Pirani Gauge

Abstract

The thermal conductivity gauge implements a model of power dissipation for accurately measuring gas pressure. The envelope surrounds a gas volume, and the sensor wire is positioned within the gas volume. The controller provides a model of power dissipation from the thermal conductivity gauge, including power loss due to conductive heat loss from the sensor wire termination junction, radiative loss from the sensor wire toward the gas envelope, and pressure-dependent conductive heat loss from the sensor wire through the ambient gas. The controller then applies a power input to the sensor wire to heat it, and calculates a total power dissipation W during application of the power input. T , sensor wire temperature T s , and the envelope temperature T e The gas pressure in the envelope is measured as W T , T s and T e , as well as a model of power dissipation.

Description

[Technical Field]

[0001] Related Applications This application is a continuation of U.S. Application No. 18 / 045,685, filed October 11, 2022, the entire teachings of which are incorporated herein by reference. [Background technology]

[0002] Because the rate of heat transfer through a gas is a function of gas pressure, measurements of the rate of heat transfer from a heated sensing element to a gas under certain conditions 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 in a Wheatstone bridge network or other circuit, which serves to heat the sensing element and measure its resistance. In many Pirani gauges, a temperature-sensitive resistor is connected as one arm of the Wheatstone bridge. The temperature-sensitive resistor is exposed to the vacuum environment in which the pressure is to be measured.

[0003] A conventional Pirani gauge is calibrated to several known pressures to determine the relationship between the pressure of the gas and the power lost to the gas or bridge voltage. Then, assuming that termination and radiation losses remain constant, the unknown pressure of the gas can be determined directly by the power lost to the gas or related to the bridge voltage in a bridge balance. Summary of the Invention

[0004] An exemplary embodiment includes a thermal conductivity gauge comprising an envelope surrounding a gas volume, a sensor wire positioned within the gas volume, and a controller. The controller can be configured to provide a model of power dissipation or power dissipation from the thermal conductivity gauge, the model including power loss due to conductive heat loss from the sensor wire termination junction, radiative loss from the sensor wire toward the gas envelope, and pressure-dependent conductive heat loss from the sensor wire through the ambient gas. The controller can then apply a power input to the sensor wire to heat it, and calculate a total power dissipation W during application of the power input. T , sensor wire temperature T s , and the envelope temperature T e The controller may measure the measured W T , T s , and T e , as well as a model of power dissipation, the gas pressure within the envelope may further be determined.

[0005] The thermal conductivity gauge may be a Pirani gauge. The controller may: 1) calculate the total power dissipation W during the application of the power input at a subsequent time; T , sensor wire temperature T s , and the envelope temperature T e and 2) determining a change over time in at least one of the termination loss factor G and the radiation loss factor E based on the subsequent values.

[0006] The controller also: 1) calculates the total power dissipation W as the power input varies; T and the sensor wire temperature T s and 2) measuring multiple separate values ​​of the total power dissipation W T and the sensor wire temperature T sand 3) determine values ​​of the termination loss factor G and the radiation loss factor E based on the mathematical fit. The envelope temperature Te may be maintained at a constant value as the power input varies. The controller may be further configured to output a notification to remove and replace the sensor wire based on comparing at least one of the termination loss factor G and the radiation loss factor E to a reference value. The controller may be further configured to 1) determine a gas containment factor A based on the mathematical fit, where the gas containment factor A is dependent on the type of gas in the enclosure, and 2) determine a measurement of the gas pressure in the enclosure based on the gas containment factor A.

[0007] The controller calculates 1) the sensor wire temperature T over a given time period. s Based on the change in the sensor wire C S 2) Determine the heat capacity of the sensor wire C S The controller may be further configured to determine a measurement of the gas pressure within the enclosure based on the heat capacity of the sensor wire C based on a rate of cooling of the sensor wire temperature Ts over a given period of time. S The controller may determine a measurement of the gas pressure during an increase in the gas pressure within the enclosure.

[0008] Further embodiments include methods of operating a thermal conductivity gauge with a sensor wire in a gas volume within an envelope. A model of power dissipation from the thermal conductivity gauge can be provided, the model including power loss due to conductive heat loss from the sensor wire termination junction, radiative loss from the sensor wire toward the gas envelope, and pressure-dependent conductive heat loss from the sensor wire through the ambient gas. A power input can be applied to the sensor wire, and during application of the power input, the total power dissipation W T , sensor wire temperature T s , and the envelope temperature T e The gas pressure in the envelope can then be calculated by multiplying the measured W T , T s , and Te , as well as a model of power dissipation.

[0009] The zero offset of a thermal conductivity gauge is determined by 1) evacuating the envelope to essentially zero pressure, 2) applying a power input to the sensor wire, and 3) measuring the total power dissipation W during the application of the power input. T , sensor wire temperature T s , and the envelope temperature T e 4) measuring the terminal loss factor G and the radiation loss factor E in the power dissipation model, T , T s , and T e and determining a temperature compensation value for the sensor wire as a function of the temperature compensation value. The termination loss factor G may correspond to heat loss in a termination post during application of power input to the sensor wire, the termination post being coupled to the sensor wire. The radiation loss factor E may correspond to radiation loss by the sensor wire during application of power input to the sensor wire. A temperature compensation value may be determined that compensates for variations in at least one of the sensor wire temperature and the envelope temperature, the temperature compensation value being a function of at least one of the termination loss factor G and the radiation loss factor E, and a measurement of the gas pressure based on the temperature compensation value may be determined.

[0010] Further embodiments include a method of operating a thermal conductivity gauge, wherein a power input can be applied to the sensor wire of the thermal conductivity gauge when an enclosure containing the sensor wire and the envelope exhibits substantially zero pressure. T , sensor wire temperature T s , and the envelope temperature T e can be measured during application of power input. S The heat capacity of the sensor wire temperature T over a given time period s The gas pressure measurement can then be determined based on the change in the sensor wire C S The thermal capacitance of the sensor wire can be determined based on measurements of the thermal capacitance of the sensor wire and the power input applied to the sensor wire.

[0011] Sensor Wire C SDetermining the heat capacity of the enclosure may be based on a rate of cooling of the sensor wire temperature Ts over the given period of time. Determining the measurement of the gas pressure may occur during an increase in gas pressure within the enclosure.

[0012] A further embodiment includes a thermal conductivity gauge comprising an envelope surrounding a gas volume, a sensor wire positioned within the gas volume, and a controller, the controller configured to: 1) apply a power input to the sensor wire of the thermal conductivity gauge when an enclosure containing the sensor wire and the envelope exhibits substantially zero pressure, and 2) control a total power dissipation W during application of the power input to heat the sensor wire. T , sensor wire temperature T s , and the envelope temperature T e and 3) measuring the sensor wire temperature T over a given time period. s Based on the change in the sensor wire C S 4) Determine the heat capacity of the sensor wire C S and determining a measurement of gas pressure within the enclosure based on a measurement of the thermal capacity of the sensor wire and the power input applied to the sensor wire.

[0013] The foregoing will become apparent from the following more detailed description of exemplary 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 the embodiments. [Brief explanation of the drawings]

[0014] [Figure 1A] FIG. 1 is a circuit diagram of a prior art Pirani gauge. [Figure 1B] 1B is a graph illustrating the response of the Pirani gauge of FIG. 1A. [Figure 2A] 1 illustrates a prior art Pirani gauge including a compensation wire. [Figure 2B] 1 illustrates a prior art Pirani gauge including a compensation wire. [Figure 3]2A-2B illustrate the prior art Pirani gauge of FIGS. 2A-2B mounted within a chamber. [Figure 4] 1 illustrates a prior art thermal conductivity gauge sensor used in an exemplary embodiment. [Figure 5A] The sensor of FIG. 4 is illustrated in more detail. [Figure 5B] 5 is a graph illustrating the response of the sensor of FIG. 4. [Figure 6] 10 is a plot illustrating the contribution of "zero pressure" losses to the overall heat dissipation in a sensor in one embodiment. [Figure 7] 10 is a plot depicting power dissipated at zero pressure versus wire temperature in one embodiment. [Figure 8A] 10 is a plot depicting power consumption in a sensor of a gauge in one embodiment. [Figure 8B] 10 is a plot depicting power consumption in a sensor of a gauge in one embodiment. [Figure 9] FIG. 1 depicts the interaction between a heated sensor wire and gas molecules. [Figure 10A] 1 is a plot of power as a function of pressure in one embodiment. [Figure 10B] 1 is a plot of power as a function of pressure in one embodiment. [Figure 11] FIG. 2 is a block diagram of a gauge circuit in one embodiment. [Figure 12] 1 is a plot of normalized pressure over time in one embodiment. [Figure 13] 1 is a plot of sensor temperature over time in one embodiment. [Figure 14] 1 is a plot of sensor temperature over time in one embodiment. [Figure 15A] 10 is a plot of sensor temperature over time in a further embodiment. [Figure 15B] 10 is a plot of sensor temperature over time in a further embodiment. [Figure 15C]10 is a plot of sensor temperature over time in a further embodiment. [Figure 15D] 10 is a plot of sensor temperature over time in a further embodiment. [Figure 16] 1 is a plot of (1 / T) vs. P in one embodiment. [Figure 17] 1 is a plot of heat capacity as a function of wire temperature. [Figure 18] 1 is a plot of normalized pressure over time in one embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0015] A description of exemplary embodiments follows: The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety.

[0016] Exemplary embodiments include thermal conductivity gauges, such as Pirani gauges, and methods for operating them. A conventional Pirani gauge is described below with reference to Figures 1-3, and an additional gauge is described below with reference to Figure 4. Such gauges may be implemented in exemplary embodiments described below with reference to Figures 5A-18.

[0017] Pirani gauges that maintain a constant sensor wire temperature have been used to perform pressure measurements between 1E-4 Torr and 1000 Torr. A typical Pirani gauge that provides a constant sensor wire temperature during operation relies on a Wheatstone bridge connected to the sensor wire. The power required to maintain the wire at a constant temperature is used to provide a pressure measurement. Maintaining a constant temperature in the sensor wire is desirable because it allows for a faster response to pressure steps without having to wait for a temperature change to occur. A constant wire temperature also provides a pressure-independent signal baseline offset that can be subtracted from the actual signal, providing a purely pressure-dependent portion of the signal by itself.

[0018] In a typical constant-wire-temperature Pirani gauge, the temperature of the wire is maintained at a constant temperature by passing a pressure-dependent electrical heating power through it. Because the amount of power required to keep the wire at a constant temperature is pressure-dependent, a simple power measurement is used to provide a pressure measurement. This design relies on a Wheatstone bridge to regulate the wire temperature during operation by maintaining its temperature-dependent resistance.

[0019] 1A is a circuit diagram of a prior art Pirani gauge 100. The pressure sensor is connected as one arm of a Wheatstone bridge 110 with a temperature sensitive resistor R S R3 is typically a temperature-sensitive resistor designed so that the temperature rise due to the current i3 is negligible. R2 and R1 are typically fixed resistors. The sensor wire R S and typically R3 is exposed to the environment in which the pressure is to be measured. The environment is contained within an envelope where the sensor wire R S extends through a pair of feedthroughs. Alternatively, R3 may also be contained within the envelope via one or more additional feedthroughs.

[0020] The resistance values ​​of resistors R1, R2, and R3 are determined by the pressure-dependent voltage V ブリッジ is applied to the top of the bridge, and V 左 =V 右 In this case, the sensor wire R S The resistors of are fixed and chosen to be equal to (R1*R3) / R2. The voltage V ブリッジ is V 左 and V 右 The voltage difference between V and V is automatically controlled by an operational amplifier to maintain zero volts. 左 From V 右 The bridge is considered to be balanced when the potential drop across is zero. In bridge balance, the following conditions exist: a)is=i3, (1) b) i1 = i2 (2) c) isRS = i1R1, (3) d) i2R2=i3R3 (4) e) Dividing Equation 3 by Equation 4 and using Equations 1 and 2, we get f) RS = βR3 (5), where β = R1R2 (6). g) Therefore, in bridge balance, RS is a constant fraction β of R3. h) To achieve the steady state condition of RS at any given pressure, the following equation (7) must be satisfied: i) Power input to RS = power radiated by RS + power loss termination of RS + power loss in gas due to RS (7)

[0021] Sensor resistor R S The amount of power required to keep the temperature and resistance constant increases with pressure, so the voltage V ブリッジ also depends on pressure. This relationship is S voltage V over the pressure range in the chamber occupied by ブリッジ This is illustrated in FIG. 1B, which is an exemplary plot of the voltage V ブリッジ exhibits an S-curve over a range of pressures. Conventional Pirani gauges are calibrated for some known pressures and then applied to an unknown pressure, P x and the power loss into the gas, or more conveniently into the bridge voltage. Then, assuming that the termination and radiation losses remain constant, we determine the relationship between the unknown pressure P of the gas x can be determined directly by the power dissipated in the gas or can be related to the bridge voltage at the bridge balance.

[0022] The Pirani gauge 100 provides a simple configuration for measuring pressure and allows the sensor wire resistance to be adjusted in a simple manner. 左 =V 右 ), a simple op-amp circuit can be used, allowing the circuit to be built at low cost. However, to provide compensation for different ambient temperatures outside the chamber, the desired signal response (i.e., V ブリッジTo provide the proper temperature dependence (vs. pressure) a resistor of very specific value must be added to the gauge head during calibration.

[0023] 2A-2B illustrate a prior art Pirani gauge 200 that includes a compensation wire Rc. The gauge 200 is equivalent to the Pirani gauge 100 described above, but the addition of the compensation wire Rc allows the gauge 200 to compensate pressure readings for ambient temperature variations. Such ambient temperature variations are caused by the sensor wire Rc that encompasses the chamber in which pressure is measured. S The temperature difference between the wire and the envelope wall (not shown) is varied by adding a compensation wire resistor R, as shown in Figure 2B. C is wrapped around a smaller envelope within the chamber and allowed to reach temperature T2, which is in thermal equilibrium with room temperature. The resistances in the bridge (R3 and R4) and the compensation wire Rc then adjust the difference between temperatures T1 and T2 (T1 is the temperature of the sensor R) while the Wheatstone bridge remains balanced as T2 changes. S The wire temperature of the sensor wire R is adjusted so that it remains constant. S The power dissipated in the gas by the pressure sensor depends on this temperature difference, so a measurement of this power dissipation provides a pressure measurement that is independent of the ambient temperature.

[0024] In fact, the compensation wire R C exhibits variations between different gauges. Therefore, each implementation of gauge 200 must be individually adjusted by adjusting the resistance value during testing and calibration to provide a temperature difference (T1 to T2) that remains constant as the ambient temperature changes. Furthermore, the compensation wire R C The winding of the compensation wire R can be expensive and difficult to complete. C may also be wrapped internally around the gauge within a thin-walled envelope, making it exposed to the gas environment.

[0025] 3 illustrates the prior art Pirani gauge 200 described above in a further view as mounted within a chamber 290 (not shown to scale). S and compensation wire R C A portion of the gauge 200, including the compensation wire R, extends into the chamber 290 through the feedthrough flange 220, while the remainder of the Wheatstone bridge remains outside the chamber 290. C The compensation wire R C The gauge 200 is mounted within the pressure sensor volume on a thin-walled can 240 that facilitates stabilization of the pressure sensor. The gauge 200 requires at least four feedthroughs 210 through the feedthrough flanges, namely, two feedthroughs for the sensor wires R. S and two other feedthroughs are connected to the compensation wire R. C Connect the

[0026] The Pirani gauge 200 exhibits several drawbacks. In particular, calibrating the gauge 200 can be difficult and arduous. The gauge 200 must undergo calibration for proper temperature compensation, which involves selecting appropriate resistor values ​​and ensuring that the values ​​T1-T2 remain constant regardless of room temperature. The Wheatstone bridge requires fine tuning for temperature compensation. While maintaining the values ​​T1-T2 can be achieved if the calibration procedure is performed properly, the calibration procedure does not allow for the use of nominal resistor values. Rather, each gauge must be manually adjusted and configured with specific resistors, which are high-precision components.

[0027] Due to the strict implementation of the Wheatstone bridge-based temperature control, the gauge 200 does not allow for changes in sensor wire operating temperature (or resistance) during operation, but instead provides a single operating temperature.

[0028] Pressure and sensor wire R S Although there is a linear relationship between the power required to keep the bridge voltage V ブリッジAlthough the bridge voltage indicates pressure based on the measurement of V, this bridge voltage is not linearly related to pressure, as shown in Figure 1A. There is a large baseline offset (e.g., due to radiation and termination losses) and the V vs. pressure ブリッジ This, combined with the nonlinear response of the sigmoidal curve, results in an S-shaped curve that makes calibration difficult and reduces accuracy when interpolating measurement results.

[0029] 4 illustrates a thermal conductivity gauge 400 in a further embodiment, focusing on the sensor portion of the gauge. The gauge 400 includes a sensor wire R secured within a chamber 490 via a wire mount 406. S The chamber 490 includes a wire 405 (also referred to as a filament). The wire 405 connects to a gauge circuit 450 through a terminal 412 that extends into the chamber 490 via a single feedthrough 410 (e.g., electrically connected through an air-to-vacuum feedthrough connection). The opposite node of the wire 405 can be connected to a ground, such as an envelope 480 that surrounds the chamber 490. A temperature sensor 470 (e.g., a thermistor) can be positioned on or near the envelope 480 to measure the temperature of the envelope 480 and / or the ambient temperature outside the chamber 490.

[0030] In contrast to gauge 200 described above with reference to FIGS. 2-3, gauge 400 provides a sensor with a simpler configuration. Gauge 200 requires only a single feedthrough 410 to chamber 490. Furthermore, because temperature compensation can be provided using temperature sensor 470 in combination with gauge circuitry 450, compensation wires may be omitted from gauge 400. Gauge 400 therefore enables a sensor with a simpler, more compact structure that requires less labor to assemble. Gauge 400, as well as further embodiments of thermal conductivity gauges usable in exemplary embodiments, are described in U.S. Pat. No. 10,845,263, the entire teachings of which are incorporated herein by reference.

[0031] Many conventional thermal conductivity gauges utilize a Wheatstone bridge circuit to (1) control sensor wire temperature and (2) access pressure-related bridge voltage (Vb) measurements via a factory-based calibration procedure, as described above. Some gauges rely on constant sensor wire temperature and high-speed analog temperature control for real-time pressure tracking. While bridge voltage measurement is a common calibration path in such gauges, this approach does not provide an opportunity to monitor or track the thermal characteristics of the sensor during manufacturing and operation. While Pirani sensor pressure readings are expected to operate over a wide ambient temperature range, they are often sensitive to ambient temperature fluctuations.

[0032] Conventional gauges handle ambient temperature compensation in one of two ways: (1) by adding a temperature-sensitive compensation resistor to the bridge (i.e., temperature-independent Vb during assembly), or (2) by determining a temperature correction factor during test / calibration in an oven-based test vacuum system (e.g., a temperature- and / or pressure-controlled environment). A typical pressure calibration procedure generates or simply verifies a lookup table of bridge voltage (Vb) versus pressure (P), which is then stored in the gauge / transducer's electronic control unit. Sensor wire temperature is typically not included in the pressure calculation because wire temperature is controlled but not actively or accurately measured during operation. Envelope temperature is sometimes used for temperature correction of pressure readings. Calibration coefficients used for temperature compensation are typically measured over a narrow pressure range in an oven-based test vacuum system during long procedures and do not provide adequate temperature compensation across the entire pressure range of commercial sensors because they cannot adequately account for the varying heat loss mechanisms that exist across the entire pressure range of operation. In addition to envelope temperature changes due to ambient temperature fluctuations, self-heating due to higher power dissipation at higher pressures can cause the envelope to operate above ambient temperature, as discussed later. Some commercial products focus on temperature compensation features to minimize the effect of self-heating on pressure readings.

[0033] Exemplary embodiments described below may implement processes for manufacturing and / or calibrating thermal conductivity gauges that improve the calibration and operation of the gauges. Such embodiments may implement sensor hardware such as that described above.

[0034] FIG. 5A illustrates a thermal conductivity gauge 500 in an exemplary embodiment. The gauge 500 may incorporate features of the thermal gauge disclosed in the above-referenced U.S. Pat. No. 10,845,263. The sensor is configured with the optional addition of a shield 515. The sensor wire 505 may be connected between a terminal 512 (embodied as a feedthrough pin) and the shield 515. The shield 515 provides a conductive path to ground and surrounds at least a portion of the sensor wire 505, protecting the sensor wire 505 from physical damage from contaminants from the process environment and providing a thermal boundary condition for the sensor wire 505. When used in combination with a hot cathode gauge, the shield 515 may also serve to shield the sensor wire from radiation from the hot filament. In such a configuration without the shield 515, the sensor wire may experience a large change in baseline radiation offset. An insulator 511 may surround the terminals 512 at the feedthrough 510 to ensure a seal within a chamber 590 enclosed by the envelope 580. The terminals 512 further connect to a controller 550.

[0035] The sensor wire 505 may be a small diameter (e.g., 0.001 inch or 0.002 inch) filament and may be twisted into a coil (e.g., a 0.010 inch diameter coil). The operating temperature T1 of the sensor wire 505 may be selected to have a target temperature T1 of at least 20°C above room temperature to provide adequate sensitivity to pressure changes. The temperature of the sensor wire 505 may be held at a constant value during operation, thereby improving the response speed to pressure changes. This constant temperature T1 may be controlled by applying a control power input (W to distinguish from pressure P) to terminal 512 to drive the sensor wire 505 to the target resistance value. TThis can be achieved by applying a resistance vs. temperature (designated as Ω). The relationship between the resistance of the sensor wire 505 and the temperature can be determined for the sensor wire 505 based on previous measurements of the same wire type. This relationship can be used to calibrate the gauge 500. As shown in FIG. 5B, the required power input W T also varies as a function of the pressure in chamber 590. This function exhibits a linear region where pressure can be measured most accurately. For gauges that use a bridge circuit, the bridge may fix the operating temperature of the wire, and the temperature may not be measured but may be assumed to be constant. However, this assumption may not always hold true, especially during pressure transients.

[0036] To improve the operation and calibration of the thermal conductivity gauge, the exemplary embodiment reduces the total power dissipation (W T ), sensor wire temperature (T s ), and envelope temperature (T e ) may utilize real-time measurements of multiple measurands, including pressure measurements. Heat loss mechanisms in Pirani sensors are well understood, and applicable thermal models are widely available in the technical literature. However, conventional Pirani gauges do not implement thermal or physical models that would improve the manufacturing and measurement capabilities of Pirani gauges. Thermal conductivity gauge fabrication, calibration, and pressure measurements benefit from thermal models in several ways, as described below.

[0037] Total power dissipation W T represents the heat transferred from the sensor wire to the surrounding envelope through several mechanisms, including termination losses of gas molecules, radiation losses, and thermal conductivity, and the total power dissipation W T is related to the gas pressure and is parameterized by both the sensor wire and envelope temperatures. According to well-established thermal models, W T increases in direct proportion to the gas pressure and the temperature difference between the sensor wire and the envelope wall. Detailed mathematical formulas correlating power dissipation to gas pressure and temperature are listed below: Gas Power Dissipation (W g) can be isolated from the total power dissipated by the sensor wire during operation and is based on the well-known thermophysical properties of a heated sensor wire immersed in a gas. Gas power loss is directly proportional to the thermal conductivity of the gas, which in turn is proportional to the gas pressure. When the gas power loss is known, the accuracy of pressure calculations and the effectiveness of temperature compensation improve. Pirani sensors are also described as thermal conductivity sensors and provide an indirect measurement of pressure, i.e., it depends on the chemical composition of the gas. W g W T The ability to mathematically separate pressure from temperature simplifies pressure calculations, improves temperature correction algorithms, provides the ability to calculate pressure for other gases (i.e., gases different from the calibration gas), and provides a route for predictive maintenance.

[0038] Sensor wire temperature T s can be determined based on the measured resistance across the sensor wire and represents the operating temperature of the sensor wire, and the total power dissipation W T and gas power dissipation W g Without sensor wire temperature measurement, the Pirani gauge may not be able to distinguish between power changes due to fluctuations in pressure or wire temperature. Wire temperature control (analog or digital) is never perfect, and changes in wire temperature due to pressure transients can occur at any time. Real-time sensor wire temperature T s The measurement allows the exemplary embodiment to isolate changes in gas power dissipation. The sensor wire temperature measurement is also necessary to provide accurate, temperature-compensated "zero pressure" power measurements as described below and to derive temperature coefficients without the need for an oven-type test vacuum system.

[0039] The power dissipation mechanisms that drive heat loss away from the heated wire are distinct at different pressure ranges. -3 At pressures below 10 Torr, gas conductivity losses are negligible, so heat dissipation is dominated by radiation and termination losses. -3In the range of ∼10 Torr, heat transfer is closely correlated with the change in gas thermal conductivity with pressure. Finally, above 10 Torr, heat loss is dominated by gas conduction, but is also influenced by increases in gas temperature and convection. Each of these heat loss mechanisms is described in further detail below.

[0040] "Zero pressure" loss (high vacuum range, P<1E-6 Torr) "Zero pressure," as used herein, refers to the absence of any detectable gas density by a thermal conductivity gauge. In the absence of any detectable gas density, heat dissipation from the sensor wire is dominated by two independent mechanisms: termination loss and radiation loss. At high vacuum levels, the total power dissipation, W T can be expressed as follows: W T =W 終端 +W 放射 (8) During the ceremony, W 終端 = power dissipated in the termination support (i.e., termination losses), and W 放射 = power dissipated by radiation (i.e., radiation losses). End support posts may refer to support posts (e.g., wire mounts 406 as shown in FIG. 4) directly connected to each end of the sensor wire. 終端 and W 放射 The relative contributions of are affected by the surface emissivity characteristics, the bulk thermal conductivity of the sensor wire, the dimensions (eg, length and diameter) of the wire, the operating temperature of the wire, and the operating temperature of the envelope.

[0041] FIG. 6 is a plot illustrating the contribution of zero pressure drop to the overall heat dissipation in an exemplary sensor. This plot shows that zero pressure drop occurs at the normal reference temperature of operation of the sensor wire (i.e., typically T), provided the sensor wire remains clean and polished. 基準 This emphasizes the observation that the pressure drop is typically dominated by end losses at T (where T is about 100°C) and the contribution from radiation is low.s 4 Since radiation losses increase with the temperature of the sensor wire, the termination losses (T s (which increases with

[0042] Termination loss: W 終端 The termination posts are thermally sunk into the sensor envelope and are maintained at the ambient temperature T during operation. 周囲 As a result, the thermal power transfer from the wire to the pillar, W 終端 A constant flow of heat is generated. The termination posts are thermal anchors with a large thermal capacity (or thermal mass) and thermal conductivity to the envelope. The heat rejected to the terminations is replenished by an electric heater circuit to maintain a constant wire temperature (i.e., a constant resistance, Rs).

[0043] In a thermal model, the termination loss can be mathematically expressed as: W 終端 =G*(T s -T e ) (9) During the ceremony, G = termination loss coefficient (ELC) T s = temperature of the wire (R s (derived from T e = envelope temperature

[0044] Since the temperature of the envelope (where the sensor wire is thermally submerged) can increase above ambient when self-heating is set at the highest pressure, equation (9) includes the ambient temperature, T 周囲 , and envelope temperature, T e A distinction is introduced between T and T to account for possible discrepancies between the envelope and ambient temperatures caused by self-heating. e will continue to be used throughout the thermal analysis.

[0045] The above functional form is the W T and T sThe linear relationship between ELC and G indicates that the total heat dissipation is dominated by termination losses. ELC can be a function of: 1) sensor wire material (substrate wire and coating), 2) sensor wire dimensions, 3) support post dimensions, 4) support post material, 5) post thermal connection to header, and 6) notch characteristics. ELC(G) can be expected to remain approximately constant if the mechanical properties of the sensor do not change over time (i.e., no material is consumed or accumulated). ELC can also be expected to be repeatable from unit to unit.

[0046] Radiation loss:W 放射 The heated sensor emits electromagnetic radiation into the surrounding structure (blackbody emission). The rate of energy loss due to such a process depends on 1) the temperature of the wire (non-uniform distribution), 2) the emissivity of the surface material of the wire, and 3) the temperature of the surrounding structure (approximately T e In a thermal model, the radiation loss can be mathematically expressed as: W 放射 =E*(T s 4 -T e 4 ) (10) During the ceremony, E = Radiation Loss Coefficient (RLC) T 基準 = reference temperature of the wire (derived from Rs) T e = envelope temperature The above equation shows the non-linear relationship between radiated power and temperature (e.g., absolute temperature). RLC is directly proportional to the area and emission coefficient of the sensor wire surface.

[0047] Figure 7 shows the T e Zero pressure at the sensor vs. T = 20°C s 1 is a plot depicting the power dissipation at T s reaches a high temperature value, the effect of radiation losses is s This can be clearly seen as an increase in slope with increasing . The power obtained from the graph above was fitted to the following functional form: W T(zero pressure)=G*(T s -T e )+E*(T s 4 -T e 4 ) (11) The coefficients derived from the nonlinear fits shown by the traces are shown in Table 1. [Table 1]

[0048] The measurements and calculations described above offer several advantages. In particular, T , T s , and T e Measurement of T allows for the calculation of the G and E thermal coefficients of each individual gauge (1) during the calibration process or (2) during sensor operation (i.e., each time the sensor is operated and stabilized at zero pressure). The validity of Equation (11) can be experimentally verified, and as Equation (11) is depicted, T s or T e It can be demonstrated that identical values ​​of the G and E coefficients are obtained that track power variations for either

[0049] Based on equation (11), T s or T e can be varied to determine the G and E coefficients. Implementations of Pirani circuits, such as the exemplary embodiment gauges described below, allow for sensor wire temperature variations and can deliver fresh G and E values ​​(at the factory and in the field) in seconds. In contrast, deriving G and E from Te variations requires an oven-based test vacuum system, an expensive and time-consuming process. Calculating G and E in the factory or in the field is particularly simple in exemplary embodiments because it allows for variation of sensor wire temperature over a wide range. Total power can be measured at multiple wire temperatures while remaining in high vacuum, and G and E that fit the functional form of equation (11) can be calculated. Without variable wire temperature capability, measuring G and E could be achieved by varying Te in an oven-based test vacuum system, which is a much slower process.

[0050] Furthermore, under zero pressure conditions, W T , T s , T e Measurement of G allows for the determination of thermal coefficients, G and E, which offers several advantages. In gage manufacturing, determining G and E in the factory allows for real-time incoming material qualification, improving manufacturing yield and preventing unacceptable material from entering the production floor. Measurement of termination loss and emission coefficients, in exemplary embodiments, can provide a means for establishing incoming material inspection procedures and preventative failure reporting. Such embodiments may implement all-digital power control and power and temperature measurement, or may implement a hybrid configuration including an analog temperature controller. Such embodiments may also measure power and temperature in real time, including configurations with a bridge as described above, which may be achieved by adding additional test points to the bridge circuit to measure the current to and voltage across the sensor wire. G and E coefficients can be tracked during production as part of statistical process control (SPC) analysis of incoming material characteristics.

[0051] Measurements also provide operational benefits: determining G and E in the field (variable T of the sensor) s The use of a metering setting (using the metering setting) allows for the detection of sudden increases in E related to contamination (affecting minimum detectable pressure performance) or sudden changes in G that may be due to corrosion or contamination buildup on the sensor wire and may indicate an imminent end of life (and the need for preventative maintenance). The G and E coefficients can be tracked during operation to provide predictive maintenance notifications, as described in more detail below. Additionally, access to G and E, and the ability to upgrade the thermal coefficients of the gauges in the field, provides improved zero pressure measurement and minimum detectable pressure (MDP) specifications that are less dependent on ambient temperature. Tracking G and E is a substantial feature for improving zero pressure measurement specifications in an exemplary embodiment.

[0052] Gas loss As the gas pressure around the sensor wire begins to increase, the gas molecules begin to contribute to the total power loss. The total power dissipated is now expressed as: W T =W 終端 +W 放射 +W ガス (12) During the ceremony, W 終端= Power dissipated in the terminal pole (terminal loss) W 放射 = power dissipated by radiation (radiation loss) W ガス= Power dissipated by gas (gas thermal conductivity losses) Energy transfer from the heated wire to the gas molecules is pressure dependent, an effect that is utilized in thermal conductivity gauges (TCGs) to derive gas pressure. Because heat transfer to gas molecules is species (heat capacity, mass, and accommodation coefficient) dependent, all thermal conductivity gauges are essentially indirect pressure measurement sensors. From equation (12), and to determine the amount of power transferred to the gas molecules, the zero pressure power loss must be known and subtracted from the total power. Accurate pressure measurement always requires "knowing" the zero pressure power loss, which requires knowing G and E for the sensor to adjust to temperature changes in the wire or envelope. Knowing G and E allows the TCG to be calculated. s or T e This allows zero to be accurately subtracted when either

[0053] FIG. 8A shows the power consumption at the sensor for a given gauge and at several different envelope temperatures from 0 to 60°C, and T 基準 = 100°C. As shown, power consumption across the entire pressure range decreases as the envelope temperature increases. It is also clear that the change in power as a function of temperature depends on the pressure range.

[0054] Figure 8B shows the T e Gas W as a function of pressure at 20°C ガス1 is a plot depicting the power dissipated by the gas at zero pressure W from the total pressure data. T For P<1 Torr, the gas power and W ガス There is a strict linear relationship between P and P, and the slope of the linear response is proportionally related to the gas accommodation coefficient.

[0055] Low pressure operation, P≦1 Torr Figure 9 depicts the interaction between the heated sensor wire and gas molecules. At low pressure, gas molecules collide with the surface of the hot wire. All molecules are heated to an average temperature T g (and their corresponding Maxwellian energy distributions). At low pressures (i.e., the mean free path of molecular collisions is larger than the characteristic dimensions of the sensor), the temperature of the gas molecules reaching the wire is the envelope temperature, T g =T e If self-heating is not in place, T e =T 周囲 Molecules that reach the wire typically reside on the surface for a short residence time (related to the accommodation factor) and then leave the filament at a high temperature close to the wire temperature.

[0056] The accommodation factor is typically defined as the probability of the energy transfer process: at low pressures, heated molecules emitted from the wire undergo multiple collisions with the envelope wall, and their temperature rises to T before another collision with the sensor wire occurs. g =T e and energy is effectively transferred from the wire to the wall. The net power transfer is gas power dissipation.

[0057] In a thermal model, the power dissipated by the gas under these low pressure conditions is expressed as: W g =A*[(T s -T g ) / T g 1 / 2 ]*P (13) During the ceremony, W g= power dissipated by gas molecules A = Gas Coefficient - species dependent. Includes accommodation coefficient. T s = sensor wire temperature - reference temperature value. T g = temperature of gas molecules reaching the sensor wire. T at low pressure g =T 周囲 =T e (i.e., in the absence of self-heating) P = gas pressure

[0058] Equation (13) gives the W at low gas density values. ガス and P.

[0059] FIG. 10A is a plot showing that the linear relationship of Equation (13) exists for pressures <1 Torr in the "Gas Loss" trace corresponding to N2 gas. FIG. 10B shows a similar relationship through data extracted with a power measurement circuit. The A coefficient is s , T e (=T ガス ), and W T After measuring, it can be calculated from the linear region of the plot using equation (13). Table 2 shows the e and T s The value of A calculated from equation (13) using the settings is shown. [Table 2] A consistent A value can be calculated and, using equation (13), T s and T e Under typical combinations of g can be used to calculate

[0060] Therefore, under zero pressure conditions (W T , T s , T eMeasurement of the A factor allows for the determination of the thermal coefficient A (also called the gas accommodation coefficient). This determination can provide several advantages. For example, measuring A during production can provide a measure of the accommodation coefficient of the sensor wire for N2 gas. Monitoring the A factor can be part of the qualification process for incoming materials, particularly for use as sensor wire, and can prevent unsuitable materials (e.g., dirty or poor surface quality) from entering the production floor. In calibrating gauges, a consistent A factor valid over a wide range of pressures and temperatures (W T , T e , T s ) allows low pressures to be calculated over a wide pressure range (e.g., <1 Torr) from a single A value stored in the electronic control module. The A factor can be calculated from a single test pressure measurement, eliminating the need to use multiple pressure set points (e.g., cycle time reduction). When the A factor is available, low pressure calibration and measurement can be simplified.

[0061] Further refinement can be achieved during the measurement process, for example by using equation (13) to calculate a single stored A coefficient, total power, and measured temperature, T e and T s Using the equations (11) and (13), it is possible to calculate the temperature-compensated pressure. Equations (11) and (13) provide specific temperature coefficients for both zero pressure power and gas power temperature compensation. Relying on thermal models and their thermal coefficients for all different heat dissipation mechanisms effectively expands the temperature and pressure ranges over which the Pirani sensor can be temperature compensated. The temperature coefficients utilized are related to verifiable physical phenomena, providing additional insight into the quality of the manufacturing materials and their integrity.

[0062] The exemplary embodiments described herein are directed to the use of (W T , T s , T eBased on a thermal model of gas thermal conductivity as described above, exemplary embodiments can characterize the thermal properties of the gauge and provide faster and easier calibration procedures, more accurate pressure measurement algorithms, wider range temperature compensation of pressure readings, and improved tracking of sudden pressure transients (e.g., steps and pulses).

[0063] Envelope temperature T e Measurement of the temperature can be performed with a variety of thermometers thermally coupled to the envelope wall. Thermistors, temperature diodes, and platinum resistors are some examples of thermometers compatible with this application. The thermometers can be located on the vacuum or air side of the envelope. Measurement of the electrical heating power delivered to the sensor can be accomplished in several ways through various circuit implementations.

[0064] 11 is a block diagram of a gauge circuit 1100 that may be implemented in an exemplary embodiment of a thermal conductivity gauge, where electrical heating power is delivered to the sensor wire 1105 from a power supply 1110, while through a digital feedback loop, a microprocessor 1120 controls the current (I s ) to achieve a target sensor resistance R0. The target resistance R0 is determined by the desired sensor wire temperature T s The voltage Vs across the sensor wires is digitally measured by the microprocessor 1120 and can be varied at any time to adjust for different temperatures. s is known by the microprocessor 1120, the sensor wire resistance R S and total power dissipation.

[0065] During operation, the temperature T of the sensor wire 1105 s can be set by selecting a target sensor wire resistance R0 that corresponds to the desired temperature. In contrast to Wheatstone bridge gauge implementations, T scan be varied by the microprocessor 1120 during calibration and in the field to derive or verify the thermal coefficients G, E, and A. The power supply 1110 is configured so that the microprocessor 1120 controls I s Through W T A digital measurement of the voltage across the sensor wire 1105 provides both the total power and the wire resistance. The wire resistance can then be fed back to the temperature control loop and the resistance error signal can be used to close the loop. The temperature control loop can be fully digital processed by the microprocessor 1120. The voltage measurement can be digital and can use a high-resolution, high-speed analog-to-digital converter in the microprocessor 1120.

[0066] 5A, the controller 520 may implement some or all of the measurement, calculation, and calibration functions described above and may incorporate the gauge circuitry 1100 described above with reference to FIG. 11. For example, the envelope 580 may surround the gas volume to be measured and the sensor wire 515 may be positioned within the gas volume. The controller 520 may be configured to provide a model of the power dissipation from the thermal conductivity gauge 500, the model including conductive heat losses from the sensor wire termination junctions (e.g., W 終端 ), radiation losses from the sensor wire towards the gas envelope (e.g., W 放射 ), pressure-dependent conductive heat loss from the sensor wire through the ambient gas (e.g., W ガス ), the controller 520 may then apply a power input to the sensor wire 515 to heat the sensor wire 515, and calculate a total power dissipation W T , sensor wire temperature T s , and the envelope temperature T e The measured W T , T s and T e Based on the power dissipation model, as well as the power dissipation model, the controller 520 can determine the gas pressure within the envelope 580 .

[0067] To provide predictive maintenance and field calibration, at subsequent times, the controller 520 may calculate the total power dissipation W during application of the power input. T , sensor wire temperature T S , and the envelope temperature T e Based on the subsequent values, the controller 520 may determine a change in at least one of the termination loss factor G and the radiation loss factor E over time.

[0068] The controller 520 also calculates the total power dissipation W as the power input varies. T and the sensor wire temperature T s and then measure the total power dissipation W T and the sensor wire temperature T s Based on the mathematical fit, the controller 520 may determine values ​​for the termination loss factor G and the radiation loss factor E. During this process, the envelope temperature T e may be maintained at a constant value. The controller 520 may output a notification to remove and replace the sensor wire (or a larger component of the gauge that houses the wire) based on a comparison of at least one of the termination loss coefficient G and the radiation loss coefficient E to a reference value. Based on the mathematical fit, the controller may also determine a gas containment coefficient A, which may depend on the type of gas in the enclosure 580, and then determine a measurement of the gas pressure in the enclosure 580 based on A.

[0069] As will be explained in more detail below, the controller 520 also determines the thermal capacitance C of the sensor wire based on changes in the sensor wire temperature Ts over a given period of time. S and then determine the heat capacity C S The controller 520 may determine a measurement of the gas pressure within the enclosure based on the rate of cooling of the sensor wire temperature Ts over the given time period. S and may determine measurements of the gas pressure during the increase in gas pressure within the enclosure 580.

[0070] When implementing the features described above, a thermal conductivity gauge can exhibit several advantages. T , T s , T e The measurements allow the controller to fully characterize and optimize the gauge based on a thermal model. Thermal coefficients, including but not limited to G, E, and A described above, can be derived at the factory and updated in the field when the three measurements are available within the gauge.

[0071] Thermal coefficients generated at the factory during calibration can have several uses. For example, such thermal coefficients can be used for qualification of incoming materials. Factory quality control can set limits on acceptable values ​​for thermal coefficients and reject unsuitable materials that do not meet those limits. Such quality control procedures ensure more consistent product performance is delivered to customers. Traditional sensor wire qualification procedures are often limited to measuring wire resistance, which is not sufficient to ensure the most consistent unit-to-unit performance.

[0072] Thermal coefficients can also be used to provide improved minimum detectable pressure (MDP) performance. Pressure measurements at the low end of the range depend on accurate recording of zero offset. While some conventional gauges track zero offset, none have the ability to correct for it in real time as sensor wire or ambient temperature changes. Zero offset drift limits the MDP specifications of all commercially available products. As a result, users must update their instruments' zero offset periodically, preferably whenever they reach zero pressure (by unit button press, digital signal input, or command). Access to G and E coefficients allows gauge users to reduce zero offset checks because the instrument can update the zero offset for sensor wire and envelope temperature variations and based on accepted thermal models for zero pressure power dissipation.

[0073] The thermal coefficients can further be used to simplify pressure calibration at low pressures. The ability to separate gas power dissipation and calculate pressure using the A thermal coefficient along with physics-based temperature compensation can minimize the number of test points required during low-pressure calibration. The thermal coefficients generated at the factory during calibration can also be used to simplify the pressure calculation to essentially a single linear equation that accounts for temperature changes in both the sensor wire and the envelope. Such a mathematical implementation allows for easy switching to pressure calculations for other gas species by simply modifying the A thermal coefficient to match the other species being measured.

[0074] Furthermore, the thermal coefficient can be used to perform temperature compensation for both the temperature fluctuations of the sensor wire and the envelope. Reliance on known heat dissipation models allows for improved temperature compensation over a wider range of temperatures and pressures. Such thermal coefficients can also be used to improve the time response of the Pirani sensor. Conventional sensors generally rely on temperature control loops to precisely control the sensor wire temperature, but the sensor wire temperature can deviate from the target during events such as pressure steps or pulses. Real-time, accurate measurement of the sensor wire temperature can detect such deviations from the target value and take them into account in the calculation of pressure.

[0075] The ability to update thermal coefficients originally collected and recorded in the field and at the factory provides a better opportunity to detect changes in thermal characteristics that may indicate end of life or the need for complete recalibration or repair. T , T s , T e The added ability of the gauge to vary the sensor wire temperature over a wide range, combined with access to measurements for thermal modeling, provides additional capabilities to simplify the calibration procedure, which is typically performed in slow oven-type vacuum systems. e The change in value can be performed quickly without the need for any special vacuum system.s Replace with a fast change in value.

[0076] Zero Offset Adjustment Pirani gauges are the workhorse of the vacuum processing industry, typically used to measure gas pressures over the range of 1E-4 to 1E3 Torr. To ensure accuracy at the lowest pressures (i.e., P<1E-2 Torr), periodic "zero offset" (ZOA) adjustments must be performed to compensate for drift due to contamination or corrosion of the sensor wire and ambient or sensor wire temperature changes. The zero offset adjustment (ZOA) procedure is typically performed while the gauge is exposed to high vacuum levels (e.g., P≦1E-6 Torr).

[0077] The ZOA can be activated in the field in several different ways. For example, a "zero" button may be available somewhere on the electronics module. The user presses the button under high vacuum conditions, and a new ZO correction value is stored in memory and used for subsequent measurements. A digital input pin may be available to activate the ZOA. A logic pin may be connected to a PLC or ionization gauge that controls the activation of the ZOA event. Alternatively, the ZO command may be available through a digital communication interface. For older gauges without microprocessor control, a potentiometer may be adjusted until the pressure reading is properly zeroed at high vacuum. Such a ZOA procedure is stored in the controller's memory and then generates a new ZO correction value used to correct all subsequent pressure readings. For accurate operation, the ZOA may be essential for all pressure readings (P<1E-2 Torr).

[0078] While ZO drift can be minimized, it may not be practical to eliminate it. Vacuum practitioners recognize the need to frequently zero Pirani gauges. Therefore, a solution that reduces the frequency of ZOA would provide substantial benefits. The exemplary embodiments described below provide a new ZOA methodology, based on a thermal model for heat dissipation, that provides several advantages over thermal conductivity gauges, including: a) Deterioration of the minimum detectable pressure function. b) Improved accuracy at P<1E-2 Torr. c) Specific ambient temperature correction of the ZO correction value (i.e. reducing the frequency of ZO adjustments). d) The ability to update the zero offset correction temperature coefficient in the field (i.e., life extension), referred to herein as "Deep Zero Offset Adjustment" (DZOA). e) The ability to track changes in sensor wire characteristics due to corrosion or contamination (i.e., opportunities for repair and predictive maintenance), leading to extended life.

[0079] The physics-based causes of ZO drift are explained below, and we discuss how the above improvements can be realized in a thermal conductivity gauge that includes the following features: a) Thermal model-based calibration and pressure measurement procedure. b) Three necessary and sufficient measurements: total power dissipation (W T ), sensor wire temperature (T s ), and envelope temperature (T e ) access. c) Specially designed temperature coefficient for zero offset compensation. d) New ZOA options: Standard DOA (updates ZO corrections) and Deep ZOA (updates ZO corrections and their temperature coefficients).

[0080] Conventional gauges, as explained above, rely primarily on the implementation of a Wheatstone bridge circuit, with the bridge voltage (V b ) as the primary pressure-related measurement related to pressure via calibration. ZO adjustment, in this case, simply measures the bridge voltage at high vacuum, stores that ZO correction voltage in memory, and subtracts that same value from all future bridge voltage measurements. Manufacturers often recommend frequent ZOA events, especially in polluted environments. The ZOA also needs to measure accurate pressure at P<1E-2 Torr when the ambient temperature changes by a few degrees.

[0081] Most conventional gauges include such a ZOA function, but as explained above, T , T s , or T e , nor do they use calibration or pressure measurement methods based on thermal models for heat dissipation. Conventional gauges also do not derive or use temperature coefficients that are specifically calibrated and dedicated to the ZO correction value. Some commercial gauges include some level of temperature correction or compensation of the pressure reading, but these approaches are limited to addressing the self-heating issue at atmospheric pressure.

[0082] Returning to Figure 10A, the "Total Loss" trace shows an S-curve of total power dissipation versus pressure over the typical operating range of a Pirani sensor. Heat dissipation in a Pirani sensor is governed by well-known thermal processes. Equation (12) above shows the total power dissipated by the sensor wire given a steady pressure and sensor wire temperature. The first two terms, W 終端 and W 放射 is independent of pressure and the support column (W 終端 ) and radiation losses from the wire to the surrounding (cooler) wall (W ra ) which can be referred to as "zero pressure power loss" and can be expressed as T via Equation 2. s and T e It is mathematically related to W 終端 corresponds to the termination loss, and W 放射 The term quantifies the radiation loss. Both terms are related to T through the thermal coefficients, G and E, expressed in equation (11) above. s and T e Depends on W T (P=0) is a power offset that represents the power dissipated by the sensor wire in the absence of gas molecules or gas thermal conductivity to the wall.

[0083] By definition, zero pressure total power loss, W T (P=0) or WT(P=0) contribute a constant power offset to the total sensor wire power, independent of pressure, and gas (W ガス) The zero pressure total power loss is the fundamental root cause of the need for ZOA functionality in all Pirani sensors.

[0084] In Figure 10A, the "Total Loss" trace follows the total power dissipation, which includes all three terms in equation (12). As shown, the total power curve has a constant power offset, W(P=0) ≈ 400 mW. The total power exceeds that constant offset as the gas pressure increases, significantly above 1E-3 Torr on the graph. The zero pressure power of the gauge depends on several variables: (1) T e , (2) T s and (3) sensor wire conditions, including dimensions and surface finish.

[0085] The "gas loss" trace in Figure 10A represents the loss of gas from the surrounding gas via thermal conductivity, W ガス To separate the power dissipated in T (P=0) is subtracted. W at pressures below about 1 Torr ガス The linear behavior of the response vs. P provides a simple means to calculate pressure (via a linear equation) and perform temperature compensation. In fact, at low pressures, W ガス can be expressed as follows: W ガス =W T -W T (P=0)=A*P*(T s (t)-T e ) / T e -1 / 2 (14)

[0086] As explained above, W ガス Separating the W of the sensor provides a convenient and simple calibration and pressure calculation procedure compared to previous approaches. T (P=0). Changes in power offset not captured by ZOA are ガス This can cause calculation errors and lead to inaccurate pressure calculations.

[0087] It would be advantageous to minimize the zero-offset contribution to the total power. In the example shown in Figure 10A, the power consumed by the gas (through thermal conductivity) coincides with a zero pressure-power offset at P ≈ 2E-2 Torr. This can be used to calculate the low pressure W ガス Measurements below 1E-2 Torr are generally taken to provide an accurate value of W T This explains why we need accurate and up-to-date tracking of (P=0). In other words, for pressures in the E-4 Torr range, ガス contributes less than 1% of the total power dissipation, which means that a 1% uncorrected drift in power offset will be reported as a change in pressure on the order of E-4 Torr.

[0088] W T (P=0) is periodically refreshed using the ZOA procedure, exposing the gauge to high vacuum pressure, and T (P=0) must be recorded. However, not all vacuum processes have access to the necessary high vacuum levels as frequently as may be required to provide consistent and accurate low pressure measurements.

[0089] According to equation (14), W T (P=0) is a function of both Ts and Te. The thermal coefficients, G and E, can be determined at the factory as part of the sensor calibration procedure, and T s or T e , and measure its dependence on either G or E. Both thermal coefficients are derived from a mathematical fit as described above, stored in memory, and can then be used to adjust the zero pressure power offset for temperature changes. Calculating and storing the independent thermal coefficients G and E at the factory as part of the calibration process, which is lacking in conventional approaches, not only provides a means to perform temperature correction of the power offset, but also provides a baseline measurement of sensor wire characteristics, including cleanliness and size.

[0090] Exemplary embodiments can implement one or more ZOA processes. In a first, faster ZOA process, the gauge is moved to a value WT (P=0), T s and T e The device is exposed to high vacuum pressure conditions long enough to measure and store in memory. This is a ZOA process that does not involve changes in Ts or Te. The thermal coefficients G and E are not updated, but T is calculated according to equation (14). e and T s by W T Available records can be used to track changes (P=0).

[0091] In the second, longer process, called the "Deep ZOA," the first ZOA process is performed as above, with the addition that the G and E coefficients are increased by T s The temperature is refreshed by cycling through several values ​​of T and measuring (WT(P=0), Ts) at a constant Te value, which is also recorded. The function of T (WT(P=0) vs. T follows the functional form of Eq. (14). s (constant T e The mathematical fit of (in) provides updated values ​​of G and E for the gauge. This update allows the user to achieve two goals: a) Refreshes the temperature coefficients G and E to continue to provide accurate low pressure readings after changes occur in the bulk and surface properties of the sensor wire. b) Tracks changes in G and E and reports increases that may require sensor PM replacement during the vacuum chamber's next preventive maintenance cycle. This predictive maintenance capability is not available with conventional gauges.

[0092] (W(P=0), T s , T e With the new set of W values ​​and the updated G and E coefficients, the exemplary embodiment can continue to track the change in zero pressure offset with ambient temperature according to equation (14) above. The plot of FIG. 7 shows the W values ​​leading to the updated thermal coefficient values. T (P=0) vs. T sFigure 7 shows the curve fit of the graph. Table 1 above shows the coefficients derived from the nonlinear fit shown by the trace in Figure 7. The "Deep ZOA" process therefore provides new G and E coefficients, as well as the opportunity to diagnose end-of-life issues. In contrast to the original ZOA process, which provides a new intercept for zero power, the "Deep ZOA" provides both the intercept and slope for zero power versus temperature.

[0093] A change in G indicates a change in thermal conductivity from the sensor wire to the post. This change suggests a change in dimensional and bulk thermal conductivity due to etching, corrosion, or coating (i.e., contamination). A change in E suggests a change in emissivity in the sensor wire surface material. This change indicates a change in surface properties due to etching, corrosion, or coating. In an exemplary embodiment, the gauge controller stores acceptable boundaries for G and E values ​​for its sensors and can issue repair and maintenance notifications if the thermal coefficients approach or exceed those limits.

[0094] The ZOA solution described above can offer several advantages. For example, the thermal coefficients G and E, measured during factory calibration and stored in the gauge's memory specifically for ZO temperature compensation, provide superior ZO temperature compensation. The initial ZOA process described above involves: 1) obtaining the three relevant measurements (W(P=0), T s , T e This approach improves on previous approaches in that it 1) collects and stores the G and E thermal coefficients, and 2) leverages the G and E thermal coefficients to continuously perform temperature compensation of the ZO. Furthermore, the "deep" ZOA process offers an additional improvement that allows the G and E coefficients to be refreshed as the sensor wire temperature changes during operation. The updated coefficients effectively extend the gauge life, providing consistent temperature compensation of the ZO and accurate low-pressure readings over a longer period of time. Deep ZOA also provides the opportunity to compare G and E values ​​with the sensor's recommended limits to issue repair and predictive maintenance alerts.

[0095] Gauge response time during fast pressure transients Conventional Pirani gauge electronics rely on a Wheatstone bridge resistor network circuit (see Figure 1A) to operate a heated sensor wire (or heating element for a MEMS device) at a constant temperature. An analog feedback loop continuously adjusts the heating power directed by the electronics to the sensor wire, balancing the bridge while the sensor wire operates at a constant temperature (typically around 100°C). The bridge circuit adjusts for the electrical resistance of the sensor wire, which is related to the operating temperature through factory calibration. The bridge voltage V b is measured and used to calculate pressure based on a factory-generated (or verified) calibration curve or lookup table. While the sensor is exposed to near-constant gas pressure conditions, the ability of the balanced resistor bridge to control the sensor wire temperature is minimally challenged. However, sudden pressure transients (e.g., steps and pulses) can cause the wire temperature to temporarily deviate from the nominal value. The magnitude and duration of the deviation depend on two factors: 1) the bandwidth of the temperature regulation feedback loop, and 2) the thermal capacity of the filament assembly. Prior art Pirani gauges do not monitor the temperature of the wire sensor, but rather assume that the temperature is substantially constant. In prior art gauges, temperature deviations are not measured or detected, and bridge voltage transients are always treated as being induced by pressure changes at an assumed constant filament temperature.

[0096] The gauge in the exemplary embodiment improves the ability to accurately track fast pressure transients in real time, which can benefit vacuum processing applications. A common pressure transient event in a vacuum chamber is the fast venting process to atmospheric pressure that occurs in a load lock. During fast venting, the influx of gas into the sensor chamber suddenly increases thermal conductivity from the heated wire to the adjacent wall, causing a sudden drop in wire temperature that is not detectable by any conventional gauge. A feedback loop responds by delivering additional heating power for two independent purposes: 1) returning the filament to its nominal temperature (i.e., a contribution dependent on gas pressure), and 2) adjusting the heating power delivery to the increased thermal conductivity demands (i.e., a contribution dependent on gas pressure). Conventional gauges do not detect the change in wire temperature that occurs during the transient, instead assuming that the filament temperature does not change and that the bridge voltage transient is due solely to gas thermal conductivity / pressure changes. In other words, because the filament temperature needs to be restored, pressure reporting during the transient is inaccurate and delayed. The response time associated with temperature recovery is related to the sensor's power delivery capability, the feedback loop bandwidth, and the thermal capacity of the sensor assembly. Pirani sensors with lower thermal capacity specifications perform better in tracking fast transients. Minimizing thermal capacity often drives the design of the sensor wire and explains the enhanced dynamic response of MEMS sensors. MEMS sensors have some of the lowest Cs values ​​in the industry and are referenced by applications where fast pressure transients are experienced. Exemplary embodiments may be compatible with all types of thermal conductivity sensors, including wire designs and MEMS-scale designs. The process described herein may also be applied to sensors where the controller maintains the thermal element at a coexisting temperature, or where the temperature of the heating element is pressure-dependent. This model works in all of these cases.

[0097] Exemplary embodiments provide a method for measuring pressure using a thermal conductivity gauge based on a thermal model. While the temperature of the sensor wire and envelope may be constantly measured, and the power delivered to the sensor wire may also be measured, the pressure calculation algorithm includes an additional thermal coefficient representing the thermal capacity of the sensor wire to isolate any power directed to restore the sensor wire temperature during a pressure transient. Including the contribution of the thermal capacity term in the pressure calculation improves the dynamic response of the Pirani sensor during measurement of fast gas pressure events. The amount of power directed to restore the sensor wire temperature is proportional to both the thermal capacity of the sensor wire and the rate of change of the wire temperature. Fast wire temperature measurements are beneficial in providing a more accurate measurement of the heating power driven by thermal capacity. Several methods for measuring the thermal capacity coefficient of the sensor wire are also described. Such methods can be deployed during manufacturing procedures. Periodic measurements of the thermal capacity of production units provide an additional route for qualifying incoming materials and for removing unsuitable materials from the production line.

[0098] The above is explained as the total power (W T ), sensor wire temperature (T s ), and envelope temperature (T e ) measurement, combined with a methodology to calibrate and calculate pressure based on a thermal model. In the following, this solution is extended by including an additional term in the total power equation, which accounts for the heating power directed at the sensor to re-adjust its temperature during pressure transients.

[0099] Heat Capacity Correction The thermal capacitance of the sensor wire assembly plays an important role in the dynamic response of the Pirani sensor to pressure transients. The thermal capacitance of the sensor wire assembly is defined as: C s =Q T / ΔT (15) During the ceremony, C s is the thermal capacitance of the sensor wire assembly (Example: The specific heat capacity of tungsten is 132 J / K kg) Q T is T s is the amount of energy required to change by ΔT. The total power consumed by the sensor wire assembly during operation is the sum of the power dissipated in gases, radiation, and termination posts, as well as the T s One may also consider the power delivered to adjust for sudden changes in T (i.e., when the adjusted sensor wire temperature is compromised). s If (t) is not constant, the total power, W T (t) is not constant, even for fixed gas pressure, and the power delivered to correct for sensor wire temperature must be included in the total power equation. W T (t)=W 終端 +W 放射 +W ガス +C s [dT s / dt] (16) W T (t)=G*(T s (t)-T s )+E(T s 4 (t)-T e 4 )+A*P*(T s (t)-T e )T e -1 / 2 )+C s *[dT s / dt] (17)

[0100] In the above equation, C s [dT s / dt] is an additional power term that separates the heating power spent on changing the wire temperature. s The amount of energy required to increase the current by dQ = Cs*dT can be obtained from equation (15). s is.

[0101] The heat capacity of the sensor wire assembly is an important thermal coefficient when considering the dynamic response of thermal conductivity gauges. The heat capacity includes not only a contribution from the specific heat capacity of the sensor wire, but also some additional contributions from the mounting post. During a pressure transient (e.g., a pressure burst), the sensor wire typically cools momentarily, and the feedback loop responds by adding additional heating power to restore the desired temperature. This introduces errors into the pressure calculation unless the extra power associated with the sensor wire temperature fluctuations is isolated and accounted for in the power equation. Traditional Pirani gauges use T s , and therefore cannot distinguish between gas pressure transients and the resulting wire temperature changes. Thermal capacitance can be particularly important in pressure calculations based on the model described herein if the sensor wire is not operating at a constant temperature, or if the thermal capacitance is very large, or if the bandwidth of the heating circuit is very small.

[0102] Figure 12 is a plot of normalized pressure versus time, illustrating the improvement in dynamic response that can be achieved in an exemplary gauge when the heat capacity coefficient is incorporated into the pressure calculation above. The diamond trace represents the actual pressure transient reported by the capacitance manometer. The square trace represents the pressure transient measured without considering the last term in equation (17). The circle trace shows the reported pressure when the full equation is considered, as in equation (17). Such an improvement in time response is particularly beneficial for sensors with large heat capacity or low-bandwidth heater circuits. The ability to measure fast transients using a large heat capacity sensor allows for the design of more robust gauges, including additional materials (e.g., thicker wire) that can withstand process chemistries and result in longer life.

[0103] C s Measurement-cooling time constant heat capacity C s is important to calculate the time required for the sensor wire to cool down when the power is cut off. The time required for the sensor wire to cool down after the power is cut off is given by the following equation: T s (t)=T e +(T s、公称 -T e )*e -(a*t / Cs) (18) During the ceremony, T s (t) is the time-varying sensor wire temperature, T e is the final temperature (cold wire), T s、公称 is the initial and nominal wire temperature (hot wire), C s is the thermal capacitance of the sensor wire assembly, a is the thermal conductivity coefficient, G+A*P*T e -1 / 2 is. The cooling time of the sensor wire will be faster if the heat dissipation (e.g., termination losses and gas thermal conductivity) is increased or if the heat capacity is reduced. In fact, the time constant of the cooling process is given by the quantity T(P)=C s / a=Cs / (G+A*P*T e -1 / 2 ) (19)

[0104] Equation (19) shows the cooling time constant as a function of gas pressure, with the longest time constant occurring under zero pressure conditions.

[0105] C s Measurement - Pressure Rise C s can be used to determine the time for the sensor wire assembly to achieve a desired temperature under a specified heating power delivery step. As shown above, the temperature rises exponentially under constant power, and the time constant increases with pressure as less power is available to heat the sensor wire.

[0106] A first approximation for the heat capacity of a wire is the dimensions and specific heat capacity of the W material (e.g., length 2 inches, diameter 0.0005 inches, specific heat capacity 132 J / KgK, density 19300 Kg / m 3, Cs=1.64E-5 J / K). This number is expected to underestimate the heat capacity of the entire sensor assembly since the supports are expected to contribute to the overall heat capacity. Using this calculated number for Cs and the average G=5E-6 W / K for the zero pressure condition, this suggests the following time constant: T(P=0)=1.64E-5 / 5E-6≒3.3(seconds)

[0107] This suggests that under zero pressure conditions the filament will remain hot for many seconds after power is removed or turned off, and the time decreases proportionally with increasing pressure. Conversely, it takes longer to heat the filament in proportion to higher gas pressures.

[0108] C s Measurement: Calorimetry judgment A straightforward way to perform heat capacity measurements is to perform calorimetry at zero pressure. In a calorimetry experiment, an electrical heating power step is applied to the sensor wire assembly to measure its temperature increase versus time, T. 基準 (t) is applied while tracking. For each measurement, the power dissipated in thermal conductivity is subtracted from the total power (i.e., the termination losses at zero pressure are subtracted). The remaining power (used to heat the sensor wire assembly) is then integrated and divided by the temperature increase it causes, resulting in a direct measure of the sensor wire heat capacity, C s At zero pressure,

number

[0109] Power W T If is stepped and controlled to a constant value during heating, the temperature of the sensor wire assembly increases according to the following equation: T s (t)=T e +(W T / a)*(1-e (-t / Τ)) (twenty one) During the ceremony, T is C s / a, the time constant of the temperature increase, a is the thermal conductivity coefficient, G+A*P*T e -1 / 2 and P is the gas pressure.

[0110] Figure 13 is a plot of sensor wire temperature versus time, with current (power) steps, T s The results of a calorimetric experiment where the temperature is increased from 90 to 100 °C are shown. The sensor starts at 90 °C and the heating current is T s = 100°C. Since the resistance of the sensor wire does not change significantly over this temperature range, constant power delivery can be assumed and the data can be fit to equation (21). This fit shows that: 1) T = C s 1) / G = 5.468 seconds, 2) G = 5.2E-6 W / K, and 3) Cs = 2.85E-5 J / K. Here, the measured value exceeds the calculated value of 1.64E-5 J / K, revealing that the heating above ambient temperature extends beyond the sensor wire, i.e., into the sensor wire assembly. Therefore, C s may be referred to as the thermal capacity of the sensor wire assembly.

[0111] Figure 14 shows an additional calorimetric experiment where Ts is a plot of the sensor temperature over time, increasing from 20°C to 100°C. The time constant is 5.49 seconds (C s =2.86E-5), which is in close agreement with the data discussed above.

[0112] 15A-15D are plots of sensor temperature over time, ranging from 90 to 110°C (i.e., nominal operating T) at gas pressures from zero to 0.1 Torr. 基準 Figure 1 shows a series of time constants for a common sensor over a 20°C band around C. As shown, the time constant decreases as the pressure increases due to the additional power required to maintain the wire at the required temperature. In all cases, C s is the known value of G, A, P, and T e was calculated using the following relationship: T=C s / (G+A*P*T e -1 / 2 ) (twenty two) During the ceremony, G is 5.2E-6W / K, A=0.00366

[0113] Table 3 below shows the calculated Cs values ​​at different pressures. The consistency of the Cs values ​​suggests that equation (22) is an appropriate physical model for the time constant. [Table 3]

[0114] FIG. 16 is a plot of (1 / T) versus P, which according to equation (23) below should result in the following linear relationship: (1 / T)=(G / Cs)+(A*T e -1 / 2 / Cs)*P (23) During the ceremony, Intercept = G / Cs (Equation 20), Cs = 5.2E-6 / 0.1742 = 2.98E-5 J / K Slope = A*T e 1 / 2 / Cs, (Equation 21) gives A=0.00437.

[0115] For a known G value, C s The intercept of 1 / T vs. P can be used to calculate , and the slope can be used to derive A.

[0116] Figure 17 is a plot of heat capacity as a function of wire temperature. Heat capacity C s is the temperature T s Dependence on Cs(T s In one example, the thermal capacity can be further characterized by several different T sThe value can be calculated using 10°C sensor wire temperature steps (i.e., + / - 5°C) around the target temperature. The linear dependence of heat capacity on Ts is shown in Figure 17 as follows: C s (T s )=5.1E-8[J / K 2 ]*T s [K]+9.629E-6J / K C s (T s =373K)=2.87E-5J / K The dependence of Cs on the sensor wire temperature is T s The temperature gradient due to the wire is most likely related to changes in the wire. As the temperature of the wire increases, more assemblies are engaged, increasing the heat capacity of the extended thermal system.

[0117] Summary of the process for determining heat capacity In view of the above, an exemplary process for determining the thermal capacity of a sensor wire is as follows. a) Determine α. Measure wire resistance vs. temperature in the absence of self-heating. b) Determine G and E. T at zero pressure 基準 Power W as a function of T Measure and determine ε from E. c) Power measurement W in the intermediate and linear pressure ranges of the low pressure range T Determine A from (P). d) Two reference temperatures, T 低 From T 高 The exponential time constant for heating the wire at zero pressure between s Determine the following.

[0118] The power delivered to the sensor is expressed according to equations (16) and (17) above. For a brand new gauge and a narrow temperature range around ambient temperature, the contribution from radiation losses is 10%, allowing equation (17) to be further simplified. W T (t)=Go *(T s (t)-T e )+A*P*(T s (t)-T e )T e -1 / 2 )+C s *[dT s / dt] (24) where G o is the linear temperature coefficient of zero pressure power loss including radiation loss over a narrow temperature range typical of the operating range of a Pirani sensor (i.e., 0-60 °C).

[0119] Power term C s *[dT s / dt] provides an effective method of subtracting the gas-dependent heating power (dissipated in regulating the sensor wire temperature) from the total power consumed by the sensor. The remaining power can then be used to accurately calculate the gas pressure during a fast pressure event, such as an overpressure or atmospheric vent event. As mentioned above, the heater can only provide power, so [dT s / dt]>0, equation (17) applies.

[0120] Including the heat capacity thermal coefficient in the design, calibration, and pressure calculation of a Pirani sensor offers several distinct advantages, as explained below.

[0121] High-speed Pirani sensors are typically designed with small heating elements, especially on the MEMS scale. In wire-based designs, small wire diameters are generally preferred to minimize termination losses due to thermal conductivity and improve response times due to reduced thermal capacitance. From a thermal modeling perspective, the reduced size addresses the fact that small sensors have a smaller thermal capacitance of the sensor wire assembly, recover faster from temperature changes in the sensor wire, and require less heating energy to restore the nominal sensor wire temperature. By additionally measuring the sensor wire temperature and taking into account the thermal capacitance term (in equation (17)), exemplary embodiments can provide fast time response to fast events, such as atmospheric venting, even with larger sensor wire constructions.

[0122] Figure 18 is a plot of normalized pressure versus time, demonstrating the performance of the heat-capacitance-compensated sensor in the exemplary embodiment, as opposed to a MEMS-scale prior art sensor. The diamond trace is an actual pressure transient curve measured by a capacitance-type manometer with a 10-millisecond response time. The triangle trace is the pressure response measured with a high-speed MEMS-scale Pirani gauge. The circle trace is the response of a standard Au-coated tungsten wire Pirani, including 1) real-time sensor wire temperature measurement and 2) heat-capacitance compensation, as shown in the last term of Equation 13. The square trace represents a wire Pirani gauge with a high-speed temperature control system. As shown, this sensor eventually works toward catching up with the pressure transient, but lags (i.e., underestimates the pressure) until the heater circuit operates to restore the wire temperature. The inclusion of the heat-capacitance term for the sensor wire temperature measurement and pressure calculation allows a gauge with a larger sensor wire to rival the dynamic response of one of the fastest conventional Pirani sensors in the exemplary embodiment.

[0123] In particular, larger sensor wires are longer and have a larger diameter, naturally packing in more metal material. The larger diameter means a more robust mechanical design, better able to withstand the vibrations common in vacuum systems. The larger diameter also means enhanced robustness against reactive chemicals that can erode metal surfaces, providing longer sensor life in the presence of corrosive species.

[0124] The exemplary embodiment also provides a calibration advantage. During calibration, the heat capacity, C sPerforming a measurement of not only provides the thermal coefficients necessary to perform more accurate pressure calculations via equation (17), but also provides another measure of the bulk thermal properties associated with the sensor wire structure. Heat capacity measurements can be used to track the manufacturing process looking for changes in the thermal properties of the sensor wire. Sudden changes or long-term drift in the sensor's heat capacity indicate manufacturing issues such as variations in wire dimensions or material composition.

[0125] Exemplary embodiments also benefit gauge-based measurements. The inclusion of the sensor's thermal capacitance in the pressure calculation, Equation (17), combined with real-time sensor wire temperature monitoring, provides faster pressure measurement response and accuracy in the event of a pressure transient. Pirani sensors are routinely used in load lock stations where fast venting is the norm, and fast response is essential to improve speed and accuracy in these events.

[0126] While exemplary embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and detail can be made therein without departing from the scope of the embodiments encompassed by the appended claims.

Claims

1. A thermal conductivity gauge comprising: an envelope surrounding the gas volume; a sensor wire positioned within the gas volume; a controller; The controller providing a model of power dissipation from the thermal conductivity gauge, the model including power loss due to conductive heat loss from a sensor wire termination junction, radiation loss from the sensor wire towards the gas envelope, and pressure dependent conductive heat loss from the sensor wire through the ambient gas; applying a power input to the sensor wire to heat the sensor wire; During said application of said power input, the total power dissipation W Ｔ , sensor wire temperature T ｓ , and the envelope temperature T ｅ and measuring The measured W Ｔ , T ｓ , and T ｅ determining a gas pressure within the envelope based on the power dissipation model; a thermal conductivity gauge configured to:

2. The thermal conductivity gauge of claim 1 , wherein the thermal conductivity gauge is a Pirani gauge.

3. The controller At a subsequent time, during the application of the power input, the total power dissipation W Ｔ , sensor wire temperature T ｓ , and the envelope temperature T ｅ measuring subsequent values ​​of determining a change over time in at least one of a termination loss factor G and a radiation loss factor E based on the subsequent values; The thermal conductivity gauge of claim 1 further configured:

4. The controller As the power input varies, the total power dissipation W Ｔ and the sensor wire temperature T ｓ measuring a plurality of distinct values ​​of The total power dissipation W Ｔ and the sensor wire temperature T ｓ determining a mathematical fit to said plurality of distinct values ​​of determining values ​​for the termination loss factor G and the radiation loss factor E based on the mathematical fit; The thermal conductivity gauge of claim 1 further configured:

5. The thermal conductivity gauge of claim 4 , wherein the envelope temperature Te is maintained at a constant value as the power input varies.

6. 5. The thermal conductivity gauge of claim 4, wherein the controller is further configured to output a notification to remove and replace the sensor wire based on comparing at least one of the termination loss factor G and the radiation loss factor E to a reference value.

7. The controller determining a gas containment factor A based on the mathematical fit, wherein the gas containment factor A is dependent on the type of gas in the enclosure; and determining a measurement of gas pressure within the enclosure based on the gas containment coefficient A; The thermal conductivity gauge of claim 4 , further configured to:

8. The controller the sensor wire temperature T over a given period of time ｓ Based on the change in the sensor wire C Ｓ Determine the heat capacity of The sensor wire C Ｓ determining the measurement of gas pressure within the enclosure based on the heat capacity of the The thermal conductivity gauge of claim 1 further configured:

9. The controller determines the cooling rate of the sensor wire C based on the rate of cooling of the sensor wire temperature Ts over the given time period. Ｓ 9. The thermal conductivity gauge of claim 8, wherein the gauge determines the heat capacity of

10. The thermal conductivity gauge of claim 8 , wherein the controller determines the measurement of gas pressure during an increase in the gas pressure within the enclosure.

11. 1. A method of operating a thermal conductivity gauge comprising a sensor wire within a gas volume within an envelope, the method comprising: providing a model of power dissipation from the thermal conductivity gauge, the model including power loss due to conductive heat loss from a sensor wire termination junction, radiation loss from the sensor wire towards the gas envelope, and pressure dependent conductive heat loss from the sensor wire through the ambient gas; applying a power input to the sensor wire; During said application of said power input, the total power dissipation W Ｔ , sensor wire temperature T ｓ , and the envelope temperature T ｅ and measuring The measured W Ｔ , T ｓ , and T ｅ determining a gas pressure within the envelope based on the power dissipation model; A method comprising:

12. The method of claim 11 , wherein the thermal conductivity gauge is a Pirani gauge.

13. At a subsequent time, during the application of the power input, the total power dissipation W Ｔ , sensor wire temperature T ｓ , and the envelope temperature T ｅ measuring a subsequent value of determining a change over time in at least one of a termination loss factor G and a radiation loss factor E based on the subsequent values; The method of claim 11 further comprising:

14. As the power input varies, the total power dissipation W Ｔ and the sensor wire temperature T ｓ measuring a plurality of distinct values ​​of The total power dissipation W Ｔ and the sensor wire temperature T ｓ determining a mathematical fit to said plurality of distinct values ​​of determining values ​​of a termination loss factor G and a radiation loss factor E based on the mathematical fit, such that the model of power dissipation incorporates the termination loss factor G and the radiation loss factor E; The method of claim 11 further comprising:

15. As the power input varies, the envelope temperature T ｅ The method of claim 14 , wherein is maintained at a constant value.

16. 15. The method of claim 14, further comprising selectively removing and replacing the sensor wire based on comparing at least one of the termination loss factor G and the radiation loss factor E to a reference value.

17. determining a gas containment factor A based on the mathematical fit, wherein the gas containment factor A is dependent on the type of gas in the enclosure; and determining a measurement of gas pressure within the enclosure based on the gas containment coefficient A; The method of claim 14 further comprising:

18. the sensor wire temperature T over a given period of time ｓ Based on the change in the sensor wire C Ｓ determining the heat capacity of The sensor wire C Ｓ determining the measurement of gas pressure within the enclosure based on the heat capacity of the enclosure; The method of claim 11 further comprising:

19. The sensor wire C Ｓ Determining the heat capacity of the sensor wire temperature T over the given time period ｓ 20. The method of claim 18, wherein the cooling rate is based on a

20. 20. The method of claim 18, wherein determining the measurement of gas pressure occurs during an increase in the gas pressure within the enclosure.

21. The zero offset of the thermal conductivity gauge is evacuating the envelope to substantially zero pressure; applying a power input to the sensor wire; During said application of said power input, the total power dissipation W Ｔ , sensor wire temperature T ｓ , and the envelope temperature T ｅ and measuring The termination loss factor G and the radiation loss factor E in the power dissipation model are defined as W Ｔ , T ｓ , and T ｅ and determining the value as a function of The method of claim 11 , further comprising modeling by:

22. 22. The method of claim 21, wherein the termination loss factor G corresponds to heat loss in a termination post during application of the power input to the sensor wire, the termination post being coupled to the sensor wire.

23. 22. The method of claim 21, wherein the radiation loss coefficient E corresponds to radiation loss by the sensor wire during application of the power input to the sensor wire.

24. determining a temperature compensation value that compensates for variations in at least one of a sensor wire temperature and an envelope temperature, the temperature compensation value being a function of at least one of the termination loss factor G and the radiation loss factor E; determining the measured value of gas pressure based on the temperature compensated value; 22. The method of claim 21 further comprising:

25. 1. A method of operating a thermal conductivity gauge, comprising: applying a power input to the sensor wire of the thermal conductivity gauge when an enclosure containing the sensor wire and the envelope exhibits substantially zero pressure; During said application of said power input, the total power dissipation W Ｔ , sensor wire temperature T ｓ , and the envelope temperature T ｅ and measuring the sensor wire temperature T over a given period of time ｓ Based on the change in the sensor wire C Ｓ determining the heat capacity of The sensor wire C Ｓ and determining a measurement of gas pressure within the enclosure based on the measurement of the thermal capacity of the enclosure and the power input applied to the sensor wire.

26. The sensor wire C Ｓ 26. The method of claim 25, wherein determining the heat capacity of is based on a rate of cooling of the sensor wire temperature Ts over the given period of time.

27. 26. The method of claim 25, wherein determining the measurement of gas pressure occurs during an increase in the gas pressure within the enclosure.

28. A thermal conductivity gauge comprising: an envelope surrounding the gas volume; a sensor wire positioned within the gas volume; a controller; The controller applying a power input to the sensor wire of the thermal conductivity gauge when an enclosure containing the sensor wire and the envelope exhibits substantially zero pressure; During the application of the power input to heat the sensor wire, the total power dissipation W Ｔ , sensor wire temperature T ｓ , and the envelope temperature T ｅ Measure the sensor wire temperature T over a given period of time ｓ Based on the change in the sensor wire C Ｓ Determine the heat capacity of The sensor wire C Ｓ determining a measurement of gas pressure within the enclosure based on the measurement of the heat capacity of the enclosure and the power input applied to the sensor wire. A thermal conductivity gauge configured as follows:

29. The controller measures the sensor wire temperature T over the given time period. ｓ Based on the cooling rate of the sensor wire C Ｓ 30. The thermal conductivity gauge of claim 28, wherein the gauge determines the heat capacity of

30. 30. The thermal conductivity gauge of claim 28, wherein the controller determines the measurement of gas pressure during an increase in the gas pressure within the enclosure.

31. 1. A method of operating a thermal conductivity gauge comprising a sensor wire within a gas volume within an envelope, the method comprising: The zero offset of the thermal conductivity gauge is evacuating the envelope to substantially zero pressure; applying a power input to the sensor wire; During said application of said power input, the total power dissipation W Ｔ , sensor wire temperature T ｓ , and the envelope temperature T ｅ and measuring The terminal loss coefficient G and the radiation loss coefficient E are Ｔ , T ｓ , and T ｅ and determining the value as a function of and modeling by providing a model of power dissipation from the thermal conductivity gauge, the model incorporating the termination loss factor G and the radiation loss factor E; applying a power input to the sensor wire; During said application of said power input, the total power dissipation W Ｔ , sensor wire temperature T ｓ , and the envelope temperature T ｅ and measuring The measured W Ｔ , T ｓ , and T ｅ determining a gas pressure within the envelope based on the power dissipation model; A method comprising:

32. 32. The method of claim 31 , wherein the model of power dissipation further includes power loss due to conductive heat loss from a sensor wire termination junction, radiative loss from the sensor wire towards the gas envelope, and pressure-dependent conductive heat loss from the sensor wire through ambient gas.

33. 32. The method of claim 31 , wherein the termination loss factor G corresponds to heat loss in a termination post during application of the power input to the sensor wire, the termination post being coupled to the sensor wire.

34. 32. The method of claim 31 , wherein the radiation loss coefficient E corresponds to radiation loss by the sensor wire during application of the power input to the sensor wire.

35. determining a temperature compensation value that compensates for variations in at least one of a sensor wire temperature and an envelope temperature, the temperature compensation value being a function of at least one of the termination loss factor G and the radiation loss factor E; determining a measurement of gas pressure based on the temperature compensated value; 32. The method of claim 31 further comprising:

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