Abstract:
A method of producing a temperature sensing device is provided. The method includes forming at least one silicon layer and at least one electrode or contact to define a thermistor structure. At least the silicon layer is formed by printing, and at least one of the silicon layer and the electrode or contact is supported by a substrate during printing thereof. Preferably, the electrodes or contacts are formed by printing, using an ink comprising silicon particles having a size in the range 10 nanometres to 100 micrometres, and a liquid vehicle composed of a binder and a suitable solvent. In some embodiments the substrate is an object the temperature of which is to be measured. Instead, the substrate may be a template, may be sacrificial, or may be a flexible or rigid material. Various device geometries are disclosed.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    THIS invention relates to a temperature sensing device and a method of producing such devices. In particular the invention relates to a negative temperature coefficient thermistor. 
         [0002]    Printing of functional inks has a long tradition in the electronics field. For example, pigment based inks are used to screen-print interconnections and resistors on printed circuit boards. In these applications the thick film inks used consist of a vehicle and pigments of silver and carbon respectively, where the pigment particles can have a dimension in the nanometer range. 
         [0003]    Traditionally most functional materials have been printed by conventional printing techniques, such as screen printing. More recent developments are aimed at printing not only the passive components of a circuit, but also active components. For example, printed nanoparticulate silicon components are disclosed in International patent application WO 2004/068536, which discloses the printing of semiconducting layers in active devices like solar cells and transistors. However, a commonly known example for an application of semiconducting thick-film pastes is the fabrication of a temperature dependent resistor, known as a thermistor. Such devices are generally considered to be passive electronic components. Of particular relevance here are thermistors which have a negative temperature coefficient of resistance, commonly known as NTC thermistors, meaning that their electrical resistance decreases approximately exponentially with increasing temperature. 
         [0004]    Existing thermistors of this general type are composed of pastes comprised of a powder of a compound semiconductor material and a binder material, such as a glass frit. This paste is either screen printed onto a ceramic substrate or cast to form a green body, after which it is sintered at high temperature to form a massive layer or body of semiconductor material. Invariably, because of distortion during the thermal treatment, further trimming of the material to obtain the correct resistance is required before metallization, in the case of thick-film thermistors. 
         [0005]    The fabrication processes used place limitations on the substrate materials that can be used, precluding the use of many lightweight, flexible materials such as paper and polymer film. Traditionally, thick-film inks used for the fabrication of thermistors are composed of heavy metal sulphides and or tellurides, such as lead sulphide, and are not compliant with modern legislation such as the European Restriction on Hazardous Substances (ROHS). Recently introduced alternative materials include compositions of mixtures of rare earth and transition metal oxides, such as manganese oxide. Thermistors based on silicon are usually cut from heavily doped silicon wafers, and have a positive temperature coefficient of resistance. 
         [0006]    It is an object of the invention to provide an alternative temperature sensing device and a method of producing such devices. 
       SUMMARY OF THE INVENTION 
       [0007]    According to the invention there is provided a method of producing a temperature sensing device, the method including forming at least one silicon layer and at least two conducting electrodes or contacts to define a thermistor structure, at least the silicon layer being formed by printing, and at least one of the silicon layer and conducting electrodes or contacts being supported by a substrate material during printing thereof. 
         [0008]    The temperature sensing device may be a negative temperature coefficient (NTC) thermistor. 
         [0009]    For the purposes of the invention, “printing” should be interpreted in its broadest sense as any method of depositing a liquid or colloidal mixture on a solid substrate, and hence includes coating methods such as drop casting, slit coating, spin coating and spraying. 
         [0010]    Although direct patterning, by printing a design or coating through a stencil is desirable, this is not necessary if the substrate material has the correct size and form. 
         [0011]    Specifically the definition of printing should include all types of: relief printing, including but not limited to flexography and letterpress; intaglio processes such as gravure printing; and planographic printing, such as lithography, xerography, and thermography. 
         [0012]    Planographic printing methods envisaged include all offset printing processes in which the design is first transferred to a blanket roll, such as offset lithography and offset gravure printing, or to a tampon as in pad printing. 
         [0013]    Finally, the term printing should encompass traditional stencil methods which are commonly defined as printing, and screen printing in particular, as well as non-contact printing methods such as ink-jet printing, aerosol, spraying, and electrohydrodynamic spraying. 
         [0014]    At least the silicon layer, and preferably the electrodes or contacts, should be deposited by printing as defined above. 
         [0015]    Said at least one silicon layer and at least two conducting electrodes or contacts may be applied directly to an object of which the temperature is to be measured, so that the object itself forms the substrate. 
         [0016]    Alternatively the substrate may be any metallic, or otherwise electrically conducting body, such that the substrate forms one of the contacts for the thermistor. 
         [0017]    Otherwise the substrate can be any material or combination of materials upon which the contacts and the silicon layer can be deposited. 
         [0018]    In one preferred embodiment, the substrate comprises a flexible sheet, which may for example be composed of a solid film such as a metal foil or polymer sheet; a fibrous material such as paper and felted materials; or a woven fabric. 
         [0019]    In the case of a metallic or conducting substrate which does not form one of the contacts to the device, the surface of the substrate may be rendered non-conducting by the application of an intermediate insulating layer, either in the form of a paint, ink, varnish or lacquer, or through commonly known surface treatment processes such as oxidation, carburization, nitridation or anodizing. 
         [0020]    In another preferred embodiment the substrate comprises a rigid sheet, which may be composed of a solid material such as a metal sheet, glass or polymer sheet or semiconductor wafer; a composite containing fibrous or particulate material such as paper and felted materials; or a composite containing woven fabric. 
         [0021]    By way of example only, possible materials from which the substrate can be composed include copper, aluminium, gold, silver, alloys thereof, silicon, germanium, silicon carbide, flint glass, crown glass, borosilicate glass, quartz, paper card, cotton, glass fibre, polyimide, polyester and its derivatives, other plastics, cellulose, and many other materials. 
         [0022]    Where the body for which the temperature to be measured does not form the substrate, the substrate may form a permanent support for the thermistor structure. 
         [0023]    Alternatively the substrate may form a temporary support or template for the thermistor structure during the production thereof. 
         [0024]    In this case, the substrate may either be sacrificial, and be removed by chemical, thermal or mechanical means after printing of the thermistor structure, or it may form a reusable template. 
         [0025]    In a preferred embodiment the silicon layer is formed from an ink comprising silicon particles and a liquid vehicle composed of a binder and a suitable solvent. In some cases, depending on the printing process, the solvent may be omitted, or additional compounds commonly used in the formulation of inks, such as siccatives or stabilisers, may be added. 
         [0026]    The silicon particles should have a size in the range 10 nanometres to 100 micrometres, and preferably should be nanoparticles with a characteristic size between 50 and 250 nanometres. 
         [0027]    The silicon nanoparticles should preferably have a surface which allows the transport of electrical charge between particles. This may be achieved through a suitable termination of surface dangling bonds by oxygen, hydroxyl or hydrogen species as described in International patent application WO 2007/004014. 
         [0028]    Electrical conduction through the silicon nanoparticle network formed within the printed silicon layer is presumed to occur by a hopping percolation process, in which the transfer of charge between the individual particles or clusters of particles, or the semiconductor material and the conducting electrode, is limited by thermally activated processes. Hence the temperature coefficient of the resistance is predominantly determined by the particle characteristics, especially at their surfaces and interfaces. Modification of the surface, either by the introduction or removal of trapped states by the adsorption of other species, particularly small molecules which are easily ionized; or the varying of the thickness of an interfacial barrier caused by partial oxidation or adsorption of another material, specifically large organic molecules, can therefore also be used to alter the temperature response of the material. 
         [0029]    Another mechanism known to contribute to the temperature dependence of the resistance is the thermal generation of carriers in intrinsic or lightly doped semiconductors. It is therefore desirable to choose the appropriate doping level of the silicon particles, either by fabricating them from conventionally doped n- and p-type material or adsorbing a fully ionized ionic species onto the surface as described in International patent application WO 2007/023362. 
         [0030]    Suitable silicon nanoparticles can be produced by mechanical attrition of bulk silicon, or by any other method, such as the pyrolysis of any silane gas, including monosilane and disilane and their derivatives, in which full oxidation is prevented by the exclusion of oxygen, or the reduction of the sub-stoichiometric oxides as described in International patent application WO 2009/125370. 
         [0031]    The overall transport of electrical current through the silicon layer follows a percolation path between interconnecting particles and clusters of particles. Therefore the nominal, or room temperature, resistivity is chiefly governed by the microstructure of the silicon layer, and particularly the number of particle interconnections. This can be modified not only by the choice of printing process and its parameters, but by the modification of the ink composition, through variation of the silicon to binder ratio or the addition of either an insulating phase such as silica or other ceramic nanoparticles, or conducting metallic nanoparticles. 
         [0032]    The method may include the addition of at least one additional conducting path into the silicon particle layer by the modification of the ink composition, by varying the silicon to binder ratio, or the addition of either an insulating phase such as silica or other ceramic nanoparticles, or a conducting or semiconducting phase to the ink, thereby effectively to add a relatively temperature independent internal resistance in parallel with the temperature dependent resistance of the thermistor structure. 
         [0033]    The addition of extra conducting paths into the silicon particle layer has the effect of adding a relatively temperature independent internal resistance in parallel with the temperature dependent material of the thermistor structure. This combination may also be used to modify the temperature sensitivity of the device. 
         [0034]    In an extension of this idea, the additional phase may comprise nanoparticles of differently doped silicon, or of another semiconductor material. 
         [0035]    In an alternative approach, a printed temperature sensor may be fabricated with an internal temperature independent resistor printed, using a conducting ink, in parallel with the temperature dependent resistance of the thermistor structure. 
         [0036]    Similarly the nominal resistance of the printed temperature sensor can be increased by printing a temperature independent internal resistance in series with the temperature dependent resistance of the thermistor structure. 
         [0037]    The silicon powder to binder ratio in the inks used should be sufficient to allow a measurable electrical conductance in the nominal operating range of the device, but low enough to maintain structural integrity of the silicon layer. 
         [0038]    The nanoparticle fraction in the ink may range from 5% to 95%, but best performance is achieved above when the concentration of nanoparticles is significantly greater than the lower percolation thresholds, with a practical limit of around 25%. 
         [0039]    Between the lower and upper percolation thresholds, the resistance may be simply adjusted by variation of the fraction of silicon nanopowder in the ink. Our results show this region to broadly correspond to between 25% and 60% of silicon nanopowder particles in the ink by volume. 
         [0040]    The best reproducibility is obtained for high particle to binder ratios, above the higher percolation threshold where the material properties vary only weakly with the fraction of silicon in the ink. This can be achieved with a silicon fraction above 60% and preferably in excess of 80%. 
         [0041]    The ink vehicle may be comprised of any commonly used ink-base, composed of an organic binder and its appropriate solvent. 
         [0042]    The binder may be a soluble polymer such as polystyrene or cellulose acetate butyrate, or an autopolymerising monomer such as acrylic emulsion or as described in WO 2007/072162 a natural oil, such as linseed or calendula oil, or a fatty acid. 
         [0043]    In one embodiment and in the examples described below, the binder used was a commercial screen printing ink base, comprising a water-based acrylic emulsion, and the solvent was propylene glycol. 
         [0044]    Other binder and solvent combinations which have been shown to be suitable include: refined linseed oil with commercial lacquer thinners, acetone or similar; polystyrene with chloroform; and cellulous acetate butyrate with chloroform. 
         [0045]    With the exception of devices in which the substrate forms one of the electrical contacts, it is preferred to produce the electrical contacts in a similar manner as the silicon layer, so that they are directly patterned by printing. For this purpose any commonly available conducting ink, such as silver, gold or graphite based screen printing pastes or metallic nanoparticle based inks, may be used. 
         [0046]    Alternatively, the contacts may be formed by one of a number of established thin film deposition processes, such as sputtering, evaporation, or chemical vapour deposition. Equally, electroplating or electroless plating may be applied. 
         [0047]    In such cases, the contacts may be patterned to the correct form by chemical or electrochemical etching, laser scribing or otherwise removing material to form the desired shape. 
         [0048]    In one preferred embodiment, the contacts have a circular geometry so that the radial electrical path of the thermistor structure ensures that the resistance measured is averaged over all directions relative to the printing direction, thus eliminating the effect of any lateral anisotropy in the printing process. 
         [0049]    Generally because of the high resistivity of the printed silicon material, the aspect ratio of the thermistor device should be low, so that the distance between any two contacts used to supply the current should be small in comparison to the width of the semiconducting pathway between the contacts. 
         [0050]    Preferably, the aspect ratio of the thermistor device is less than 1/30, and more preferably less than 1/1 000. 
         [0051]    In one embodiment this can be achieved by a multilayer structure, comprising a layer of printed silicon material between two layers of conducting material, as illustrated in  FIG. 1  of the accompanying drawings. In such a device the resistance is measured through the thickness of the silicon layer, in a direction perpendicular to the plane of the silicon layer. Consequently, the area of such a temperature sensor can be extended almost indefinitely and may take any arbitrary shape. 
         [0052]    In general, however a series of coplanar electrodes or contacts are preferred because of the simplicity of the manufacturing process. In this case at least two conducting contacts are deposited using any suitable process either on to the silicon layer, or firstly onto the substrate and subsequently overprinted with the silicon layer. These two geometries may be referred to as top-contact or bottom-contact devices respectively. 
         [0053]    For devices with coplanar contacts, the specific geometries indicated in  FIGS. 2 to 8  below may be applied to increase the width to length ratio. 
         [0054]    In one embodiment, two elongated parallel contacts which extend side by side are deposited in a pattern defining a spiral or meandering path to cover a relatively large area, thereby to allow the average temperature of a correspondingly shaped area of the substrate to be monitored 
         [0055]    In another embodiment, two interdigitated electrical contacts, each having a plurality of elongate strips or fingers which extend parallel and adjacent to one another to define a serpentine gap, are connected or bridged by a layer of printed particulate silicon. 
         [0056]    The layer of printed particulate silicon may be structured to follow the serpentine gap between the electrodes, or may form a continuous layer over the serpentine gap between the electrodes. 
         [0057]    In another embodiment, four electrical contacts, two of which are used to supply electrical current to the temperature sensing device and two of which are used to monitor voltage in use, are deposited in either a conventional linear four-point geometry or any of the commonly used van der Pauw geometries to obtain a higher accuracy. 
         [0058]    The invention extends to a temperature sensing device produced by the above defined methods. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0059]      FIG. 1  is a schematic side view of a multi-layer temperature sensing device according to the present invention; 
           [0060]      FIG. 2  is a schematic diagram showing the arrangement of a first embodiment of a printed thermistor according to the invention, with a spiral configuration; 
           [0061]      FIG. 3  is a schematic diagram showing the arrangement of a second embodiment of a printed thermistor according to the invention, with an interdigitated configuration; 
           [0062]      FIGS. 4 &amp; 5  are schematic diagrams showing the arrangement of third and fourth embodiments of a printed thermistor according to the invention, with concentrically arranged contacts; 
           [0063]      FIG. 6  is a schematic diagram showing the arrangement of a fifth embodiment of a printed thermistor according to the invention, having a four electrode configuration; 
           [0064]      FIG. 7  is a schematic diagram showing the arrangement of a sixth embodiment of a printed thermistor according to the invention, having four electrical contacts connected by a layer of printed particulate silicon for which a van der Pauw method can be used to determine the electrical resistance; 
           [0065]      FIG. 8  is a schematic diagram showing the arrangement of a sixth embodiment of a printed thermistor according to the invention, similar to the embodiment of  FIG. 7  but having extended contact arms; 
           [0066]      FIG. 9  is a graph showing an Arrhenius curve for an example of a thermistor of the design shown in  FIG. 6 ; 
           [0067]      FIG. 10  is a graph showing an Arrhenius curve for an example of a bottom-contact thermistor of the design shown in  FIG. 5 ; 
           [0068]      FIG. 11  is a photograph of an embodiment of a negative temperature coefficient thermistor formed according to the method of the invention; and 
           [0069]      FIG. 12  is a photograph of a variation of the interdigitated thermistor shown in  FIG. 11 . 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
       [0070]      FIG. 1  shows a schematic sectional side view of a basic multi-layer thermistor structure according to an example embodiment of the present invention. 
         [0071]    The thermistor structure is formed on a substrate  10  and comprises a first metallic layer  12 , a layer of particulate silicon  14  printed onto the first metallic layer  14 , and a second metallic layer  16  deposited onto the layer of particulate silicon  14 . As indicated above, the substrate  10  can take many forms, but will typically comprise a flexible sheet, which may, for example, be composed of a solid film such as a metal foil or polymer sheet; a fibrous material such as paper and felted materials; or a woven fabric. These examples are provided merely for illustrative purposes and are not intended to be limiting. The metallic layers and the particulate silicon layer are preferably deposited by printing as defined above. 
         [0072]    In the embodiment of  FIG. 1 , the substrate  10  is either non-conducting or, if conducting, does not serve as an electrical contact to the thermistor structure. In this embodiment, the first and second metallic layers  12  and  16  serve as conducting electrodes or contacts, to which respective wires or other conductors  18  and  20  can be connected. 
         [0073]    Several example embodiments of thermistors produced by the methods of the invention are described below with reference to  FIGS. 2 to 8 . 
         [0074]    The first embodiment, as shown in  FIG. 2 , is a bottom-contact two-terminal thermistor. This embodiment includes two elongate conducting contacts  22  and  24  formed on a substrate  26 , which extend side by side and which may be arranged in a pattern such as a spiral to cover a relatively large area. The contacts are connected or bridged by a layer  28  of printed particulate silicon having an elongate spiral shape and which partially overlies the respective contacts, the whole structure being supported by the substrate. Electrical connections can be made to the contacts  22  and  24  as required. 
         [0075]    Instead of the illustrated squared-off spiral shape, the contacts and the bridging layer of particulate silicon may follow another parallel meander or curved spiral path. The thermistor structure may cover a relatively large area, to allow the average temperature of a large and possibly irregularly shaped area of the substrate  26  (or an object to which the substrate  26  is attached) to be monitored. 
         [0076]    A similar top contact device may be fabricated by simply reversing the deposition sequence, with the layer of particulate silicon being printed first and the contacts being deposited over it. In an alternative approach, the silicon strip may form a continuous layer deposited on or underneath the contact strips. 
         [0077]      FIG. 3  is an illustration of an interdigitated two terminal thermistor consisting of two interdigitated electrical contacts  30  and  32 , which are connected or bridged by a layer  34  of printed particulate silicon. The contacts  30  and  32  each have a plurality of elongate strips or fingers  36  and  38  which extend parallel and adjacent to one another to define a serpentine gap over which a layer of silicon ink is printed to form the layer  34  and to connect the two sets of electrodes. The number and length of the contacts or electrodes and their fingers may be varied to cover any desired area. The thermistor is printed on a substrate  40 . 
         [0078]    This silicon layer  34  may be structured to follow the gaps between the electrodes as shown, or may form a continuous layer. The device may be either a bottom-contact or top-contact device, depending on the order of deposition of the materials as described above. 
         [0079]      FIG. 4  shows an embodiment in which the electrical path of the thermistor is in the radial direction of a circular structure having an inner electrical contact  42  and a concentric ring-shaped outer contact or electrode  44 . The contacts are connected by an annular layer of printed particulate silicon  46 . The thermistor is printed on a substrate  48   
         [0080]      FIG. 5  shows a similar embodiment to that of  FIG. 4 , in which the two contacts comprise a solid inner circle  50  and a concentric outer ring  52  deposited in a coaxial geometry. A printed particulate silicon layer  54  forms a second concentric ring, bridging the two contacts. However, in the device of  FIG. 5  the inner electrode contact  50  is extended radially outwardly to a first electrical contact pad through a gap in the outer contact  52 . The outer contact is also extended outwardly to a second electrical contact pad  58 . The structure is printed on a substrate  60 . The concentric ring defined by the printed silicon layer  54 , which bridges the annular gap between the two contacts, may be either complete or broken (as illustrated). 
         [0081]    The example embodiments of  FIGS. 4 and 5 , which may be fabricated as either top-contact or bottom-contact devices, are specifically adapted to printing processes. The radial electrical path of these thermistor structures ensures that the resistance measured is averaged over all directions relative to the printing direction, thus eliminating the effect of any lateral anisotropy in the deposition process. 
         [0082]    For higher accuracy, thermistor devices adapted for use in the well known four point resistance measurement technique may be desirable. This may be achieved by a device having four coplanar electrodes as indicated in  FIG. 6 . This device has two finely structured inner electrodes  62  and  64  between which the potential difference is determined and two additional electrodes  66  and  68  through which a current is supplied. All four electrodes are connected by an over-printed layer  70  of printed particulate silicon. The device is formed on a substrate  72 . Each of the inner electrodes  62  and  64  has an enlarged contact pad at each end thereof. 
         [0083]    The two inner electrodes  62  and  64  are used to measure the potential difference in the particulate silicon layer, and may be very finely printed. The outer electrodes  66  and  68  are used to supply an excitation current and may be relatively large compared to the inner electrodes. In the simplest variation of this geometry, as illustrated, the silicon layer  70  is simply printed as a thick strip bridging the four electrodes in a central area of the device. 
         [0084]    An alternative to the four point resistance method is to use any of the well-known van der Pauw geometries, such as the circular design shown in  FIG. 7  or the “Greek cross” geometry shown in  FIG. 8 . 
         [0085]    In the printed thermistor device of  FIG. 7 , four equispaced wedge-shaped electrical contacts  74 ,  76 ,  78  and  80  are provided, connected by a layer  82  of printed particulate silicon having a solid circular shape. The device is printed on a substrate  84 . The four contacts are arranged symmetrically in a circular pattern with a space in the centre of the pattern which is filled by the layer of printed silicon. To obtain the highest accuracy, this latter layer should have a circular form and be centrally located. However, this is not essential, and adequate devices can be produced by printing a continuous layer of silicon onto or underneath the electrodes. 
         [0086]    In the device of  FIG. 8 , four electrodes  86 ,  88 ,  90  and  92  are deposited symmetrically on a substrate  94 . A layer  96  of particulate silicon is deposited in a central region of the device between the contacts. The layer  96  has a Greek cross geometry, with the tips of the arms of the cross partially overlying the respective electrodes and defining two perpendicular silicon paths between the electrodes. 
         [0087]    Further well known variations of the van der Pauw geometry which can be defined by thermistors of the invention include structures which combine the geometrical features of these two basic forms, such as a clover leaf or Maltese cross. 
         [0088]    A novel method of determining the temperature dependent resistance, made possible by the use of printing to fabricate the devices, is to extend the principles of the van der Pauw technique by having the same symmetrical electrode structure forming top and bottom contacts. Any of the two-contact designs presented above can be used to determine the resistance through the bulk of the silicon layer in an analogous method to the standard four-point van der Pauw technique. Similarly, four-electrode configurations applied as both top and bottom contacts will give an even higher accuracy and stability of the resistance measurement. 
         [0089]    Furthermore, any of the above designs, or similar arrangements of electrodes, can be arranged in an array over a large area on the substrate to form a pixellated sensor which will allow the temperature distribution over a given area to be mapped. 
       Example 1 
       [0090]    In a first example a negative temperature coefficient thermistor was produced according to the design shown in  FIG. 6 . Four silver electrodes or contacts were deposited on 80 g/m 2  wood-free paper sheet substrate by screen-printing using Du Pont 5000 silver conductor. The separation between any two adjacent electrodes was 2 mm. After allowing the silver ink to dry for approximately one day under ambient conditions, silicon ink was drop-cast to form a connection between all four electrodes of the device. The silicon nanoparticles used in the ink were milled from a boron doped p-type silicon wafer, according to the method disclosed in WO 2009/125370. These particles were mixed with a commercially available acrylic screen-printing base in a ratio of 95% silicon by weight, and the consistency of the ink was adjusted by thinning with propylene glycol. 
         [0091]    The completed device was cut out from the larger sheet of paper to form a small flexible device of size approximately 15 mm by 10 mm. In preliminary tests, the room temperature current/voltage characteristics were determined by both four-point and two-point techniques. For testing its temperature response, this device was fixed with adhesive tape to the outside of a glass beaker of diameter 65 mm, such that the paper substrate was between the printed thermistor device and the glass, and so that the axis of the device followed the circumference of the glass. 
         [0092]    To calibrate the temperature dependence of the resistance, the beaker was filled with iced water and heated on an electric hotplate, while the temperature of the water was measured with a digital thermometer. For convenience the resistance was simply measured with a digital multimeter. 
         [0093]      FIG. 9  shows the resistance temperature response of the thermistor on an Arrhenius scale. In the temperature range indicated, the device exhibits a logarithmic temperature coefficient, commonly referred to as a beta value, of 2 210±30K. 
       Example 2 
       [0094]    In a second example a negative temperature coefficient thermistor was produced, also according to the design shown in  FIG. 5 . Silver contacts were deposited on a substrate comprising a sheet of 80 g/m 2  wood-free paper by screen-printing using Du Pont 5000 silver conductor. The diameter of the inner electrode was 5 mm, and the separation between the two electrodes was 0.5 mm. After allowing the silver ink to dry for approximately one day under ambient conditions, a silicon layer was screen-printed over the gap between the electrodes, using silicon nanoparticles milled from 2503 grade metallurgical silicon according to the method disclosed in WO 2009/125370. These nanoparticles were mixed with a commercially available acrylic screen-printing base in a ratio of 88% silicon by weight, and the consistency of the ink was adjusted by thinning with propylene glycol. 
         [0095]    The completed device was cut out from the larger sheet of paper to form a small flexible device of size approximately 20 mm by 15 mm. Silver wires were soldered to the contact pads to form secure permanent connections. Current/voltage characteristics were measured for the device, in the temperature range 50K to 350K, using a Lake Shore 7700 Hall measurement system, and associated cryostat, under zero magnetic field conditions. The resistance/temperature characteristics shown as an example in  FIG. 10  were determined from the slope of the voltage/current characteristics at low excitation current. Over an extended temperature range, there are at least two Arrhenius coefficients, of typically 1 000K at liquid nitrogen temperatures and 2 000K around room temperature. Further studies of similar devices indicate a third beta value of approximately 10 000K which is apparent at temperatures above 350K. The combination of these different beta values in different ranges allows the printed silicon thermistors to be applied over a wide range of temperatures. 
       Example 3 
       [0096]      FIG. 11  is a photograph of a negative temperature coefficient thermistor according to the design shown in  FIG. 3 . In this case the silicon is printed as a solid block over the interdigitated silver contacts, but only the area of silicon deposited between the contacts contributes to the temperature dependent resistance. For a low resistance, the length to width aspect ratio of the silicon semiconductor should be low, ideally less than 1/1 000. In this example, the silver contacts comprise 25 individual electrodes, with 24 gaps between adjacent electrodes, each gap having a length of 16 mm and the width of each gap (the separation between adjacent electrodes) of 0.25 mm. 
         [0097]    In contrast to the device of Example 2, which is a high resistance device and has a length to width aspect ratio of approximately 1/30 (given by the ratio of the transverse gap between the conductors to the circumference of a circle defining the gap between the conductors in  FIG. 5 ), the design of the present Example has an aspect ratio of 1/1 600, and a correspondingly lower resistance for the same silicon layer thickness. 
         [0098]    The silver contacts were deposited by screen printing on 160 gsm paper board substrates using Du Pont 5000 Silver Conductor. After allowing the silver ink to dry for approximately one day under ambient conditions, a silicon layer was screen-printed over the gap between the electrodes, using silicon nanoparticles milled from 2503 grade metallurgical silicon according to the method disclosed in WO 2009/125370. These nanoparticles were mixed with a commercially available acrylic screen-printing base in a ratio of 80% silicon by weight, and the consistency of the ink was adjusted by thinning with propylene glycol. 
         [0099]    The final thermistor was then packaged as a discrete component according to the method disclosed in South African provisional patent specification 2010/06533, with the silver contacts being allowed to protrude from the plastic lamination. Tests of many such devices were conducted in a box oven, over a temperature range from 20° C. to 60° C., yielding a consistent beta value of 2 000 K with a statistical variation of ±100 K. Typical resistances, depending on the thickness of the silicon layer, are 100 kΩ. Detailed analysis of the conductance from low temperature measurements using a Lake Shore 7700 system, over an extended temperature range from 15 K to 350 K, showed three characteristic beta values of approximately 20 K, 650 K and 1 900 K. 
       Example 4 
       [0100]      FIG. 12  is a photograph of variation of the interdigitated thermistor described in Example 3, according to the basic design of  FIG. 3 , which is extended over a larger area, and which takes its form as a graphic design. As an example a full size human handprint was chosen as the design, but any other abstract or pictorial design could have been selected without restriction. 
         [0101]    A plurality of silver tracks, with their common connections forming the outline of the hand, are screen printed, using Du Pont 5000 silver conductor on various colours of 180 gsm paper board, to form the interdigitated electrodes. The gaps between the electrodes are adjusted to fit the shape of the design, and range from 0.5 mm to 1 mm. Silicon ink, comprising 80% by weight of nanoparticles milled from 2503 grade silicon according to the method disclosed in WO 2009/125370, is printed in different positions to form both the graphic design and a set of thermistors connected in parallel. Equally the whole area of the hand could have been printed in silicon, but this was not done to allow an illustration of the principles of construction and operation of the thermistor. After printing, the thermistor was packaged as a discrete component according to the method disclosed in South African provisional patent specification 2010/06533, with the silver contacts being allowed to protrude from the plastic lamination. Typical resistances for this design, depending on the thickness of the silicon layer, are between 20 and 40 kΩ, and the beta value is consistent at 2 000±100 K.