Patent Publication Number: US-11656139-B2

Title: Thermal conductivity gauge

Description:
RELATED APPLICATION 
     This application is a continuation of U.S. application Ser. No. 15/955,266, filed Apr. 17, 2018. The entire teachings of the above application(s) are incorporated herein by reference. 
    
    
     BACKGROUND 
     Because the rate of heat transfer through a gas is a function of the gas pressure, under certain conditions, measurements of heat transfer rates from a heated sensing element to the gas can, with appropriate calibration, be used to determine the gas pressure. This principle is used in the well-known Pirani gauge, in which heat loss is measured with a Wheatstone bridge network, which serves both to heat the sensing element and to measure its resistance. In a Pirani gauge, a temperature-sensitive resistance is connected as one arm of a Wheatstone bridge. The temperature-sensitive resistance is exposed to the vacuum environment whose pressure is to be measured. 
     A conventional Pirani gauge is calibrated against several known pressures to determine a relationship between pressure of a gas and the power loss to the gas or the bridge voltage. Then, assuming end losses and radiation losses remain constant, the unknown pressure of a gas may be directly determined by the power lost to the gas or related to the bridge voltage at bridge balance. 
     SUMMARY 
     Example embodiments include a thermal conductivity gauge for measuring gas pressure. The gauge may include a sensor wire, a resistor, and a controller. The sensor wire may be positioned within a chamber and coupled to a terminal and a ground. The resistor may be coupled between the terminal and a power input. The controller may be configured to apply the power input to the resistor and adjust the power input, as a function of a voltage at the terminal and a voltage at the power input, to bring the sensor wire to a target temperature. The controller may further determine a measure of gas pressure within the chamber based on the adjusted power input. 
     In further embodiments, the resistor and sensor wire may have an equivalent resistance at the target temperature. The sensor wire may be coupled to a grounded envelope encompassing a volume of the chamber. The sensor wire may be coupled to the envelope via a shield extending through the volume of the chamber. The controller may be further configured to 1) determine a compensation factor based on an envelope temperature external to the chamber, and 2) determine the measure of gas pressure as a function of the compensation factor. The resistor may be a first resistor, and a second resistor and a switch can be connected in parallel with the first resistor, where the controller selectively enables the switch. 
     In still further embodiments, the gauge may be implemented in combination with an ion gauge (e.g., a hot cathode gauge or a cold cathode gauge) within the chamber. Feedthroughs of the gauge and the ion gauge extend through a common feedthrough flange. The gauge occupies a single feedthrough of the feedthrough flange, where the terminal is the single feedthrough. The controller can selectively enable the ion gauge in response to detecting the measure of gas pressure from the thermal conductively gauge below a target threshold. The controller may be further configured to determine a compensation factor based on heat generated by the ion gauge, the controller determining the measure of gas pressure as a function of the compensation factor. The controller may selectively disables the ion gauge in response to detecting the measure of gas pressure from the thermal conductively gauge above a target threshold. 
     In yet further embodiments, the sensor wire is supported within a removable housing extending between the terminal and the ground. 
     Further embodiments can include a method of measuring gas pressure. A power input can be applied through a resistor and sensor wire connected in series, where the sensor wire is coupled to a terminal and a ground within a chamber, and the resistor is coupled between the terminal and a power input. The power input can be adjusted, as a function of a voltage at the terminal and a voltage at the power input, to bring the sensor wire to a target temperature. A measure of gas pressure can then be determined within the chamber based on the adjusted power input. 
     Still further embodiments can include a thermal conductivity gauge for measuring gas pressure, including a circuit and a controller. The circuit includes a sensor wire and a resistor coupled in series, the sensor wire being positioned within a chamber. The controller may be configured to 1) apply a power input to the circuit; 2) adjust the power input, as a function of a voltage across one of the sensor wire and the resistor, to bring the sensor wire to a target temperature; and 3) determine a measure of gas pressure within the chamber based on the adjusted power input. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments. 
         FIG.  1 A  is a circuit diagram of a prior art Pirani gauge. 
         FIG.  1 B  is a graph illustrating a response of the Pirani gauge of  FIG.  1 A . 
         FIGS.  2 A-B  illustrate a prior art Pirani gauge including a compensation wire. 
         FIG.  3    illustrates the prior art Pirani gauge of  FIGS.  2 A-B  implemented within a chamber. 
         FIG.  4    illustrates a sensor of a thermal conductivity gauge in an example embodiment. 
         FIG.  5 A  illustrates the sensor of  FIG.  4    in further detail. 
         FIG.  5 B  is a graph illustrating a response of the sensor of  FIG.  4   . 
         FIG.  6    is a diagram of a thermal conductivity gauge in an example embodiment. 
         FIGS.  7 A-C  are graphs illustrating response of the thermal conductivity gauge at different envelope temperatures. 
         FIGS.  8 A-D  are plots illustrating response of the gauge implementing temperature compensation. 
         FIG.  9 A  is a diagram of a thermal conductivity gauge in a further embodiment. 
         FIG.  9 B  is a diagram of a thermal conductivity gauge in a still further embodiment. 
         FIGS.  10 A-B  illustrate response of a thermal conductivity gauge with and without baseline correction. 
         FIG.  11    illustrates an assembly including a thermal conductivity gauge implemented in combination with a hot cathode ion gauge. 
         FIG.  12    is a diagram illustrating the feedthroughs implemented by the assembly of  FIG.  11   . 
         FIGS.  13 A-C  illustrate a housing supporting a sensor wire for use in a thermal conductivity gauge. 
     
    
    
     DETAILED DESCRIPTION 
     A description of example embodiments follows. 
     Pirani sensors with constant sensor wire temperature have been employed to perform pressure measurements between 1E-4 and 1000 Torr. Typical Pirani gauges that provide a constant sensor wire temperature during operation rely on a Wheatstone bridge in connection with the sensor wire. The electrical power required to keep the wire at a constant temperature is used to provide a measure of pressure. Maintaining a constant temperature at the sensor wire is desirable as it allows faster response to pressure steps as there is no need to wait for temperature changes to take place. Also, having constant wire temperature provides pressure independent signal baseline offsets that can be subtracted from the actual signal to provide the pure pressure dependent part of the signal by itself. 
     In a typical constant wire temperature Pirani gauge, the temperature of a wire is kept at a constant temperature by running pressure dependent electrical heating power through it. Since the amount of electrical power needed to keep the wire at a constant temperature depends on pressure, a simple power measurement is used to provide a pressure measurement. This design relies on a Wheatstone bridge to regulate wire temperature by maintaining its temperature dependent resistance during operation. 
       FIG.  1 A  is a circuit diagram of a prior art Pirani gauge  100 . The pressure sensor comprises a temperature sensitive resistance R S  connected as one arm of a Wheatstone bridge  110 . R 3  is typically a temperature sensitive resistance designed to have a negligible temperature rise due to the current i 3 . R 2  and R 1  are typically fixed resistances. The sensor wire R S  and typically R 3  are exposed to the environment whose pressure is to be measured. The environment is encompassed within an envelope through which the sensor wire R S  extends via a pair of feedthroughs. Alternatively, R 3  may also be included within the envelope via an additional one or more feedthroughs. 
     The resistance values of resistors R 1 , R 2  and R 3  are selected such that when a pressure-dependent voltage V Bridge  is applied to the top of the bridge, at which V left =V right , the resistance of the sensor wire R S  is fixed and identical to (R 1 *R 3 )/R 2 . Voltage V Bridge  is automatically controlled by an operational amplifier to maintain the voltage difference between V left  and V right  at zero volts. When the potential drop from V left  to V right  is zero, the bridge is considered to be balanced. At bridge balance, the following conditions exist:
 
 i   s   =i   3 ,  (1)
 
 i   1   =i   2   (2)
 
 i   s   R   s   =i   1   R   1 ,  (3)
 
 i   2   R   2   =i   3   R   3   (4)
 
     Dividing Eq. 3 by Eq. 4 and using Eq. 1 and 2 gives
 
 R   s   =βR   3   (5) where
 
β= R   1   R   2   (6)
 
     Thus, at bridge balance, R S  is a constant fraction β of R 3 . 
     To achieve a steady-state condition in R S  at any given pressure, Eq. 7 below must be satisfied:
 
Electrical power input to  R   S =Power radiated by  R   S +Power lost out ends of  R   S +Power lost to gas by  R   S   (7)
 
     Because the amount of electrical power required to keep the sensor resistor R S  at a constant temperature and a constant resistance increases with pressure, voltage V bridge  depends on pressure as well. This relationship is illustrated in  FIG.  1 B , which is an example plot of voltage V bridge  over a range of pressure within a chamber occupied by R S . As shown, the voltage V bridge  exhibits an S-curve over the pressure range. A conventional Pirani gauge is calibrated against several known pressures to determine a relationship between unknown pressure, P x , and the power loss to the gas or more conveniently to the bridge voltage. Then, assuming end losses and radiation losses remain constant, the unknown pressure of the gas P x  may be directly determined by the power lost to the gas or related to the bridge voltage at bridge balance. 
     The Pirani gauge  100  provides a simple configuration for measuring pressure, and allows for adjusting a sensor wire resistance in a simple manner. A simple op-amp circuit can be used to null the bridge (V left =V right ), allowing the circuit to be built at a low cost. However, in order to provide compensation for different ambient temperatures outside the chamber, resistors of highly specific values must be added to the gauge head during calibration to provide the desired signal response (i.e., V bridge  versus pressure) and proper temperature dependence. 
       FIGS.  2 A-B  illustrate a prior art Pirani gauge  200  including a compensation wire Rc. The gauge  200  is comparable to the Pirani gauge  100  described above, but the addition of the compensation wire Rc allows the gauge  200  to compensate pressure readings against ambient temperature fluctuations. Such ambient temperature fluctuations change the difference in temperature between the sensor wire R S  and the envelope walls (not shown) encompassing the chamber in which the pressure is to be measured. As shown in  FIG.  2 B , the compensation wire resistor R C  is wound around a smaller envelope within the chamber and allowed to reach a temperature T 2  having thermal equilibrium with room temperature. The resistances in the bridge (R 3  and R 4 ) and in the compensation wire Rc are then tuned such that as T 2  changes, and while the Wheatstone bridge remains balanced, the difference in temperature T 1 -T 2  (where T 1  is the wire temperature of the sensor R S ) remains constant. Because the power dissipated by the sensor wire R S  to the gas depends on this temperature difference, a measurement of this power dissipation indicates a pressure measurement that is independent of ambient temperature. 
     In practice, the compensation wire R C  exhibits variability among different gauges. Thus, each implementation of the gauge  200  must be individually tuned by adjusting resistance values during testing and calibration to provide a temperature difference (T 1 -T 2 ) that remains constant as the ambient temperature changes. Further, the winding of the compensation wire R C  can be expensive and difficult to complete. In order to provide fast response, the compensation wire R C  can also be wound internally to the gauge in a thin walled envelope and become exposed to the gas environment. 
       FIG.  3    illustrates the prior art Pirani gauge  200 , described above, in a further view as implemented within a chamber  290  (not shown to scale). A portion of the gauge  200 , including the sensor wire R S  and the compensation wire R C , extends into a chamber  290  via a feedthrough flange  220 , while the remainder of the Wheatstone bridge remains outside the chamber  290 . The compensation wire R C  is mounted inside the pressure sensor volume on a thin-walled can  240  that facilitates stabilization of the compensation wire R C  while the room temperature changes. The gauge  200  requires a minimum of four feedthroughs  210  through the feedthrough flange: two feedthroughs connect the sensor wire R S , and another two feedthroughs connect the compensation wire R C . 
     The Pirani gauge  200  exhibits several disadvantages. In particular, both assembly and calibration of the gauge  200  can be difficult and laborious. In order to assemble and operate the gauge  200 , the compensation wire R C  must be wound and attached to electrical connectors at the feedthrough flange  220 . Once assembled, the gauge  200  must undergo calibration for proper temperature compensation, including selecting the proper resistor values and ensuring that the value T 1 -T 2  remains constant regardless of the room temperature. The Wheatstone bridge requires fine tuning for temperature compensation. Maintaining the value T 1 -T 2  can be achieved if the calibration procedure is properly executed, but it does not allow the use of nominal resistor values. Rather, each gauge must be manually tuned, and is configured with specific resistors that are high-accuracy components. 
     Further, the sensor of the gauge  200 , including the sensor wire R S  and can  240 , is large and bulky. In order to achieve convection at high pressures, the can  240  must have a large volume to allow convection to set in as pressure goes above approximately 100 torr. One reason for this requirement is that the sensor wire R S  is not wound or coiled, and the can  240  has a large inner diameter. 
     A Pirani gauge may be useful a sensor to control enabling and disabling of an ionization gauge (not shown). However, due to its size and use of multiple feedthroughs, the gauge  200  may be unsuitable for use in combination with an ionization gauge. An ionization gauge occupies several feedthroughs and substantial volume adjacent to a feedthrough flange, leaving minimal space and feedthroughs for a Pirani gauge. Moreover, temperature compensation is generally required to run a Pirani gauge inside the envelope of an ionization gauge. As the ionization gauge is turned on, the walls of the ionization gauge envelope warm up, making it necessary to add temperature compensation as the difference between T 1  and T 2  changes due to an increasing T 2 . The use of an internal compensation wire requires feedthroughs, while the addition of an external compensation wire adds complexity to the design. 
     Due to the rigid implementation of temperature control based on a Wheatstone bridge, the gauge  200  does not allow for a change of the sensor wire operational temperature (or resistance) during operation, instead providing a single temperature of operation. 
     Even though there is a linear relationship between pressure and the power required to keep the sensor wire R S  at constant temperature, the gauge  200  indicates pressure based on a measurement of the bridge voltage V bridge , which, as shown in  FIG.  1 A , is not linearly related to pressure. The combination of a large baseline offset (due to radiative and end losses, for example) with a non-linear response of V bridge  on pressure leads to an S-shaped curve that makes calibration difficult and less accurate while interpolating the measurement results. 
       FIG.  4    illustrates a thermal conductivity gauge  400  in an example embodiment, with attention to a sensor portion of the gauge. The gauge  400  includes a sensor wire R S    405  (also referred to as a filament) fixed within a chamber  490  via a wire mount  406 . The wire  405  connects to the gauge circuit  450  (described in further detail below) via a terminal  412  that extends into the chamber  490  through a single feedthrough  410 . An opposite node of the wire  405  can be connected to a ground, such as an envelope  480  encompassing the chamber  490 . A temperature sensor  470  (e.g., a thermistor) can be positioned at or near the envelope  480  to measure temperature of the envelope  480  and/or ambient temperature outside the chamber  490 . 
     In contrast with the gauge  200  described above with reference to  FIGS.  2 - 3   , the gauge  400  provides a sensor having a simpler configuration. The gauge  200  requires only a single feedthrough  410  into the chamber  490 . Further, a compensation wire may be omitted from the gauge  400 , as temperature compensation can be provided using the temperature sensor  470  in combination with the gauge circuit  450 . Thus, the gauge  200  enables a sensor having a simpler, more compact structure that requires less labor to assemble. 
     The gauge circuit  450  provides further advantages over the gauge  200 . The principles on which the gauge circuit  450  operate are described below with reference to  FIGS.  5 - 6   . 
       FIG.  5 A  illustrates a portion of the gauge  400  in further detail. Here, the sensor is configured with the optional addition of a shield  415 . The sensor wire  405  may be connected between the terminal  412  (embodied as a feedthrough pin) and the shield  415 . The shield  415  provides a conductive path to ground, as well as surrounds at least a portion of the sensor wire  405 , protecting the sensor wire  405  from physical damage from contaminants from a process environment and providing a thermal boundary condition for the sensor wire  405 . The shield  415 , when used in combination with a hot cathode gauge, may also serve to shield the sensor wire from the radiation from the hot filament. In such a configuration absent the shield  415 , the sensor wire may experience a large change in the baseline radiation offset. An insulator  411  may surround the terminal  412  at the feedthrough  410  to ensure a seal within the chamber  490 . The terminal  412  further connects to the gauge circuit  450 . 
     The sensor wire  405  may be a filament of a small diameter (e.g., 0.001 in. or 0.002 in) and twisted into a coil (e.g., a coil 0.010 in. in diameter diameter). The operational temperature T 1  of the sensor wire  405  can be selected to have a target of  20 C or more above room temperature to provide adequate sensitivity to pressure changes. The temperature of the sensor wire  405  can be held at a constant value during operation, which can improve the speed of response to changes in pressure. This constant temperature T 1  can be achieved by applying a controlled power input (designated P W  to distinguish from pressure P) at the terminal  412  to bring the sensor wire  405  toward a target resistance value. A relation between the resistance and temperature of the sensor wire  405  can be determined for the sensor wire  405  based on previous measurements of the same wire type. This relation can be used for calibrating the gauge  400 . As shown in  FIG.  5 B , the required power input P W  also varies as a function of the pressure of the chamber  490 . This function exhibits a linear region in which the pressure can be measured most accurately. 
       FIG.  6    is a diagram of the gauge  400  with attention to the gauge circuit  405 . In view of the relation between the resistance and temperature of the sensor wire  405 , the gauge circuit  450  can maintain the sensor wire  405  at temperature T 1  during operation. To do so for a selected operational wire temperature T 1 , the corresponding wire resistance can be calculated based on known calibration curves for the wire type. The resistance of the sensor wire  405  at the selected temperature is thus R S (T 1 ). 
     In order to control the resistance of the sensor wire  405  at different pressures, the gauge circuit  450  can include a resistor R 1  connected in series with the sensor wire  405 . To simplify analysis, the resistance of R 1  can be selected to be equal to the resistance of R S  at the selected temperature T 1 :
 
 R   1   =R   S ( T   1 )  (8)
 
     A variable voltage source Vh can be connected to the resistor R 1  opposite the terminal  412 , and the voltage at the terminal Vt and the voltage source Vh can be compared to determine an adjustment for the voltage source Vh. In one embodiment, the gauge circuit  450  can provide this comparison and adjustment with an amplifier  452 , a comparator  460 , and a voltage controller  465 . The comparator  460  compares the values of 2*Vt (provided by the amplifier  452 ) and Vh, and outputs a comparison result to the voltage controller  465 . The voltage controller  465  then adjusts Vh until 2*Vt is equal to Vh:
 
 Vh= 2* Vt   (9)
 
     When the above condition is met, the resistance of the sensor wire  405  matches the resistance of R 1 , and the wire is at temperature T 1 . The electrical P W  power required to heat the sensor wire to temperature T 1  is then a function of Vh and R 1  as follows:
 
 Pw=Vh   2   /R   1  or  Pw= 4 Vt   2   /R   2   (10)
 
     The value P W  at this state can be used to calculate pressure based on an observed relationship between pressure and heating power. In example embodiments, this relationship can be linear over a pressure range extending up to approximately 1 Torr, as illustrated in  FIGS.  7 A-B , described below. Thus, with the resistor R 1  and sensor wire  405  R S  having resistance values selected in accordance with equation (8), the gauge circuit  450  can apply the voltage input Vh to the resistor R 1 , and adjust the power input P W  as a function of a voltage across the resistor R 1  (i.e., Vh and V t ) to satisfy equation (9). In doing so, the sensor wire  405  is brought to the target wire temperature T 1 . A measure of the power input P W  at this state can be determined by equation (10). Comparing the adjusted power input P W  against a known power/pressure relation, a measure of gas pressure within the chamber  490  can thus be determined. 
     The gauge circuit  450  presents one solution for adjusting the temperature of the wire to T 1 , which ensures that the resistance of the sensor wire  405  matches that of resistor R 1  regardless of the gas pressure exposed to the wire. The comparator  460  and voltage controller  465  provide a feedback loop to measure the differential between Vh and 2*Vt and adjust Vh until the difference is zero and R 1 -R S (T 1 ). The comparator  460 , amplifier  452  and voltage controller  465 , or other circuitry providing comparable operation, may be implemented in analog and/or digital circuitry. 
       FIG.  7 A  is illustrates a response of an example 0.001 in diameter sensor wire implemented in a thermal conductivity gauge such as the gauge  400 . The log-log plot shows the change in power response to pressure within a chamber as a function of temperature of the envelop housing the chamber. The plot includes four curves, where each curve corresponds to the same wire temperature (100 C) but different envelope temperatures. As shown, the four curves share a common range of pressure (approximately 1E-3 Torr to 1 Torr) where the relation between power input and pressure are substantially linear. 
       FIG.  7 B  illustrates the response of the 0.001 in diameter sensor wire in further detail. Here, the linear range of the lowest and highest envelope temperatures (22 C and 54 C) is shown in isolation. This plot demonstrates how the linear range of the curves is affected by envelope temperature, where a higher envelope temperature corresponds to a lower power input at a given pressure. Both plots can be matched closely with a linear trend estimation as shown. Thus, the power input P W  required to heat the sensor wire  405  to temperature T 1  is a function of the temperature difference T 1 -T 2 . 
       FIG.  7 C  illustrates a response of an example 0.002 in diameter sensor wire. In contrast to the 0.001 in diameter wire described above, the 0.002 in diameter wire exhibits higher power dissipation, thereby requiring a higher power input. However, the thicker wire also provides a response usable for determining pressure, and may confer advantages during installation and operation due to its higher durability. The sensor wire may be composed of one or more different materials based on the application and working environment of the gauge. For example, a sensor wire made of nickel may be advantageous for use in reactive environments, a tungsten sensor wire may have higher durability, and a platinum sensor wire may be suitable when lower emissivity is desired. 
     The results shown in  FIGS.  7 A-C  can be used to provide for envelope temperature compensation of pressure measurements in a thermal conductivity gauge. For example, with reference to  FIG.  4   , the sensor wire  405  exhibits a response comparable to the response illustrated in  FIGS.  7 A-C . The response may be determined based on measuring the sensor wire itself or may be defined from the wire type. A data set corresponding to this response may be collected and compiled into a lookup table cross-referencing power input, pressure, and envelope temperature. When the gauge  400  operates as described above, the resulting power input P W , along with a measure of the envelop temperature detected by the thermal sensor  470 , can be applied to the lookup table to determine the pressure of the chamber  490 . Alternatively, the wire response may be used to derive an equation relating the power input, pressure, and envelope temperature, such as an expression for the linear trend estimation shown in  FIG.  7 B . Thus, by applying data for power input versus pressure across different envelope temperatures, such as the data shown in  FIGS.  7 A-C , a measure of power input at a gauge can be used to determine chamber pressure in a manner that compensates for different temperatures of the envelope. In contrast to the gauge  200  described above, which requires controlling the temperature difference between ambient and sensor temperatures, the gauge  400  measures the ambient or envelop temperature T 2  independently (e.g., via the thermal sensor  470 ), and uses this temperature data to interpret the power measurement when determining pressure. 
       FIG.  8 A  illustrates a response of a thermal conductivity gauge with and without temperature compensation. Similar to the plots of  FIGS.  7 A-B , the power response of a given sensor wire at two different envelope temperatures (25 C and 54 C) is shown. Additionally, temperature-compensated versions of the power response are shown, which exhibit a nearly identical curve. Thus, as a result of the temperature compensation, the power input applied to the sensor wire can be used to determine the pressure accurately across a range of different envelope temperatures. 
     An approach for calculating a temperature-compensated power value is as follows: 
     An uncompensated plot of power input and pressure, as shown in  FIG.  8 B  (e.g., based on a direct sensor signal response), can be divided into three sections 1) baseline at high vacuum (at left), 2) linear response (Log, Log) (at center), and 3) Convection response (˜10 torr to ATM) (at right). The baseline response is made up of two loss mechanism that are constant over the entire pressure range: 1) R L , Radiation loss, and 2) C L , Convective end loss. Thus, the total baseline loss can be expressed as:
 
Total baseline loss= R   L   +C   L , where
         a) Radiation loss R L =εσ(T 4   wire −T 4   case ), where ε=emissivity, σ=Boltzmann&#39;s constant   b) Convective loss C L =Gπr 2 (T wire −T case )/L, where G=thermal conductivity of wire, r=radius of wire, L=length of wire       

     In the linear response region, L R =KP, (Log L R =log K+P), which is nearly temperature independent (T/sqrt(T)). 
     In the convection region, hot sheaths of gas inhibit thermal transfer, and the response flattens out. Yet the response also has a Δ T and like Δ T 4  dependence and can be modeled. The temperature coefficient of the baseline loss regions can be corrected with an equation that has the delta T and delta T to the fourth terms:
 
Delta  T  Power Baseline=( c+dΔT+eΔT 4);
         where c, d and e can be determined from thermal cycling and fitting population.       

     The entire sigmoid response function can be modeled as a logistics-type sigmoid function, thereby enabling the device to be temperature-compensated with the known physics of the regions:
         a) Logistics sigmoid function=1/(1+e −x ), replacing the e −x  term with the physics of the device.   b) Linear region=KP K=constant, P=pressure   c) Boundary conditions:
           i. a=atmospheric power level   ii. b=baseline offset power level   
               

     
       
         
           
             
               
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     Expressing the atmospheric and baseline power levels as a function of temperature provides the following: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
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     Based on the above equations, an equation to calculate pressure from measured power can be expressed as follows:
 
Pressure ( T )=( a ( T )/ K )/(1/(power− b ( T ))−1)
 
     To calibrate a gauge to provide accurate parameters in the equation above, the power may be measured at atmosphere and baseline at a nominal pressure. A plot of example temperature-compensated power curves, utilizing the above equations, is shown in  FIG.  8 A . Here, a pair of temperature-compensated power curves is compared against a pair of uncompensated power curves for the same temperatures (25 C and 54 C).  FIG.  8 C  illustrates a comparison between a single power curve, temperature-compensated and uncompensated, within a high-pressure convection region. Similarly,  FIG.  8 D  illustrates a comparison between a single power curve, temperature-compensated and uncompensated, within a high-vacuum baseline region. 
       FIG.  9 A  is a diagram of a thermal conductivity gauge  900  in a further embodiment. The gauge  900  may incorporate one or more features of the gauge  400  described above. A circuit  902  includes a transistor  910 , a resistor R 1 , and a sensor wire  905  (R S ) connected in series between a voltage source VP and ground. The circuit  902  extends, in part, into a chamber  990 , where the sensor wire  905  may be configured as described above with reference to  FIG.  4   . A thermal sensor  970  (e.g., a thermistor) detects the temperature T 2  of an envelope  980  encompassing the chamber  980 . 
     A controller  950  may be configured to receive a measure of voltages V H  and V T  opposite the resistor R 1 , as well as an indication of the temperature T 2  from the thermal sensor  970 , and outputs a control signal V C  to control current through the transistor  910 . The controller  950  may incorporate features of the gauge circuit  450  described above, and may be implemented in analog and/or digital circuitry. For example, the controller  950  may include an analog-to-digital converter (ADC) for converting V H , V T  and T 2 , to digital values; a proportional-integral-derivative controller (PID) controller for determining the control voltage V C  based on the digital values; and a digital-to-analog converter (DAC) for generating the control voltage V C  to the transistor  910 . 
     Prior to operation, the gauge  900  may be configured comparably to the gauge  400  described above. Further, the resistance value of resistor R 1  may be selected based on the room-temperature resistance of the sensor wire  905 , where the room-temperature resistance can be used to calculate the resistance of R 1  required to maintain the operational temperature T 1  of the sensor wire, where “tempco” is a temperature coefficient that indicates the change in resistance with temperature:
 
 R   1   =R   S (room temperature)+ T   1 *tempco* R   S (room temperature)(or  R   1   =R   S (room temperature)(1+ T   1 *tempco)  (11)
 
     In operation, the controller  950  can maintain the sensor wire  905  at temperature T 1  by adjusting the control voltage V C , thereby controlling the power input at the resistor R 1 . The controller  950  can determine adjustment to the control voltage V C  through a process comparable to the process for determining voltage Vh described above with reference to  FIG.  6   . In particular, the voltages VT and VH can be compared to determine an adjustment for the voltage source provided by the transistor  910 . The controller  950  adjusts V C  until 2*V T  is equal to V H . When this condition is met, the resistance of the sensor wire  905  matches the resistance of R 1 , and the wire is at temperature T 1 . The electrical power P W  required to heat the sensor wire to temperature T 1  is then a function of V H  and R 1  as described above in equation (10). The power input P W  at this state can be used to calculate pressure based on an observed relationship between pressure and heating power as illustrated in  FIGS.  7 A-B  and  8 . Thus, with the resistor R 1  and sensor wire  905  R S  having resistance values selected in accordance with equation (8), the controller  950  can apply the power input P W  to the resistor R 1 , and adjust the power input P W  as a function of a voltage across the resistor R 1  (i.e., Vh and V t ) to satisfy equation (9). In doing so, the sensor wire  405  is brought to the target wire temperature T 1 . A measure of the power input P W  at this state can be determined by equation (10). Comparing the adjusted power input P W  against a known power/pressure relation, a measure of gas pressure within the chamber  990  can thus be determined. The controller  950  may output an indication of P W  to enable this determination, or may be configured to determinate pressure via a lookup table or further calculation, thereby outputting a pressure value. In doing so, the controller  950  may also use the envelope temperature T 2  to determine a temperature-compensated pressure value as described above. 
     The controller  950  provides a digital control loop that enables the gauge  900  to be configured to operate with a desired wire temperature in a range of possible temperatures. By changing the multiplication factor between Vt and Vh, a target wire temperature can be selected as follows:
 
 Vh=xVt  where  x  is  a  multiplication factor
 
     To derive x: 
     At Tnominal (room temperature), R 1 =Rs (R 1  connected in series with the sensor wire Rs). At any other temperature, the temperature coefficient of the wire can be used to calculate Rs(T):
 
 Rs ( T )=(1+ a *( T set− T nominal)) Rs , (where  a  is the temperature coefficient of the wire type to be used)
 
     The relationship between Vh and Vt can be expressed as a simple resistive divider equation:
 
 Vt =[ R 1/( R 1+ Rs ( T ))] Vh  
 
Inserting Rs(T):
 
 Vt =[ R 1/( R 1+(1+α*( T set− T nominal)) Rs )] Vh  (using  R 1= Rs )
 
 Vt =[ R 1/( R 1+(1+α*( T set− T nominal)) R 1)] Vh  
 
 Vt =[ R 1/( R 1*(1+(1+α*( T set− T nominal)))] Vh  
 
 Vt =[1/((1+(1+α*( T set− T nominal)))] Vh  
 
 Vt =[1/((2+α*( T set− T nominal))] Vh  
 
 Vh =(2+α*( T set− T nominal))* Vt  
 
 x =(2+α*( T set− T nominal))
 
     (2+α*(Tset−Tnominal)) is the multiplication factor (x) in the digital loop that can be applied to change the temperature of the wire depending on the customers&#39; requirements and process. 
     Example values that may be implemented in the calculations above are as follow: 
     α=0.0048 (TC for tungsten) 
     Tset=100, Tnominal=75 
     Vh=2.36*Vt; x=2.36 
     Tset=125 Tnominal=25 
     Vh=2.48*Vt; x=2.48 
     Thus, using a calculated multiplication factor x, the wire temperature can be configured for a given application of the gauge  900  without changing the values of resistors R 1  or R S . 
       FIG.  9 B  is a diagram of a thermal conductivity gauge  901  in a further embodiment. The gauge  901  may include the features of the gauge  900  of  FIG.  9 A , with the addition of a resistor R 2  that can be selectively connected in parallel with the resistor R 1  via a switch  934 . The switch may be controlled by the controller  950  or may be manually configured. In alternative embodiments, one or more additional resistors may be selectively connected in series with, or in parallel with, the resistor R 1 . The resistor R 1  may also be replaced with a variable resistor. 
     Further, the temperature of the wire can be adjusted by using a variable multiplication factor. For example, R 1 =Rs may be set at ambient temperature. When the wire is at the desired temperature (Vh=2*Vt), the multiplication factor x can be used to adjust the temperature such that Vh=x*Vt, where x=(2+tempco*(Ttarget−Tambient). Under such an implementation, only the ambient resistances of the sensor (Rs) must be matched to R 1 . 
     In some applications, an adjustable resistance provided by the gauge  901  may be advantageous. For example, the gauge  901  may be used in multiple settings requiring different operational temperatures of the sensor wire  905 .  FIG.  10 A  illustrates one such application, where the power response of the sensor wire  905  over pressure is shown for two different operational temperatures T 1  (100 C and 120 C) of the sensor wire  905 . The sensor wire  905  exhibits a lower power response at 100 C than at 120 C. To correct for this difference, as shown for example in  FIG.  10 B , the values of resistors R 1  and R 2  may be selected such that (1) the resistor R 1 , absent R 2 , exhibits a target response from the sensor wire  905  when T 1  is at a first operational temperature (e.g., 100 C); and (2) the total resistance of R 1  and R 2  connected in parallel exhibits a comparable response from the sensor wire  905  when T 1  is at a second operational temperature (e.g., 120 C). As a result, the gauge  901  can provide for operation at different values of T 1  while achieving a comparable response for determining pressure. 
       FIG.  11    illustrates an assembly  1100  including a thermal conductivity gauge  1120  implemented in combination with an ion gauge  1130 . The ion gauge  1130  includes an electron source  1105 , an anode  1120 , and an ion collector electrode  1110 . The electron source  1105  (e.g., a hot cathode) is located outside of an ionization space or anode volume. The anode structure includes a cylindrical wire grid  120  around posts  112  and  114 , defining the ionization space in which electrons  1125  impact gas molecules and atoms. The ion collector electrode  1110  is disposed within the anode volume. Electrons travel from the electron source  1105  to and through the anode, cycle back and forth through the anode  1120 , and are consequently retained within, or nearby to, the anode  1120 . Further embodiments may utilize an ion gauge having a cold cathode electron source. 
     In their travel, the electrons  1125  collide with molecules and atoms of gas that constitute the atmosphere whose pressure is desired to be measured. This contact between the electrons and the gas creates ions. The ions are attracted to the ion collector electrode  1110 , which is connected to an ammeter  1135  to detect current from the electrode  1110 . Based on a measurement by an ammeter  1135 , the pressure of the gas within the atmosphere can be calculated from ion and electron currents by the formula P=(1/S) (I ion /I electron ), where S is a coefficient with the units of 1/Torr and is characteristic of a particular gauge geometry, electrical parameters, and pressure range. 
     The gauge  1120  may be configured as described above with reference to  FIGS.  4 - 10   . Due to the low pressures at which a typical ion gauge operates, the assembly  1100  benefits from the thermal conductivity gauge  1120 , which can measure higher pressures than the ion gauge  1130 . Further, the thermal conductivity gauge  1120 , via a controller  1150 , may control a switch for the ion gauge  1130 , enabling the ion gauge  1130  (e.g., at power sources  1113 ,  1114 ) when the measured pressure falls below a given threshold, and disabling the gauge  1130  when the measure pressure rises above a given threshold. As a result, the ion gauge  1130  can be prevented from operating at pressures that may cause damage to it. Conversely, the controller  1150  may receive input from the ion gauge  1130  (e.g., from ammeter  1135 ), enabling the gauge  1120  when the pressure rises above a threshold and disabling the gauge  1120  when the pressure falls below a threshold. 
     In response to the heat generated by the ion gauge  1130  during operation, the thermal conductivity gauge  1120  may be further configured to compensate for temperature fluctuations caused by this heat. For example, to the extent that the ion gauge  1120  raises the temperature of the envelope, the thermal conductivity gauge  1120  may compensate for this temperature change as described above with reference to  FIGS.  7 A-C  and  8 . This approach may also be applied to temperature changes measured at other points relative to the ion gauge  1130 . For example, a thermal sensor may be implemented at the ion gauge  1130  to measure temperature, and this measured temperature can be correlated to the power response of the thermal conductivity gauge  1120  to determine a compensation factor based on heat generated by the ion gauge, thereby enabling the gauge  1120  to determine the measure of gas pressure as a function of the compensation factor. 
     When implemented in combination, the thermal conductivity gauge  1120  and ion gauge  1130  may be assembled such that feedthroughs of each gauge extend through a common feedthrough flange  1145 . An example feedthrough flange  1145  is illustrated in a top-down view, in  FIG.  12   . The ion gauge  1130  uses several feedthroughs of the flange  1145 . In contrast, the thermal conductivity gauge  1120 , as configured as described above, requires only a single feedthrough  1160 . This single feedthrough  1160  accommodates a feedthrough pin, and the sensor wire R S  is connected between the feedthrough pin and a ground (e.g., the envelope or a post). Because the gauge  1120  only requires a single feedthrough of the flange  1145 , and an ion gauge may leave at least one feedthrough unused in an existing assembly, the gauge  1120  may provide a further benefit in that it can be retrofitted into such an existing assembly with minimal alteration to the assembly. 
       FIGS.  13 A-C  illustrate a housing  1300  supporting a sensor wire  1305  for use in a thermal conductivity gauge such as the gauges  400 ,  900  described above.  FIG.  13 A  illustrates a side cross-section of the housing  1300 , and  FIG.  13 B  is an perspective view of the housing  1300 . The housing  1300  may include conductive end caps  1320  to which the sensor wire  1305  can be connected. The sensor wire may be retained at each end by being compressed between the end caps and a tube  1350 , thereby making the electrical connection. The tube  1350  can be of a non-conductive material (e.g., glass or ceramic), and connects the end caps  1320 . Depending on a desired level of thermal transfer between the sensor wire  1305  and the chamber, the tube  1350  may be closed or slotted. 
       FIG.  13 C  illustrates a top-down view of the housing  1330  as positioned within a chamber. The housing  1300  provides a number of advantages. For example, the rigid structure of the tube  1350  protects the wire from damage during installation and operation. Further, the end caps  1320  may accommodate a bracket or post within the chamber, allowing the housing  1300  to be quickly and easily installed, removed and replaced. 
     While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments encompassed by the appended claims.