For Reference

NOT TO BE TAKEN FROM THIS ROOM

THE UNIVERSITY OF ALBERTA

A LINEAR TEMPERATURE CONTROLLER FOR DESORPTION SPECTRUM STUDIES

by

(c) OPAS CHUTATAPE

A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES AND RESEARCH IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

DEPARTMENT OF ELECTRICAL ENGINEERING

EDMONTON, ALBERTA SPRING, 1973

~

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ATRAIRIA 30 YTI2AIVIMU SHI

Ha TASsH ¥ . a ;

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THE UNIVERSITY OF ALBERTA FACULTY OF GRADUATE STUDIES AND RESEARCH

The undersigned certify that they have read, and recommend to the Faculty of Graduate Studies and Research, for acceptance, a thesis entitled A LINEAR TEMPERATURE CONTROLLER FOR DESORPTION SPECTRUM STUDIES submitted by OPAS CHUTATAPE, in partial fulfilment of the requirements for the degree of Master

of Science.

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iii

ABSTRACT

The processes governing the sierra of an energetic particle when it collides with and penetrates a solid surface are exceedingly complex. Parameters such as particle type, energy, target material and orientation can be well specified and yet it is still extremely difficult to accurately predict target behaviour under any given bombardment condition. Much, however, can be learned about bombardment processes by Studying the behaviour of the trapped particles as they re-evolve from the target material at elevated temperatures and a well-defined temp- erature-time profile can considerably facilitate evaluation of particle-

Solid interaction.

This thesis describes the design and construction of a control system for linearly varying the temperature of a solid target as a function of time. First, the characteristics of the heating process and of the System were investigated. Then the mathematical model of the process was derived and used to describe the system behaviour, leading to the design and construction of an electro-mechanical controller. The whole system was analysed by a frequency response method which indicated that compensation was necessary. The compensated system was finally tested and its

specifications were compared with those previously set.

The controller was tested by generating post-bombardment de- sorption spectra from a stainless steel target which had been previously

inactivated with both argon and helium ions. In comparing the activation

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energies for desorption from stainless steel with earlier work, discrepancies arise, particularly at the higher temperatures. Deficiencies in adequately controlling the target temperature in these earlier

Studies and different target configurations may account for these

differences.

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ACKNOWLEDGEMENTS The author wishes to thank his supervisors, Dr. R.P.W. Lawson and Dr. J.F. Vaneldik, for their teaching and guidance during the

course of this work and throughout the writing of this thesis.

The staff and students of the Electrical Engineering Depart- ment are to be praised for making the author's stay in the Department both enjoyable and stimulating. The author is particularly indebted to Dr. P. Bryce and Mr. R. Schmaus of the High Vacuum Laboratory for

many helpful discussions.

The financial support received from the Canadian International

Development Agency is gratefully acknowledged.

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CHAPTER

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2.5 faa Zed

vi

TABLE OF CONTENTS

INTRODUCTION Preliminary Remarks Mathematical Analysis Background

Objective and Scope of the Thesis

HEATING PROCEDURE AND DETERMINATION OF PROCESS TRANSFER FUNCTION Introduction

Heating Procedure and Background Information

Previous Work Reviewed

Thermal System Configurations

2.4.1 Ultra-high vacuum chamber

2.4.2 Filament and target arrangement Thermocouple Accuracy Considerations Final Thermocouple

Mathematical Modelling of the Heating Process

2.7.1 Energy balance equations and the

behaviour of the process

23

23

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S20

320

vii 2.7.2 Linearization and representation of the process

2.7.3 Approximation of the transfer

function of the process

CONSTRUCTION OF CONTROL SYSTEM

Introduction

Schematic Diagram of the Control System

Type of Controller

Circuit Details

3.4.1 Ramp function generator

3.4.2 Comparator

3.4.3 The proportional plus integral controller

3.4.4 Trigger and triac circuits

Form of the Transfer Function of Each

Block

3.5.1 Comparator

3.5.2 Controller

3.5.3 Trigger and triac circuits

Block Diagram Representation of the

Control System

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CHAPTER IV

CHAPTER

CHAPTER

VI

6.1 G.2 o.3 6.4

viii ANALYSIS AND DESIGN Introduction Determination of the Frequency Response 4.2.1 Experimental procedure 4.2.2 Results Adjustment of Controller Gains Phase Lead Compensation Network

Pole Shifting

RESULTS OF TEMPERATURE CONTROL Introduction

Step Response

Ramp Response

Accuracy and Errors in the Measurement

of Temperature

THE STUDY OF DESORPTION SPECTRA Introduction

Apparatus

Experimental Method

Results

6.4.1 Desorption spectra

6.4.2 The determination of activation

energies

101 101 101 103

mio

Tad tay Ly 119 149 119

127

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CHAPTER VII Fel ive

BIBLIOGRAPHY

ix

6.4.3 Comparison to previous results by

Burch®

CONCLUSIONS Summary

Suggestions for Further Work

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Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

Figure 2.8

Figure 2.9 Figure 2.10

Figure 2.1]

LIST OF FIGURES

Diode plate current as a function of filament current. |

Cross section of the UHV chamber showing the thermal system configurations. | Temperature-emf characteristic curve of type

R thermocouple.

Thermistor bridge circuit.

Block diagram of the heating process. Electrical analog network of the heating process.

Transient responses of the thermal system to step filament currents.

Plotted curves for the determination of poles of the system:

Curve I, plot of loalc(t)-c(~)|/|c(0)-c(~)|vs. t, Curve II, asymptote of curve I,

Curve III, average of rog( She - (142,207 099%) 4 VScat)

Plot of curves I, II, and III in linear scale. Electrical analog for cooling process of the target.

Cooling curve of the target.

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Log-Log plot between Veplts) and I,.

Curves between Vip (tg) and I.

Block diagram representing the thermal

system.

Schematic diagram of temperature control

system.

Simplified diagram of control system.

Ramp function generator.

Comparing bridge circuit.

Instrument set up for measuring and

attenuating thermocouple emf.

Input network of the recorder.

Simulation of the transfer function

“ie pe i

Low drift dc. amplifier of inverted gain Ky.

K

Low drift dc amplifier of non inverted gain Ko. Integrator.

Summing amplifier.

Trigger and triac circuits for controlling of filament current.

Turn on characteristics of SCR and triac.

Load voltage waveform.

Block diagram of the electrometer and recorder.

Page 47

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Figure 3.16 Block diagram of the control circuit. 76 Figure 3.17 Curve plotted between I, and Vee 78 Figure 3.18 Block diagram representing the trigger and

triac circuits. 79 Figure 3.19 Block diagram of the linearized system. 80 Figure 4.1 Instrument set up for frequency response test. 84 Figure 4.2 Bode diagram of the recorder and electrometer. 85 Figure 4.3 Bode diagram of trigger and triac circuits. 87 Figure 4.4 Block diagram of the control system with

calculated transfer functions. 89 Figure 4.5 Total response of elements from the trigger

circuit forward to the recorder. 90 Figure 4.6 Bode diagram of the open loop transfer function

for Ko=l (solid lines) and that of the compen-

sated system (dotted lines). 94 Figure 4.7 Insertion of compensation network. 97 Figure 4.8 Root locus of the system. 99 Figure 5.1 Step response of the compensated system. 102 Figure 5.2 Ramp function responses Of the compensated

System at various ramp speeds. 104-109 Figure 5.3 Ramp function response of the compensated

system adjusted at K=400, K,=150, T,=70. 110

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Error signal (V-) for a ramp input. Filament current (I,) for a ramp input. Bombarding electron current for a ramp input.

Thermistor bridge calibration curve. Differentiating circuit.

Helium desorption spectra for incident ion energies of 100 to 500 ev, at

14

constant dose 1x10 ions/cm, heating rate

6503-0/5eC, Helium desorption spectra for incident ion

energies of 600-800 ev, at constant dose

14

1x10 ions/cm“, heating rate 7.12°C/Sec.

Argon desorption spectra for incident ion

energies of 200, 500 ev, at constant

14

dose 1x10 ions/cmé and heating rate 5.25°C/Sec.

Argon desorption spectra for incident ion

energies of 800 ev, at constant dose

14 2

1x10" ions/cm” and heating rate 6.7°C/Sec.

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CHAPTER I INTRODUCTION 1.1 Preliminary Remarks

In the study of outgassing and surface properties of metals and semiconductors an inert gas ion such as helium at different doses and energies may be used to bombard the surface producing defects to its atomic lattice. The gas atom finally either becomes trapped within the metal Or escapes through the surface with reduced kinetic energy |. Post bombardment heating of the target” is a useful technique for studying the trapping mechanism and location of injected ions. Heating causes escape from the trapping configuration, migration to the surface and effusion from the target. The desorbed gas pressure measured in the

system when plotted with time is referred to as a "desorption spectrum".

Mathematical analysis of the desorption spectra is of a reasonably tractable nature, when the surface temperature is a specified

function of time. The information obtained from the analysis includes:*

a) the number of the various desorbing phases and the

population of the individual phases;

b) the activation energy of desorption of the various phases and

c) the order of the desorption reaction

Four temperature functions that were used to analyze the

desorption spectra are’

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4 T,fu(t-(n-1)at)} ]

Generally speaking, thermal inertia associated with the surface produces an exponential function of time [T=T,+1'(1-e-*/*)) rather than a step function temperature increase. Then analysis of the desorption

becomes complex and this temperature function is rarely used.

The linear and reciprocal temperature functions are the most widely used functions which will considerably simplify most of the analysis. The fourth temperature function is also of some importance and a temperature displacement schedule approximating to this function has been employed by

and Kelly’. It was also used to analyze the desorption

Burtt et al. from a continuum of heterogeneous sites of different desorption energies where the linear and reciprocal temperature/time function lead to a

quantitatively intractable evaluation’.

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1.2 Mathematical Analysis Background

P.A. Redhead® has given a detailed analysis of methods for determining the activation energy, rate constant and order of reaction from the desorption experiments using two heating schedules, i.e. a linear and a reciprocal time/temperature variation. In addition G. Carter’ describes fully the generality of the numerical technique for the analysis of continuous energy spectra and its application to various other investigations involving a variety of surface temperature/time schedules.

Some important results will be quoted here to show the advantages of a

linear temperature/time function.

The Maximum Desorption Rate

The rate of desorption from a unit surface area is

N(t) = - $2 =v, o” exp (- fr) (1.1)

desorption rate (molecules /cm-/sec)

where N = O = number of molecules desorbed (molecules/cm*) n = the order of the desorption reaction Va oe rate constant E = the activation energy of desorption (K cal/mole) R = gas constant (1.986x1079 K cal/mole °K)

T = absolute temperature (°K)

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: oD nortrb Bry cyte ; \Snfy bpAD070T De = | p » t c nt Ta4 a ; | TST if TO Vt BS 'SAHSE ivi ©¢ by | . : neyoar f F ve pout Ada) |\UMB Cul Wile s/c r ati op Jeet ainnindsn nebenls wwyey SB patvioyvnalr 2n0fr¢enyd : wy }o* wad id ha fils 0 U# P pets V ' i. d 2 = oF yen bayoun sa bi TW ivesod Ine7toORn! % eae cet on YCoCHT Sa i a t yh ut ¥ Wal bets i bt a 1 ; r une At sts narsatossd mum xe 1 onl 2 25 aur it b {ile fiw & TiO Mei Jive Sy 70 Sab of \ a i fi : +f ; i) ( V6 t r= ae = : ra } a +h J i? ; : . f path Mock wn [bis _ rare Pe ie bey | 042) ii 29) 279 | nt } STAY TOES 4 jue =. Ht L tg ; Fenk safuaatan) Khalsa tat i. agereme a saseen - = . MOVES UNOS ON) DSayOZSD SS yosioOn to 190 = a) i

nabyo 28

Angitenoo Ss5¥

n

(afom\!so 4) nofiqyozeb +o Virions sof isytios a4g = Ff

a\iao X © Op06@. I} dneserion, a6

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ni

4

For a linear change of sample temperature with time (T=T tbt) and assuming that E is independent of o, the above equation is solved to find the temperature (T,) at which the desorption rate is maximum.

Then :

E/RT = (v4/b) exp(-E/R tT) For n = 1 (1.2) = (20 v,/b) exp(-E/RT (1.3a) pe ie p? bOVneoss O.V = R= exp(-£/RT,) (1.3b)

where c= initial surface coverage

o,= coverage at T

p p

For a first order desorption process in which the desorption rate depends linearly upon o, i.e. there is no interaction between adsorbed molecules in the desorption process, the relation between E and Ty is very

13

nearly linear and, for 10 ~ > v4/o > 10° (oK7!), is given to + 1.5% by

Vv E/RT, = tn ba Bag oe GA (1.4)

taking the first order rate constant v, = 10!3 secu!,

Carter derives the temperature at the maximum rate as :

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alee 7

7 ; sah ol» ah a T mae vay 2t | byte gawrsad morysi at Sd ,. 2290010 Mors iWeoe ony fi eafuns at

Of vot .bas yond yeen

dae OF = rv Sng22m09 et67-V9b19 Jyevk? sda ohn

iminixam atid 4699 wieroamas ‘oflt-aay iygb 493159

5 In order to obtain the initial site population o,, equation A ed EE integrated to give

iF

. E ASG expl -v, {| exp{ - prt dt] (1.6) 0

This is eventually solved as :

o bE dEcombleeey 7 p Te

Thus the initial site population Oy can be deduced from the

maximum rate itself.

For the second order reaction the rate equation becomes : r E (1.8) dt ~~ ¥2o expt- pF} ;

The approximate expression for the maximum desorption rate is

given as

It can be seen that the complicated expressions are solved and approximated by simpler ones to obtain the required information when an appropriate temperature/time function is assumed. It is therefore

desirable to have a linear temperature/time relation for simplifying the

bevioe sis enofersrqxs batsorfquo2 5 ‘tedd 992 ad neo : pe OC ;

'

rane.*

1 ait Afstdo oF 2enc ysl qniz vd" betentxo1q gee ihe : as va i : re é 4

oy

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6

analysis of desorption spectra. Furthermore, the linear temperature/time relation will clearly distinguish different peaks on a desorption spectrum which will help determine the order of the reaction simply by visual

akamination >:

1.3 Objective and Scope of the Thesis

This thesis describes the design of a controller capable of heating a stainless steel sample at a linear rate from room temperature (25°C) to the sample melting point with due regard to simplicity and

economy. The prime requirements are:

1) Linearity in the temperature range of interest from

25°C up to 1200°C. 2) Variable heating rate from 5°C/sec to 25°C/sec.

The required specifications of the controller may be separated

into two parts as follows: a) Transient response requirements

In general it is desirable that the transient response be sufficiently fast and be sufficiently damped. For a step response from

25°C up to approximately 1200°C the following quantities are required:

1) Rise time (t.): The time required for the response to rise

from 10 to 90% of its final value should be less than 5 sec.

2) Settling time (t.): The time required for the response to decrease to and stay within 2% of its final value should

be less than 15 sec.

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) sat to 2porteor+e73gge Bet Npst VF

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eon f HAS __e Tatil ta Ten een} ndbitcie -it ' i PMPWOTOT Sin wv Ousf VLSI Hmt XONNGH OF HH 7 oe : } amt ant +} wre 4.4 a , HS Trubs; Sm ay Sf} tf ri} omrs 92ih 7, >

t:%o YOO oF Of mov? -

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7

3) Maximum overshoot (M,): Maximum overshoot should be less than 5% of the input amplitude, i.e., less than 60°C which corresponds to a damping ratio of between 0.7 and

Oe b) Steady state response

The output ramp response of the system should exactly follow various input ramp speeds but with constant steady state error in temperature. Although no stringent limit on this error is required,

it should be kept small.

After designing of the controller, its stability and per- formance are investigated, and final specifications are determined. The final system is later compensated to obtain the required stable per- formance. Results are then presented in the form of linear temperature versus time curves. Some desorption spectra obtained by use of these linear temperature/time functions are shown to demonstrate the capability of the controller. The results are compared with those obtained

previously.

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5 5

3 9 =~ =a 2 w 7 “—— Lab w ~ - * + ca ‘v wv —* nw oe > —_

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CHAPTER II

HEATING PROCEDURE AND DETERMINATION OF PROCESS TRANSFER FUNCTION

2.1 Introduction

In this chapter a suitable heating method is chosen. There- after the "plant" is arranged according to this method and the actual transfer function of the thermal system is determined. The outline of

this chapter is as follows:

Section 2.2 describes the heating procedure together with

some background information.

Section 2.3 reviews the previous heating method and the

results obtained by Burch®

Section 2.4 describes the ultra high vacuum chamber and shows

the arrangement of the thermal plant components.

Section 2.5 considers thermocouple accuracy and choice of

thermocouple.

The actual thermocouple used is described in the concluding portion of section 2.6 and in the last section (2.7), the actual transfer

function of the thermal system is determined.

2.2 Heating Procedure and Background Information

An electron beam is selected as the heat source to heat the

<.