# Patent

## Title
Method and test system for fast determination of parameter variation statistics

## Abstract

A method and test system for fast determination of parameter variation statistics provides a mechanism for determining process variation and parameter statistics using low computing power and readily available test equipment. A test array having individually selectable devices is stimulated under computer control to select each of the devices sequentially. A test output from the array provides a current or voltage that dependent on a particular device parameter. The sequential selection of the devices produces a voltage or current waveform, characteristics of which are measured using a digital multi-meter that is interfaced to the computer. The rms value of the current or voltage at the test output is an indication of the standard deviation of the parameter variation and the DC value of the current or voltage is an indication of the mean value of the parameter.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
The present Application is related to U.S. patent application Ser. No. 11/961,520 entitled “METHOD AND SYSTEM FOR ISOLATING DOPANT FLUCTUATION AND DEVICE LENGTH VARIATION FROM STATISTICAL MEASUREMENTS OF THRESHOLD VOLTAGE”, filed contemporaneously herewith by the same inventors and assigned to the same Assignee. The present Application is also related to U.S. patent application Ser. No. 11/462,186 entitled “CHARACTERIZATION ARRAY AND METHOD FOR DETERMINING THRESHOLD VOLTAGE VARIATION”, filed on Aug. 3, 2006 and issued as U.S. Pat. No. 7,423,446, and U.S. patent application Ser. No. 11/736,146 entitled “METHOD AND APPARATUS FOR STATISTICAL CMOS DEVICE CHARACTERIZATION”, filed on Apr. 17, 2006 and issued as U.S. Pat. No. 7,397,259, each having at least one common inventor and assigned to the same Assignee. The disclosure of each of the above-referenced U.S. patent applications is incorporated herein by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention is related to device characterization methods and circuits, and more particularly to a method and system for determination of parameter variation statistics for devices within a test array.
2. Description of Related Art
Parameter variation/process variation has become increasingly significant as processes have shrunk. Simulation can only provide a level of confidence in the overall yield of design or production, but testing is typically required to determine the true variation of device parameters for particular geometries and processes.
For the reasons given above, test arrays are typically fabricated either on production wafers or as independent test models, to characterize devices for both design verification and production testing purposes. The determination of process and/or parameter variation statistics is a time-consuming and computationally intensive process, especially when a large number of test devices must be evaluated. On the order of 100 samples per computed distribution must be collected over the range of operating parameters to be measured in order to provide a reasonably accurate model, and then the statistics must be computed from the sample values.
Therefore, it would be desirable to provide a faster method and test system for determining parameter variation statistics.
SUMMARY OF THE INVENTION
The above objectives of providing a faster method and system for determining parameter variation statistics for a test array of devices is accomplished in a computer performed method and computer controlled test system. The method is a method of operation of the test system, which may be at least partially embodied in program instructions stored in computer-readable storage media for execution in a test workstation computer system.
The test system and methodology sequentially enable an array of devices under computer control. A test output from the array produces a voltage or current dependent on a device parameter for which a statistical variation is to be determined. The sequentially activation of each device in the array produces a voltage or current waveform at the test output, which is then measured with a digital voltmeter interfaced to the computer. The rms value of the voltage or current provides an indication of the standard deviation of the parameter, and the DC value of the voltage or current provides an indication of the mean value of the parameter.
The foregoing and other objectives, features, and advantages of the invention will be apparent from the following, more particular, description of the preferred embodiment of the invention, as illustrated in the accompanying drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1A is a schematic diagram of a transistor parameter characterization circuit, and FIG. 1B is a schematic of a transistor characterization array, that may be used in test methodologies and systems according to embodiments of the present invention.
FIG. 2A is a schematic diagram of a resistor characterization circuit, and FIG. 2B is a schematic of a characterization array in accordance with an embodiment of the invention, that may be used in test methodologies and systems according to embodiments of the present invention.
FIG. 3 is a flow chart of a method in accordance with an embodiment of the present invention.
FIG. 4 is a pictorial diagram of a wafer test system in which methods in accordance with an embodiment of the present invention are performed.



DETAILED DESCRIPTION OF PREFERRED EMBODIMENT
The present invention relates to a process/device characterization method and system that use a digital multi-meter, voltmeter and/or current meter to provide indications of standard deviation and/or mean values of device parameter variation within an array of devices. A test array circuit provides a current or voltage output that provides an indication of at least one device parameter/device characteristic. The devices are sequentially selected to generate a waveform at the test output(s). The waveform(s) is measured using the digital multi-meter, voltmeter and/or current meter to obtain rms and DC average values, which provide a direct indication of the standard deviation and mean of the device parameter distribution, respectively. By using a digital metering device, statistical computation overhead is virtually eliminated as compared to sampling each device and computing the statistics from the sampled distribution. Variations in the resistance of resistors, threshold voltage and other characteristics of transistors, and capacitance of capacitors and transistor terminals can all be measured using the techniques of the present invention.
The method is a computer-performed method embodied in a computer program having program instructions for carrying out the method by controlling a characterization array and performing the above-described voltage and/or current measurements. The variation in device characteristics are determined from the measurement data retrieved from a multi-meter, voltmeter or current meter interfaced to a workstation computer system. The method of the present invention dramatically reduces the amount of time to characterize device parameter variation within an array, permitting greater flexibility in making measurements over large numbers of operating conditions.
Referring now to FIG. 1A, a characterization circuit in accordance with an embodiment of the present invention is depicted. Transistor N1 is a device under test for which the threshold voltage VT is to be determined. Transistor P1 and current source I2 form a source-follower that imposes a constant VDS value across the channel of transistor N1, since the amount of current diverted through P1 is fixed by I1 and I2, any change in VS results in an equal change in VD in order to keep VGS of P1 constant. Transistor P1 is generally a thick oxide device having a long channel and operated in the saturation region. Current source I1 fixes the channel current IDS through transistor N1. A constant voltage VG is imposed on the gate of transistor N1. Therefore, any variation in the threshold voltage (ΔVT) of device N1 will appear directly as an opposite change in source voltage (ΔVS) in the depicted measurement circuit, since ΔVG=0, ΔIDS=0 and therefore Δ(VGS−ΔVT)=0.
Referring now to FIG. 1B, a characterization array 20 in accordance with an embodiment of the present invention is shown. Characterization array 20 is a test integrated circuit integrated on a die, a wafer kerf or other integrated circuit location that may be experimental only, or occupy one or more die or kerf locations in a production wafer. An array of transistors including device under test DUT is operated in a controlled manner via signals provided by scan latches 22. Although the exemplary embodiment uses scan latches 22 to apply the control signals, it is understood that registers controlled via a control interface or other suitable circuit may be provided to control the operation of characterization array 20. Further, it is understood that although the exemplary embodiment supplies signals to external equipment via pads VGP, IDP and VSP, one or more of the external devices used to operate and evaluate device under test DUT may be integrated within characterization array 20. For example, any or all of voltage source VG, current source I21 and a voltage measurement circuit for measuring the voltage at pad VSP can be integrated on a wafer including characterization array 20.
Signals provided from scan latches 22 select a unique row and column associated with one of the transistors, e.g., device under test DUT. The selection of a row is made by a logical “1” applied to the gate of one of current steering transistors NI1-NI4 and simultaneously to a gate of a corresponding one of source voltage sense transistors NS1-NS4. Scan latches 22 are programmed such that only one row is selected at a time, i.e., all gates of transistors NI1-NI4 and NS1-NS4 are set to logical “0” other than the gates corresponding to the selected row. The selection of a column is made by enabling a transmission gate, e.g., transmission gate 24 that passes a reference gate voltage provided at pad VGP to the gates of all of the transistors in a column of the transistor array. A corresponding transmission gate 23 is also enabled and applies the output of amplifier A1 to the drain of each transistor in the selected column. The gate of a corresponding drain voltage sense transistor ND1-ND4 for the selected column is also set to a logic “1”, and provides a sense path for sensing the drain voltage of a column at the inverting input of amplifier A1. Scan latches 22 are sequentially programmed such that only one column is selected at a time, i.e., all transmission gates are disabled and drain voltage sense transistor ND1-ND4 gates are set to logical “0” other than the enabled transmission gates corresponding to the selected column and the gate of the corresponding rain voltage sense transistor ND1-ND4. The selection is performed at a constant rate and therefore a waveform of equal interval values corresponding to the threshold voltage VT appears at output test point VSP. Sequential selection in the context of the present invention, does not mean that physical order must be maintained, only that the devices are selected in sequence so that their characteristics are reflected in the generated waveform(s).
The source follower circuit described with reference to FIG. 1A is included within characterization array 20, but includes amplifier A1, which forces the drain-source voltage (VDS) to be a constant value for each selected transistor in the array. For example, when transistor DUT is selected by enabling transmission gates 23 and 24, along with transistors ND4, NI2 and NS2, transistor ND4 applies the drain voltage of transistor DUT to the inverting input of amplifier A1. Simultaneously, transistor NS2 applies the source voltage of transistor DUT to the gate of source-follower transistor P10, which controls the voltage at the non-inverting input of amplifier A1. The feedback loop acts to hold the drain-source voltage of transistor DUT constant by tracking any changes in the source voltage sensed from the selected row and adjusting the drain voltage supplied to the transistors in the column by an equal amount. Only one of the transistors in the array is conducting current at any time. Current provided from the output of A1 is directed through transmission gate 23 through the channel of transistor DUT and through transistor NI2 to an external stable current source I21. Since the current output of amplifier A1 is supplied to the drains of each transistor in a selected column, but only one selected row has a return path enabled via one of transistors NI1-NI4, only one device is selected for characterization for each valid combination of row and column selection signals provided from scan latches 22.
The above-described characterization array 20 thus provides a mechanism for sequentially selecting each device in the array and sensing changes in the source voltage VS at pad VSP for a fixed operating point set by the channel current IDS permitted through pad IDP and the gate voltage VG applied at pad VGP. By setting different valid selection combinations in scan latches 22, each transistor in the array is selected and a value of VS is measured and collected by a meter such as an external computer-controlled digital voltmeter (DVM) or digital multi-meter (DMM). The present invention concerns the determination of statistical descriptions of threshold voltage variation or other characteristic variation such as IDS variation obtained by replacing current source I21 with a digital current meter (DCM) and forcing fixed voltages at each of the terminals of device under test DUT. RMS measurements obtained from the meter are used as a direct indication of the standard deviation of the variation of the device characteristics and DC (average) measurements obtained from the meter provide a mean value for the characterization array. The mean values between multiple devices can thus be statistically compared to further characterize larger numbers of devices.
Referring now to FIG. 2A, a characterization array 20A for characterizing resistance variation is shown. Resistors R1-RN are individually and sequentially selected using pass gate pairs (transmission gates) TG1A, TG1B through TGNA, TGNB and providing a constant current through the selected resistor using current source I21A. Pass gates TG1A-TGNA provide a voltage source from test point VFORCE that is sufficient to saturate current source I21A for any resistance value of resistors R1-RN plus the corresponding resistance of the selected one of pass gates TG1A-TGNA. Pass gates TG1B-TGNB provide a sense output at test point VHI so that the resistance of pass gates TG1A-TGNA has no impact on the measured output, which is the voltage between test points VHI and VLO. Scan latches 22A control the sequential selection of resistors R1-RN so that a voltage waveform corresponding to the resistance of resistors R1-RN is produced across test points VHI and VLO. Therefore, the standard deviation of the distribution of the resistance of resistors R1-RN is obtained from an RMS measurement from a meter connected across test points VHI and VLO and a measure of the mean is obtained from the measured DC (average) voltage.
Referring now to FIG. 2B, a characterization array 20B for characterizing capacitance is shown. Capacitors C1-CN may be capacitors formed from metal layers of the circuit implementing characterization array 20B, or may be gates of transistors. If transistor gate capacitances are measured, the drain and source terminals must generally be biased in some manner, since the capacitance generally varies non-linearly with the transistor operating point. The above-incorporated U.S. patent application Ser. No. 11/736,146 entitled “METHOD AND APPARATUS FOR STATISTICAL CMOS DEVICE CHARACTERIZATION”, and issued as U.S. Pat. No. 7,397,259, describes biasing techniques for measuring transistor terminal capacitance in detail. The present invention directly measures the statistics of an array of capacitances rather than measuring individual capacitance values as is described in the above-referenced U.S. patent application.
First, a set of pass gates TG1D-TGND are all enabled by de-asserting each control output of scan latches 22B to force a first terminal of all of capacitors C1-CN to ground. The other terminal of capacitors C1-CN is a commonly connected node that is continually charged and discharged by the switching action of pass gates TG20, TG21 and TG22, which are operated by non-overlapping clock phases Φ1 and Φ2 provided from a non-overlapping clock generator 24. Thus, during the calibration interval, the current flowing through a resistor R20 connected between pass gates TG20 and TG21 during clock phase Φ1 is the current required to charge the total capacitance of capacitors C1-CN plus any parasitic capacitances to VDD from ground, since during clock phase Φ2, the commonly connected terminals of capacitors C1-CN is discharged to ground. The current flowing through resistor R20 during clock phase Φ2 is zero. Non-overlapping clock generator 24 operates at a high frequency, e.g., 10 MHz and the average current flowing through resistor R20 is dependent on the frequency F of non-overlapping clock generator 24, according to ICAL=FVDDCTOT, where CTOT is the total capacitance at the commonly connected node of capacitors C1-CN. The reference current value ICAL can be captured with a DVM connected to the outputs of a pair of low-pass filters LPF1 and LPF2 that have inputs connected to the terminals of resistor R20. The difference between the output voltages of low-pass filters LPF1 and LPF2 is RFVDDCTOT during the calibration interval. Low-pass filters have a passband that does not pass the switching frequency of non-overlapping clock generator 24, but does not filter the frequency at which scan latches 22B are operated to sequentially select capacitors C1-CN for testing during the capacitance statistics measurement, so that the rms value correctly reflects the standard deviation of capacitance. Low-pass filters LPF1 and LPF2 may be integrated on a die including characterization array 20B or may be provided externally as part of the measurement apparatus.
Next, the statistics of the capacitances of capacitors C1-CN are measured by operating scan latches 22B to sequentially enable pass gates TG1C-TGNC. Corresponding pass gates TG1D-TGND are each disabled as the scan proceeds. Since clock phase Φ1 is applied directly to capacitors C1-CN by pass gates TG1C-TGNC as each is enabled and has a value of VDD at that time, during clock phase Φ1, the current through resistor R20 is IMEAS=FVDD(CTOT−CSELECTED), where CSELECTED is the capacitance of the capacitors selected for measurement. Thus, the average DC deviation from the difference in output voltages of low-pass filters LPF1 and LPF2 to the difference in output voltages of low-pass filters LPF1 and LPF2 during the selection of capacitors C1-CN is an indication of the mean value of the capacitances of capacitors C1-CN. The rms value of the variation in the difference in output voltages of low-pass filters LPF1 and LPF2 during the selection of capacitors C1-CN is an indication of the standard deviation of the capacitances of capacitors C1-CN.
Referring now to FIG. 3, a method according to an embodiment of the invention is depicted in a flowchart. First, the test operating conditions for the characterization array are set, including power supply voltages, temperature and calibration, if required by the measurement (step 40). Next each device is selected in turn by clocking the selection values through scan latches (step 42). The test output voltage and/or current levels are measured with a digital multi-meter (step 44). (Alternatively, a DVM or DCM may be employed, depending on the output value to be measured.) Then, the rms value of the voltage/current level(s) from the multi-meter are retrieved and stored in computer memory. The standard deviation of device parameter variation is determined from the measured rms value (step 46). Finally, the DC average value of the voltage/current measurement is retrieved from the multi-meter and stored in computer memory. The mean value of the device parameter variation is determined from the measured DC average value (step 48).
Referring now to FIG. 4, a wafer test system in which a method according to an embodiment of the invention is performed, is shown. A wafer tester 30 includes a boundary scan unit 31 for providing stimulus to a die or kerf circuit 32A on a wafer under test 32, via a probe head 33 having electrical test connections 33A to die 32A. Wafer tester 30 also includes a digital multi-meter DMM, which may be part of a parametric measurement unit that also includes a programmable voltage source PVS and a programmable current source PCS, that are all coupled to die 32A via probe head 33 electrical test connections 33A. In the embodiment illustrated in FIG. 1B, the output of programmable voltage source is connected to pad VGP, the output of programmable current source PCS is connected to pad IDP and the input of digital multi-meter DMM is connected to pad VSP. In the embodiment illustrated in FIG. 2A, programmable current source PCS provides current source I21A and the input of digital multi-meter DMM is connected across terminals VHI and VLO. In the embodiment illustrated in FIG. 2B, digital multi-meter DMM is connected across the outputs of low-pass filters LPF1 and LPF2.
A workstation computer 38, having a processor 36 coupled to a memory 37, for executing program instructions from memory 37, wherein the program instructions include program instructions for executing one or more methods in accordance with an embodiment of the present invention, is coupled to wafer tester 30, whereby the measurements described above are performed and measurements collected and stored in memory 37 and/or other media storage such as a hard disk. A CD-ROM drive 35 provides for import of program instructions in accordance with embodiments of the present invention that are stored on media such as compact disc CD. Workstation computer 38 is also coupled to a graphical display 39 for displaying program output such as distributions of the threshold voltage for devices in the characterization array provided by embodiments of the present invention. Workstation computer 38 is further coupled to input devices such as a mouse 34B and a keyboard 34A for receiving user input. Workstation computer may be coupled to a public network such as the Internet, or may be a private network such as the various “intra-nets” and software containing program instructions embodying methods in accordance with embodiments of the present invention may be located on remote computers or locally within workstation computer 38. Further, workstation computer 38 may be coupled to wafer tester 30 by such a network connection.
While the system of FIG. 4 depicts a configuration suitable for sequential test of a plurality of dies on a wafer, the depicted system is illustrative and not a limitation of the present invention. Probe head 33 may be a multi-die full wafer probe system, or may comprise multiple probe heads for simultaneously testing multiple wafers on a single or multiple die basis. Additionally, while boundary scan control of the characterization array is illustrated, the techniques of the present invention may also be applied to execution of test code from a processor incorporated on wafer 32 with appropriate current and voltage sources and voltage measurement circuitry provided on wafer 32, as well. The resultant generated display or data exported from workstation computer 38 may take the form of graphical depictions of the threshold voltage variation across the characterization array, or may graphical or numerical statistical distribution information that describes the threshold voltage variation.
While the invention has been particularly shown and described with reference to the preferred embodiments thereof, it will be understood by those skilled in the art that the foregoing and other changes in form, and details may be made therein without departing from the spirit and scope of the invention.

## Claims

1. A computer-performed method for characterizing device parameter variation in an array of devices, the method comprising:
under control of a computer system, sequentially selecting devices within said array as a selected device under test;
producing a voltage or current waveform at a test output of the array of devices corresponding to a value of a particular device parameter of the selected device, wherein the voltage or current waveform is generated at the test output by action of the sequentially selecting;
measuring at least one of a DC value or a root mean square value of a variation of the voltage or current waveform during the sequentially selecting with a digital meter interfaced to the computer system; and
storing the at least one of the DC value or the root mean square value of the variation of the voltage or current waveform in a memory of the computer system as an indication of a statistic of the device parameter variation;
wherein the measuring measures a root mean square value of variation of the waveform as an indication of a standard deviation of the device parameter variation.

2. A test workstation computer system including a memory for storing program instructions for characterizing device parameter variation within a characterization array, a processor for executing said program instructions, an interface that couples the processor to control logic that performs device selection within a characterization array circuit, and a digital meter interfaced to the processor and coupled to a test output of the characterization array, wherein said program instructions comprise program instructions for:
sequentially selecting devices within said characterization array as a selected device under test, wherein the test output of the characterization array produces a voltage or current waveform corresponding to a value of a particular device parameter of the selected device, and wherein the voltage or current waveform is generated at the test output by action of the sequentially selecting;
measuring values of the voltage or current waveform with the digital meter during the sequentially selecting;
reading the values of the voltage or current waveform from the digital meter after completion of the sequentially selecting; and
storing a result of the reading in storage within the test workstation computer system as an indication of a statistic of the device parameter variation;
wherein the digital meter measures a root mean square value of variation of the waveform as an indication of a standard deviation of the device parameter variation.

3. A computer program product comprising a non-transitory computer-readable storage media encoding program instructions for characterizing device parameter variation within an array for execution by a workstation computer including an interface that couples a processor or the workstation computer to a control logic that performs device selection within a characterization array circuit, and a digital meter interfaced to the processor and coupled to a test output of the characterization array, wherein said program instructions comprise program instructions for:
sequentially selecting devices within said characterization array as a selected device under test, wherein the test output of the characterization array produces a voltage or current waveform corresponding to a value of a particular device parameter of the selected device, and wherein the voltage or current waveform is generated at the test output by action of the sequentially selecting;
measuring values of the voltage or current waveform with the digital meter during the sequentially selecting;
reading the values of the voltage or current waveform from the digital meter after completion of the sequentially selecting; and
storing a result of the reading in storage within the test workstation computer system as an indication of a statistic of the device parameter variation;
wherein the digital meter measures a root mean square value of variation of the waveform as an indication of a standard deviation of the device parameter variation.