Vacuum/volume 34/number 8/9/pages 785 to 789/1984 0042-207X/8453.00+ .00 Printed in Great Britain Pergamon Press Ltd

A pressure gauge utilising the electron diffusion process and microcomputer control J Lucas a n d T Go to , Department of Electrical Engineering & Electronics, University of Liverpool P.O. Box 147, Liverpool L69 3BX, UK

received 1 November 1983; in final form I February 1984

A pressure gauge suitable for use with vacuum systems has been researched for the pressure region 10 -3 to 100 torr. The gauge functions by examining the diffusion process of electrons travelling across a uniform electric field. The measured parameters are the fraction of emitted current (I/Io) reaching the anode and its partition (I 1/1=) between a central disc and an outer annulus of the anode. These two measurements uniquely specify the gas pressure within an experimental error of i 5 % over the entire pressure range. A back illuminated thin film produces a stable electron current source having a long operating life. The gauge requires a calibration curve to be produced for each gas and results have been obtained for hydrogen, carbon monoxide and argon. The parameter I/I o shows less than a 20% variation between gases at a given pressure, whilst although the parameter I~/1= has a similar shape in all the gases, the variations are much larger at the same pressure. The use of a microcomputer system, together with a look up table for each gas, has enabled the gauge output to be directly converted into a pressure reading and displayed. A special feature of the gauge is the fast response time ( < 100 ps) to pressure transients.

1. Introduction

The gauges ~ listed in Table 1 may be used for measuring gas pressures in vacuum systems for the pressure range 10 -12 to 760 torr. For low pressures the ionization or Knudsen gauge may be used. The ionization gauge requires calibrating for each gas whilst the Knudsen gauge indicates closely the absolute pressure of both gases and condensable vapours. For the mid-pressure range the Pirani gauge is suitable. This gauge requires calibration but is very useful when readings of pressure fluctuations are required. For the high pressure range the diaphragm gauge is used, and this is an absolute gauge. The bending of the diaphragm may be measured by a bridge circuit to give a voltage output proportional to gas pressure. A very successful commercial version of this gauge is the Baratron 2. Alternatively the dia- phragm may be operated in a null deflection mode by cancelling out the gas pressure with an equivalent pressure on the opposite side of the diaphragm. This technique allows the accurate and absolute reading McLeod gauge to be used to measure the gas pressure but without the contamination effects of the mercury.

Table I. Suitable pressure gauges

Type of gauge Pressure range (torr) Comment

Ionization down to 10- 12--*available up to ~ 1 Calibrated Knudsen 10- %-* 10- 3 Absolute Pirani ~ 10-3--*up to 100 or even higher Calibrated Diaphragm 10-2--,760 and higher Absolute

The object of this paper is to describe a gauge suitable for operation under clean conditions over the pressure range 10- 3 to 100 torr. It has to be calibrated for each gas but once calibrated, the use of a microprocessor allows a direct reading of the gas pressure to be displayed. The time response of the gauge is extremely fast being less than 100 ps.

2. Principle of operation

Electrons whilst travelling in the direction of a uniform electric field will diffuse radially. If the electrons are emitted from a point source at the centre of the cathode then these electrons when

arriving at the anode will have a mean radial displacement (r2j from the centre of the anode. This is illustrated in Figure 1.

I

The magnitude 3 of r 2 is represented by

r--i= 4 D, d 2 V (1)

where D,= radial diffusion coefficient, = mobility,

d =distance between electrodes and

V = voltage.

The parameter D,/p has been extensively measured in gases and has been shown 4 to be solely a function of E/p( = V/pd), where p is the gas pressure reduced to 0:C temperature. The values 3 for H 2, CO, Ar and He are given in Figure 2. These curves illustrate the nature of D,/p in common gases. For low E/p, the values are highest in the inert gases whilst at high E/p all gases have similar

785

J Lucas and T Goto: A pressure gauge util izing the electron diffusion process

I I ,

+ I %';)" I Anode I, + 12

- I I I C a t h o d e

/ Point electron source

Figure I. Illustrations of operating principle of the gauge.

lO Ar

,

0 O5

O O2

F I I I ~ ! t I t I o01

O I O2 0 5 I Z 5 IO 20 50 I00 200 5 0 0

E / p ( V c m ' t o r r - ' a t O ° C )

Figure 2. The relation be[ween D/y and E,'p (defined in equation (1)1

values. If E and d are kept constant then (1) shows that r 2 is a

function of D,/p i.e. E/p. Since E is constant then r 2 increases as p

decreases. Hence a measurement of r 2 may be used as an indication of the gas pressure. A simple way to experimentally

realize r 2 is to measure 11/I 2, the ratio of electron current to the inner and outer sections of the anode, as shown in Figure 1.

The magnitude 5 of the anode current (I) is given by

4v I = I ° C + 4v

where r = electron drift velocity,

c = root mean square speed of the electrons, x c/c/c ~ , where c is the random speed of the electrons

and I o = current emitted under same electrical conditions but in I )a¢ l~O.

The values of v and C are specified for the electrons in the vicinity of the cathode surface, where the electron energy is determined by the emission energy of the electrons from the cathode surface. For this condition 5

2 v = ~

where

and

6) ~pp Lo

e = electron charge, m = electron mass, L 0 = m e a n free path for collisions at pressure of I torr at O°C

c = electron random speed.

electron drift velocity is again solely a function of E/p for The each gas so that

I 3 m C

- - ~ = l + 8 e L o ( c ) E ( p [2)

Equation (2) shows that 1 is a function of gas pressure, decreasing as the gas pressure increases. This measurement will also provide an indication of the gas pressure when calibrated for each gas.

Although unique curves are obtained for measurements of r z and I/I o as a function ofp at fixed E and temperature for each gas, there is no universal curve for all gases. Hence a calibration curve is necessary. A few years ago, this would have been a serious restriction but, because of the microcomputer, it is possible to store a look up table in the memory so that a radial diffusion measurement may be instantaneously produced as a pressure measurement on a digital display. The limitation of the gauge is that it is mainly useful for pure gases or known gas mixtures (e.g. laser gases). However it can be easily calibrated if a mixture is commonly used.

One attractive feature is the fast response because it oper- ates with electron beams. The response time is r=d/r, where v is the electron drift velocily. Even at a low E/p value (~0.1 V c m - I t o r r - l ) where the electron drift velocity is the slowest 5, the response time of the gauge is z ~- 10-Ss for most gases. Even allowing for electronic circuit delays an overall response time of 100 ps is easily achievable 6.

3. Construction

A schematic diagram of the gauge is shown in Figure 3. This particular experimental model has been mounted on a 3 in. uhv flange. The assembly consists of an anode, a cathode and a guard ring. The electrode separation (d) is 1.25 cm and the electrode diameter is 4.45 cm. The guard ring is cylindrical in shape having an id of 4.45 cm and a height of 0.62 cm. The mounting bases for the electrodes form part of the guard ring structure such that equipotential planes exist at n - 0 , kd, ½d, :~d and d, and produce a reasonably uniform electric field between the electrodes. Computer simulation v has shown that for all values of r < 2.1 cm the field distortion was less than 0.1 o]. All parts have been made from non-magnetic stainless steel and the whole structure mounted from the base plate on stainless steel screwed rod and electrically insulated by glass spacers. The anode is electrically connected to earth potential.

3.1. Anode. The anode consisted of a base plate (which forms part of the guard ring structure), an outer electrode and an inner electrode. The electrodes were insulated from the base by

786

J Lucas and T Goto: A pressure gauge utilizing the electron diffusion process

Faraday cage

t 11 114

Quartz d isc~ )~ "1 ~ ~ I ~;:~ --Cathode 1!

I L I ~ - l l + h" fire

I' ~ II--Gtass/metaL seat

Figure 3. Schematic diagram of pressure gauge.

LpStobiUzed ower suppty I

R~

rn r~ RA

f node (virtual earth)

' ~// 'Io-I 1 I~ I Cathode

+ o V z

Figure 4. The electron current measuring gauge.

precision ground glass spacers and formed a flat surface with a 0.1 mm gap separating them. The outer electrode had an od of 4.45 cm, whilst the inner electrode has a Faraday cage type structure. The entrance to the cage was selected to be either 1.25 cm od or 0.625 cm od. Fine strands of tungsten wire (0.2 mm od and 0.4 mm spacing) were welded across the entrance in the anode plane to give a uniform field condition across the full anode surface. The whole anode was coated with carbon black to reduce electron reflections.

3.2. Guard ring. A single guard ring was used having the same id as the od of the anode surface. The guard ring height was 0.62 cm and combined with two 'half sections' on the anode and cathode base plates to give a gap separation of 1.25 cm. This structure was convenient for experimenting with longer electrode gaps as additional guard rings could readily be introduced.

3.3. Cathode. The cathode is also shown in Figure 3. It has been designed to form part of the guard ring structure. The cathode has a central 3 mm dia hole and the central region is machined to fit a 3 cm dia quartz disc of 2 mm thickness. The quartz disc has a push-in fit to maintain a flat cathode surface. A fine layer of silver dag seals in the edge of the glass and metal. The entire cathode is coated with a Pd film. The thickness over a central 3 mm dia of the disc is 100 A thick and elsewhere is 1000 A thick. The election source is obtained by the back illumination of the central region of the quartz disc with uv light. A cylindrical screen attached to the back of the cathode prevented stray uv light from reaching the other electrodes and producing stray electron currents. The source ofuv light was a pen ray lamp s and was placed close to the cathode by using a glass/metal seal and quartz flat mounted centrally into the 3 in. dia uhv flange.

4. Experimental arrangement

A stainless steel vacuum chamber was constructed. It was evacuated with a 2 in. oil diffusion pump (with a rotary backing pump), isolated from the chamber by a liquid nitrogen cold trap and attained a background pressure less than 1 x 10 -6 torr. The system was operated either sealed for pressures above 0.1 torr or with a continuously flowing gas at pressures below 0.1 torr. The gas pressure was measured on three gauges, namely, a Baratron gauge (10- ] to 100 torr), a McLeod gauge (10- 3 to 1 tort) and an

ionization gauge (10-6 to 10- a torr). Gases of commercial purity were used.

The electron current measuring arrangement is shown in Figure 4. The anode currents lj and 12 were measured using stabilized electrometer amplifiers 9. These devices produce output voltages which are proportional to the input current, such that

V 1 = RARB 11 R1

and

V 2 = R.ARB I2 . R2

The values of R A and R B were 101° Q and l04 f2 respectively whilst R~ and R 2 were known fractions ofR s (1.0, 0.3, 0.1, 0.03 or 0.01 ) to allow accurate measurements of the ratio 11/I 2 over a wide range, i.e. from (100:1 to 1 : 100). The anodes were maintained at earth potential throughout the experiment and the currents Ij and 12 measured. The total emission current 1 o was set at a known reference level (nominal value , , -2 .10-1°A) in vacuum by adjusting the position of the lamp behind the thin film.

5. Experimental results

Experimental results have been obtained for both 1~/12 and l = I~ +12 as a function of pressure (normalized to 0=C)in three gases--hydrogen, argon and carbon monoxide, These gases represent the molecular, atomic and electron attaching gases used in gaseous electronics research. The results are shown in Figures 5, 6 and 7 for hydrogen, argon and carbon monoxide respectively. The curves for l i / l 2 initially show a decrease to a minimum and then a rapid rise as p increases, whilst l ( = 11 + I21 simply decreases as p increases. The shapes of 11/I 2 are similar in hydrogen and carbon monoxide because of their similar D,/la values at low E/p, whilst the minimum value in argon exists at a larger pressure because of the higher D,/la values at low E/p (see Figure 2). The rapid rise will occur at higher pressure values where D,/~ approaches thermal energy values common to all gases. The curves for I show a similarity in all three gases falling to a value of I / l o =0.18--0.14 at a pressure of 10 torr and Ill o =0.08-*0.06 at a pressure of 100 tort. In order to obtain smaller ratios for I , / l 2 at high gas pressures a smaller central collecting anode is required. A

787

J Lucas and T Goto: A pressure gauge uti l iz ing the electron diffusion process

• First rneosurement ~'I_Z x Second meosurement / I z

I - - r = 1 . 2 5 cm /o J - - - r -0625 cm /~

o ~--'--'a~-----~_~ II,+ I~l ~6 .... ...~ / ~ -

/ " % ,,,'"

1 -. . ~ . . . . I . .% o i I . I ,my-~- I I

I0-3 10 -2 tO -n I

Torr

Figure 5. Response of gauge to hydrogen.

' %

K

+ o.,

001 I0 10 2

, , , / 8

/ .

Ot

I 10 -3 L0 -2 I0 -I t 10

% x

r~ H

Torr

Figure 6. Response of gauge to argon ( H terms are defined in Section 6).

I / ! i /

f I0 ~1 ~[

° _o_°_,.,_-,-°-°4-.<::1--.-.- - I

i 1 I I Ioo~ 0 110_3 10_2 IO-'

Torr

Figure 7. Response of gauge to CO.

I IO 10 2

reduction of the radius from 1.25 to 0.625 cm produces the results also shown in Figure 5 for hydrogen. The results have clearly shown that the gas pressure in the range 10-2 to 100 torr can be accurately measured from values of the anode currents I~ and I~ for a suitable choice of size of the central collecting anode, provided I o is initially set at a constant value. The rate ofchange of 1~/I 2 and I with pressure are such that between them they unambiguously indicate the pressure. At high pressures an accuracy of 1% is easily attainable whilst even at low pressures an error of no more than 5% is obtained. The currents 11 and 12 were stable over long periods of time. It was customary to set I o each

day, although it only showed a slow variation. The thin film only required renewal after about 1 yr of operation.

6. The microcomputer system

In order to make this pressure gauge more attractive to the user it has been operated with a BBC microcomputer system 11. The electrical arrangement is shown in Figure 8. The voltages are fed into the microcomputer by using the analogue to digital converters available on the microcomputer. The two gauge voltages V z and V~ are directly connected to separate channels, A digital port output is used to operate reed relay switches in order to select the amplifier resistances R 1 and R 2 (see Figure4) necessary to generate input voltages in the range 0.3-1 V. This maintains high accuracy in these measurements. A third voltage input (V3) is provided by a platinum resistance thermometer in order to record accurately the temperature. The computer program is entered via the keyboard and stored on the floppy disc. Operating instructions are also given via the keyboard, and the results are listed on the visual display unit (vdu). The program is written in the Basic language. The calibration curves shown in Figures 5 to 7 are stored on floppy disc and are used to convert the input voltage readings (V 1 and V2)into a pressure measurement. The Lagrange second order interpolation polynominaP ° using three consecutive calibration points was suitable for this analysis. The pressures pl and P2 were evaluated from the measurements of I~/I 2 and I and the weighted average (p) produced such that

p= (wlpl + w2p2)/(wl + w2)

with

,5 log(I1/I2) ,5 log(/) . wl = ~ p p, and w 2 = Ap !p,

Values for w/w~ + w 2 are shown in Figure 6. The visual display unit (vdu) allows all the input and computed parameters to be displayed, especially gas type, temperature and pressure.

7. Summary

An electron beam gauge has been demonstrated for (+5°0) reading the gas pressure over a wide range (10-2 to 100 torr). Ifa higher pressure range is required the device can be designed to either have a longer electrode separation or a smaller central collecting disc in the anode. The device has a fast time response

PlOt ~num resistance thermometer

V3

AmpLif ier

L_

V2-- Ampl i f ie r I--

R2 I Rt v

ADC ADC ADC ADC D~gita/ por t

BBC m~crocompu ter I "t"--'~

L T

2,

Z 2

SeLect

VDU ] Keyboard

Figure 8, Circuit for microcomputer operalion.

788

J Lucas and T Goto. A pressure gauge utilizing the electron diffusion process

being much less than 100/~sec. The output currents are stable and the thin film electron source only requires replacing after operating for a period of 1 yr.

The main disadvantage of the device is that it requires calibration. One of the two parameters of the pressure (i.e. using I) is not too sensitive to the gas type and shows a similar variation between gases as is found in the ionization or Pirani gauges. The other mode of pressure evaluation (11/I2) although having a similar variation with gas pressure is totally dependent on knowing the gas type.

The construction of the gauge is simple and it can be manu- factured at low cost. However in order to provide automatic operation it is necessary to use a microprocessor based system. The BBC microcomputer system used is very convenient and such systems are now readily available in most laboratories. A custom microcomputer board without the keyboard, vdu and floppy disc could be used at a greatly reduced cost.

References

1 G F Weston, Vacuum, 29, 277 (1979); Vacuum, 30, 49 (1980). 2 Baratron Type 170M-7A, MKS Instruments Inc, Burlington, Mass, USA. 3 L S Lakshmindrasimha and J Lucas, J Phys D, 10, 313 (1977). '~ J RActon and J D Swift, Cold Cathode Discharge Tubes, Heywood, London, 1963, p 80, p 21. s j Limbcek and J Lucas, Solid St Electron Decice, 2, 161 (1978). 6 j Lucas and N C Kucukarpaci, J Phys D, 12, 703 (1979).

R W Crompton, M T Elford and J Gascoiyne, Aust J Phys, 18, 409 (1965). s Pen ray lamp, Ultra Violet Products lnc, San Gabriel, California, USA. 9 j H Leck and W E Austin, Electronic Engrg], 32, 106 (1960). =o D G Moursund and C S Duris, Elementary Theory and Application oJ Numerical Analysis, McGraw-Hill Company, New York (1967L =J BBC Microcomputer (Model B) System, c/o Vector Marketing, Dennington Estate, Wellingborough, Northants NN8 2RL.

Acknowledgements

The authors wish to thank Professor J H Leek for his invaluable discussions of the overall problem.

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