Chapter 4
4— 1 Introduction
Ae mentioned in Chapter 1, it was proposed to investigate the effects of the deposition parameters on the electrical properties of R F sputtered silicon dioxide films at 10GHz. Factorially designed experiments not only enable the effects of the parameters to be deter
mined but also indicate the extent, if any, of interactions that may occur between the parameters. The purpose of this chapter is to give a brief description of the technique, but more detailed information may be found in references (41»42,43,44) . a copy of an internal report written b y the author on the subject is given in Appendix
4-2 Terminology
In order to simplify explanation of the technique, some terms in common use in factorial design will be defined.
1) Factor«- This denotes any parameter of an experiment that may be varied.
2 ) Level of a Factor»- The level of a factor is the value of a parameter used in a particular experiment.
3) Treatment«- The set of levels of all factors used for a given trial is called the treatment or treatment combination.
4) Response»- The numerical result of a trial is termed the response.
5) Effect of a Factor«- The effect of a factor is the change in response produced by changing the level of the faotor.
6) Mnin Kffect (Moan Difforenco) ond Interactional- Tho main
effect (mean difference) is defined as tho effect of a factor averaged over all levels of the other factors. If the effect of one factor is different over the different levels of another, then the two factors are said to interact.
4-3 Contrast Between Classical Method and Factorial Design Method
In a two-factor experiment, the classical approach to determine the effects of the factors is to vary each parameter separately until the conditions yielding the "best" result are obtained. If the two factors interact, then this best result will not be the optimum. Factorial design overcomes this by considering the combinations of all levels of all factors. The simplified design is one in which each factor is allocated two levels. Assessment of the response of all treatment combinations in a two-factor two level experiment there-
p
for requires 2 - 4 trials to be performed. The main effect of each factor is the average of the calculated effects at the different levels of the other, and will be zero if no interaction exists. Be cause of experimental error, even if these effects do not exist, it is still likely that some numerical value will be obtained. For this reason it is necessary to apply statistical analysis to the results in order to determine the significance of the effects.
4-4 Statistical Analysis of the Results
To obtain tho significance of a result, the calculated effect must be compared with the experimental error. An estimate of tho error may be found by duplicating each trial. For each treatmont,
the variance of the mean response con be calculated. Although the means of each response will be different, the vorianco will only differ because of sampling fluctuations. Thus, all samples of all moans are assumed to have the same vorianco. It is therefore possible to use the variance of all treatments to give a reliable estimate of the variance of a single result. The error in calcul ating the main effects and interactions may then be obtained. It is shown in Appendix 2 that the error of all effects and interactions are the same for a fully replicated design. For this reason it is termed the standard error and is given by
standard error «
where s » standard deviation of a single result n2 ■ number of treatments i». ecu.A m e a n
As the main effect is the difference of two moans, the t-test may be applied to determine the probability that the two means are
merely samples drown from the same population, a low value indicating a highly significant effect. Another statistical test which may be used is the F-teot. Both methods are discussed in Appendix 2. If some previous knowledge of the effects does exist and it is known that some of the interactions are not present, then these interactions may themselves be used to estimate the experimental error. This is particularly useful for large designs where higher order interactions can be assumed not to exist.
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4— 5 Comments
Informetion gained from factorial experiments can also bo usod to optimize processes. The approoch is ono of determining the "path of steepest ascent". Time has not allowed optimization of the process investigated and the reader should consult references 41 and 42 for further information. For large designs, the calcul
ations become laborious. A computor programme (see Appendix 2) has b e e n written to perform the analysis of two level designs. The
programme can handle up to four faotor experiments, single or duplicated, and the analysis is performed b y the F-test.
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Chapter 5
INITIA L MEASURESNTS OF THE PROPERTIES OF RF SPUTTERKI) SILICON DIOXIilK
5-1 Introduction
Before commencing the factorially designed experiments, it was thought advisable to perform some low frequency measurements on silicon dioxide in order to compare the quality of the films obtained with those described by other workers. It was during this work that the use of silicone vacuum grease, mentioned in Chapter 3, was found to be particularly benefi ;ial.
Unknown to the author at this stage of the work, there were two faults on the sputtering system. These were faulty earthing of the vacuum chamber top plate upon which the oscillator stood and incorrect operation of the Penning gauge used for measuring the sputtering pressure. The evidence for, and correction of, these faults is out lined in Appendix 1. The results given in this chapter are for films deposited at 10 Torr as indicated by the Penning gauge. It is
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