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"PLASTIC DEFORMATION OF GALLIUM ARSENIDEbyIKECHUKWU UDEVI-ARUEVORUM.Sc (Physics), University of NigeriaNsukka, 1983B.Sc (Physics), University of NigeriaNsukka, 1980A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FORTHE DEGREE OF MASTER OF SCIENCEinFACULTY OF GRADUATE STUDIESDepartment of Metals and Materials EngineeringWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAOctober 1991\u00A9 Ikechukwu Udevi-AruevoruIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature) Department of /A= 7-409--L r a /V7/77-6- /e/eiltr E- ifvf 9//VE 6The University of British ColumbiaVancouver, CanadaDate  C 57/77 i)/DE-6 (2/88)11AbstractThe present investigation was undertaken to determine the validity of Haasen's model ofplastic deformation for GaAs over an extended range of temperatures and to observe the relationbetween the dislocation density in the deformed samples and the deformation variables. Theexperimental results show a discrepancy with the predictions of the model. This discrepancy andalso the different values of the activation parameters reported in the literature was explained interms of the contributions of temperature induced effects to the plastic strain rate .The dislocation densities in the deformed samples obtained by counting dislocation etch pitsindicate that the density of dislocations in deformed GaAs is directly related to the applied stress,the plastic strain rate, the test temperature while being inversely related to the applied strain rate.Table of ContentsAbstract ^ iiTable of Contents ^ iiiList of Tables viList of Figures ^ viiAcknowledgements ix1. Introduction ^ 11.1 Crystal Structure and Dislocations in GaAs ^ 11.2 Stress - Strain Curves of f.c.c. Metals 41.3 Dislocations and Macroscopic Deformation Variables ^ 82 Literature Review ^ 92.1 Experimental Study 92.2 Theoretical Studies ^ 102.2.1 The CRSS Model 102.2.2 Haasen's Model ^ 112.3 The Yield Point 142.3.1 Dynamical Recovery ^ 152.4 Application of Haasen's Model ^ 16iii3 Objectives ^ 204 Experimental Procedure ^ 214.1 Determination of The Specimen Orientation ^ 214.2 Specimen Preparation and Testing ^ 234.2.1 Compression Tests Specimens 234.2.2 Compression Testing Apparatus ^ 234.2.3 Compression Testing Procedure 254.3 Tensile Tests ^ 264.3.1 Preparation of The Tensile Tests Specimens ^ 264.3.2 Tensile Testing Apparatus ^ 274.3.3 Tensile Testing Procedure 274.4 Dislocation Etch Pit Density ^ 304.4.1 Chemical Polishing ^ 304.4.2 Etching of The Specimens 315 Observations ^ 325.1 Compression Tests Results ^ 325.1.1 Stress - Strain Curves 325.1.2 Temperature and Strain Rate Dependence of m and U ^ 44ivV5.1.3 Dislocation Density - Compression Tests. ^  545.2^Tensile Tests ^  595.2.1 Tensile Stress - Tensile Strain Curves ^  595.2.2 The Temperature Dependence of The Yield Stress ^  595.2.3 Dislocation Density - Tensile Tests. ^  646^Discussion ^  706.1^Yield Drop  716.2^Temperature and Strain Rate Dependence of m and U ^  736.3^Stress - Strain Curves ^  786.3.1 Compression Tests  786.3.2 Tension Tests ^  806.3.3 The Relation Between The Dislocation Density and Macroscopic DeformationVariables ^  827^Conclusions  848^Suggestions for Further Work ^  85References ^  87List of Tables5.1^Temperature, Yield and Recovery stresses for Series A Compression Samples. ^ 405.2(a) Temperature vs Yield Stress for Series B Compression Samples. ^ 415.2(b) Temperature vs Recovery Stress for Series B Compression Samples. ^ 425.3^Comparison of Sample Elongations for Series B Samples. ^ 435.4(a) Temperature Dependence of (2+m) Values From Present Study  525.4(b) (2+m) and u Values Reported in The Literature. ^  525.5(a) Temperature vs n values obtained from present study ^  535.5(b) Strain Rate Dependence of esD values ^  535.6^Dislocation Etch Pit Densities From Series B Compression Samples. ^ 555.7^Temperature vs Yield Stress for Tensile Tests Samples. ^ 635.8^Dislocation Etch Pit Densities From Tensile Tests Samples  655.9^Comparison of Present Results With Results Reported in The Literature(Compression Tests). ^  79viList of Figures1.1 a 60\u00B0 Dislocations in The Shuffle Plane. ^ 21.2 a 60\u00B0 Dislocations in The Glide Plane. 31.3 Shear Stress - Shear Strain Curves for Pb Single Crystals. ^ 51.4(a) Temperature Dependence of The CRSS of Pb Single Crystals 61.4(b) Flow Stress Ratio vs Temperature for Pb Single Crystals. ^ 62.1 Comparison of Weiss's and Schroter's Results. ^ 184.1 X-Ray Diffraction Pattern From Specimen Orientation Tests. ^ 224.2 Compression Jig and The Tube Furnace. ^ 244.3 Tensile Sample and The Tensile Jig. 295.1 Stress - Strain Curves From Compression Tests. ^ 355.2 Resolved Shear Stress - Shear Strain Curves From Compression Tests. ^ 365.3 Recovery stress from Resolved Shear Stress - Shear Strain Curves ^ 375.4 Comparison of The Yield Stress for The Two Compression Tests Samples. ^ 385.5 Yield Stress vs Temperature for Series B Samples. ^ 395.6 In of Yield Stress vs In of Strain Rate. ^ 485.7 In of Yield Stress vs 1/Temperature. 495.8 In of Recovery Stress vs 1/Temperature. ^ 50vii5.9 In of Recovery Stress vs 1/Temperature. ^ 515.10 Dislocation Etch Pits in an as Received Compression Sample ^ 565.11 Dislocation Etch Pits in a Deformed Compression Sample 575.12 Dislocation Etch Pits in a Deformed Compression Sample ^ 585.13 Tensile Stress - Tensile Strain Curves. ^ 605.14 Plastic Strain at Fracture vs Temperature From Tensile Tests. ^ 615.15 Yield Stress vs Temperature From Tensile Tests ^ 625.16 Dislocation Etch Pits in an as Received Tensile Sample. ^ 665.17 Dislocation Etch Pits in a Deformed Tensile Sample 675.18 Dislocation Etch Pits in a Deformed Tensile Sample. ^ 685.19 Dislocation Etch Pits in a Deformed Tensile Sample. 69viiiixAcknowledgementsI am grateful to my supervisors, Dr Fred Weinberg and Dr I.V. Samarasekera for their support andencouragement in the course of this work, to Johnson Matthey electronics Co. Ltd for providingthe GaAs samples used in the experiments, to Bob Butters, H. Tump, Laurie Frederick and MaryMager for their assistance and patience and finally to my colleagues in particular, to Chris Parfenuik,G. Lockhart, A. Boateng, S. Kumar, Gang Liu and C. Muojekwu for their encouragement.11INTRODUCTIONGaAs is a direct band gap III - V compound semiconductor which has found extensiveapplication as substrates for electronic devices, FET transistors, lasers etc. The utility of GaAsdevices is however limited by1.A high grown - in dislocation density (usually about 104 to 105 dislocations/cm2).2. An inhomogenous distribution of these dislocations in the material.Dislocations have a direct effect on the electrical properties of devices because they alter the density,mobility and lifetime of electrical carriers and indirectly through their interaction with impuritiesand other crystalline defects. Thus dislocations in GaAs are of major importance in the technologyof semiconductor devices.1.1 Crystal Structure and Dislocations in GaAs.The Bravais lattice of GaAs is f.c.c. and the crystal structure consists of alternate f 111 )planes of positive and negative ions which leads to a polarity in the stacking of the (111} planes.The structure may also be considered as a layered structure, each layer consisting of two (111)planes connected by three covalent bonds per atom. In contrast to f.c.c. metals, GaAs is brittleat low temperatures due to it's covalent bonding and becomes increasingly plastic at temperaturesabove 0.4T. where T. is the congruent melting temperature. The crystal is grown using eitherthe Liquid Encapsulated Czochralski (LEC) technique or the Bridgeman method.The dislocations are generated by thermoelastic stresses accompanying growth. They may alsobe generated in the crystal during device fabrication and in devices operating at elevatedtemperatures.2The dislocations in GaAs can either be positive or negative (a or 13) 60' dislocations andscrew dislocations. Dislocations lying between the widely spaced ( 111) planes are called theshuffle set while those lying between the narrowly spaced (111) planes are called the glide set.Figs 1.1 and 1.2 show the a 60' dislocations in the shuffle and glide planes respectively.Fig. 1.1. An a 60' dislocation in the shuffle plane showing a row of dangling bonds,reference (1).3Fig 1.2 An a 60'dislocation in the glide plane, reference (1).The dislocations contain a dense array of unpaired dangling bonds along the edge of theextra half plane of atoms. These dangling bonds are unpaired electrons and are responsible formost of the electrical properties of dislocations. Dislocation motion may occur either betweentwo layers or between two (111 } planes constituting a layer. Dislocations moving between twolayers are referred to as the shuffle dislocations while those moving between ( 111 ) planes arecalled glide dislocations. The glide dislocation may dissociate into two Shockley partials inthe same manner as in f.c.c. metals. However a direct dissociation of a shuffle dislocation intopartials is difficult since this would produce dislocations with high fault energies. In addition,glide and shuffle dislocations differ in the directions of the broken bonds occuring in their cores.Dislocation climb in GaAs differs from that in f.c.c. metals. Because of it's double occupancy,a jog as an elementary source of point defects produce di- vacancies on non-conservativemovement. These double vacancies are less mobile than the single vacancies which is contraryto experience with f.c.c. structures.41.2 Stress - Strain Curves of f.c.c. Metals.Although the crystal structure and dislocation properties of diamond structure materialsdiffer from that of pure f.c.c. metals, the plastic properties of GaAs may be correlated with thecorresponding behaviour of f.c.c. metals. The observed similarities in the stress - strain curvesof f.c.c. and diamond structure metals and also the fact that the arrangement of dislocations asobserved by a TEM study of work - hardened Ge crystals are similar to those found atcorresponding points in the hardening curves of Cu, Au, and Ni - Co alloys suggests that it isthe geometry of the slip planes, the interaction between the slip systems and dislocation reactionsthat determine the dislocation structure and work - hardening during uniaxial deformation (2).The present investigation is concerned with the deformation of GaAs at hightemperatures. There is little information or theory in the literature related to the deformation ofionic crystals such as GaAs at high temperatures. Following the premise that the plasticdeformation of diamond structure semiconductors is essentially the same as that of f.c.c. metals,for which there is a large body of observations and theory, the observed plastic behaviour ofGaAs can be related to the behaviour of f.c.c. metal crystals.seI1I5Resolved shear strainFig. 1.3 The resolved shear stress - shear strain curves for lead single crystals, ref(3).The deformation of f.c.c. metals at high homologous temperatures is described in aninvestigation of lead single crystals (3,4). Typical resolved shear stress - shear strain curves forlead in the temperature range of 78 to 550\u00B0K (0.13 to 0.92 of the melting point temperaturerespectively) are shown in Fig. 1.3. The onset of plastic flow decreases appreciably withincreasing test temperature. The initial linear work hardening region is not clearly defined anddecreases in length with increasing temperature. The major part of the deformation curve at200\u00B0K and above, shows a progressively decreasing rate of work hardening, associated withrecovery. At the highest temperatures, the maximun stresses reached are very low with verylittle working hardening being evident. The decrease of the CRSS with temperature for easyglide orientations is shown in Fig. 1.4(a).Plastic deformation of lead single crystals as a function of temperature for easy glideand &lt;100&gt; orientations&gt;. (a) CRSS (4), (b) flow stress ratio (3).59 + 69 Pb(easy glide)6005000^100^200^300^400Temperature \u00B0K100^200^300^400^500Temperature \u00B0KFig. 1.4(b)6100908070Nft 6050U 403020100Fib. 1.4(a)critical resolved shear stress&lt;100&gt; annealed in situ59 Pb .4\u2018 \u00B059 Pb +0.05%Sn -59 Pb + 0.1%Snaaa cse7Above 300\u00B0K, it is shown that the CRSS of &lt;100&gt; oriented crystals is effectively thesame as easy glide. The flow stress ratio for lead crystals oriented for easy glide is shown inFig. 1.4(b). The flow stress drops with increasing temperature above 300\u00B0K. With &lt;100&gt;orientations, the flow stress above 300\u00B0K is a little lower for easy glide as shown in the figure.The theories of deformation of f.c.c. single crystals generally divides the deformationinto three stages. After elastic strain has occured, stage I of plastic deformation, called easyglide occurs. This is characterised by a very low rate of work hardening and is associated withthe occurence of single slip across the entire cross section of the sample. At high homologoustemperatures, stage I is generally not observed.Following stage I, deformation continues into stage II. In this stage, slip occurs on theprimary and secondary slip systems. This stage is one of strong strain hardening with a hardeningcoefficient that is about ten times that of stage I. The ratio of the work - hardening coefficientto the shear modulus of the material is essentially independent of temperature and the appliedstress and is weakly dependent on the specimen orientation. The ratio is insensitive to theimpurities present in the material and is of the same order of magnitude for all f.c.c. metals. Thelinearity of the stress - strain curve in stage II is explained by assuming that the formation ofCottrell- Lomer barriers continues throughout this stage which leads to a decrease in the slipdistance with increasing strain. The duration of stage II is temperature dependent. Thetemperature dependence arises because the yield stress in general increases with decreasingtemperature. Consequently the stress necessary for the activation of secondary slip systems alsoincreases as the temperature decreases. At low temperatures, most of the stress - strain curveis dominated by stage II while at high temperatures, it may not be fully developed before theonset of stage III.8Stage III starts when stage II deviates from linearity with increasing strain in the stress- strain curve. In stage III the work hardening coefficient decreases with increasing strain dueprimarily to dynamic recovery occuring during deformation. With increasing test temperatures,the transition strain between stage II and stage III decreases until stage II cannot be identifiedat the highest temperatures. The dynamic recovery in this stage is associated with the thermallyactivated rearrangement of the dislocations in the specimen during deformation. This couldinclude cross slip of screw dislocations and the collapse of Cottrell - Lomer dislocations. Theseprocesses reduce the internal stress fields and hence the work hardening coefficient. The stressfor the beginning of stage III decreases logarithmically with increasing temperature which canbe accounted for by the temperature dependence of the activation energy for cross slip whichvaries inversely with temperature (5).1.3 Dislocations and Macroscopic Deformation Variables.The deformation properties of materials having f.c.c. structures follow a regular pattern.Each material exhibits essentially the same characteristics and in the same order but only differsin the stress and temperature needed to cause the dislocation reactions which controls the givenbehaviour. The ultimate goal of a study of deformation behaviour is to correlate the dislocationdensity in the specimen with easily determined macroscopic deformation variables. For GaAs,the dislocation density is determined by chemically etching the sample to produce dislocationetch pits. On { 100 ) surfaces, the etch pits appear as elongated hexagonal shapes. The dislocationdensity in as grown LEC GaAs crystals is between 104 to 105 dislocations /cm2. The pits oftenare arrayed in clusters forming cell boundaries. The dislocation densities are higher at the centerand near the edge of a { 100 } wafer, and in &lt;110&gt; directions on the surface . The grown indislocations have been shown to be highly stable by Gallagher and Weinberg (6), with noapparent movement up to annealing temperatures of 900\u00B0C. They also showed a direct correlationbetween the etch pits and dislocations using cathodoluminesence imaging of the dislocations.92LITERATURE REVIEWDislocations in GaAs have a marked effect on the properties of GaAs devices. It has beenshown that n- type Ge can be made p- type by deforming the crystal plastically and the applicationof an external stress alone is sufficient to cause diode degradation (1). The decrease in light outputof GaAs lasers has been related to the kinetic properties of dislocations in the GaAs which areconsidered to be non - radiative recombination centers. Most of the dislocations in GaAs whichaffect its electrical and optical properties are produced during crystal growth. As a result a studyof the generation and multiplication of dislocations during crystal growth could lead to better controlof the density and distribution of the dislocations in GaAs used for devices. In this investigation,the generation and multiplication of dislocations have been examined both experimentally andtheoretically.2.1 Experimental Study.During crystal growth, thermal gradients in the crystal generates local thermoelasticstresses. When the stresses exceed the critical resolved shear stress (CRSS) of the material,dislocations are generated and propagate through the crystal. Attempts to reduce the dislocationdensity have followed two directions.1. The thermoelastic stresses can be reduced by reducing the thermal gradients in the crystal.This can be done by changing the thermal environment in the crystal grower by increasing theamount of encapsulant in the liquid or by using a different growth procedure such as VerticalBridgman growth.2. Increasing the CRSS of the material by solid solution hardening. It has been reported (7) thatadding In dopants to LEC grown GaAs crystals at concentrations up to 10 20/cm 3 significantlyreduced the dislocation density.10However, although the dislocation density is reduced, the interaction of dislocationswith the impurities leads to a range of complex effects in semiconductors devices. Directmeasurements of the temperature distributions in the melt and solid during solidification aredifficult to make due to the high temperatures involved and particularly the high pressures forGaAs growth. This makes a direct experimental correlation between dislocation density andthermal conditions during growth difficult.2.2 Theoretical Studies.Mathematical heat transfer models have been developed to determine the thermoelasticstresses in growing GaAs crystals. Dislocation models have been used to estimate the localdislocation density from the local stresses. Two dislocation models have been considered.2.2.1 The Critical Resolved Shear Stress Model.In the plastic deformation of f.c.c. single crystals, the onset of plastic flow is givenby the yield stress. For easy glide, with the stress resolved along the slip plane in the slipdirection , the onset of plastic flow is given by the critical resolved shear stress (CRSS). Thegeneration and multiplication of dislocations in single crystals occurs when the local stressexceeds the CRSS. The number of dislocations produced increases as the excess local stressincreases. For deformation of single crystals at higher temperatures and when more thanone slip system is operative, the region of easy glide (stage I) is not observed and the CRSSis thus not clearly defined in the stress strain curve . In addition, the high temperature stress- strain curves have a progressively decreasing slope which makes selection of the yieldstress approximate. The application of the CRSS criteria to diamond structure materials hasbeen questioned as well as the effect of temperature on the dislocation density (8). Thesefactors suggest that the CRSS criteria for dislocation generation and multiplication may notbe suitable for GaAs.112.2.2 Haasen's Model.Haasen's model of plastic deformation (2), often referred to as the dynamicdislocation model, is based on the fact that as a material is progressively deformed elastically,part of the strain is progressively relaxed by plastic deformation.The total strain in the material at any given time is given by the following equationet(t)=ep (t)+e,i(t)^ [1]Where et (t), c (t), and eel (t) are the total strain, plastic and elastic strains respectively.The plastic strain rate in the deforming body is given by the Orowan equationi i =Nbv^ [2]where N is the dislocation density, b the Burgers vector and v the average dislocationvelocity.Dislocation multiplication occurs in the specimen in proportion to the density ofmobile dislocations and the average distance travelled by these dislocations. Themultiplication process is defined bydN =8Nvdt^ [3]where 8 is a multiplication parameter assumed to depend on the effective stresssince the dislocation velocity depends on the effective stress. 8 is given by12S = Kden.^ [4]where the effective stress is by definition given by((TA \u2014 A /VI)^ [5]K is the multiplication constant, G A is the applied stress, AN 112 is the internal stressat the location of an individual dislocation and m is the stress exponent of the dislocationvelocity. In diamond structure materials, m is a small number, with values usually between1 and 3, and the dislocation velocity is strongly dependent on temperature and weaklydependent on stress (2). In contrast, in f.c.c. metals, m is a large number usually greater than16, the dislocation velocity is strongly dependent on stress and weakly dependent ontemperature (9).The equation for the dislocation velocity v, is expressed in terms of an Arrheniustype equation since the generation and propagation of dislocations is a thermally activatedprocess as well as being stress activated.v =B(T)(6A \u2014AN 1/2)m^ [6]whereB (T) = Bo exp(\u2014U IkT)^ [7]13B(T) is a temperature dependent viscous term describing the changes in the frictionalresistance of the lattice to the propagation of dislocations. B o is a constant for a givenmaterial, U is the activation energy for the generation of dislocations, k is the Boltzmann' sconstant and T is the test temperature. In contrast, the corresponding equation for thedislocation velocity for f.c.c.metals is given byCT jm,,.(_[8]Ge is the effective stress on the dislocation, to is related to the magnitude of the viscousdrag on the moving dislocations by the short range obstacles and m is the stress velocityexponent. In this model, to and m are considered material constants. In equations [6] and[8], the internal stress is assumed to fluctuate with a wavelength that is of the order of themean distance between the dislocations. However in equation [8], the assumption is furthermade that this separation is so large that thermal fluctuations do not assist the applied stressin overcoming the internal stress. This results in a temperature independent flow stress exceptfor the small indirect dependence through the temperature dependence of the elasticconstants.Using equations [1], [2], [3], [4] and [6], the macroscopic stress - strain - timerelationship for a deforming specimen is given by a solution of the following simultaneousequations.14dN^U^i)m+1^ [9]dt =NKBoexP(\u2014if (GA \u2014 AN-I m 1 dcTAde = ONbBo exp(--kT )(GA\u2014 AN2 4 U dt[10]Where 9 is a geometrical factor, and G is the rigidity modulus of the material. Theequations are solved subject to the initial conditions that at t = 0, e = 0 and N = N o (whereNo is the grown - in dislocation density).2.3 The Yield Point.The model allows the existence of two yield points for the deforming specimen. Theupper yield point is defined as the stress at which the initial dislocations present in the specimenbegin to move while the lower yield point corresponds to the stress at which the movingdislocations begin to interact with each other (beginning of work hardening). The model accountsfor a pronounced yield point in a constant strain rate test using equation [1] as follows. Initiallyalmost all the applied strain is elastic with few dislocations present moving at high speeds. Withfurther deformation the dislocations multiply and the plastic term increases while the elasticterm decreases, becomes zero and sometimes negative as the stress goes through the upper yieldpoint . Further dislocation multiplication leads to dislocation interactions which produces a risein stress resulting in a lower yield point (2).The temperature and strain rate dependence of the upper and lower yield points can bederived from equations [1], [9] and [10] with the assumption that AN 1' &lt;&lt; a A and is given by15(A 2Cm )2+m .--^( ^U ^)aY =^e\"exb Bo^p (2 + m)kTwhereCm=  (1 + \u2014212+1-1 2m^2[12]cry is the stress at the upper or lower yield point, A and Cm are constants. The modelallows the calculation of the macroscopic deformation variables in terms of the three physicalparameters B(T) , A and K using equations [9] and [10] while equation [11] is used for estimatingm and U.2.3.1 Dynamical Recovery.Haasen's model of plastic deformation has been extended to include the temperatureand strain rate dependences of the stress at the beginning of dynamic recovery (15). Usinga relation first proposed by Mohamed and Langdon (15), for the description of the steadystate creep of materials at high temperatures, the temperature and strain rate dependence ofthe stress at the beginning of dynamic recovery is given by'Ell; AkT (Gb )3 .^(QSD)G Gb 7 Eexp kT[13]16Here, n is the stress exponent, G is the shear modulus, b is the Burgers vector,yis the stacking fault energy while QSD is the activation energy of self diffusion. Equation[13] has been applied to the interpretation of the dynamical recovery of the elementaland compound semiconductors.2.4 Application of Haasen's Model.Haasen' s model has been used extensively to predict stress - strain curves , creep curvesand dislocation densities and to estimate values of m and U for the elemental semi- conductorsSi and Ge (10,11,12). Because of the close similarity between the crystal structure and electronicbonding of the elemental and compound semiconductors having the sphalerite structure, themodel has been successfully applied to GaAs, InSb, InP, and ZnS to estimate m and U. (13-24).However the use of equations [9] and [10] to predict the stress - strain curve and dislocationdensity for GaAs is limited because values of the parameters A, B(T) and K are not known.Themodel assumes that all the dislocations in the specimen undergoing deformation are mobile.This assumption limits the application of the model to small strains. Also the model assumesimplicitly that the dependence of the dislocation velocity on stress and temperature is separable.17The different values of U and m reported when the model was applied at differenttemperatures and strain rates to the same material were attributed to experimental errors and tothe different experimental techniques used in those studies (2,10,12). Weiss (25), whileinvestigating the inflection point of creep curves of germanium observed a temperaturedependent stress exponent m(T) and a stress dependent activation energy U(a). He modifiedHaasen's model to take this into account by replacing the stress exponent in equation [6] by atemperature dependent term given bym(T) [14]His results are shown in Fig. 2.1 as dashed lines in which the stress associated with theyield point determined from the modified model is plotted as a function of 7.1 . Schroter, Brion,and Siethoff (25), in their study of the temperature and strain rate dependence of the lower yieldpoint in silicon and germanium extended the temperature range investigated by Weiss. Theydeformed silicon and germanium in compression in the temperature range 900\u00B0C to 1300\u00B0C and450\u00B0C to 920\u00B0C respectively and strain rates 10 -2 /s to 10-5 /s. They report that for silicon, thestress exponent of the dislocation velocity (m), and the activation energy for the generation ofdislocations (U), are independent of temperature and applied stress respectively in agreementwith Haasen's model. However their results for germanium are in reasonable agreement withthe results of Weiss and are shown in Fig. 2.1 by the solid lines.20E1E 10210.S18900 600 700 \u2022 600^SOO9^10^11^12^13If% K' lFig 2.1 Yield stress vs temperature derived from inflection points in creep curves of germanium(dotted lines) at the strain rates indicated (25). The results of Schroter et al for the lower yieldpoint in germanium are indicated by the solid lines (25).The non linear dotted lines of Weiss differ by a small amount from the solid curves ofSchroter et al. There is no clear explanation for this difference and also the different resultobtained for silicon. Deformation studies on GaAs have been reported (13,15,16,18) which werecarried out in the temperature range of 350'C to 600T. The temperature and stress dependenceof m and U were not determined in these investigations.19The ability of Haasen's model to predict the dislocation density in a specimen undergoingplastic deformation is limited because separate experiments are required to estimate B(T), Aand K in the equation for dislocation density. The density of mobile dislocations in f.c.c. metalscan be estimated from a model of plastic deformation by Alden (9,26) which has been comparedto experimental data at low temperatures with considerable success. However dislocations inreal crystals have been shown to have a fine structure closely related to the crystal structure(27). For GaAs, there are two interpenetrating sublattices of Ga and As forming the f.c.c.structure which gives rise to two types of densely packed glide planes which are not equivalent.In addition, the covalent bonding of GaAs results in a high concentration of energy in thedislocation core and a pronounced Peierl's potential. On the basis of the significant differencesbetween GaAs and f.c.c. metals, it is unlikely that the Alden's model is applicable to GaAs.203OBJECTIVESThe objectives of this research was to extend the range of temperatures generally studied(usually less than 600\u00B0C) in the uniaxial plastic deformation of GaAs using compression and tensiontests and thus determine(a) The temperature and strain rate dependence of the yield stress.(b) The activation parameters characterizing the beginning of plastic deformation andobserve their temperature and strain rate dependence. With this data, the validity of Haasen's modelfor the deformation of GaAs will be tested over an extended range of temperature.(c) To obtain the dislocation densities in the deformed samples by etching the samples andcounting the etch pits. Using these results, the dislocation density will be correlated with themacroscopic deformation variables.214EXPERIMENTAL PROCEDUREThe gallium arsenide single crystals used in the investigation were provided by JohnsonMatthey Co Ltd. They consisted of two sets of seed crystals having square cross sections of 36.0mm 2(series A) and 17.64mm 2 (series B) respectively and wafers of GaAs crystals produced by the LECmethod.4.1 Determination of The Specimen Orientation.The specimen orientations were determined using the Laue back reflection technique.Samples cut from the tensile and compressive specimens were polished and attached to a verticalspecimen holder. X-rays were generated at a copper target using a Phillips X-ray machine. Thex-ray beam was passed through a 0 5mm diameter pinhole and impinged on the samplepositioned 3cm from a flat photographic film placed normal to the incident x-rays and betweenthe x-ray source and the sample. The exposure time was 20minutes at 30kV and lOrnA. Afiducial mark made on the film related it's orientation with respect to the sample. A typical x-raydiffraction pattern is shown in Fig. 4.1.The spots are observed to have four fold symmetry. The normals to the reflecting planeswere plotted on a stereographic projection using a stereographic net and a Greninger chart. Bycomparing the stereographic projection with a standard projection, the spots were identifiedand the orientation of the sample surface was established as ( 100 ).22Fig. 4.1 Typical x-ray diffraction pattern obtained in the specimen orientation tests.4.2 Specimen Preparation and Testing.4.2.1 Compression Tests Specimens.A paste of Valtron AD 1210 ingot mounting adhesive was formed by mixing theresin and hardener in the ratio 10 : 1 . Using the paste , the seed crystals were glued to agraphite board one at a time and allowed to dry for about 10 hours. The assembly of thesample on the graphite board was subsequently mounted horizontally on a diamond sawcutting machine. The cutting speed of the diamond blade was set at 2000rpm and thedimensions of the compression specimens were specified on the machine. By operating thecutting machine in the automatic mode, specimens having the set dimensions were cutthrough a vertical motion of the diamond saw head. After each cutting process, the machinecauses the horizontal base which supports the graphite board to move towards the diamondsaw head a horizontal distance equal to the set dimensions and the cutting process is repeated.The dimensions of specimens in series A were 6.0mm x 6.0mm x 10mm, and the dimensionsof series B were 4.2mm X 4.2mm x 15.9mm. The specimens were separated from the graphiteboard and the adhesive by heating in a solution of glacial acetic acid. The hot acid weakensthe adhesive thus releasing the specimen. The specimens were subsequently polished usinga solution of 5 vol % bromine in methanol.4.2.2 Compression Testing Apparatus.The apparatus used for the compresssion tests is shown in Fig. 4.2. It consists of astainless steel cage into which the test sample is placed as shown. The compression jig isattached to long steel rods which connects it to the load cell and cross head on an Instronmachine.23quartz cylinderto load cellasbestos liningspecimenresistance wireto cross head of lnstron24The furnace temperature was measured using a chromel -alumel thermocouple soldered tothe test jig beside the specimen.The specimen was heated using a resistance tube furnaceand the furnace temperature was recorded on a chart recorder. All tests were conducted inthe presence of a helium atmosphere.Fig 4.2 Section of the tube furnace enclosing the compression jig.254.2.3 Compression Testing Procedure.Before each test, the Instron machine was calibrated using a dead weight followedby the calibration of the chart recorder using a voltage generator. The specimen was thenplaced between the two faces of the compression jig lubricated with graphite, with thedeformation axis of the sample parallel to &lt;100&gt;. The furnace tube was lowered to enclosethe compression jig and the specimen. The furnace was turned on and set to the testtemperature and the helium gas flow rate set at 35cc/min. When the furnace temperaturereached steady state, the specimen was deformed at a constant cross head speed. Thetemperature range for the compression test extended from 400\u00B0C to 800\u00B0C while the crosshead speeds (CHS) were varied from 2.12 x 10 -3 cm/s to 8.5 x 10-5cm/s. For each test, thedeformation was stopped after a limited amount of plastic deformation occured. After thefurnace has cooled to room temperature, the specimen was removed from the test jig andetched in KOH to determine the dislocation density in the specimen. At the end of each test,the set point temperature was compared with the steady state furnace temperature recordedby the chart recorder.The difference between the two temperatures was not greater than \u00B13 degrees Celsius in all the experiments.264.3 Tensile Tests.4.3.1 Preparation of the Tensile Tests Specimens.The tensile tests samples were cut from 7.62cm diameter wafers with a thickness of0.8mm to the shape shown in Fig. 4.3(a). The samples were roughly shaped by sand blastingand finished by grinding the edges with a diamond saw. To do this, an aluminum platesample was made having the same shape as the tensile specimens. This was then used as atemplate to mark the shape onto a tape fastened to the GaAs wafer. The tape was cut witha razor blade and the residual tape around the test sample shape removed. This was done onboth sides of the GaAs wafer. A fine sand blasting jet cut through the wafer around the edgeof the tape fastened to the surface roughly outlining the test sample .The finishing process was carried out using two glass slides ground to have the samedimensions as the tensile specimen. The glass slides were heated on a hot plate and Lakesideresin was melted onto the surface of each glass slide. The sample was placed between theglass slides, forming a sandwich assembly which was cooled to room temperature. Theassembly was then mounted vertically on a grinding machine and by a horizontal motion ofthe assembly, the upper edge was progressively ground using a high speed diamondimpregnated grinding wheel. After each pass, the assembly was raised in small vertical stepsof 0.5mm and the process continued until a good surface finish was obtained. The processwas then repeated on the opposite edge of the sample. In this way, tensile specimensmeasuring 15mm x 4mm x 0.8mm were produced. After grinding the assembly was heatedon a hot plate and the specimen was separated from the glass slides after the wax melted.The wax residue on the specimen was removed using methyl alcohol and the specimenpolished in a 5% bromine / methanol solution , swabbing the surface gently during polishing.274.3.2 Tensile Testing Apparatus.The tensile samples were mounted in the molybednum tensile testing grips shownin Fig. 4.3(b). Tests were carried out in an Instron with the upper molybednum rod of thegrips attached to the load cell and the lower to the crosshead. The sample and the test gripswere contained in a quartz tube which was filled with helium during testing to reduceoxidation of the sample . The quartz tube was surrounded with a resistance heated tubefurnace powered through a temperature controller. Chromel/alumel thermocouples werewelded to the upper and lower grip assembly and were used to determine the test temperature.4.3.3 Tensile Testing Procedure.Initial tests showed that the tensile specimens tended to slip from the grips or deformslightly as they were loaded in the furnace and heated prior to testing. To overcome this, asmall titanium guide was attached to the grips to prevent lateral movement of one grip withrespect to the other. In addition the tensile samples were cemented to the flat grip surfacesusing a high temperature cement (ceramabond 571 powder mixed with the liquid). Thetensile axis of the samples were parallel to the &lt;100&gt; direction.The sample fastened to the grips was aligned in the Instron. The heating furnace wasthen lowered to surround the test assembly and turned on. Helium gas flow through theassembly tube was set at 35cc/min. When the furnace temperature reached steady state atthe test temperature (between 400 and 750\u00B0C), the sample was deformed in tension at aconstant cross head speed (CHS) which varied between 8.5 x 10-3 and 4.2 x 10-5 cm/sec. Allthe test samples were pulled to fracture, recording the load as a function of time. Examinationof the samples after each test showed that elongation and hence plastic deformation tookplace only in the gauge length, defined as the free specimen length between the upper andlower grips. After the test was completed and the test assembly cooled, the fractured sample28sections were fitted together at the fracture surfaces and the total strain in the gauge lengthmeasured. The measured strain was then compared to the strain during plastic deformationdetermined from the cross head movement. The sample sections were then polished andetched to determine the dislocation density in the deformed sample.U 29gauge length/(a)(b)Fig 4.3 (a). Shape of tensile sample, (b) Tensile jig to hold sample.304.4 Dislocation Etch Pit Density.Both as received sections of GaAs and sections of test samples after deformation wereused for dislocation etch pit density measurements. The samples were initially cleaned byimmersing them in boiling trichloroethane, then boiling acetone and finally boiling isopropylalcohol for five minutes in each liquid. The specimens were then throughly washed with distilledwater and rinsed with methanol.4.4.1 Chemical Polishing.Chemical polishing was carried out in two stages. In the first stage, the specimenwas immersed in 15m1 of a 1 :1 : 1 solution of hydrogen peroxide, ammonium hydroxideand distilled water for about three minutes, then washed in distilled water and rinsed inmethanol. This removed a thin surface layer of the sample. In the second stage, a solutionof 1 : 4 bromine in acetic acid was gently swabbed across the specimen surface using akimwipe swab until the specimen had a mirror surface. The specimen was then washed withdistilled water and rinsed with methanol.314.4.2 Etching of the Specimens.The GaAs specimens were etched one at a time in a nickel crucible. The sample atroom temperature was covered with a layer of KOH pellets, a nickel cover placed on thecrucible and the crucible placed in a muffle furnace set at 530\u00B0C. The crucible was left inthe furnace for times ranging from 8 to 12 minutes depending on the specimen size. In thefurnace, the potassium hydroxide melted and etched the crystals.After the specified etching time, the crucible was removed from the furnace and cooled toroom temperature. After cooling, the potassium hydroxide was washed off the specimenusing running water and the specimen dried with methanol.The etched specimen was thenexamined for etch pits using an optical microscope at various magnifications.325OBSERVATIONSHaasen's model of plastic deformation relates microscopic dislocation properties tomacroscopic deformation variables. Recently the validity of the model for some materials over anextended range of temperature has been questioned. This research was undertaken to test the validityof Haasen's model for GaAs. The model was tested by applying equation [11] to the compressiontest results. The results of the compression and tension tests also allowed a comparison of themagnitudes of the temperature and strain rate dependence of the yield stresses for the GaAs wafersand the seed crystals. The distribution and density of dislocations in the deformed specimens werealso observed.5.1 Compression Tests Results.5.1.1 Stress - Strain Curves.Typical stress - compressive strain curves at 600\u00B0C and 700\u00B0C test temperatures areshown in Fig. 5.1. The stress and compressive strain were determined from the load andcrosshead movement data and the initial dimensions of the sample. The curves show a shortinitial transition region which varied between samples, followed by a linear section and thena section with progressively decreasing slope as the strain increased. As expected, the curveat 600\u00B0C lies above the 700\u00B0C curve. Deviation from linearity is gradual and occurs at ahigher stress for the 600\u00B0C curve as compared to that for 700\u00B0C.On the basis of the plastic strain which occured in the samples as a result ofdeformation, determined after completion of the test, elastic deformation occured in theinitial transient. The linear section is taken as stage II during plastic deformation and the33section with decreasing slope as stage III. Since the samples have &lt;100&gt; parallel to thedeformation axis , in which case multiple slip systems are operative, stage I should not beobserved in the stress strain curve.The resolved shear stress - shear compressive strain curves were derived from thestress - strain curves using.S = acosA,cos9^[15]where S is the resolved shear stress while cos A. cos 4) is the Schmid factor. Thesamples were oriented with the (100) plane in the compression plane. Slip occurred on the{111) planes in &lt;110&gt; directions. The angle A. , between the normal to the {111) and thecompression direction is 54\u00B0 44\" and that between the &lt;110&gt; direction and the compressionaxis 9 , is 45\u00B0. Accordingly the Schmid factor is 0.409. The resolved shear stress is themeasured stress times the Schmid's factor while the resolved shear strain is the measuredcompressive strain times the reciprocal of the Schmid's factor.Examples of the resolved shear stress - resolved shear strain curves for series Bcompression tests samples between 500\u00B0C and 800\u00B0C test temperatures are shown in Fig.5.2. The linear stage II is observed to shorten rapidly with increasing test temperature,followed by a curved portion with progressively decreasing slope. The slope of stage IIdecreases with increasing test temperature. The transition from the linear stage II to non -linear stage III of the stress strain curves is not clearly defined. The transition point is takenas the intersection of two straight lines, one drawn along the linear portion and the otherdrawn tangent to the curved portion as shown in Fig. 5.3. This is termed the recovery stresswhich is the resolved shear stress at the start of dynamical recovery. The yield stresses and34the stresses at the beginning of dynamical recovery determined as a function of temperatureand strain rates are listed for series A samples in Table 5.1 while that of series B samplesare listed in Tables 5.2 (a) and (b). In Table 5.1, we note that the yield stress drops from10.08 MPa at 400\u00B0C to 3.02 MPa at 750\u00B0C for a CHS of 4.2 x cm/s. Increasing the CHSto 8.5 x 104 cm/s increases the yield stress at 500\u00B0C to 9.58 MPa. The yield stress valuesfor the B samples (Table 5.2(a)) with the larger length/width ratio vary between 7.55 MPaat 400\u00B0C and 3.47 MPa at 800\u00B0C for a CHS 4.2 x 104 cm/s. The yield stress increases athigher values of CHS and decreases with lower values. Comparing the results in Tables 5.1and 5.2 (a), it is noted that the yield stress values are significantly lower for the B seriescompared to the A series.The difference between the A and B series is attributed to the lower length/widthratio of the A series . It has been shown (28), that below a length/width ratio of about 2.0,end effects significantly raise the apparent yield stress. Series A specimens has a length/widthratio of 1.67 which is below the critical value while series B specimens has a length/widthratio of 3.8. The temperature dependence of the yield stress of the series B samples for thethree strain rates examined are shown in Fig. 5.5. Highest values of yield stress are obtainedfor the highest strain rate. At 500\u00B0C, the yield stress corresponding to strain rate of 0.333 x104/s is appreciably lower than the others.Each sample after deformation was measured and the change in length due todeformation compared to the change in length determined from the Instron chart recordingthe load and elongation during deformation. The results for series B samples are listed inTable 5.3. The measured change in length Al is observed to be lower than the valuedetermined from the Instron chart by 4 to 29 %.I^I20^40^60^80^100 120 140 160 180035Compressive strain x 10'3Fig. 5.1 Typical stress - compressive strain curves obtained in the compression testsfor the test temperatures indicated and a CHS Of 4.2 x 10-4 cm/sec. (Sample numbers 7B and10B).3660200^400^600^800Resolved compressive shear strain x 10 4Fig. 5.2 Resolved shear stress - Shear compressive strain curves for the testtemperatures indicated 'C and a CHS of 4.2 x 10 4 cm /sec.(S ample numbers 4B,7B,10B and13B).0 100^200^300^400Resolved shear strain x 10 43720 - stage III16 - recovery stress12 -246001.67stage II8yield stress-00^4Fig. 5.3 Determination of the recovery stress from the resolved shear stress - shearstrain curves for the temperature and strain rate indicated (Sample number 7B).38300^500^700^900Temperature (degrees Celsius)Fig. 5.4 Comparison of the yield stress against temperature for the two sets ofcompression tests specimens for the length/width ratios indicated.(CHS = 4.2 x 104 cm/s).39Temperature (degrees Celsius)Fig. 5.5 Temperature dependence of the yield stress for the strain rates indicated ( x10-4 /sec), for the series B compression tests specimens.40Temperature \u00B0C Sample Yield Stress(MPa)TM(MPa)Strain Rate x10-4/sCHS(cm/sec) x10-4400 lA 10.08 48.52 1.67 4.2500 2A 9.58 52.42 3.33 8.5600 3A 8.07 29.23 1.67 4.2650 4A 5.55 27.47 1.67 4.2700 5A 4.79 17.89 1.67 4.2750 6A 3.02 15.12 1.67 4.2Table 5.1 Temperature dependence of the yield stress and the recovery stress for theseries A compression tests specimens (Sample dimensions 6.0 x 6.0 x 10.0mm)41Temperature \u00B0C Sample Yield stress(ay) (MPa)In c StrainRate x10-4/sCHS (cm/sec)400 1B 25.52 17.05 8.33 2.1 x 10-3400 2B 7.55 15.84 1.67 4.2 x 10-4500 3B 4.29 15.27 0.33 8.5 x 10-54B 6.74 15.72 1.67 4.2 x 10-45B 16.33 16.61 8.33 2.1 x 10-3600 6B 3.27 15.00 0.33 8.5 x 10-57B 5.51 15.52 1.67 4.2 x 1048B 12.25 16.32 8.33 2.1 x 10-3700 9B 2.04 14.53 0.33 8.5 x 10-510B 4.08 15.22 1.67 4.2 x 10-411B 9.19 16.03 8.33 2.1 x 10-3800 12B 1.53 14.24 0.33 8.5 x 10-513B 3.47 15.06 1.67 4.2 x 10-4Table 5.2(a). Temperature dependence of the yield stress for series B compressiontests specimens (Specimen dimensions 4.2 x 4.2 x 15.9mm)42Temperature \u00B0C Sample 'till(MPa)In TH1 StrainRate xCHS (cm/sec)104/s400 1B 50.02 17.72 8.33 2.1 x 10-3400 2B 43.39 17.59 1.67 4.2 x 10-4500 3B 17.35 16.67 0.33 8.5 x 10-54B 35.22 17.38 1.67 4.2 x 10-45B 40.83 17.52 8.33 2.1 x 10-3600 6B 11.84 16.29 0.33 8.5 x 10-57B 15.72 16.57 1.67 4.2 x 1048B 25.52 17.05 8.33 2.1 x 10-3700 9B 6.34 15.66 0.33 8.5 x 10-510B 10.41 16.16 1.67 4.2 x 10-411B 13.48 16.42 8.33 2.1 x 10-3800 12B 3.27 15.00 0.33 8.5 x 10-513B 6.53 15.69 1.67 4.2 x 10-4Table 5.2(b). Temperature dependence of the recovery stress for series B compressiontests specimens (Specimen dimensions 4.2 x 4.2 x 15.9mm)43Temp.\u00B0C Sample Al(chart) mmAl(sample) mmCHS (cm/sec)400 1B 3.05 2.69 2.1 x 10-3400 2B 4.83 4.32 4.2 x 10-4500 3B 4.78 4.06 8.5 x 10-54B 3.25 3.02 4.2 x 10-45B 6.35 5.18 2.1 x 10-3600 6B 1.63 1.45 8.5 x 10-57B 2.41 2.29 4.2 x 10-48B 5.84 5.61 2.1 x 10-3700 9B 1.37 0.97 8.5 x 10-510B 2.74 2.51 4.2 x 10411B 9.40 * 5.89 2.1 x 10-3800 12B 3.05 2.67 8.5 x 10-513B 4.45 4.14 4.2 x 10-4Table 5.3 A comparison of sample elongations determined from Instron chart andby a direct measurement of changes in sample length (* sample fractured).445.1.2 Temperature and Strain Rate Dependence of m and U.In the previous theoretical consideration of deformation, an expression wasdeveloped for the yield stress as a function of the material parameters and the test conditions(equation [11]), and reproduced belowA 2C fm^U.-L-m^\" p ^GY = bBo^Ex ( (2 + m)kT )On taking the natural logarithm of the above equation, we obtain1 Aln a =^(2Cm ) ^1 U Y 2+mln ^ +bB0 2+mln i + (2+m)kT [16]At constant temperature, U is assumed constant independent of the applied stress,then equation [16] may be written aslnay=C+ (2 +m) lniwhereC ^1^ ln(A2Cm j+ ^U2 + m bBo (2 + m)kTFrom equation [17], In ay should be linearly dependent on lni with a slope givenby (2\u00B1m) . Values of In cry were plotted as a function of In i in Fig. 5.6 for the compression[17][18]tests samples (Table 5.2(a)). The solid lines were obtained by a least squares fit of the(2 +m)(in(i\u2014M0-)+1ni)A 2C\u201E,D =45experimental results. The magnitude of (2+m) for any given test temperature is given by thereciprocal of the slope of the fitted line and the results are listed in Table 5.4(a). since theresults at 400 and 800\u00B0C are only based on two points, the values listed are uncertain.For a constant strain rate and variable temperature, equation [16] may be written asU InaY =D +(2+m)kT[19]where D is a constant given by[20]from equation [19], In ay should be linearly dependent on -;,- with a slope given by(2 + where k is the Boltzman's constant. Values of .F , were estimated usingu m)kU (2 + m) = k.slope[21]Values of In ay are plotted against 1 / T for three strain rates in Fig. 5.7, the solidlines being a best fit of the experimental points. From the resulting slopes (2,u--7-n) is determinedfrom equation [21], giving values of 0.19, 0.13 and 0.13 eV for the strain rates of 0.33, 1.67and 8.33 x 104 Is respectively.46By a similar analysis using equation [13], the strain rate dependence of the stress atthe beginning of dynamic recovery is given byn In ti,,,= Constant + In i^ [22]From equation [22], In t should be linearly related to In i with a slope givenby ,T1 . Values of in.% are plotted against lni for the various test temperatures in Fig.5.8. The solid lines are a least squares fit of the experimental results. The magnitudesof n are obtained from the reciprocals of the slopes of the curves and are listed in Table5.5(a).The temperature dependence of the recovery stress is similarly obtained from equation[13] asn In tm = Constant +Thus MT,,, is linearly related to 1/T with a slope given by.slope = Q7k-QSD... - = k .slopenValues of in t,,, are plotted against 1/T in Fig. 5.9 for the three strain rates. The solidQ.,lines represent a least squares fit of the experimenatl results. From the resulting slopes, -,7were estimated and the values are listed in Table 5.5(b).QSD^ [23]kT47The present results for (2+m) are compared with values reported in the literature inTable 5.4(b). It is observed that the present results are a little higher than the reported valuesfor other specimen orientations. This difference may be associated either with the differentorientations of the specimens or due to residual strain in the sample. Note that the pre-strainedusample listed in Table 5.4(b) has a high value for (2+m). Values for (2_\u2014,i) from the presentresults are correspondingly lower than the reported values.48-11^ -9^ -7In strain rateFig. 5.61n yield stress vs In strain rate for the test temperatures indicated \u00B0C.491^1.4^1.8^2.2^2.6^31 / Temperature x 10 -3Fig 5.71n of the yield stress vs the reciprocal of the test temperature for the strainrates indicated x 104/s.50-8 -7-9In strain rate-10-1 11817.51716.51514.514Fig. 5.81n of the recovery stress vs In strain rate for the test temperatures indicated\u00B0C.lfremperature x 10 -3Fig 5.9 In of the recovery stress vs the reciprocal of the test temperature for the strainrates indicated x 10-4 /s.5152Temperature \u00B0C) TT,,(2+m)400 0.323 3.33500 0.404 4.40600 0.485 4.44700 0.565 4.15800 0.646 3.965.4(a).Crystal Orientation TT,\u201EU (2+m)(2 + m ) eV&lt;110&gt; 0.41 - 0.58 0.45 3.2&lt;123&gt; 0.45 - 0.51 0.45 3.1&lt;123&gt; 0.46 - 0.62 0.35 3.5&lt;123&gt; 0.35 - 0.58 0.31 6.5*Table 5.4(b).Values of (2+m) determined from the present data for &lt;100&gt; oriented crystals (Table5.4(a)). Reported values of U/(2+m) and (2+m) for the crystal orientations indicated arelisted in Table 5.4(b). The value with the asterisk is for a pre - strained sample (15).Temperature \u00B0C TT\u201E,n500 0.40 3.8600 0.48 4.2700 0.57 4.3800 0.65 2.3Table 5.5(a)Strain Rate x 104 /s QSDneV0.333 0.191.67 0.208.33 0.17Table 5.5(b).53Tables 5.5(a) and 5.5(b) n and 92--: values obtained from the present study.545.1.3 Dislocation Density - Compression TestsThe dislocation density in the undeformed and deformed compression tests sampleswere obtained by etching the samples and counting the etch pits. An example of the etch pitdensity and distribution in an as received sample after etching in KOH for eight minutes isshown in Fig. 5.10. The etch pits are clearly defined with hexagonal symmetry. There is avariation in etch pit size and some overlapping of the pits. The etch pit density was countedto be 4.0 x 104 /cm2 which is within the range of the values reported for as grown GaAscrystals.After deformation, the etch pits were not as clearly defined and had an appreciablyhigher density than that of the as received sample. An example is shown in Fig. 5.11 for asample tested at 600\u00B0C at a strain rate of 8.33 x 10-4 /s. There appears to be two categoriesof etch pits on the surface. One consists of large elongated faceted pits, and a large numberof small black pits. The density of the large pits were counted to be 1.5 x 105 pits/cm2 whichis close to the as received etch pit density. The estimated density of the small pits is 4.42 x106 pits/cm2 . These pits may be associated with the dislocations resulting from plasticdeformation. The small pits appear to be arrayed in lines which might correspond to sliplines. Another example of a compression sample deformed at 600\u00B0C at a slower strain rateis shown in Fig. 5.12. The etch pit distribution is similar to that of Fig. 5.11 with similarlarge and small pits but with a slightly higher density. The dislocation etch pit densities indeformed compression tests samples (series B) are listed in Table 5.6.55Temp.\u00B0C Sample Strainratex 104 Is6A \u2014 ay(MPa)ep Calculatedetch pitDensityx 106 /cm2Observedetch pitDensity(large)x 105 /cm2Observedetch pitDensity(small)x 106 /cm2large small400 1B 8.33 25.01 0.096 1.88 1.46500 4B 1.67 40.16 0.172 3.40 9.4 3.58600 6B 0.333 15.10 0.095 2.89 0.89 4.3600 8B 8.33 24.58 0.255 4.66 1.5 4.42700 9B 0.333 10.01 0.047 4.90 4.47800 12B 0.333 4.90 0.199 6.45 6.12Table 5.6. Dislocation etch pit density in deformed compression test samples (seriesB), GA \u2014 CTy is the difference between the final stress in the sample and the yield stress, epis the plastic strain in the sample.Fig 5.10 Dislocation etch pits in an as received GaAs sample (set B). Etching timewas 8 minutes. Magnification X 175.5657Fig 5.11 Dislocation etch pits in a deformed GaAs sample (strain rate = 8.33 x 10 4 /s, testtemperature = 600\u00B0C). Magnification X 600, Specimen number 8B.58Fig 5.12 Dislocation etch pits in a deformed GaAs sample. (strain rate = 3.33 x 10-5/s, test temperature = 60(YC.) Magnification X 950, Specimen number 6B.595.2 Tensile Tests.5.2.1 Tensile Stress - Tensile Strain Curves.A typical stress - strain curve for GaAs at 700\u00B0C strained at 1.67 x 10 -4 /s is shownin Fig. 5.13. The curve show a linear stage II followed by a non - linear stage III with aprogressively decreasing slope. All the samples fractured at the end of the deformationwithout any apparent necking. The plastic strain at fracture as a function of temperature insamples which deformed plastically is shown in Fig. 5.14. The data available is limited.However the results show that considerable plastic deformation occurred prior tofracture. Up to 93 % plastic strains were observed depending on the test temperature andstrain rate.5.2.2 The Temperature Dependence of The Yield Stress.The values of yield stresses obtained in the present study are shown in Table 5.7.The temperature dependence of the yield stresses for the two strain rates considered is shownin Fig. 5.15. The yield stress for the higher strain rate is significantly above the corresspondingvalues for the lower strain rate. The recovery stress was obtained from the stress - straincurves in a manner similar to that shown in Fig. 5.3 and the results obtained in the presentstudy are shown in Table 5.7.600^20^40^-2^60^80Tensile strain x 10Fig. 5.13 Typical stress - strain curve obtained in tension tests for the test temperatureindicated *C and a strain rate of 1.67 x 10'/s (sample number T12).61400^500^600^700^800Temperature (degrees Celsius)Fig 5.14 The percentage plastic strain at fracture as a function of test temperaturefor the strain rates indicated x 10 -4 /s . 65624321.5450^550^650^750Temperature (degrees Celsius)Fig 5.15 Resolved yield stress as a function of temperature for the strain ratesindicated x 104/s.63Temp. \u00B0C Sample Yieldstress(MPa)TB/MPaA 1(chart)mmA 1 (sample)mmStrain ratex 10-4 /sCHS(cm/sec)400 Ti F F 4.2 x 10-5T2 F F 4.2 x 10-4T3 F F 2.1 x 10-3500 T4 3.65 7.43 3.3 2.95 0.167 4.2 x 10-5T5 F F 4.2 x 10-4T6 F F 2.1 x 10-3600 T7 2.91 5.66 3.73 2.74 0.167 4.2 x 10-5T8 4.85 10.25 5.1 3.68 1.67 4.2 x 10-4T9 F F 2.1 x 10-3T10 F F 8.5 x 10-3700 T11 2.47 5.84 3.4 2.67 0.167 4.2 x 10-5T12 4.26 8.16 6.6 5.89 1.67 4.2 x 10-4T13 F F 2.1 x 10-3T14 F F 8.5 x 10-3750 T15 2.13 6.57 3.89 2.97 0.167 4.2 x 10-5T16 3.52 7.34 2.46 1.63 1.67 4.2 x 10-4Table 5.7 Measured values of the yield stress, the recovery stress ,the chart andsample elongations for the temperatures and CHS indicated (F = Samples fractured duringelastic deformation).645.2.3 Dislocation Density - Tensile Tests.The dislocation densities in the tensile samples were estimated following the sameprocedure used for the compression test samples. The appearance and distribution of etchpits in an as received tensile sample is shown in Fig. 5.16 which as expected, is similar tothat of the compression test sample. The pits are hexagonal and tend to overlap in clusters.The etch pit density in an as received sample was estimated to 1.2 x 104/ cm 2.The deformedsamples when etched in KOH did not produce the well defined faceted pits as in the samplebefore deformation. An example of a deformed etched surface for a test temperature of500\u00B0C and strain rate of 1.67 x 10 -4 /s is shown in Fig. 5.17. The pits are small and withoutclearly defined facets. Some have shiny bottoms, others, dark bottoms. The density of theetch pits was estimated to be 2.86 x 106 pits/cm2.Increasing the test temperature to 600\u00B0C, and etching the samples after deformationproduced small etch pits similar to those obtained at 500\u00B0C. Examples of samples tested at600\u00B0C at strain rates of 1.67 x 10-4 and 8.33 x 10 A /s are shown in Figs. 5.18 and 5.19. Theetch pit densities were estimated to be 6.91 x 10 5 and 1.04 x 106 pits /cm2 respectively. Theresults of the etch pit density measurements are listed in Table 5.8.65Temp.\u00B0C Sample aA \u2014 ay(MPa)ep strain ratex 10-4/sEstimatedetch pitdensity /cm2Observedetch pitDensity /cm2500 T5 1.67 2.86 x 106600 T7 1.84 0.424 0.167 1.94 x 107 2.8 x 107600 T8 9.76 0.507 1.67 1.65 x 107 6.91 x 105600 T9 8.33 1.04 x 106Table 5.8 Dislocation etch pit density in deformed tensile samples ,GA \u2014 ay is thedifference between the final stress in the sample and the yield stress, 4 is the plastic strainin the sample.Fig 5.16 Dislocation etch pits in an as received GaAs wafer. Etching time was 10minutes. Magnification X 175.6667_4.4\u25A0011r;Nee- t140,106Ce-4, 'IC11 \"41t^j,^\u2022,;11,10.104,1C2J.,._^r^,Cry Z -3\u00B0'\u2018147441i14\".Fig 5.17 Dislocation etch pit density in a deformed GaAs wafers.(strain rate = 1.67x 104 /s, test temperature = 500\u00B0C). Magnification X 865, Sample number T5.68Fig 5.18 Dislocation etch pit density in a deformed GaAs wafer.(strain rate = 1.67 x10-4 /s, test temperature = 600\u00B0C). Magnification X 427, Sample number T8.00\u2022\u2022 0\u2022t14P^\u202260 e'llkh'(-0^lile0\u20220 \u2022'PA ore IA.\u2022e\u2022\u2022I0Fig 5.19 Dislocation etch pits in a deformed GaAs wafer (strain rate =8.33 x 10 4 /s,test temperature = 600\u00B0C) Magnification X 968, Sample number T969706DISCUSSIONThere exists in the literature, conflicting reports on the magnitude of the parameterscharacterising the beginning of plastic deformation of GaAs and also on the temperature and strainrate dependence of these parameters. Most of the values reported were obtained within a narrowrange of temperature and this makes it difficult to resolve the differences in the reported values.Also most of the results reported were for specimen orientations favourable to single slip and thestress - strain curves showed a pronounced yield drop. It was thus widely claimed that the yielddrop phenomena is a typical feature of the stress - strain curves of GaAs. The temperature, stressand strain rate dependence of the dislocation density in deformed GaAs specimens have also beena subject of strong interest. This research was directed toward finding a link between the resultsreported in the literature, and to observe the relation between the dislocation density and deformationvariables. An explanation of the results obtained in the present study and those reported in theliterature was sought on the basis of the microscopic theory of dislocations.It was found in the course of the experiments that preparation of the test samples anddeforming the GaAs at high temperatures was more difficult than anticipated. GaAs is highly brittleat low temperatures, resulting in sample failure during sample preparation. Compression sampleswere made from seed crystals provided by Johnson Matthey, since cutting facilities were notavailable, The internal strains in the crystals provided and the overall quality were not clearlydefined. Etching the deformed samples for delineating dislocations was difficult and nonreproducible, which makes the observations of the etch pit density partly ambiguous. Edge grindingof the tensile samples also proved difficult due to sample breaking during grinding or during handlingfor cleaning and fitting into the tensile grip system.6.1 Yield Drop.The stress - strain curves for both the compression and tension tests show a smoothtransition from elastic to plastic deformation. No yield drop was observed in all theexperiments.The yield drop phenomena has been a subject of increasing controversy and anumber of theories have been proposed to explain the phenomena.The yield drop phenomena has been accounted for in terms of the amount of initial andpotentially mobile dislocations that are present in the specimen prior to deformation. In thistheory, the application of an external stress causes the generation of dislocations which adds aplastic term to the applied strain rate. The elastic term thus decreases while the plastic termincreases. The stress then goes through a maximum (upper yield point) and may even fall tozero were it not for work hardening which limits the multiplication of dislocations and allowsthe stress to rise again. (lower yield point). In agreement with this model, the magnitude of theyield drop decreases with increasing temperature and the extent of pre - strain present in thesample prior to deformation.The yield drop has also been explained in terms of Cottrell's theory where it is associatedwith an unpinning stress. In this theory, the dislocations are considered to be surrounded byimpurity atmospheres which pins them strongly to the lattice. The stress required to unpin thesedislocations from the atmospheres is then assumed higher than the stress they require to movethrough the lattice, hence the yield drop. This theory has been used to explain the yield dropphemomena in many metals (29).71In GaAs, the grown - in dislocations do not move under an applied stress (6) and theirrole as sources of new dislocations remains unclear. The parabolic stress - strain curves obtained72in the present study are then associated with the activation of multiple slip systems whichgenerates a high dislocation density prior to yielding. The result is that changes in the dislocationdensity before and after yielding and thus changes in the dislocation velocity are not significantand this suppresses the yield drop.736.2 Temperature and Strain Rate Dependence of m and U.The temperature and strain rate dependence of m and U may be correlated directly tothe temperature and strain rate dependence of the dislocation types that are effectively presentand active during the deformation process.Two pertinent questions arise.1.What dislocation types are present in the crystal during the deformation process and whichare rate controlling.?2.What is the temperature and strain rate dependence of m and U for these types of dislocations.?Recent experiments on dislocation velocities in semiconductors (16,17,30,31,32,33)have shown a stress dependence of the dislocation velocity below a specific critical stress whichdepends on the crystal and also on the dislocation type . Below this stress, the resulting velocityequation may not be properly described by a simple power law. In germanium for example, theresults of velocity measurements show that for 60\u00B0 dislocations, a plot of the log of the dislocationvelocity versus the log of the applied stress is linear for applied stresses above 2kp/mm 2 whilefor stresses below 2kp/mm2, the curves show a large and temperature dependent slope. (30,33).Similarly for silicon, the activation energy of the 60\u00B0 dislocations and the stress exponent arestress and temperature dependent respectively for stresses below 3kp/mm 2 However the resultsfor screw dislocations show the activation energy and the stress exponent to be stress andtemperature independent respectively for stresses greater than 0.4kp/mm2 (11,30,35).It is this breakdown in the power law equation that is responsible for the apparentconfusion in the literature on the \"correct\" magnitudes of m and U obtained from experimentsperformed at different temperatures and strain rates. In the temperature and stress interval inwhich dislocation velocities have been measured in GaAs (16), dislocations were shown tohave the lowest mobility compared to a and screw dislocations hence their motion was thoughtto be rate controlling. However the absolute values of the activation energy obtained in74macroscopic deformation experiments differed from the activation energy of any of theindividual dislocation types. The results of Steinhardt and Haasen (18) on the creep rates ofGaAs indicates that the average creep rate depends on some suitable combination of the velocitiesof the different dislocation types. It was shown in that study that the macroscopic activationenergy should be defined by1U = 2\u2014 (Ua + US)[21]where Uo, and Us are the activation energy for the a and screw dislocations respectively.Recently, Rabier and Boivin (5), have shown that the density of screw dislocations in a deformedGaAs specimen depends on the deformation temperature. In that study, they showed that at lowtemperatures, the deformation substructures of GaAs single crystals consists mainly of screwdislocations while at high temperatures, the substructure shows a low density of screwdislocations. The transition from a substructure where the density of screw dislocations is lowto one where it's density dominates was explained in terms of the temperature dependence ofthe activation energy of cross slip. At high temperatures, the activation energy is low, hencecross slip takes place readily and opposite screw segments annihilate each other. At lowtemperatures, cross slip is more difficult to activate and this leads to an accumulation of screwdislocations in the primary glide plane. Thus the contribution of screw dislocations to the totaldislocation density and hence to strain hardening depends on the test temperature. It is thisproblem related to the crystal structure of GaAs that limits the comparison of m and U obtainedat different temperatures and strain rates.The present results show that the magnitude of (2+m) is temperature dependent withvalues ranging from 3.33 at 400\u00B0C to 3.96 at 800\u00B0C.while changes in the values of the activation75energy obtained in the present study are not so pronounced. This variation in the magnitudesof (2+m) from 400\u00B0C to 800\u00B0C. is qualitatively in agreement with the temperature dependenceof the rate sensitivity of the flow stress at high temperatures obtained for ZnS (34). In ref (34),the stress sensitivity of the strain rate increased with temperature in the temperature range ofabout 200\u00B0C to 370\u00B0C before decreasing with temperature down to 540\u00B0C.The present results are not in agreement with that of Schroter et al on germanium. (25). Theyreport that m decreased with increasing temperature. It was also shown in ref (25) that whilem and U depends on temperature and strain rate respectively for germanium, m and U doesnot show the same dependence in silicon.In comparison with macroscopic deformation experiments, the results of dislocationvelocity measurements show that only the velocity of screw dislocations may be describedapproximately by the simple power law relation of equation [6] for all the stress intervalspresently investigated. The discrepancies in the results of macroscopic deformation experimentsmay then be explained in terms of the stress and temperature dependence of dislocation typeswhose motion is rate controlling. In Ge 60\u00B0 dislocations have been shown to be rate controlling(12) while for Si the motion of screw dislocations are rate controlling.(11). The temperatureand stress dependence of m and U for germanium compares favourably to the temperature andstress dependence of the 60\u00B0dislocations in germanium while the constant values of U and mfor silicon may be due to the fact that no asymmetry has been observed in the temperature andstress dependence of the velocities of screw dislocations (32,35) . It has been suggested thatthis may be due to it's strong covalent bonding which induces a very high Peierls stress. Thescatter in the values of U and (2+m) obtained in the present results and also in those listed inTable 5.4(b) may be associated with structural changes that occur in the specimens duringplastic deformation and due to the large temperature and strain rate variations not allowed for76in the equations derived by Haasen (2). The assumption of a constant activation energy for theparameters characterising the beginning of plastic deformation implicit in the model presumesthat dislocations are driven mainly by a single mechanism at all temperatures and strain rates.The effect of thermal activation on the generation and motion of dislocations and hencein the plastic flow of metals is seen in the precipitous rise of the yield stress of most of therefractory b.c.c. metals (iron, tungsten, tantalum etc.) on decreasing the deformation temperaturebelow room temperature .This result has also been observed both for single and poly-crystallinematerials and is thus not attributable to the presence of grain boundaries. On defining thedeformation stress as the stress that causes the dislocations to move a large distance comparedto their mean separation, these results indicate that the deformation stress is a sum of two terms,a plastic term and a thermal term. For any given structure and specimen orientation, thedeformation stress is constant. Thus for the same strain rate and temperature, repetitiveexperiments using identical specimens will produce the same yield stress. (the plastic componentof the deformation stress). On changing either the strain rate or the deformation temperature,we change not the deformation stress but it's components. Increasing the temperature increasesthe thermal term while reducing the plastic term. This is manifested by a reduced yield stress.Increasing the strain rate increases the plastic term while reducing the thermal term and hencean increased yield stress.The agreement of the experimental results with the equations of Haasen' s model at lowtemperatures and high strain rates arises because under these conditions, the thermal componentof the deformation stress is not significant, consequently the dislocations in the specimen aredriven mainly by a single mechanism, in this case the applied stress. On increasing thetemperature or reducing the strain rate, we obtain a gradual transition from plastic to viscousdeformation, for then, localised obstacles to the dislocations may be overcome purely by thermalfluctuations and also the diffusion of point defects contributes significantly to the plastic flow.77All of these processes, in addition to the applied stress, compete effectively for the rate controllingmechanism and consequently, equation [11] ceases to be a correct description of the stress andtemperature dependence of the plastic strain rate and this limits the validity of the results obtainedusing this model under these conditions.The critical stress dependence of the dislocation velocity below which the power lawrelation breaks down may be associated to a transition from a single mechanism controlleddeformation to a multi - mechanism controlled deformation. Thus this critical stress defines thetransition stress above which the equations of Haasen's model holds. Below this stress, theequations of the model have to be modified to account for the contributions of temperatureinduced effects to the plastic strain rate.6.3 Stress - Strain Curves.6.3.1 Compression Tests.The general shape of the compression stress strain curves shown in Fig. 5.1 isconsistent with similar results reported in the literature (36,37). The magnitude of the yieldstress observed in the present investigation drops appreciably with test temperature andvaries with strain rate (Table 5.2(a)). The present results of the compressive resolved yieldstress of GaAs are compared to reported values in Table 5.9. At 700\u00B0C and for roughlysimilar strain rates , the measured yield stress is 4.08 MPa compared to the reported valueof 2.8 MPa, At other temperatures, the measured values are also appreciably higher than thereported values.The high values of the yield stress obtained in the present study are difficult to accountfor . It is possible that they are associated with the condition of the test samples. The sampleswere cut from seed crystals with a diamond saw. The seed crystals themselves were cut froma large crystal boule with a diamond saw. As a result all the sample surfaces were cut andin the process of cutting, internal strains may have developed in the samples. It is not clearwhether these strain were alleviated at the test temperatures prior to deformation. Thesamples were not annealed at high temperatures due to the potential loss of arsenic byevaporation. Internal strains could lead to higher yield stress. We note that at the highesttest temperature (800\u00B0C) and lowest strain rate (0.33 x 10-4/s), the yield stress drops to 1.53MPa. appreciably lower than the value at the higher strain rate. The present high values ofthe yield stress are thus attributed to internal strains in the starting material which could notbe eliminated in a controlled manner. There was no other manner of preparing samples inthe present investigation.7879In the present study, for test temperatures of 500\u00B0C, plastic deformation was observedwith some recovery (stage III) at high stress values. This differs from reports (15) that stageIII may not be observed below 550\u00B0C prior to fracture.Temp\u00B0C Strain ratex 104 /s.Orientation Present ResultsMPaReported ResultsMPa600 1.67 [100] 5.51not stated [100] 6.9700 1.67 [100] 4.081.0 [100] 2.80800 1.67 [100] 3.47900 1.0 [100] 2.45Table 5.9 Comparison of present results with values reported in the literature, ref(37).806.3.2 Tension Tests.The values of the resolved yield stress for GaAs, given in Table 5.7 are shown tovary appreciably with temperature and strain rate similar to that observed in the compressiontests. In a number of samples, as indicated, fracture occured before the onset of plasticdeformation, particularly at the higher strain rates and lower temperatures. This is a reflectionof the brittle characteristic of GaAs at lower temperatures. Comparing the yield stress of thetensile samples with the compression samples (Tables 5.7 and 5.2(a)), It is observed that forthe lower test temperatures, the values in tension are below that observed in compression.At the slowest strain rates, comparing tension and compression values of 3.65 and 4.29MPa at 500\u00B0C, 2.91 and 3.27 MPa at 600\u00B0, 2.47 MPa and 2.04 MPa at 700\u00B0C. The differencedecreases at the higher temperatures. In general, it is assumed that the resolved yield stressin tension and compression should be the same. It is not clear why the difference is observedin the present case. It is postulated that the compression test samples contain internal strainsprior to deformation. The tension tests samples have polished faces and were chemicallypolished after careful shaping which likely eliminates or markedly reduces internal strainsand this could account for the difference.In Table 5.7, the increase in length of the tensile gauge length at fracture A/ asdetermined fron the Instron chart is compared to Al measured from the sample after fittingthe fractured pieces together as carefully as possible. The measured lengths of the fracturedsamples are consistently smaller than the chart values by between 10 and 30 %. This indicatesthat tensile strains are introduced during testing in addition to the strains in the sample. Thisthen accounts for the shallow slope of the elastic portion of the stress strain curves and makesquantitative evaluation of stress strain curves in which strain plays a significant roleuncertain.81A direct comparison of the resolved yield stress in tension between the present resultsand reported values cannot be made since values for GaAs of [100] orientation at hightemperatures have not been reported.Also, a more detailed comparison of the stress strain curves determined in this investigationwith the plastic deformation model as proposed by Haasen (2) appears to be of limited value.The strains measured, only approximate the actual strains produced in the sample. In additionthe temperature and strain rate dependence of the flow stress is required. As reported inTable 5.7, all of the samples deformed at strain rates higher than 1.67 x 10 -4 Is fracturedduring elastic deformation . The strain rate dependence of the flow stress thus cannot bedetermined from the present data.826.3.3 The Relation Between The Dislocation Density and MacroscopicDeformation Variables.The relation between the dislocation density in a deformed specimen and themacroscopic deformation variables has been a subject of strong interest. In the investigationof the high temperature deformation of GaAs by bending (6), it was shown that a markedincrease in dislocations occured after small strains. The dislocations were detected usingcathodoluminescence. It was also demonstrated in undeforned GaAs that there is a directcorrelation with etch pits and dislocations on (100) surfaces of GaAs.Without assuming any definite mechanism for the multiplication of dislocations, itseems reasonable to assume that there exists a functional relation between the dislocationdensity in a deformed specimen to the applied stress, the strain rate, the plastic strain andthe deformation temperature. This functional relation is expressed empirically below.p =kAaaibepTd [22]where k, a, b, c and d are constants to be determined. In the above equation, Ac istaken to be the difference between the applied stress and the yield stress of the specimenwhile E, 4, and T are the strain rate, plastic strain and deformation temperature respectively.The physical question then is at what point during the plastic deformation of a crystal dothe dislocations begin to significantly multiply. The results of dislocation experiments(41,42) indicate the existence of a threshold stress. In this study, this threshold stress wastaken to be the yield stress of the specimen.The constants in equation [22] were determined from the present data. Values of theparameters were substituted in the equation and using Newton's method, the equations were83differentiated with respect to each of the variables and the resulting equation solved for theconstant terms. On this basis the functional relation between the dislocation density and thedeformation variables was found to be398 8 .A00.023ep0.0817, 1.32^ [23]p = \u00A30.093This result show that the dislocation density is directly related to the applied stress,the plastic strain in the specimen, and the deformation temperature while being inverselyrelated to the strain rate ( a lower strain rate being equivalent to an increased temperature).Values of the dislocation density for a range of temperatures and strain rates werecalculated from the test variables giving the results shown in Table 5.6. The experimentalobservations of the etch pit dislocation density after plastic deformation in compression arealso listed in Table 5.6. Assuming the small pits to be associated with dislocations arisingfrom plastic deformation and the large pits with grown in dislocations in GaAs. The observedsmall pits are compared to the calculated dislocation etch pit density.The values for the etch pit dislocation densities from the tensile test samples are listedin Table 5.8. Using the constants from the compression tests data, values of the dislocationdensities were calculated using two tensile tests data and the results compared with themeasured values in Table 5.8.847Conclusions1.The stress and temperature dependence of the activation energy (U) for the generation ofdislocations and the stress exponent (m) of the dislocation velocity obtained from macroscopicdeformation experiments correlates directly to the stress and temperature dependence of thedislocation types whose motions are rate controlling.2. Haasen's model of plastic deformation is not applicable to GaAs in the temperature range(400\u00B0C - 800\u00B0C) investigated in the present study.3. The critical stress dependence of the dislocation velocity below which the power lawequation breaks down, marks a transition stress above which the deformation model of Haasenholds.4. The differences in the various values of U and m reported in the literature are not due toexperimental errors as has been claimed, but are due to the different temperatures and strain ratesunder which the results were obtained.5. The dislocation density in a deformed GaAs sample is directly related to the applied stress,the plastic strain and the test temperature while being inversely related to the applied strain rate.858SUGGESTIONS FOR FURTHER WORKHaasen's model of plastic deformation remains the most consistent dislocation model fordiamond structure materials. However, at high temperatures the model has to be modified to accountfor the contributions of temperature to the plastic strain rate.The process of this modification may be aided by finding answers to the following basicquestions.What processes contributes to the plastic strain rate at high temperaturesHow can we describe the contributions of each of these processes quantitatively.How do these processes relate to each other. For instance are they parallel dependent orindependent processes etc.The fact that the constants B(T), A, K, in the equations of the model are not known forGaAs limits the application of the model to GaAs. The constant A may be obtained using equation[5] as followsaA = oeff + AN2Thus a plot of oA Vs N112 should give a straight line whose slope is A. 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