the present invention. For simplicity, the structure and operation of only one sensor is discussed, but, like the other experimental examples, the preferred method and apparatus for conducting testing involves using a plurality of sensors disposed on a sensor array and coupled with an electronic platform, as represented in FIG.  16 E. The most common technique for measuring the dielectric constant of a material is, as noted above, forming a capacitor with the material to be tested in between two plates. Forming a sandwich-type capacitor and obtaining measurements from such a capacitor, however, is often a cumbersome operation, especially when used with liquid samples. Furthermore, the geometry of the capacitor needs to be well defined; the user should know the exact thickness of the capacitor layers, position the plates, and maintain these dimensions throughout the testing. 
     As shown in FIGS. 16C and 16D, a preferred sensor structure for dielectric measurement according to the present invention is a planar capacitor having interdigitated electrodes  160 . The interdigitated electrodes look somewhat like two interlocking combs where the “teeth”  162  do not touch each other. Note that because the thermal characteristics of the substrate  164  are not a concern when measuring electrical properties, the substrate supporting the electrodes  160  can have any thickness (i.e., it does not have to be a thin membrane). However, it is desirable that the substrate  164  should have low dielectric losses under the desired measurement conditions and not exhibit any phase transitions or other unusual behavior. Thus, the electrodes  160  themselves can be printed on glass sheet, quartz, sapphire, or any other desired inert substrate material. 
     The advantage of the interdigitated electrodes is that the material sample&#39;s dimensions do not affect the output of the sensor because the capacitors formed by the wires of the interdigitated electrodes  160  are so small; as long as the thickness of the material placed on the electrode  160  is a few times larger than the spacing between the electrode wires, the thickness of the material sample is no longer important because the electric field is virtually zero at a distance that is several times the spacing between the wires  162 . For example, if the spacing between wires  162  in the electrodes is 5 microns, the electric field is reduced roughly by a factor of 10 for every 10 μm of distance away from the surface. The wire spacing is preferably kept as small as possible so that the capacitance can be kept large enough to measure easily. More particularly, the capacitance obtained from a given sensor will be in the range of L 2 /D (in picofarads pF), where L is the length of one side of a square sensor and D is the spacing between the wires, both in units of centimeters. For this example experiment the electrode  160  dimensions for use in the sensor array of the present invention was a 2 millimeter square sensor with a 5 micron wire spacing, which will give capacitance readings of around 10-15 pF. However, the electrodes  130  can any have dimensions to obtain a capacitance range meeting the user&#39;s own specifications. 
     For example, the sensor array used in the experiment shown in FIG. 16B was fabricated from 1000 Å Cr metal on a 5″ square glass substrate using a standard photomask blank as a starting substrate. The starting substrate is preferably purchased pre-coated with the metal and a photoresist. The photoresist was patterned by contact printing from a master photomask, and the exposed Cr metal was etched away chemically. The resulting interdigitated electrodes  130  cover a 2 mm square and contain lines and spaces of 5 μm. 
     FIG. 16E is a simplified block diagram representing a materials characterization system having a sensor array that is designed for measuring dielectric properties. Like the other embodiments described above, the sensor array is controlled by an electronic platformn via a multiplexer that directs electronic signals to and from selected sensors. The electronic platform can measure the complex impedance across each capacitor to determine the capacitance, resistance and complex dielectric constant of the materials on each sensor. For example, the capacitance of a sensor can be measured in less than 0.1 seconds using a conventional capacitance/resistance meter or impedance analyzer. The multiplexer can scan the electrodes  160  in any order and any combination rapidly, as explained in previous examples. Alternatively, a separate drive circuit can be provided for each sensor so that the sensors can be measured simultaneously. The capacitance and losses due to the various interconnect circuitry, including wires, signal routing means  129 , etc., can be measured with the sensor array  10  removed from the apparatus. Subsequent measurements with a sensor array  10  in place can then be corrected to separate the impedance of the electrodes  160  from the impedance due to the interconnects. 
     Because dielectric spectroscopy does not necessarily involve measuring the thermal properties of the material, monitoring the material temperature is not necessary if measuring the dielectric constant alone. However, the interdigitated electrode structure can be combined with, for example, a resistance thermometer  166 . This combined structure can monitor changes in the dielectric constant during a chemical reaction while simultaneously monitoring thermal events such as exotherms. The combined electrode/thermometer structure preferably has the thermometer placed in the center of the electrode to provide the most accurate temperature reading. By conducting the dielectric and thermal measurements simultaneously, more information is made available from a single experiment. In addition, the glass transition of the cured resin can be measured by operating the system in Dynamic Thermal Analysis modes as described above. 
     More specifically, the scans shown in FIG. 16B were obtained by coupling selected sensors to an SRS 560 LCR meter (inductance/capacitance resistance meter) operated at a 1 kHz frequency. Although one preferred operation mode includes repeated measuring the capacitances of multiple sensors in the array  10  during a single experiment, the data shown in FIG. 16B was acquired one sample at a time. The LCR meter was coupled to a selected sensor&#39;s contact pads  14  via two wires attached to micropositioners. Once the sensor was contacted, a fluid sample was applied directly to the sensor, and measurements were recorded manually once per minute, for a total time of ten minutes. The capacitance of the leads, before connecting them to a sensor, was approximately 1 pF. The capacitance of a bare sensor with the leads was approximately 15-20 pF. The capacitance of a sensor with one of the epoxy components placed on top of it was typically 30-40 pF immediately following application of the sample. 
     The epoxy used in the specific example shown in FIG. 16B is Devcon 5-minute epoxy. In the experiments conducted on the individual epoxy components, denoted A and B in the figure, fresh samples of the components were removed from the storage tube immediately before being applied to the sensor. When a mixture of A and B was tested, the two components were removed from their tubes and mixed for approximately 30 seconds before being applied to the selected sensor. A large reduction of the sensor capacitance can be seen for the sample of the mixed epoxy, corresponding to setting, while the capacitance for the individual components A and B change by much smaller amounts. 
     Determining the dielectric properties of materials in and of themselves can also be important. For example, integrated circuits often includes dielectric layers separating multiple wires from each other to minimize or eliminate cross-talk, and it has been found that lower dielectric constant materials, which do not polarize easily, allow signals to propagate more quickly. Thus, conducting dielectric spectroscopy according to the claimed invention allows rapid screening of many materials to find materials that have the optimum dielectric properties. 
     Experimental Example 
     Surface Launched Acoustic Wave Sensors 
     FIGS. 17A and 17B show an example of a surface launched acoustic wave sensor  170  for measuring material properties such as viscosity, density, elasticity, and capacitance. An electrode in the surface launched acoustic wave sensor may also have interdigitated fingers  172 , in this case for launching and measuring transmission of acoustic energy. Further, like the examples shown in FIGS. 16C and 16D and described above, the interdigitated structure of the sensor electrodes in FIGS. 17A and 17B can measure the dielectric constant and the conductivity of the material, if desired. 
     In this example, surface launched acoustic wave sensors can be fabricated on thin silicon-nitride or etched silicon membranes  174  similar to those described above. A piezoelectric material  176 , such as zinc oxide, is then deposited as a thin layer on top of the membrane to produce an acoustic wave sensing device. The physical dimensions of the electrode, such as its thickness, size, and configuration, can be adjusted so that the electrode operates in, for example, a surface acoustic wave (SAW) resonance mode, a thickness shear mode (TSM), a flexural plate wave (FPW) resonance mode, or other resonance mode. When the electrode acts as a resonator, its resonating response is affected by, for example, the sample&#39;s viscosity and density. U.S. application Ser. No. 09/133,171 to Matsiev et al, filed Aug. 12, 1998, describes mechanical resonators in more detail and is incorporated by reference herein. 
     Thus, because the surface launched acoustic wave device shown in FIGS. 17A and 17B can serve as both a mechanical resonator and as a sensor for characterizing other material properties, such as the dielectric constant, multiple devices can be arranged in a sensor array format to screen material properties. The versatility of the surface launched acoustic wave device and other mechanical resonators make it a good choice for observing multiple materials as they undergo a chemical or physical process involving changes in viscosity, density, conductivity, molecular weight, or chemical concentration. 
     Further, the mechanical resonator can be used to measure weight or force because of its responsiveness to mechanical loading. When surface launched acoustic wave sensors are arranged in an array format, the sensor array can be used to weigh simultaneously multiple samples of powders or liquids, each sensor acting as a separate scale. As noted above, these mass measurements can be conducted simultaneously with viscosity, conductivity, and dielectric constant measurements due to the interdigitated structure of the sensor electrode. Electroplating or solution deposition could also be measured using the arrayed mechanical resonators by correlating the resonator response to mass loading. 
     The mechanical resonator structure shown in FIGS. 17A and 17B can also be used for magnetic material characterization. More particularly, the mass loading effect of the resonator can be used to measure a sample material&#39;s response to an external magnetic field. In this application, the resonators in the array are coated with the test material or materials, and the sensor array is placed in a magnetic field. Any magnetic response of the material to the magnetic field would appear as a change in the mass loading experienced by the resonator. This mass loading change damps the resonance signal from the resonator, and the amount of damping can be correlated with the material&#39;s response to the applied field. Alternatively, a mechanical actuator can be used in the same manner as the mechanical resonator, and characterization would be conducted by measuring the amount of displacement in the actuator. 
     Experimental Example 
     Electrical Transport Properties 
     Yet another set of material properties that can be measured using the materials characterization system of the present invention are the electrical transport properties of materials: electrical resistance, Hall effect resistance, magnetoresistance, and current-voltage curves showing non-linear features such as breakdown voltages and critical currents. As explained above, the “plug-and-play” format of the invention may only requires the user to change the sensor array, not the entire machine or any hardware, to measure a different material property, depending on the embodiment being practiced. The changes may occur at the sensor level; the electronic platform and multiplexer can remain generally the same regardless of the specific material characteristic to be tested. Minor variations in the electronic hardware, such as amplifiers, voltmeters, capacitance meters and the like may be needed to conduct the measurements, but these modifications can be external to the sensor array and can be conducted in the flexible electronic platform. The following discussion will focus on the specific sensor structure that is used to measure electrical transport properties; the connections between the sensor array, the multiplexer, and the electronic platform, as well as their operations, are similar to the connections and operations described above. 
     FIG. 18A show a preferred sensor structure that can measure the electrical transport properties of a material. Like the above examples, a plurality of the sensors are disposed in an array format to measure these properties for a materials library quickly. As is known in the art, resistivity is an intrinsic property that does not depend on the dimensions of the material, and resistance equals the resistivity ρ of the material times the length of a material sample L divided by the material sample&#39;s cross-sectional area A (R=ρL/A). The Hall coefficient, as is also known in the art, indicates the number of electrons or holes in a material per unit volume and indicates the sign of the charge carriers. 
     Measuring these two characteristics according to the present invention is relatively simple. The materials to be tested are formed into bars  180  having known dimensions, and the sensors used to test the material are equipped with six leads  182  that preferably contact the bar of material at both ends and in the middle, as shown in FIG.  18 A. The bars  180  themselves can be formed by depositing the library elements through a mask onto the leads  182 , or by depositing the materials on the substrate first using a mask and then printing the leads  182  on top of the bars  180 , again using a mask. In some cases, the bar  180  should be sintered or annealed after deposition, so the anticipated effects of the sintering/annealing process on the contacts should also be considered when selecting a depositing order. Like previous embodiments, the contact pads in this embodiment provide the connection between the sensor array and the electronic platform that sends and reads signals to and from the individual sensors. 
     To obtain a material&#39;s resistance, an AC or DC current is simply passed through the bar  180  and the AC or DC voltage across the bar  180  is measured using leads EC or FD, without placing the sensor array in a magnetic field. To obtain a material&#39;s Hall coefficient and magnetoresistance, the sensor array should be placed in a magnetic field B that points perpendicular to the substrate. The magnetic field B can be generated in a variety of ways. For example, a large permanent magnet or electromagnet  184  can be used to generate a magnetic field that is perpendicular to the substrate over the entire sensor array, as shown in FIG.  18 B. Any non-uniformity in the magnetic field B can be detected before conducting the materials characterization, by using an array of identical, calibrated Hall effect sensors, and this non-uniformity can be taken into account in any subsequent analysis of the data obtained from the sensor array with samples. Alternatively, as shown in FIG. 18C, an array of permanent magnets or electromagnets  186  having the same array format as the sensor array can be used in place of the single magnet. The pole portions of the magnet array are preferably placed close to the individual samples and sensors in the sensor array. As for the single magnet, the magnet array can be calibrated with an array of Hall effect sensors to detect any non-uniformities or variations in the field strengths produced by the individual magnets so that these variations can be taken into account in subsequent analysis of the data from the sensor array. 
     During testing, a current is sent through the bar  180  using contacts A and B. The material&#39;s resistance in a magnetic field, known as magnetoresistance, can be measured in the same manner as resistance except the sensor array is exposed to a magnetic field so that the sensor can measure any changes in resistance in response to the magnetic field. The Hall voltage is obtained by measuring the voltage across the width of the bar, at contacts CD or EF, and the Hall resistance is given by: 
     
       
           V   H   =IR   H   =I ( B/nec )  
       
     
     As can be seen from the equation, the Hall voltage for a given magnetic field strength corresponds to the charge carrier density (n) and the sign of the carriers (+e or −e) for the material being tested. As is well known in the art, the Hall voltage results from the forces on moving charge carriers in a magnetic field. This force, which is perpendicular to the direction of motion as well as the field direction, causes positive and negative charges to build up on opposing edges of the sample until the resulting electrical force on the moving charge carriers exactly cancels the magnetic force. This condition can be used to derive the above equation for the Hall resistance. 
     Experimental Example 
     Thermoelectric Material Properties 
     Yet another group of properties that can be measured using the sensor array of the present invention are two characteristics of materials that pertain to their desirability for use in thermoelectric cooling devices: thermopower and thermal conductivity. Thermopower will be discussed first. 
     When a temperature gradient is imposed on a material under open circuit conditions, an electric field occurs due to the diffusion of charge carriers in the temperature gradient. In equilibrium, the force on the charge carriers due to the electric field is just sufficient to counteract their tendency to diffuse in the temperature gradient. The ratio between the temperature drop and the voltage drop across a sample is known as the thermopower, S=ΔV/ΔT, and is typically measured in units of μV/K. The thermopower is a fundamental physical property of an electronic material that can provide information about a materials electronic structure and other characteristics. In addition, the thermopower is a key physical parameter for materials which are used as thermoelectric cooling devices. A large thermopower value is a desirable property for a material in cooling device applications. To search for improved thermoelectric materials using combinatorial chemistry techniques to synthesize libraries of thin films of candidate materials, it is desirable and necessary to be able to measure rapidly the thermopower of many materials. 
     The thermopower, S, can be measured using the sensor design explained above and shown in FIG. 19A by measuring the voltage drop ΔV across a bar sample  190  for a known temperature difference ΔT along the sample  190 . This can be conducted in a variety of ways. In one embodiment, as illustrated in FIG. 19B, a temperature gradient is imposed along the entire sensor array  10  by contacting two opposing edges  191 ,  192  of the array with metal blocks  194 ,  196  whose temperatures are controlled and measured. If the substrate has high thermal conductivity, such as silicon, then heat losses to radiation and convection will be relatively minor compared to the heat conduction along the substrate, and a fairly uniform temperature gradient will be produced. The gradient may be approximated as the total temperature drop divided by the width of the array, and the temperature drop across an individual sample will be the gradient times the length of the sample. In other words, ΔT sample =ΔT array  *(L sample /L array ). More precise information about the temperature drop across each sample may be obtained by including two temperature sensors next to each sample within the sensor array  10 , one near each end. 
     The above example ignores heat losses through the electrical contacts to the sensor array, which may cause the temperature profile to deviate from the preferred linear gradient form or cause most of the temperature drop to occur over a relatively small distance near the edge of the array instead of evenly across the entire array. An alternative embodiment which is not subject to this problem is shown in FIG.  19 C. In this embodiment, a chain of heating/cooling elements  198 , such as thermoelectric heat pumps, is used to impose a temperature drop across each row in the sensor array, by means of blocks of metal or other thermally conductive material that contacts both the heating/cooling elements  198  and the substrate. The elements  198  preferably alternate direction so that all of the samples in the array  190  are at the same average temperature. The structures that produce the temperature gradient on the array may be integrated into the compression plate  44 , shown in FIG. 4, used to apply pressure on the sensor array against the contacts to the circuit board. 
     In yet another embodiment, the temperature gradient can be produced by resistive heating elements that are part of the sensor array itself rather an external heating fixture. This structure is most easily accomplished if the substrate has low thermal conductance, either via a low thermal conductivity material (e.g., glass) or via a thin film substrate (e.g., silicon nitride). A large number of configurations are possible; ideally, temperature sensors are placed at both ends of each sample and a resistive heating element is placed near one end of the sample. In addition, at least two electrical connections are at the ends of the sample for measuring the thermoelectric voltage. 
     Experimental Example 
     Thermopower (Seebeck Coefficient) Measurements 
     In the embodiment of thermopower measurements proposed in co-pending U.S. application Ser. Nos. 09/210,086; 09/210,428; and 09/210,485, a temperature gradient is imposed on the substrate and samples by placing the substrate in contact with two or more temperature controlled blocks (domestic application, FIG.  19 C). This method has the advantage of affording good control over the magnitude and uniformity of the temperature gradients, but requires the use of additional apparatus beyond that included in materials characterization system of the present invention. 
     In order to demonstrate the feasibility of making thermopower measurements in an array format without the need for additional apparatus, a sensor was designed which included a resistive heater at one end of the sample, in addition to leads for current injection, longitudinal voltage measurement (resistance), and transverse voltage measurement (Hall effect). This sensor design is shown in FIG.  22 . Arrays of these sensors were fabricated using 0.2 μm sputtered nickel metallization, on a substrate consisting of a silicon wafer with 0.5 μm of thermally grown silicon oxide electrical insulation. The combined system of a material sample and the nickel leads forms a two-junction thermocouple. The net voltage across the thermocouple is given by v th =(S x −S Ni )ΔT=SΔT, where S x  is the thermopower of the sample, S Ni  is the thermopower of the nickel leads, and ΔT is the temperature drop due to the power generated by the heater. 
     When a voltage is applied to the heater, power is generated primarily in the narrow “hairpin” heater wire. The end of the sample close to the heater will be warmer than the opposite end, and a thermal voltage will be generated, which can be measured by coupling a pair of voltage leads to a sensitive DC voltmeter. Because the silicon substrate is roughly 1000 times thicker than the sample (typically 0.5 mm vs. 0.2 microns) and has high thermal conductivity (of order 1 W/cm° K), almost all of the heat generated will flow through the substrate, not the sample, and the temperature distribution for a given power level will therefore be essentially independent of the properties of the sample. Therefore, the temperature drop across a sample is determined primarily by the heater power level, independent of the thermal conductivity of the sample. 
     Thus, for a given power level, the thermal voltages generated in different samples in an array will be proportional to the total thermopower of the thermocouple formed by the sample and the nickel leads. If a sample with known thermopower is included in a materials library, then the relationship between temperature and heater power can be determined, and the data from other samples converted to absolute thermopower. Thus, although the detailed temperature distribution for this sensor design has not been calculated, this is not necessary to obtain meaningful thermopower measurements. 
     A 64-element test library was synthesized on an 8×8 sensor array. Each row contained a binary composition gradient from Bi to Sb, and all 8 rows were identical. The library was synthesized by sputtering alternating layers of Bi and Sb, each with a maximum thickness of 5 nm and with a linear thickness gradient across the library defined by a moving shutter, until a 200 nm film was built up over the entire array. The electronics used to measure the thermopower are shown in FIG. 23. A voltage generated by a digital-to-analog converter is buffered by a unity gain inverting amplifier and then applied to the heater. The thermal voltage v th  from the sample is low-pass filtered (cutoff frequency=1 kHz) and amplified (G=10 4 ) by a Stanford SRS580 low noise preamplifier, before being recorded by an analog-to-digital converter. For each sample, the heater drive voltage V H  is varied in uniform steps from V min  to V max , where V min =−V max , and the thermal voltage v th  is measured for each value of V H . The power generated by the heater is given by P=V H   2 /R H  and to a first approximation the temperature drop across the sample will be proportional to P. Therefore, we expect the thermal voltage, v th =bV H   2 , and the constant b should be proportional to the thermopower S (which is measured in μV/° K). Again, the relationship between b and S, the thermopower, can be determined by measuring a sample with known thermopower, and this relationship can be used to convert b to S for the unknown samples. 
     FIGS. 24A-C show a complete set of raw data for the BiSb test library. For each sample, v th  is plotted against V H  and is seen to describe a parabola, v th =a+bV H   2 . The offset v th =a at V H =0 is due to an input offset of the preamplifier. It can be seen from the data that the coefficient b varies widely over the BiSb library, in both magnitude and sign, but is essentially constant for a given composition. The coefficient b is plotted in FIG. 24C for the entire library. All of the observed trends are consistent with the data reported in FIG. 38 of the paper “Electric Transport Quantities of Bismuth-Antimony Alloys”, by J. Neisecke and G. Schneider, (Zeitschrift fur Naturforschung A, vol. 26, pp 1309-1315, 1971), as can be seen in FIG.  25 . The sensor data for all samples of a given composition (each column) have been averaged, and corrections have been applied to account for the thermopower of the nickel leads. The data have been normalized to −65 μV/° K at 100 atomic % Bi. 
     The sensor array structure for measuring thermal conductivity will now be discussed. Like thermopower, thermal conductivity is important for determining how efficient a given material will be for use in thermoelectric cooling devices. An ideal material in a cooling device application will have low thermal conductivity in conjunction with low electrical resistance to minimize heat leakage in the device and create a large temperature difference across the device with minimum energy consumption and heat dissipation. 
     FIGS. 20A and 20B show a preferred sensor structure for measuring the thermal conductivity of materials. As in the previous experimental examples explained above, the description will focus on the structure of a single sensor, but it is understood that multiple sensors are used in the present invention in an array format, and that sensors measuring different properties can be included on the same sensor array. Also, analysis of thermal conductivity may be useful in materials research contexts other than the search for new thermoelectric materials. 
     The preferred thermal conductivity measurement method is via vapor-deposited films, on the order of half-micron thick, on membranes, similar to the structure used for heat capacity measurements. Other methods may also be used to deposit thin film samples, such as evaporation from a solution or suspension. As in heat capacity measurements, thermal conductivity measurements preferably minimize the effects of the substrate&#39;s thermal characteristics on the overall measurement results. FIGS. 20A and 20B illustrate a preferred sensor structure  200  for measuring thermal conductivity. As can be seen in FIG. 20A, the sensor structure  200  for thermal conductivity measurements can be of similar construction and materials as the structure used in heat capacity measurements, such as a silicon-nitride membrane, so that the thermal characteristics of the material sample can be easily detected and separated from the thermal characteristics of the substrate on which the sample sits. Thus, the details of the structure will not be repeated here. 
     Referring to FIG. 20B, a desired sensor pattern is printed via any known method, such as lithography, on the membrane  202  surface opposite the surface on which the material sample  204  will be deposited. This prevents a short-circuit from forming when characterizing electrically conductive materials, such as metals. In this example, the sensor includes two wires  206 ,  208 . The specific geometry of the sensor should be optimized so that the temperature is substantially uniform along the portion  205  of the sensor  200  over which the temperature will be measured on the membrane  202  (e.g., the “active” portion). To accomplish this, the membranes  202  on the sensor array should be made relatively long and narrow to insure that heat flow in the active portion is predominantly between a second (heater) wire  208  and the nearby substrate  210 , which contains a first wire  206 , i.e., across the width of the membrane  202  (perpendicular to the heater wire  206 ) and not along the length of the wire  208 . 
     As noted above, a preferred sensor design includes two parallel wires  206 ,  208  having a known width and spaced a known distance apart. Branch leads  206   a,    208   a  extend from each parallel wire  206 ,  208  and are spaced a known distance apart for conducting voltage measurements V1 and V2 along the parallel wires. In this embodiment, the first wire  206  is used as a thermometer and the second wire  208 , which is on the membrane  202 , is used as both a heater and a thermometer. As in previously described structures, the temperature is monitored by measuring the AC or DC voltage and current of the sensor and calculating the resistance, which varies linearly with respect to temperature. 
     In a preferred structure, the first wire  206  is disposed on the solid silicon substrate  210 , near the edge of the silicon nitride membrane window  202 , while the second wire  208  is disposed on the membrane portion  202  of the substrate. The silicon in the substrate  210  acts as a large heat sink to prevent the temperature detected by the second wire  208  from rising in response to the heat generated by the first wire. If the width of the membrane  202  is kept small (e.g., less than 1 mm wide and preferably less than 100 μm wide), heat losses due to radiation may be neglected in comparison to the total heat flow through the membrane and sample, and if the thermal conductivity measurements are conducted in a vacuum, heat losses to the atmosphere due to conduction and convection may be neglected. Virtually all of the heat produced by the first wire  206  conducts through the membrane  202  and the sample  204 , in a direction perpendicular to the wires  206 ,  208 . 
     The theory behind thermal conductivity measurements will now be described with respect to the structure shown in FIGS. 20A and 20B. As noted above, thermal conductivity is a measure of how easily heat travels through a material when a temperature difference T2−T1 is imposed on a material sample. When a temperature difference ΔT=T2−T1 is imposed across a material sample, such as a bar sample, heat will flow from the warmer end of the sample to the cooler end. This heat flow J (in watts) is equal to the thermal conductance K multiplied by the temperature difference ΔT. In other words, the amount of heat flow through the sample is proportional to the temperature difference across the sample. The specific proportionality constant depends on both the sample&#39;s geometry and the thermal conductivity κ of the material, K=κ(A/L) where A is the cross-sectional area of the bar in the direction perpendicular to the heat flow, and L is the length. In this sensor, L=the distance from wire to the edge of membrane/substrate, and A=(thickness of membrane/sample)×(distance between branch leads). 
     Referring back to the sensor structure shown in FIGS. 20A and 20B, the second wire  208 , which is used as both the heater and the thermometer, carries a relatively large current I2 to generate a known power P for heating the sample and also measure the temperature of the wire; while the first wire  206  receives a small current I1 to conduct a temperature reading. The large current I2 should be large enough to cause significant self-heating in the portion of the sample around the first wire  206 , on the order of 5 to 10 degrees C. The small current I1 is preferably the smallest amount of current necessary to measure accurately the resistance of the second wire; it should not be large enough to heat the sample to any significant degree. Even though the small current I1 may cause the sample&#39;s temperature to rise a small amount, on the order of a tenth or a hundredth of a degree, this temperature change is negligible relative to the self-heating occurring on the portion of the sample on the membrane and can therefore be ignored. Further, as noted above, the silicon substrate  210  acts as a large heat sink, keeping the temperature of the sample in that area uniform and preventing the temperature of the first wire  206  from rising along with the temperature of the second wire  208 . 
     To measure the temperature difference ΔT=T2−T1, the electronic platform only has to monitor the resistance changes in the two wires  206 ,  208 . The power I 2 V 2  generated by the heater, which is equal to the total heat flux, and is input into the sample via the first wire, is known from measurements of I and V. Because the geometry of the sample is also known, the thermal conductivity of the material can be obtained from the temperature difference. Note that the thermal conductivity of the membrane  202  still has to be subtracted from the thermal conductivity measurement obtained from the combined membrane and sample, to obtain the thermal conductivity of the material, but the membrane&#39;s thermal conductivity is easily determined by sending current through the sensor without any material on it, i.e., before deposition of the material sample. 
     Experimental Example 
     Thermal Conductance/Thermal Conductivity Measurements 
     FIG. 26 shows the design and principal of operation of a thermal conductivity sensor which was fabricated and tested in an array format. The silicon nitride membrane in the tested devices was 0.4 μm thick, and the metallization was 0.2 μm thick platinum. The width of the narrowest lines in the sensor is 0.001″ (approximately 25 μm), and the distance from the wire to the edge of the membrane is 0.01″. The wire on the membrane is used as both a resistive heater and a temperature sensor. A current passed through the wire generates power P=IV=I 2 R. The sensor is designed so that almost all of this power is dissipated via heat flow through the membrane towards the nearest edge of the silicon wafer. From the heat conduction equation J=κ(dT/dx) (where J=energy flux in W/cm 2  and κ=thermal conductivity in W/cm° K), the relationship between the power P and the temperature difference ΔT between the wire and the substrate is given by P=κ(Wt/L)ΔT, where Wt is the cross sectional area of the membrane perpendicular to the direction of heat flow, and L is the distance from the wire to the edge of the substrate. For a composite structure, including the membrane plus a sample having thermal conductivity κ s  and thickness t s , power is given by the relationship P=(W/L)(κt+κ s t s )ΔT. ΔT can be determined from the wire&#39;s resistance, R=V/I=R o (1+α(T−T o )), where R o  is the resistance at a reference temperature T o  and α is the temperature coefficient for the resistance. Thus, the power is linear in T and in R, and the slope is proportional to (κt+κ s t s ). 
     This is a purely one-dimensional model, precisely valid only for an infinitely long wire and membrane parallel to an infinite wafer edge. However, the sensor shown in FIG. 26 was designed to approximate this geometry in the region where the voltage and resistance are actually being measured (between the two nodes on the membrane). This is true because the distance L from the wire to the edge of the membrane is much shorter than the total width W of the membrane and the distance between the nodes, and because the thermal conductance of the wire itself can be neglected (discussed below), so that almost all of the heat generated in the wire passes through the membrane to the nearby wafer edge. Also, as shown below, the amount of energy lost to radiation is negligible compared to the amount conducted through the membrane. 
     In conducting the experiment, it was assumed that radiation could be neglected. The following calculation checks this assumption: I 
     With no power applied to the wire, the entire sensor array and sensor are in thermal equilibrium with the environment at temperature T o , so that there is no net emission or absorption of radiation by the membrane. When the wire is heated to a temperature T&gt;T o , the net radiation emitted over the area where most of the heat flow is occurring is roughly given by P rad =εσ(T 4 −T o   4 )(LW)≈4εσT o   3 ΔT(LW), where ΔT=T−T o  is the temperature rise of the wire, ε is the net emissivity of the membrane and sample, and σ=5.67×10 −12  watts/° K 4  cm 2  is the Boltzman radiation constant. Therefore the ratio of the amount of heat lost by radiation to that lost by conduction is given by β=P rad /P cond =4εσT 3 L 2 /κt. For a good thermal conductivity measurement, a β&lt;&lt;1 is required. For the sensor geometry shown in FIG. 26, L=10 −2  cm and t=0.4×10 −5  cm Using the upper limit ε=1 for the emissivity and κ=0.15 Watts/cm° K for silicon nitride, one obtains β≈0.01; so at most 1% of the heat generated by the wire is lost to radiation. 
     Additionally, it may be shown that the heat which is conducted along the sensor wires to the wafer is small compared to the heat traveling through the membrane. The total thermal conductance of the membrane is approximately 2.4×10 −5  W/° K, while that of the wires is approximately 4×10 −7 W/° K. Although the thermal conductivity of Pt is about five times higher than that of Si 3 N 4 , the heat conduction path through the wires is so much longer and narrower than that through the membrane that these losses may be ignored to a good approximation. 
     To test the thermal conductivity sensor, an aluminum film with a thickness gradient was deposited on the back side of a 1×8 sensor array, using sputter coating from an Al target. The thickness was controlled by moving a computer-controlled shutter during deposition, yielding a film thickness which ranged from 0 to 3500 Å in 500 Å steps. 
     There are many possible ways to resistively heat the wire while measuring the resistance, in order to determine the thermal conductivity. One method is to make a series of DC current-voltage measurements, beginning with a power level which does not cause significant self heating and increasing to higher values. From a plot of P=IV versus R=V/I, the thermal conductance of the membrane and sample can be determined. In order to take advantage of the low noise and high precision which are easily attained using a lockin amplifier, however, a similar method based on AC signals was used to analyze the test library. The electronics used to make the thermal conductivity measurement is shown in FIG. 27. A 1 kHz sinusoidal voltage V was used to drive a voltage-controlled current source, as shown in FIG.  27 ( a ). (Note that all voltages discussed here are RMS). The current passing through the sensor is given by V/360 Ω, where 360 Ω was the value of the series resistor in the current source circuit. Thus, a and the sinusoidal current I=V/360 Ω was passed through the wire on the sensor membrane. A lockin amplifier was used to make a four-probe measurement of the voltage v across the wire, between the two nodes on the membrane. Increasing the AC current amplitude increases the amount of DC self-heating, the temperature, and the resistance (since the power has a DC component. Some of the detailed relationships between the different variables are shown in FIGS. 27B-D. Data for only three of the samples in the series are shown for clarity, with thicknesses of 50, 150, and 250 nm. FIG. 27B shows the nonlinear current voltage characteristic, with the faster than linear rise due to self heating. The solid line is the theoretical I-V characteristic for a 50 Ω resistance with no self-heating. The non-linear behavior in the data becomes less pronounced as the Al film becomes thicker, since heat is conducted away from the sensor more easily and less self heating occurs. FIG. 27C shows the resistance vs. the drive current, showing the quadratic increase in resistance with current. The limiting value as I→0 is the resistance at ambient temperature. If there was no self heating, the resistance would not change at all with increasing current. Again, the resistance increase is more pronounced for thinner Al films. FIG. 27D shows the power vs. resistance curve, illustrating the linear P vs. R behavior characteristic of heat loss by thermal conduction, as discussed above. For thicker Al films, more power is required to produce the same amount of temperature and resistance increase. 
     The software which controlled the measurements followed the following sequence: a particular sensor in the array is connected to the current source and lockin by closing switches in the multiplexer and matrix switch. An initial small value of I is sent to the sensor, chosen so that the amount of self heating is negligible. The resulting voltage, v, across the wire is measured by the lockin and recorded by the computer  52 . The resistance of the wire is calculated in the same way as for a DC experiment, R=v/I, P=Iv. The current amplitude I is then increased by a fixed amount, and the measurements and calculations are repeated. The drive current is typically varied by a factor of 10 from the initial to the final value in about 10 steps (corresponding to a factor of 100 variation of the total power dissipated), and the lockin is allowed to “auto scale” as necessary to maintain the signal in range. At the end of this sequence of measurements, a plot of power vs. resistance is displayed, and a straight line is fit to this plot by the computer  52 . The slope is proportional to the total thermal conductance of the sample and membrane, and is stored by the computer. All of the raw data (voltages and currents) and calculated data (power and resistance) for that sample are also stored. The multiplexer  126  then selects a new sensor, and the measurement is repeated. 
     FIG. 28 shows the best fit slope (in units of Watts per Ohm) as a function of the film thickness. The thermal conductance increases linearly with the film thickness, again in agreement with the above discussions. In order to convert this number to an absolute value of the thermal conductivity of the sample material (Al), two additional steps must be taken. First, Watts/Ohm must be converted to Watts/° K (thermal conductance). This requires accurate knowledge of the temperature coefficient of the sensor wire&#39;s resistance, since dP/dT=(dP/dR)*(dR/dT). Second, the thermal conductance must be converted to thermal conductivity. This requires accurate knowledge of not only the film thickness, but also of all of the details of heat flow in the sensor structure, which will not be as simple as the one-dimensional model described earlier and can only be obtained by detailed numerical modeling of the sensor structure. Since dR/dT was not measured and the heat flows were not numerically modeled, a precise absolute analysis of the data is not possible at this time. 
     However, we can still use the data obtained to determine the ratio of the thermal conductivities κ of silicon nitride and aluminum, and check this against the accepted values. The ratio of the thermal conductances, K, of two films, having different thicknesses, t, and thermal conductivities, κ, but the same length, L, and width, W, is given by K 1 /K 2 =κ 1 t 1 /κ 2 t 2.  Solving for the thermal conductivity ratio for this experiment, using the data from FIG. 28 for the bare membrane (400 nm nitride only) and the thickest Al sample (350 nm Al), κA Al /κ Si3N4 =(K Al /K Si3N4 )(t Si3N4 /t Al )≈[(1.7×10 −3  W/Ω)/(7.7×10 −5  W/Ω)]*(350 nm/400 nm)≈19, where it has been assumed that the thermal conductivity in watts/° K will be proportional to the slope dP/dR in watts/Ω. It is known that the thermal conductivities of Al and Si3N4 are 2.5 W/cm° K and 0.1-0.15 W/cm° K respectively, for a ratio of between 15:1 and 25:1. Thus, the measurements obtained are in fair agreement with accepted ratios of thermal conductivities. 
     It should be pointed out that it is probably possible to do thermal conductivity and heat capacity measurements on the same sensor. For example, although the heat capacity sensors are not optimized for use in thermal conductivity measurements, it has been observed that the relationship between power input, temperature, and thermal conductance still holds at least qualitatively. There may be tradeoffs in optimizing a sensor for one function or the other, but it should be possible to create a design which is a good compromise. 
     Experimental Example 
     Magnetic Material Characterization 
     The sensor array of the present invention can also characterize the magnetic properties of materials libraries, again by changing possibly only the sensor structure in the sensor array and making minor changes in electronics and including equipment for generating a magnetic field as discussed with reference to transport properties. As explained above, the sensor array of the present invention can measure the Hall coefficient of a material to determine the material&#39;s carrier concentration and sign. In the present example, generally, an array of unknown magnetic materials is placed on top of or in close proximity to an array of identically calibrated Hall effect sensors, which are made from a material with a known response to a magnetic field. An external magnetic field of variable strength is then imposed on the sample and sensor. The output of the Hall sensor is compared to the output of an identical sensor that does not contain a sample. The difference in the response of the two sensors is due to the magnetization of the sample. In a preferred embodiment, the sensors with and without the sample are connected in a differential arrangement, which greatly increases the sensitivity to the magnetization of the sample. 
     The samples may be deposited directly on a Hall sensor  210 , as shown in FIG.  21 A. In the illustrated structure, a sample  212  can be deposited on one portion  214  of the sensor, with a second portion  216  of the sensor  210  left open to serve as a reference point. The difference between the voltages V1 and V2 when the sensor  210  is placed in a magnetic field corresponds to the magnetic properties of the sample  212 . For example, the plot of the Hall voltage versus the magnetic field when there is no material on the sensor will be a straight line, but a magnetic material on the sensor  210  will cause the plot to deviate from the straight line, or will cause the straight line to have a different slope, because the sensor  210  is measuring both the external field and the field of the sample  212 . In essence, the sensor  210  used in this embodiment is a magnetic field sensor. Alternatively, the Hall sensors and the samples may be contained on two separate substrates that are pressed together during the measurement. This later method allows reuse of the Hall sensor array. 
     Another specific way in which the magnetic properties of a material can be measured is by forming a sensor array containing cantilever sensors  220 , as shown in FIG. 21B. A material sample  222  is placed on a relatively soft, flexible cantilever  224 , and then the sensor  220  is placed in a magnetic field  226  having a known field strength and field gradient. The force and/or torque due to the interaction of the field and field gradient with the permanent and/or induced magnetization of the sample will cause the cantilever  224  to deflect. The amount of the deflection will depend on the strength of the sample material&#39;s magnetic characteristics. 
     There are several ways in which the deflection amount can be measured precisely. For example, the cantilever  224  on which the sample material  222  is placed can be one half of a sandwich capacitor such that the cantilever deflection results in a capacitance change. An alternative is to place the cantilever  224  on a piezoresistor  228 , which is shown in FIG. 21B, so that the bending of the cantilever  224  strains the resistor slightly, changing its resistance value. The electronic platform can then monitor the amount the resistance changes and correlate the change with the amount of deflection. Other methods of measuring the amount of deflection in the cantilever sensors  220  can be used without departing from the scope of the invention. 
     Detailed Discussion the Software Aspects of the Invention 
     The materials characterization system of the present invention uses a control processor, computer  52 , to analyze the measurements and data gathered from the sensor array  10  for each material sample. In a preferred embodiment, the computer  52  is a personal computer, and will read and execute computer programs stored on any suitable computer readable medium for use in automatically determining material properties for materials associated with the sensor array  10 . 
     The computer  52  includes an input device, for example, a keyboard, mouse, or other data inputting device, an output device, for example a visual display, an input/output adapter for uploading and downloading data and programming information from any suitable computer readable medium, and a data input/output adapter for receiving and processing signals emitted from the sensors  12 . The computer  52  also includes a memory device, i.e., a computer readable medium. The memory device stores the computer operating system for the computer  52  and any additional applications used by the computer  52 . Those skilled in the art will appreciate that the memory device can comprise a random access memory and a read only memory formed as part thereof. Each of the above described components of the computer  52  communicate with one another through conventional means, for example a data bus bar. 
     The input/output adapter is equipped to receive data as well as computer programming instructions from any one, or combination of storage devices which may include a magnetic floppy disk, a magnetic hard disk drive, a magnetic/digital tape, and/or a CD-ROM or any other suitable storage device. The data input/output adapter includes any necessary analog to digital, and digital to analog converts needed to process the data signals received from the sensors  12 . 
     The software comprising the computer program of the present invention operates on an operating system appropriate for the personal computer on which it is installed, such as Microsoft WindowsNT® operating system. The computer program can be stored as a file on a disk drive, CD-ROM or other computer readable storage medium as a series of files. The operating program loads the appropriate file and runs the executable code contained in the file. In general, the control program of the present invention includes a series of program instructions, logic, designed to implement specific tasks. The computer program is divided into seven distinct tasks: (1) setting experimental conditions and test equipment operating parameters; (2) testing the sensor array; (3) measuring the raw data; (4) archiving the data; (5) reducing and archiving the data; (6) viewing the results of the reduced data; and (7) retrieving data and re-reducing the data. It will be appreciated that the computer program may be readily adapted to complete tasks other than those identified. 
     1. Setting Experimental Conditions and Test Equipment Parameters 
     The computer program includes instructions for setting the experimental conditions under which the sensor measurements are taken. For example, the operator can manually set the environment of the sensor array, e.g., controlling variables such as temperature, pressure, atmospheric composition, etc., and calibrating the sensor array (discussed below). 
     2. Testing the Sensor Array 
     The software identifies the sensor array  10  by a unique identifier. This unique identifier may be used to retrieve the sensor array  10  for review or further analysis once the data gathering process has been completed. 
     The computer program also identifies and stores information characterizing cells forming the sensor array  10  structure. In the disclosed embodiment, the software identifies usable and unusable cells of the sensor array  10 . Usable cells are defined as those cells that are not flagged as unusable, either automatically by the software or manually by the user. 
     Information concerning usable and unusable cells can include the location of these cells in the sensor array  10 , and these locations may be stored on the computer  52  memory storage device. It will be appreciated that this information may be stored in other memory storage devices. In the embodiment disclosed, the stored information is stored at a location and on a computer readable medium that is accessibly by a deposition software program that includes instructions for depositing the material samples onto the sensor array  10 . 
     The process for depositing the material samples onto the sensor array  10  is not performed by the computer program of the present invention. However, the steps of depositing the material samples are summarized herein to illustrate where they occur in the overall process. The deposition software and process includes the steps of (1) reading in a map of usable sensor array  10  cells; (2) mapping samples and calibration standards from the library to usable cells; and (3) writing the deposition map to a database that includes explicit and editable sample-related parameters (such as hot tip temperature, plate temperature, and solvent type). 
     As part of the array testing instructions, the software can also include instructions for calibrating the sensors. In calibrating the sensors, materials having well-known material properties such as melting point and glass transition temperatures are used as standards. In one embodiment, materials such as high density polyethylene and ethylene-butene are used as the material standards for calibrating the sensors. One of ordinary skill in the art will appreciate that these materials have well defined thermal properties. In calibrating the sensors, samples of the polyethylene and ethylene-butene materials are added to the elements of the sensor array and measured to generate corrections to the temperature calculation routine. This allows auto calibration of the sensor array  10  by finding the melting temperature of the standards and adjusting the sensor calibration to correct any variation. 
     Alternatively, the software may perform the function of calibrating the sensors to allow an accurate determination of the sample temperature. The temperature can be calculated from the sensor resistance but in order for this to be done accurately, the relationship between the resistance and the temperature must be determined. For example, if the sensor resistance is linearly related to the temperature, it is sufficient to measure the sensor resistance at two or more points and determine the change in resistance with temperature. This relationship can then be used to calculate the temperature for a given sensor resistance. 
     In one calibration method, one or more materials having well defined thermal transitions (such as glass transitions, melting points, or boiling points) at well known temperatures can be included within the library as calibration standards. From a plot of the heat capacity of the standard material sample (in either absolute or unnormalized units) versus the sensor resistance, the resistance corresponding to the transition of the material at the known transition temperature can be determined. Depending on the functional relationship between resistance and temperature, and the degree of reproducibility of this relationship from one sensor to the next, there will be some minimum number of standards that must be included in order to allow an accurate calibration to be made. In some cases a single standard may be sufficient, while in other cases two or more may be required. 
     In another calibration method, physical means are provided for heating and/or cooling the entire sensor array to a series of known temperatures. At each temperature, the voltage from each sensor is measured and stored by the computer. From a series of such measurements at several different temperatures, a calibration curve can be constructed for each sensor. 
     3. Measuring the Raw Data 
     The computer program includes software instructions that identify the sensor array by a unique identifier; import the map of usable cells and deposition library; set the operational parameters before executing the experiment; run the calibration standards for the sensors; allow an operator to select the usable cells in the sensor array  10  that are to be tested; and run or execute the experiment, i.e., gathering data from the sensors  12  and performing the analysis thereof. 
     The general steps executed by the computer program in conducting the experiment include: 
     (a) retesting the wafer (substrate) if necessary. If this step is performed, all unusable cells will be flagged automatically; 
     (b) cooling the polymer products on the wafer using operator defined ramp rates and set point temperatures over time; 
     (c) allowing a stable temperature to be reached; and 
     (d) measuring the material properties of the sample. For example, measuring the thermal properties of the samples such as the melting temperature (Tm) and glass transition temperature (Tg). 
     The software includes instructions permitting the operator to review the processed and raw data in real time. Conventional software instructions and viewing apparatus are used in performing this task. 
     When the measured data includes the thermal properties of the material sample, the thermal response data is analyzed to determine the temperatures of the material sample such as the melting temperature (Tm) and glass transition temperature (Tg). For Tg, the temperature at half height of the step function in the thermal response (plotted on the horizontal X-axis) is determined by an automated fitting routine. For Tm: The temperature (plotted on the horizontal X-axis) is determined by measuring the maximum of the melting peak in the sample thermal response. 
     A relative thermal response of the sample is calculated from the ratio of the measured first and third harmonic voltage. (This value as a function of temperature is the data that will be stored.) For comparison purposes, the operator can autoscale the data so that the sample temperature along the X-axis is the same in different plots. 
     Once the measurements have been completed, the operator may choose to either store the wafer or wash and retest it, and then log the unusable cells. The operator may repeat the experiment any number of times using different operational parameters. For instance, the operator may manually change the default operational parameters if necessary. The operator may also identify and flag any cells that to be excluded or skipped during the data gathering process, i.e., during the processing of receiving, monitoring and analyzing signals from the sensors  12 . 
     5. Archiving the Data 
     The computer program software for performing this task includes instructions for archiving both the raw and processed data using generally known techniques. It will be appreciated by one of ordinary skill in the art that the data is archived, stored, on a computer readable medium. 
     6. Reducing the Data and Archiving the Reduced Data 
     The computer program software for performing this task includes instructions for reducing and archiving both the raw and processed data using generally known techniques. The data reduction function can include statistical analysis such as finding the minimum, maximum and median data points, or other analysis adapted for reducing the number of data points analyzed or reviewed. 
     The reduction process may be performed using conventional reduction software programs such as Excel®, Kaleidagraph™ or similar software programs. The computer program instructions for data reduction also permit the operator to select the reduced data to be stored on the memory device and to adjust this data manually. 
     The instructions for reducing the data also includes logic for automatically archiving of the raw data, i.e., the compilation of and measurement of signals generated by the sensors  12 , as well as the processed data. 
     It will be appreciated by one of ordinary skill in the art that program instructions also include logic for archiving, storing, the data in the unreduced state. Generally known software instructions can be used to perform this task. Again, the data can be stored on a computer readable medium of the type generally known and used in computer and data processing systems, e.g., a CD-ROM, magnetic tape or magnetic disk. 
     7. Viewing the Results 
     Data may be viewed and analyzed using computer software package such as Excel®, Kaleidagraph™ or similar software programs. Information such as melting point and glass transition temperatures can also be determined visually from a plot of heat capacity vs. temperature by observing the location of features in the plot. 
     Retrieving the Data and Reducing the Data 
     The computer program includes software instructions for retrieving the data and reducing the data. This task is accomplished using reduction and archiving software instructions generally known in the field. 
     Description of the Software Program 
     The materials characterization system of the present invention is computer controlled and includes a software program for implementing materials characterization process previously described. In the disclosed embodiment, the computer program is stored on a computer readable medium containing software for the control of the operation of an apparatus for characterizing one or more material properties for one or more material samples. The software includes instructions for selecting a sensor or group of sensors for measurement, wherein each sensor in the array is associated with a material sample; instructions for computing, selecting and setting of test equipment operating parameters, wherein said instructions result in discrete operating parameters used to drive the test equipment; instructions for initiating a data gathering sequence, wherein the selected sensor or group of sensors are caused to measure preselected material properties; instructions for sending, receiving and monitoring signals sent to and received from the selected sensor or group of sensors; instructions for processing signals received from the selected sensor or group of sensors, wherein a specific output is generated for each signal processed; instructions for calculating an arithmetic value corresponding to a material property using the specific output generated for each signal processed; and instructions for monitoring and storing the calculated arithmetic value, signals received during said data gathering sequence, and each specific output for each signal processed. 
     The computer program instructions for calculating an arithmetic value include instructions for calculating the thermal properties of the material samples, wherein the instructions for calculating the thermal properties include instructions for calculating at least one property selected from the group of melting point, glass transition temperature, heat capacity, thermal conductivity and thermal stability. The computer also includes instructions for calculating at least one electrical transport property selected from the group of electrical resistance, Hall coefficient, magnetoresistance, thermoelectric power, and current-voltage characteristics. Further still, the computer program software includes instructions for calculating at least one material property from the group including viscosity, density, conductivity, molecular weight, chemical concentration, capacitance, dielectric constant, mass loading, elasticity, damping, tensile strength, yield strength, ductility, toughness, hardness and magnetism. The computer program software also includes instructions for calculating the magnetic properties of the material samples. The computer software includes instructions enabling the measurement of signals from two or more sensors on the same array. 
     The computer software further includes instructions for setting a runtime logic sequence for setting, limiting and monitoring the time for executing instructions for said data gathering sequence. The runtime logic sequence enables a fixed time sequence to be set for completion of the experiment as discussed herein for heat capacity measurements. 
     The computer software further includes instructions for identifying the sensor array by a unique identifier. The computer software further includes instructions for importing a map identifying the usable cells of the sensor array. This information may be stored and viewed as the location(s) of usable cells within the sensor array, stored as database or another location that is accessible by a deposition software program. 
     The computer software further includes instructions for resetting a map of the sensor array, wherein all unusable cells in the sensor array are identified. The computer software includes instructions for selectively excluding unusable cells from the data gathering sequence. For instance, the operator may select or exclude certain usable cells from inclusion in the data gathering sequence. 
     The computer software includes instructions for measuring the thermal properties of a material sample associated with the selected sensor or group of sensors. Additionally, the computer software includes instructions for calibrating the sensors. 
     Further still, the computer software includes instructions for cooling a material sample material supported on a substrate supporting the sensory array. The instructions for cooling the same include instructions for controlling the operational parameters of the test equipment such as the ramp voltage, which may be selectively chosen by the operator. 
     Alternatively, the temperature of the samples may be controlled by computer program instructions enabling the control of the temperature of the selected sensor or group of sensors. 
     The computer software includes instructions for archiving, storing, retrieving and reducing the raw data (data obtained during the data gathering sequence), wherein the instructions for reducing include an analysis algorithm. The computer software also includes instructions for archiving, viewing retrieving and reducing the processed signal data, as well as the calculated arithmetic value. 
     In an alternative embodiment, the computer program product is a computer readable medium having computer program logic recorded thereon for enabling a processor in a computer system to analyze one or more material properties of a plurality of material samples, the computer program logic includes an inputting means for enabling a processor in a computer to receive and process operator input; a selecting means for enabling the processor to drive a selected sensor or group of sensors using operator input received from the inputting means, wherein each sensor forms a sensor array and each sensor of the sensor array is associated with one or more materials samples; a driving means for enabling the processor to drive test equipment using operator input received from the inputting means; an operating means for enabling the processor to execute a data gathering sequence, wherein preselected properties are measured by the selected sensor or group of sensors for one or more material samples associated the selected sensor or group of sensors; a routing means for enabling communication between the operating means and the selected sensor or group of sensors, processing means for enabling the processor to communicate with the operating means in analyzing data signals received by the operating means; a determining means for enabling the processor to determine an arithmetic value representing a preselected material property using signals received from the operating means; and a storing means for enabling the processor to store data gathered during gathering sequence, data generated by processing means, or the arithmetic value. 
     One of ordinary skill in the art will appreciate that the computer program instructions used in controlling the material characterization system of the present invention are of the type conventionally known and used in the industry. Additionally, one skilled in the art will appreciate that fact that the necessary algorithms for performing many of the tasks and calculations required for the present invention are disclosed throughout the specification or are commonly known and used in the industry. 
     It should be understood that various alternatives to the embodiments of the invention described herein may be employed in practicing the invention. It is intended that the following claims define the scope of the invention and that the methods and apparatus within the scope of these claims and their equivalents be covered thereby. The disclosures of all articles and references, including patent applications and publications, are incorporated herein by reference for all purposes.