the following embodiments are described in order to provide a more precise understanding of the subject matter of the present invention . while the embodiments focus on a capacitative type sensor , ordinary workers in this field will readily understand that the invention is equally applicable to other forms of pressure sensor such as : ( i ) piezo - resistive , where the membrane is formed from a non - conductive material and the piezo material is in contact with the membrane . deflections of the membrane give rise to piezo - induced changes in resistivity ( and hence current , if a voltage is applied ) that can be monitored electronically . ( ii ) resonant pressure sensors , where the frequency of oscillation of the membrane depends on the pressure difference . the initial resonance could be activated by using a time - varying electrostatic force between the two electrodes . ( iii ) force compensation pressure sensors , where an electrostatic force is applied to maintain the membrane at the initial position . once again the electrostatic force between the two electrodes can be used to position the membrane . each of these sensor types has particular advantages and limitations . piezo - resistive sensors are reasonably well known and understood but require the use of exotic materials . the sensors of ( ii ) and ( iii ) are less popular but do not require exotic materials . capacitative sensors are typically robust and highly versatile and therefore the preferred embodiments will be based on this type of sensor . a brief overview of the basic operation of the sensor will be described with reference to fig2 . fig2 shows a schematic partial section of a capacitative sensor fabricated using the masked lithographic etching and deposition techniques typically used in the production of semiconductor chips . the fabrication steps are described in detail below . the sensor 30 is formed on a silicon substrate 32 , provided with sealed channels or holes 33 , on which is deposited a cmos layer 34 . a conductive layer 36 is deposited on the cmos layer 34 followed by a passivation layer 37 as illustrated . the passivation layer 37 may be an insulating or semi - conducting material . a conductive membrane 50 is spaced from conductive layer 36 to form a reference chamber 58 . roof or cap 54 covers the membrane 54 . the roof or cap 54 is provided with holes 40 , or channels or the like , so that the membrane 50 is exposed to tire pressure . the membrane 50 deflects due to differential stresses . the amount of deflection for a given pressure difference , depends on the membrane diameter and thickness , the nature of the support ( for example , strongly fixed , weakly pinned ), and the membrane material properties ( for example elastic modulus , poisson ratio , density ). both the membrane 50 and conductive layer 36 are electrodes , which develop a capacitance , c , between them which depends upon the electrical permittivity of the ambient material , e , the electrode spacing , d , and the electrode area , a . for the case where both electrodes are circular disks , c = e a / d . the sensor is then calibrated for measured capacitance versus applied pressure . fig4 , 6 , 7 , 9 , 11 , 12 , 14 , 16 , 17 , 19 , 21 , 22 and 23 show the main lithographic etching and deposition steps involved in the fabrication of a pressure sensor according to the invention . the masks associated with the successive steps are shown in fig3 , 5 , 8 , 10 , 13 , 15 , 18 and 20 . when etching photoresistive material the solid black areas of the masks are the regions that are removed by the subsequent etch . however , when etching metal and other non - photoresistive layers , the blank or unmasked areas of the mask denote the regions that are removed . skilled workers in this field will understand which masks are applied to photoresist and which are applied to non - photoresist . fig4 is section a - a ′ through the wafer 32 of a partially fabricated sensor . the silicon wafer 32 has previously been ground to the required thickness and cmos circuitry 34 is deposited on its top surface . the final cmos layer provides the bottom electrode 36 for the sensor . guard rings 42 are formed in the metallization layers of the cmos circuitry 34 . the guard rings 42 prevent air or other fluid from diffusing from the subsequently etched sealed passages 33 ( see fig2 ) through the wafer 32 to the circuitry where it can cause corrosion . the mask 70 for this first metal layer 36 is shown in fig3 , with the blank regions being etched away . as shown in fig6 , a passivation layer 37 and sacrificial layer 38 are deposited next . this is followed by masking and etching through to the silicon substrate 32 . this etch is known as the dielectric etch and the associated mask 72 is shown in fig5 . the mask represents the regions 46 that are etched . following the dielectric etch , the sacrificial layer 38 is etched away with a different etchant which also etches the holes 33 deeper into the wafer substrate 32 ( see fig7 ). referring to fig8 and 9 , the passivation layer 37 is then etched in a region 44 above the upper contact to provide an electrical pathway for the second electrode ( subsequently deposited ). as shown in fig1 , sacrificial material 48 is then deposited to fill the openings 33 into the silicon 32 made by the dielectric etch . this deposition continues until the top of the sacrificial layer 48 is level and at a height which provides the requisite gap height between the top and bottom electrodes . the first sacrificial layer 48 is then patterned and etched . the associated mask 76 is shown in fig1 . fig1 shows the deposition of the upper electrode layer 50 , also called the second metal layer . this layer is etched with the mask 78 shown in fig1 , with the blank regions being removed by the etch ( see fig1 ). the upper electrode layer 50 becomes the flexible membrane in the finished sensor . a second sacrificial layer 52 is then deposited ( see fig1 ), and subsequently etched . the relevant mask 80 is shown in fig1 . fig1 shows the deposition of the roof layer 54 . it is then etched using mask 82 shown in fig1 , with blank areas removed ( see fig1 ). the wafer is subsequently turned over for ‘ back etching ’ from the reverse side of the wafer 32 . fig2 shows a deep back etch 56 extending through to meet the openings 33 in accordance with the mask 84 shown in fig2 . the openings 33 are filled with sacrificial material 48 which is exposed by the deep back etch 56 . the sacrificial material is removed by plasma cleaning ( see fig2 ) through the deep etch 56 . as shown in fig2 , the wafer is again turned over and the sacrificial material 52 is removed through the hole in the roof layer 54 . to complete the device , it needs to be packaged , with the bottom face of the wafer being sealed . skilled workers will appreciate that there are various methods of achieving this . however , in the preferred embodiment , the bottom face of the wafer is sealed using wafer bonding , which is discussed in detail below . differential thermal expansion of the components within the pressure sensor will affect the membrane deflection and therefore the sensor output . if the sensor is used in an environment with a large temperature variation , the sensor accuracy can become unacceptable . to address this , the pressure sensor can be coupled with a temperature sensor , with the pressure sensor then calibrated as a function of temperature . to accommodate this , an embodiment of the present invention can conveniently incorporate a temperature sensor to account for temperature effects on the pressure sensor . a schematic section of the temperature is shown in fig2 . reference chamber 58 , can be etched into the same wafer substrate , but is not exposed to tire pressure like the adjacent pressure sensor ( not shown ). in these embodiments , the coupled sensors form an active and a reference sensor , the latter responding only to thermal changes . skilled workers in this field will appreciate that the reference sensor can also serve as a temperature sensor with the addition of circuitry calibrating the capacitance to the temperature . referring to fig2 , the reference sensor is made in the same way as the active sensor , except that the holes 40 are made in the membrane 50 instead of the roof layer 54 . the sacrificial material 52 between the membrane 50 and the roof layer 54 is removed with a back etch through the holes 40 in the membrane 50 . an alternative to this is to keep the membrane 50 intact and etch away the second sacrificial layer material 52 from above the active part of this layer , before deposition of the roof layer 54 . this causes the membrane 50 to be bonded to the roof 54 , and this configuration is much stiffer . therefore , the exact dimensions of the reference sensor would need to be adjusted to provide a similar capacitance change in active and reference sensors due to thermally induced stress changes in the membrane 50 . fig2 a to 27 h show perspectives of temperature compensating sensor at various stages of fabrication . as best shown in fig2 ( a ) to 27 ( d ), the reference sensor 51 is etched into the same wafer substrate 32 as the active sensor 53 . this embodiment has further increased the structural strength by adding the top cover 60 over the roof layers 54 of the active and reference membranes . the cover 60 defines separate chambers 62 and 64 over the reference and active roofs 54 respectively . in this embodiment , the roof layers 54 of each sensor stop smaller particles from contacting the membranes 50 . the top cover 60 provides much greater structural rigidity while protecting the membrane and roof guard layers 54 from damaging contact during installation . however , even with the top cover 60 , the sensor has overall dimensions that are small enough for installation in the tire valve or valve stem . as best shown in fig2 c , chamber 62 is sealed from the tire pressure , whereas chamber 64 is exposed to the tire pressure via vent 66 and channel 68 . while it has not been shown in the figures , it will be appreciated that the vent 66 extends through to the back surface of the wafer substrate 32 , where it is not sealed , but open to the tire pressure . if the sensor is wafer bonded to a sealing wafer ( as discussed below ), the sealing wafer has corresponding holes for establishing a fluid connection with the tire pressure . using the lithographically masked etching and deposition procedures of semiconductor fabrication , it is possible to manufacture a robust , low cost tire pressure sensor from micro - electro - mechanical ( mem ) based devices for use in a tpms . the membrane can be formed from a material that is capable of withstanding a wide range of environmental conditions . an advantage of such a tire pressure sensor is the relatively low cost of manufacture . the membrane can be formed in many possible geometries , for example , as a generally flat or planar shape such as a disc , or having a featured surface . fig2 is a diagrammatic representation of a capacitance sensing circuit where : c r is the capacitance of the reference capacitor ( preferably made in the same way as sensor capacitor but non - sensing ); and v 1 and v 2 are constant voltages reference voltages provided to switches 80 . these may be chosen to be two of the circuit power supplies or internal regulated supplies . these voltages are then switched onto one of each of the capacitor plates charging or discharging them . the voltage v in is fed to charge amplifier 84 , a high gain device , which amplifies the voltage to v out . v in provides a measure of charge imbalance in the circuit when it is operated as follows : connect c r to v 2 , c s to v 1 ; reset the charge amplifier 84 which forces v in to a fixed voltage v r and set the charge injector to a know state with charge q i1 . the total stored charge , q 1 , is : q 1 = c r ( v 2 − v r )+ c s ( v 1 − v r )+ q i1 connect c r to v 1 , c s to v 2 , and remove the reset from the charge amplifier 84 . the output from the charge amplifier 84 is monitored by the control 86 and feedback applied to the charge injector such that the total charge is balanced forcing v in = v r by injecting a charge of q i1 − q i2 . q 2 = cr ( v 1 − v r )+ c s ( v 2 − v r )+ q i2 feedback forces q 1 = q 2 , so that the digital output from the control 86 is : q i1 − q i2 =( v 1 − v 2 )·( c r − c s ) the control logic 86 may operate an iterative procedure to determine the required output to obtain this charge difference , at the end of which it will produce the required digital output . the voltage on c p is the same at the end of step 1 and step 2 , and so ideally , does not contribute to the digital output . optionally , these steps can be repeated and an averaging applied to the digital output to reduce random noise . furthermore , additional steps may be added to the above idealized case , in order to improve accuracy of the circuit . fig2 a to 25 d schematically show the installation of the sensor within the valve stem of a car tire . the pressure sensor can be mounted in other locations including the valve head , the tire wall , the wheel hub and so on . however , the relatively solid structure of the valve stem makes it the most convenient component for automated installation of the sensor . furthermore as the stem closer to the centre of the wheel than the rest of the tire , the acceleration forces on the sensor generated by wheel rotation are less . as best shown in fig2 b and 25 c , the sensor 96 is mounted in the valve stem 92 . a small recess is created in the valve stem wall 94 . a thin layer of hard - setting adhesive 98 is applied as a coating on the recess walls . the sensor chip 96 is then adhered into the recess with any excess adhesive removed before the adhesive 98 is cured . power can be supplied to the sensor chip 96 in a number of fashions , including , but not limited to , a long - life battery ( not shown ) located in the valve stem wall 94 , a long - life battery located in the valve head 92 , or radio frequency energy beamed to an electromagnetic transducer from an external station . the embodiment shown in fig2 a to 25 d is the latter . the pressure and temperature are sampled once per second , or at any other rate as required by legal or commercial obligations , and the results are displayed on the dashboard tire sensor display 106 , marked as level monitors 104 . if the tire pressure is outside the levels specified by the tire manufacturer for proper tire functioning , or indeed any other limits which arise from legal or commercial obligations , the specific tire 90 , or tires , will have an error shown in colour ( e . g . red ) on the car chassis symbol 102 . if the power is supplied to the sensors 96 by long - life batteries , the sensor display 106 would include a low battery indicator . this can be conveniently by illuminating the problem signal 102 in a different colour ( e . g . purple ). in a particular embodiment , the sensor has a membrane that is at least partially a conductive - ceramic compound , for example , titanium nitride , tin . the use of mems - based sensors reduces the effects of acceleration due to the greatly decreased mass . as an illustrative but non - limiting example , a tin membrane , with density of 5450 kgm − 3 , radius of 50 μm and thickness of 0 . 5 μm , should experience a force of 0 . 2 μn due to an acceleration of 1000 g ; compared with a force of 1 . 6 mn for a pressure of 207 kpa ( approximately 30 psi ), which is typical for standard tire inflation pressure . the low mass of the membrane ensures that the affect of acceleration is negligible compared to that of the pressure . tin has been found to have a surprisingly high yield strength compared with other known materials used for capacitive sensor membranes . this makes it suitable for use in a wider range of stressful , harmful or dangerous environments . this also means that under standard conditions , membranes made from tin should have greater lifetimes compared with standard capacitive pressure sensors . the sensor membrane may be composed of other conductive - ceramic compounds . in particular , metal - ceramics , for example titanium aluminium nitride ( tialn ), titanium aluminium silicon nitride ( tialsin ), tantalum nitride ( tan ), tantalum aluminium nitride ( taaln ) or the like , have suitable properties . these metal ceramics are hard wearing and form a tough , thin surface oxide . the protective oxide gives the sensors good robustness and longevity . metal ceramics are well suited to deposition by semiconductor fabrication techniques . this allows the sensor to have a thin membrane ( 0 . 5 μm to 5 μm ) with diameters ranging from about 20 μm to 2000 μm . as discussed below , thin membranes have less internal stresses from rapid cooling , and less mass for limiting acceleration effects . according to another possible embodiment , an electrode in the sensor can be provided with holes to prevent squeeze film damping . squeeze film damping occurs when the membrane deflects very close to the static electrode . the pressure of the fluid between the membrane and the static electrode rises and restricts , or damps , the membrane motion . this can severely restrict the dynamic response of the membrane . channels or apertures can let the fluid between the fixed electrode and the dynamic electrode ( membrane ) flow away from the narrowing space between them . the fluid must still remained sealed within the sensor , however , letting it escape from between the opposing faces of the membrane and the fixed electrode avoids squeeze film damping effects . residual stress in the membrane can affect its deflection and therefore the accuracy of the sensor . the fabrication process is a typical cause of residual stress . rapid cooling material from an elevated temperature , can generate thermal stresses in proportion to the material co - efficient of thermal expansion . these stresses can deform the membrane and change its deflection characteristics under fluid pressure . this in turn can affect the accuracy of the pressure reading . as discussed above , masked lithographic deposition of the conductive - ceramic membrane allows it to be very thin — typically of the order of 0 . 5 μm thick . the temperature profile across the thickness of a thin membrane is much flatter than that of a relatively thick membrane . the membrane cooling is far more uniform and the internal stresses are largely eliminated . masked lithographic deposition also allows the sensor to have a relatively thick membrane for harsh operating conditions , while still avoiding the problems of residual thermal stresses . by forming the membrane as a laminate , the separately deposited layers are individually thin enough to avoid residual stress but the final laminate is sufficiently strong . instead of depositing layers of the same conductive material , the individual layers can be selected so their collective properties provide good resistance to harsh environments . for example alternate layers of tin or tialn or various other combinations of metals and ceramics , for example , ti and tin . likewise the roof layer 54 may also composed of several different material layers , for example , silicon nitride , si 3 n 4 , and silicon dioxide , sio 2 . again , this avoids residual thermal stresses . to permit an examination of the performance of a tin membrane capacitive sensor , a series of numerical simulations have been performed using a commercial finite - element modelling package called ansys 5 . 7 ( http :// www . ansys . com ). axisymmetric models were used to reduce computational time . this required a symmetry boundary condition at the centre of the membrane , whilst the edge of the membrane was held fixed . a square mesh with one thousand nodes distributed equally across the radius was employed , and meshes with half the number of cells exhibited less than 5 % difference in the maximum stress and deflection . as discussed above , a mems fabrication procedure can be used to deposit a 0 . 5 μm thick layer of tin to form a membrane . a membrane deflection of 5 μm provides sufficient variation in capacitance . for a standard passenger vehicle , the pressure applied to the membrane is typically be in the range 0 - 45 psi , allowing for 50 % tire over - inflation . according to linear theory ( see young , w . c . and budynas , r . g ., roark &# 39 ; s formulas for stress and strain , 7 th edition , p 488 , 2002 ), the membrane radius , r , for a specific deflection , δ , and applied pressure , p , is given by : where e is the modulus ( approximately 500 gpa for tin ), t is the membrane thickness and ν is poisson &# 39 ; s ratio ( 0 . 25 for tin ). for these values it is found , from equation ( 1 ), that r ≈ 50 μm . the variation of membrane deflection with applied pressure is shown in fig3 for a membrane radius of 50 μm . the comparison between linear finite element model ( fem ) and linear theory is quite good . at very high pressure , the deflection - pressure response becomes non - linear , and it is important to include these non - linear effects when designing a working tire pressure sensor . it is possible to extend the linear range of the device by corrugating the membrane . fig2 a and 28 b illustrate a possible embodiment of a non - planar membrane 50 for use in a tpms sensor . the membrane 50 is generally circular in extent and is provided with corrugations formed as annular ridges 22 on a base region 24 . the number and spacing of annular ridges , and the individual shape of the annular ridges 22 , can vary . also , differently shaped annular ridges 22 could be provided on a single base region 24 . in the particular embodiment illustrated , the corrugations are formed to have a square - shaped cross - sectional profile . geometric parameters s , l , h and t are also illustrated and are referenced in the following equations . for a circular membrane , this amounts to superimposing a series of raised annuli on the membrane profile as illustrated in fig2 b . a theoretical model for the non - linear response for a corrugated membrane is : the variable q is referred to as the corrugation quality factor , s is the corrugation arc length , l is the corrugation period and h is the corrugation height ( refer to fig2 b ). for right - angled corrugations , s = l + 2 h . for a flat membrane , q = 1 . to include non - linear effects in the finite element calculation , the load is applied over a number of sub - steps and an equilibrium solution is sought for each sub - step . the results for the non - linear simulation and theory are also shown in fig2 . the response becomes non - linear at approximately 30 kpa , which is well below the maximum expected tire pressure . the non - linear finite element simulations match the linear and non - linear theories below and above the critical point , respectively . to assess the effect of corrugations on sensor designs , finite element models were constructed for two different corrugation periods , l = 10 and 20 μm , and two different quality factors , q = 4 and 8 . this results in a corrugation height of approximately 0 . 65 and 1 . 0 μm for q = 4 and 8 , respectively . the results in fig3 indicate that it is necessary to include non - linear effects for the pressure range considered here ; non - linearity should also be present due to the large number of rigid corners in the model . the results of the finite element simulations are compared with the theoretical model in fig3 . this shows that a corrugation factor of 8 will extend the linearity of the sensor up to an applied pressure difference of approximately 1 mpa . it also shows that the corrugation period does not have a strong effect for the configurations examined herein . the maximum von mises stress behaves in a similar manner to the membrane deflection . the stress is concentrated near the junction at the lower side of the outermost corrugation with progressively less stress on the inner corrugations ( see fig3 for a typical stress distribution ). the coefficient of thermal expansion for tin is 9 . 4 × 10 − 6 k − 1 , which means that , for the range of likely operating temperatures , thermally induced stress might alter the sensor deflection . the effect of temperature on the sensor response is examined in fig3 for a sensor with q = 8 and l = 10 mm . the range of temperatures t examined , from − 20 to + 40 ° c ., can be considered as representative of the heat - up cycle which occurs when a vehicle initiates a journey in a cold environment . it is seen that below 100 kpa pressure difference , there is a strong effect of temperature . at higher applied pressures , typical of operation , the thermal stresses are swamped by pressure - induced stresses and the temperature has little effect on the sensitivity . thus , a corrugated membrane sensor has a linear response in the region of interest . the small size of the sensor means that it is suitable for installation in wheel hub / rim valve stem and valve cap systems . as discussed above in relation to fig3 to 23 , the deep etch hole 56 needs to be sealed to maintain the fluid beneath the membrane 50 at a reference pressure . typically , the reverse side of the wafer 32 is bonded to a sealing wafer . unfortunately , simply using a polymeric adhesive to bond a main wafer to the sealing wafer is not sufficient . the reference cavity ( i . e . fluid beneath the membrane 50 ) seeks to maintain a constant pressure to ensure a minimum of calibration drift . the polymeric adhesive is permeable to air , which may result in leakage of air into the reference cavity because of the tire pressure . the flow rate across a permeable material is given by : where p 12 is the permeability of the material , a is the surface area of the material exposed to the pressure difference , δp is the pressure difference and l is the flow path length . the permeability of most polymers is of order 10 − 21 m 3 ( stp ) ms − 1 m − 2 pa − 1 , so for a pressure difference = 300 kpa , cavity radius = 50 μm , seal height = 10 μm and seal ( flow ) length = 10 μm , the flow rate is approximately 9 . 4 × 10 − 20 m 3 s − 1 . if the cavity height is 100 μm , then the total cavity volume is 7 . 9 × 10 − 13 m 3 , and approximately 100 days would be required for the reference cavity pressure to equilibrate with the tire pressure . whilst this may be suitable for testing purposes , it would make such a device unsuited to practical use . another way to seal the reverse side of the wafer is to over - mold the sensor with plastic to increase the path length for leakage . the permeability of polymers is about ten times less than that of adhesives , and so a ten - year seal would require a seal length of approximately 0 . 5 mm . this is too long for a mems device that is less than 50 μm long . to maintain the high yield and versatility of the pressure sensor as a mems device , a different sealing solution is required . wafer bonding offers the possibility of a hermetic seal at the cost of a slightly different fabrication procedure . the most prevalent forms of wafer bonding are : direct wafer bonding , anodic ( electrostatic ) bonding and intermediate layer bonding ( see table 3 ). in the first method , two ultra clean surfaces are brought into contact after they have been activated ( e . g . the surfaces are made hydrophilic or hydrophobic ); the bond forms at elevated temperatures ( near 1000 ° c .). in the second , the two wafers are brought into contact , in either vacuum , air or an inert atmosphere , and a large voltage is applied across the wafers . the bond forms because of migration of ions from one wafer surface to the other . this method has relaxed requirements in terms of surface finish , which makes it more suitable for bonding two wafers that have undergone a series of fabrication steps ; however , the high voltage may damage cmos layers . the third option employs a layer of low melting point material that is deposited on one or both wafers on the contact face . the wafers are brought into contact at moderate temperatures and the bond forms at the interface once pressure is applied . there are many different materials that may be used to form the intermediate layer ( e . g . si 3 n 4 tin ). the intermediate layer method overcomes the disadvantage of direct wafer ( high cleanliness ) and anodic ( high voltage ) bonding . the invention may also be said to broadly consist in the parts , elements and features referred to or indicated herein , individually or collectively , in any or all combinations of two or more of the parts , elements or features , and wherein specific integers are mentioned herein which have known equivalents in the art to which the invention relates , such known equivalents are deemed to be incorporated herein as if individually set forth . although the preferred embodiment has been described in detail , it should be understood that various changes , substitutions , and alterations can be made by one of ordinary skill in the art without departing from the scope of the present invention .