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Etching of Gallium Arsenide with atomic hydrogen Elzey, John W. 1992

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ETCHING OF GALLIUM ARSENIDE WITH ATOMIC HYDROGENByJohn W. ElzeyA.B., University of California, Berkeley, 1990A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEi nTHE FACULTY OF GRADUATE STUDIESDepartment of PhysicsWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIADecember 1992© John W. Elzey, 1992In 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.Department of ^PhysicsThe University of British ColumbiaVancouver, CanadaDate ^Ve/e_ 3/^/' 9 9 '2—(Signature)DE-6 (2/88)AbstractAn optical interferometric method is used to make in-situ observations ofcontinuous etching of the (100) GaAs surface during exposure to a knownconcentration of thermalised hydrogen atoms downstream from an H2 plasma.Etch rates between 3 and 9 nm/min are followed at constant temperature withinthe range 229 - 360 °C. Increasing substrate temperature leads to increased rates ofreaction. A Pt wire is used as an isothermal calorimeter to determine absolute Hatom partial pressures on the order of 5 mTorr. Analysis of etch rate dependenceon atomic hydrogen concentration verifies the surface reaction follows close to afirst order rate law with respect to the hydrogen atom concentration and anArrhenius analysis of the etch rate data yields an activation energy of 7(2) kcal/mol= 29(7) kJ/mol = 0.31(7) eV. Rate coefficients for the H + GaAs etching reactionwere found in the aforementioned temperature range to have the temperaturedependence kr = 105-7±0.7 nm min-1 Torr-1 exp(-29±7 kJ/mol)/RT. Scanningelectron microscope photomicrographs of etched samples reveal that large scale• crystallographic etching occurs resulting in textured (100) GaAs surfaces and x-rayphotoelectron spectroscopy demonstrated these surfaces were gallium-rich.Table of ContentsAbstract^Table of Contents^List of TablesList of Figures^ viAcknowledgments viiSection 1: Introduction^ 11.1 General Purpose of Study^ 11.2 Hydrogen Atoms in Silicon 21.2.1 Atomic H on the Silicon Surface^ 21.2.2 Atomic H Diffusion in Silicon 21.2.3 Atomic H Generated Platelets in Silicon^31.2.4 Atomic H Etching of Silicon^  41.3 Hydrogen Atoms in Gallium Arsenide 41.3.1 Atomic H on the Gallium Arsenide Surface^41.3.2 Atomic H Diffusion in Gallium Arsenide 51.3.3 Atomic H Generated Platelets in Gallium Arsenide^71.3.4 H2 Adsorption on Gallium Arsenide^81.3.5 Atomic H Etching of Gallium Arsenide 8Section 2: Experimental^ 142.1 Reaction Vessel^ 142.2 Sample Holder and Thermometry^ 182.3 Gallium Arsenide Samples and Silicon Nitride Mask^202.4 Hydrogen Atom Production^ 222.5 Hydrogen Atom Detection^ 232.6 Interferometer^ 27Section 3: Results^ 353.1 Measurement of the Atomic Hydrogen Concentration^353.2 Measurement of the Order of the Reaction with Respect to theConcentration of Atomic Hydrogen^ 363.3 Measurement of the Absolute Rate Constants and ActivationEnergy for Etching Gallium Arsenide with Atomic Hydrogen^383.4 Post-etch Surface Description^ 413.5 X-Ray Photoelectron Spectroscopy Result^ 44Section 4: Discussion^ 484.1 Atomic Hydrogen Adsorption on Silicon and Gallium Arsenide. ^484.2 Atomic Hydrogen Platelets in Gallium Arsenide^484.3 Atomic Hydrogen Induced Crystallographic Etching 49Section 5: Conclusion^ 51Suggestions for Further Work^ 52References^ 54Appendix 1: Slope Uncertainty Calculations^ 55Appendix 2: Preexponential and Uncertainty Determination^58ivList of TablesTable 3-1 Atomic Hydrogen Reaction with Gallium Arsenide Order Estimate at280 °C^ 37Table 3-2 Atomic Hydrogen Reaction with Gallium Arsenide Order Estimate at250 °C^ 37Table 3-3 Measured Kinetic Quantities for the Hydrogen Atom Reaction withGallium Arsenide and Subsequent Rate Constants^42List of FiguresFigure 1-1 THI and Tv tetrahedral and bond center sites for atomic hydrogen inGaAs (from L. Pavesi and P. Giannozzi55)^ 6Figure 2-1 Schematic layout of etching reactor and monitor system^15Figure 2-2 Pyrex sample holder^ 19Figure 2-3 Silicon nitride stripe orientation on (100) GaAs^ 21Figure 2-4 Platinum wire configuration for H atom detection in flow system^24Figure 2-5 Schematic of Wheatstone bridge used with Pt wire to measure thepartial pressure of hydrogen^ 25Figure 2-6 One period of a typical interferogram obtained during H atom etching of(100) GaAs at 281 °C^ 30Figure 2-7 Calculated Interferometer angular dependent intensity profile^32Figure 3-1 Plot of ln(GaAs Etch Rate) vs. ln(Hydrogen Atom Partial Pressure) at(a) 250 °C and (b) 280 °C to Estimate Reaction Order^38Figure 3-2 Arrhenius plot for the determination of the activation energy for theetching of GaAs with atomic hydrogen^ 43Figure 3-3 SEM photomicrographs of (100) GaAs etched at 205 °C from (a) side and(b) surface normalFigure 3-4 SEM photomicrographs of (100) GaAs etched at (a) 180from surface normal^Figure 3-5 SEM photomicrographs of (100) GaAs etched at (a) 280^ 45°C and (b) 205 C46°C and (b) 360 °Cfrom side^ 47Figure A-1 Slope Uncertainty Estimate Illustration^ 59Figure A-2 Preexponential Determination with Uncertainty^ 62viAcknowledgmentsThanks very much to the Mechanical Shop staff for friendly service and toSean Adams for effective and conscientious glass blowing. Mary Mager in theMetallurgical Engineering Department also proved very helpful and must becredited for the good SEM shots. Hiroshi Kato in Electrical Engineering was anexcellent guide in the fab lab and did much of the mask depositing work for me. Imust also express my gratitude to Kin-Chung Wong for daily help during myintroduction to this brand of experimental science. The extended loan of Physica 13170 1991 from Rob Kiefl was very helpful as well as several conversations. Thankstoo to George Y. Gu who I remember one day, aside from other support and help,blew many glass sample holders as fast as I could break them. Hongjun Li has alsohelped me struggle over various conceptual barriers. Ed Wishnow kindly sharedhis interferometer experience with me. I've greatly benefited from conversationswith Paul Meharg. I am lucky to work with such a capable person willing to spendhis time and brain cells explaining to me the details of what perhaps could havebeen only a section in his Ph.D. thesis. I greatly appreciate the patience of Dr. E. A.Ogryzlo.viiSECTION 1: INTRODUCTION1.1 GENERAL PURPOSE OF STUDYIt is scientifically and industrially relevant to understand the effects,including bonding details, of atomic hydrogen in and on GaAs. A myriad ofcompound semiconductor bipolar and field effect transistors as well as lasers arecurrently fabricated with the aid of various dry etching techniques1 most of whichcontain hydrogen. An understanding of the behavior of H in one crystal shouldelucidate information relative to other perhaps more complicated crystals.Furthering the understanding of surface chemistry will undoubtedly result inimprovements in device fabrication technology.Hydrogen atoms are commonly present, intentionally and unintentionallyin cleaning, growth, doping, neutralization and passivation of industrially preparedGaAs. GaAs permeates the whole of the optoelectronics industry and the reviewby Johnson et a12 of experimental results of hydrogen in crystalline semiconductorsdisplays the void in the mere determination of the binding energy parameter forhydrogen in GaAs.The etching reaction of thermalised H atoms with gallium arsenide is offundamental nature. Today, gas - solid reactions remain illusive to the theorist.The only first principles theoretical model which the author is aware of thatsuccessfully achieves etching of a semiconductor (Si) with a gas phase species (F)makes the approximation that the reaction occurs adiabatically3 (i.e. no heat iscarried away from the substrate).The objectives of the current study are to demonstrate that thermalisedatomic hydrogen does etch GaAs, to estimate the activation energy for such aprocess and to measure the absolute rate at which H etches GaAs. To ourknowledge there have been no published estimates of the absolute rate constantsfor this etching reaction.Measurement of the absolute hydrogen atom concentration separates thepresent work from non-kinetic studies of atomic hydrogen with semiconductors. Itis hoped that someday theorists can reconcile the data of this experiment withothers and provide a bona fide theory of the interaction of a semiconductor withthe ever-present, simplest of atoms: hydrogen.1.2 HYDROGEN ATOMS IN SILICON1.2.1 ATOMIC HYDROGEN ON THE SILICON SURFACEAtomic hydrogen saturates dangling bonds on silicon surfaces and tends toremove the reconstruction4. At room temperature both SiH and SiH2 are formedon the Si surface. This can only be achieved through the breaking of Si-Si bonds.At 300 °C the SiH species dominates. Even molecular hydrogen dissociates enoughat this temperature to promote H atom chemisorption which can hamper growthof epitaxial Si and SiGe films.1.2.2 ATOMIC HYDROGEN DIFFUSION IN SILICONSome convergence of theoretical and experimental studies exists todayregarding the lowest energy configuration of atomic hydrogen in crystalline silicon.Electron paramagnetic resonance, muon spin resonance experiments show that thelowest energy configuration of H in silicon is the bond center (BC) position andthere exists a secondary minimum for H at the antibonding site4 (i.e. at a site acomparable distance from the Si atom as the bond centre, but on the opposite sideof the Si atom).Atomic hydrogen produced by a remote H2 plasma is well known to diffuseinto Si at moderate temperatures (150 - 300 °C)5. Hydrogen plasma exposure isusually achieved via either a radio frequency discharge (13.56 MHz) or a lowfrequency discharge (30 KHz). Of the several states in which H exists in the Si lattice2the BC site appears to be the most energetically favourable, particularly if latticerelaxation is possible, as it is close to a surface.6The diffusion coefficient of H in Si was experimentally determined by VanWieringen and Warmoltz7 to be:D = 9.4 x 10-3 exp(-11 kcal/RT) cm2/secThe solubility, S. of H in Si for 1 atmosphere of H was also found by VanWieringen and Warmoltz to be:S = 2.4 x 1021exp(-43 kcal/RT) molecules/cm3- 10-10 molecules/ cm3 at room temperature. Experiments detect far more atomsthan this very low equilibrium value.1.2.3 ATOMIC HYDROGEN GENERATED PLATELETS IN SILICONAtomic hydrogen incorporation as a result of exposure to a remote H2plasma often leads to creation of extended defects. Johnson et a18. observed platelet(davg = 7 nm - 400 Si-H bonds) or microcrack formation (predominately along the{111) crystallographic planes and less than 0.1 gm from the surface) withtransmission electron microscopy (TEM) in crystalline Si after exposure to highconcentrations of atomic deuterium substituted for hydrogen. Johnson et al. foundthe density of platelets to be proportional to the near surface concentration ofatomic deuterium. The H generated platelets can be thought of as discs of bonded Hatom separating adjacent planes of a lattice.Johnson et al.8 concluded platelet formation in crystalline Si is due merely todiffusion of H into the crystal; not plasma or radiation damage. The first 5 nm of Sibecomes "virtually amorphous"9 while the first 200 nm suffers "severe crystallinedisorder" revealed through cross sectional TEM for H plasma treated Si crystals.Results of total energy calculations of H in Si lead Jackson and Zhangl° topostulate that a paired form of H may be responsible for the formation of this3platelet effect. J. B. Boyce et. al.11 performed nuclear magnetic resonance ondueterated crystalline silicon and obtained results consistent with the calculationsof Jackson and Zhang. Hydrogen related platelets in silicon can now be attributed tothe formation and clustering of what is commonly referred to as H2*, that is; pairsof atomic hydrogen are thought to enter Si - Si bonds by one of the H atomsbreaking the Si - Si bond and simultaneously restoring full coordination of that Siatom, while the other H atom is thought to occupy the antibonding, tetrahedralinterstitial position of the neighboring Si atom. Boyce, Johnson, Ready andWalker11 successfully used NMR on deuterated (100) Si to observe the <111>orientation of the Si-D bonds in similar D-containing platelets. The resultingplatelets are aligned along the (1111 planes.1.2.4 ATOMIC HYDROGEN ETCHING OF SILICONFeng and Oehrlein12 experimentally investigated the H atom etching ofsilicon in 1987. The above brief description of H atoms breaking Si-Si bonds (§ 1.2.1)close to the Si surface has been computationally confirmed to be plausible andsuspected responsible for H atom etching of the {111), (110) and (100) planes ofcrystalline Si13 SiH2 is found to desorb from the 16-atom cluster after a total offive zero-energy H atoms (one of which gives the surface Si atom full tetrahedralcoordination) are incident upon it.1.3 HYDROGEN ATOMS IN GALLIUM ARSENIDE1.3.1 HYDROGEN ATOMS ON THE GALLIUM ARSENIDE SURFACEH atom chemisorption on the (110) face of GaAs has been observed usingelectron energy loss spectroscopy14 after exposing the (110) GaAs surface to H atomsfrom hot filament dissociated H2. H is found to form covalent bonds with both the4Ga and the As atoms. Synchrotron radiation photoemission spectral4 found As p-like and Ga and As s-like empty states on the (110) GaAs.1.3.2 ATOMIC HYDROGEN DIFFUSION IN GALLIUM ARSENIDEB. Clerjaud et al15. hypothesized that atomic hydrogen diffuses as either aneutral or a negatively charged species in SI GaAs.The diffusion activation energy for HO in undoped GaAs was found by Rhabiet a116 to be 0.97 eV.In 1991 Johnson17 stated there has been no direct determination of theexistence of H2 in a crystalline semiconductor. Most researchers believe however:"...the most stable form of H in semiconductors is the H2 molecule."18Molecular hydrogen may be present in hydrogenated GaAs, but 1-12 is thoughtto be immobile, nearly inert and to reside at a site in GaAs with tetrahedralsymmetry, with respect to nearest neighbors (e.g. between four "neighboring" Asatoms), known as the T site19 as shown in Figure 1-1.There is another hydrogen complex, called H2*, consisting of one H in the BCsite and a second H in the T site. H2* formation is suspected to aid H diffusion inGaAs as well as hopping between T sites20. Figure 1-1, from L. Pavesi and P.Giannozzi,21 shows the various high symmetry sites in the GaAs lattice.Secondary Ion Mass Spectrometry (SIMS) profiling preceded by deuterationappears to be the definitive technique for the determination of diffusion depth of Hinto a crystalline semiconductor. The solubility of H in GaAs appears to be 2 x 1020H / cm3.22 Chevallier et al23. found in undoped GaAs the deuterium diffusionprofile to be close to an error function and a diffusion coefficient for D three timeslarger in undoped samples than that of heavily Si-doped GaAs.E. M. Omeljanovsky et al.24 determined the temperature dependence of thediffusion coefficient of atomic hydrogen in Semi-Insulating GaAs to be D = 0.02exp5e©0 HAsG aFigure 1-1. Tetrahedral (Till and Tv), antibonding and bond centre sites for atomichydrogen in crystalline GaAs (from L. Pavesi and P. Giannozzi21)6(-0.83eV/kT) cm2/sec. (Si Ea - 0.5 eV see Conyers et al). Zavada et a125. found fromSIMS profiling measurements in the 200 - 600 °C range the diffusivity, D, to be D =1.5 x 10-5 exp(-0.62 eV/kT) cm2/sec in n-type GaAs.The temperature range of interest (200 - 400 °C) is high enough such thatatomic hydrogen diffuses into the bulk GaAs readily26.Hsieh et a127. found dislocations can provide pathways for atomic hydrogendiffusion, feeding hydrogen deep into the bulk.In their study of buried n-type silicon doped GaAs layers grown by MBEdeuterated at 220 °C Caglio and co-workers28 found an increase in the roomtemperature electron mobility from 2270 cm2/ Vs (undeuterated) to 3950 cm2/ Vsaccompanied by a reduced carrier concentration. Caglio and co-workers found thediffusing deuterium concentration was independent of layer doping level but thebound deuterium concentration in the doped layer was very close to that of itssilicon concentration.1.3.3 HYDROGEN PLATELETS IN GALLIUM ARSENIDEHydrogen platelets oriented along the (111) planes have been observed inproton bombarded GaAs during tunneling electron microscope studies29.It is believed from thermal effusion spectra that atomic deuterium formscomplexes with lattice atoms and/or extended defects in bulk GaAs30. Deuteriumincorporation stemmed from exposure of the GaAs to a remote dc D2 plasma in thetemperature range of 100 - 250 °C. An unexplained high temperature thermaleffusion peak lead Stutzmann et al.30 to believe extended defects may exist in thebulk of their deuterated sample.71.3.4 H2 ADSORPTION ON GALLIUM ARSENIDEMolecular hydrogen can be considered a noninteractive, inert species withrespect to surface reactions on GaAs in the temperature range of this study. Due tothe fact that H2 molecular orbital levels and As surface atom valence orbital levelsare substantially different, H2 and As orbital overlap can not occur, so H2 does notstick to or dissociate on the (100) GaAs surface31 . Other calculations have found theactivation barrier for dissociative adsorption of molecular hydrogen to be 2.5eV32 .1.3.5 ATOMIC HYDROGEN ETCHING GALLIUM ARSENIDEOf the many steps in semiconductor device production between crystalgrowth and device testing this study focuses upon a processing essential known asetching. Etching is the removal of material (here crystalline GaAs) via somephysical or chemical reaction. The rate of reaction of the etchant with thesemiconductor as a function of temperature helps determine the feasibility ofvarious processing techniques. Etching reactions relevant to semiconductors arebetween the gas or liquid phase etchant and the solid semiconductor. Reactions ofatomic hydrogen with GaAs have been the subject of limited study through theexposure of GaAs to H in an H2 radio frequency, microwave or Electron CyclotronResonance (ECR) plasma. To date there has been no study of the morefundamental reaction between GaAs and thermalised H. This etching reaction isnot unambiguously known to occur.Several published papers have appeared describing the cleaning of GaAswith hydrogen plasmas which yield useful information pertinent to the etching ofGaAs. In general, it is found that atomic hydrogen from a plasma is effective atremoving surface contamination such as carbon and oxygen compounds. Below8some of this work is summarized primarily focusing on the technique employingan ECR plasma leading to incident energies for the impinging neutrals on the orderof 10 eV.Hydrogen discharges were found in 1981 by Smolinsky, Chang and Mayer33not to etch GaAs or its oxide. Shortly thereafter Chang and Darack34 first reportedetching of both p- and n-type GaAs, and its oxides, with a hydrogen plasmaestablishing GaAs etch rates of 20 A/min could be easily achieved. It washypothesized the reactive species in the plasma, at least with respect to the oxides,was atomic hydrogen. The sample temperature was not estimated; however, thesample was within the discharge region. It was determined by the authors that theselectivity ratio of the oxide etch over the substrate was approximately two. Changet al.35 in a later publication eventually put an upper limit on the substratetemperature during etching in an H2 plasma of 150 °C and described the resultingsurface morphology and composition. Auger Electron Spectroscopy (AES) scans ofthe etched GaAs surfaces showed no elemental segregation whereas they did claimin the same paper that indium droplets formed on hydrogen plasma etched InPsurfaces. A post-etch surface morphology comparison of Liquid EncapsulatedCzochralsky (LEC) grown GaAs with that of Molecular Beam Epitaxy (MBE) grownGaAs convinced Chang et al.35 that surface roughening is most likely a result ofinitial surface pits and defects on the LEC samples. The etched and unetched MBEsamples were reported virtually indistinguishable, whereas the LEC grown sampleswere roughened during etching.Okubora and co-workers36 in 1986 reported what they considered to bemolecular hydrogen etching of GaAs, under an AsH3 overpressure, at temperaturesin excess of 800 °C. Okubora and co-workers found no difference in etch ratesbetween undoped and Si doped n-type GaAs. We propose that they were justetching the As and evaporating the Ga. They suggested the rate limiting step in9that reaction is the evaporation of gallium for they had obtained an activationenergy, Ea=2.6 eV, in this temperature range nearly equal to the heat of evaporationof gallium. An activation energy approximately equal to the heat of evaporation ofGa is not surprising. The As removal has a very low activation energy so Asdesorbs easily. The decomposition of AsH3 into H2 and As2 can, as they suggested,be regarded as being 100%. Then applying Le Chatelier's principle one can see thatAs from the surface may feed the reaction pushing it toward the formation of AsH3resulting in As removal. Gallium eventually evaporates and the process repeats.When Ar replaced the H2 in the ambient gas mixture no etching was observed,suggesting the H2 was indeed the "etchant" and that the As evaporation at thishigh temperature was minimal due to the AsH3 overpressure. Okubora and co-workers also found, within the limits of AsH3 partial pressure of 0.75-12 Torr, theGaAs etch rate with H2 was independent of the AsH3 pressure. The H2 partialpressure was 300 Torr and 600 Torr in the two reported experiments in which theAsH3 partial pressure was varied. Okubora and co-workers proposed the first stepof the reaction kinetics involves chemisorption of atomic hydrogen, for the fractionof dissociated hydrogen should be at least 1x10-5 at 800 °C. This etching techniqueyielded "smooth... and mirrorlike" surfaces from their LEC grown undoped SI-GaAs samples. With an AsH3 overpressure they could achieve congruent loss ofGa and As, but without it they observed Ga droplet formation.In agreement with the earlier work of Chang and Darack34, Sugata et al.37showed, in 1988, that Ga and As stoichiometry is maintained during cleaning witha hydrogen radical beam from an ECR plasma as determined by auger electronspectroscopy. Their radical beam consisted of mostly H+ ions. This cleaning resultsin the reduction of the interface surface state concentration rendering it suitable forpreparing samples for MBE pretreatment. Sugata et al. believe the rate limiting stepto be the chemisorption rather than the desorption or reactant formation.1 0Reflection High Energy Electron Diffraction (RHEED) measurements suggestedcrystallinity was maintained and all cleaning was performed with the substratetemperature less than 400 °C.K.C. Hsieh et al.27 exposed thin Metallorganic Chemical Vapor Deposition(MOCVD) grown GaAs on a Si substrate to a hydrogen plasma but their etch rates(resulting in the removal of nearly all three microns of GaAs) could not beassumed to be uniform over time so no useful activation energy could be derivedfrom this data. Hsieh et al. did however find the resulting surface after a two houretch to be "pyramid-like," and after a five hour etch, in apparent contrast to thework of Chang and Darack34 and Sugata et air, metallic gallium "particles" wereseen (via TEM microscopy) to form on the surface presumably due to prolongedexposure and utter consumption of the sample under investigation. To ourknowledge this is the first report of Ga droplet formation on GaAs during ahydrogen atom etch. Previously, the droplet formation had only been reportedduring annealing36 of GaAs where the As evaporation had left a Ga rich surface.M-C. Chuang and J.W. Coburn38 were the first to report the products formedduring a hydrogen plasma etch of GaAs. They observed only volatile arsenichydrides with mass spectrometry during exposure of GaAs to hydrogen atoms froma plasma in the presence of Ar ions, but claimed no products were formed in thepresence of hydrogen atoms without simultaneous argon ion bombardment (i.e.hydrogen atoms alone appeared to not react with GaAs). They observed neithergallium hydride species with the mass spectrometer nor gallium droplet formation.AES performed on the resulting surface indicated an increased As deficiency. Thisenigma is still far from resolution since Chuang and Coburn observed no GaFfxdespite the fact that hydrogen plasmas are well known to etch GaAs.I. Suemune and co-workers39 next found the hydrogen atom etch rate ofGaAs decreased with increasing angle of incidence (from the substrate normal) of11their hydrogen ECR plasma beam and their etching even ceased after reaching adepth of 20 A for shallow incident angles apparently leaving an atomically flat (100)surface. The etch rates they (Suemune co-workers) found were approximately afactor of 100 slower than our measured etch rates with the difference merelyassumed to be attributed to vastly different hydrogen atom concentrations.J.R. Creighton40 exposed (100) GaAs at 150 K to hydrogen atoms created bydissociation of 1-12 on a hot tungsten filament. Temperature ProgrammedDesorption (TPD) studies were carried out and again (as in reference 38) no gallium-hydrides were observed. Creighton attributed the elusiveness of gallium-hydridesto surface hydride decomposition resulting in molecular hydrogen formation.By using a hot tungsten foil in the presence of H2, J.A. Schaefer et al.'"exposed GaAs to H atoms and subsequently identified, via High ResolutionElectron Energy Loss Spectroscopy (HREELS) studies, the formation anddecomposition on the surface of both arsenic and gallium hydrides. This study;however, demonstrated the resulting surfaces were gallium rich. J.A. Schaefer andco-workers42 later obtained results indicating increased hydrogen exposure leads toincreased arsenic- and gallium-hydride formation (GaH and GaH2) on the surfaceuntil the exposure was too high leading to gallium droplet formation.During their in-situ RHEED monitoring of the same cleaning process asKishimoto and co-workers43 measured the etch rate of (100) GaAs at three substratetemperatures between 300 - 500 °C. Their etch rate data corresponds to anactivation energy of 0.2 eV. The technique for the determination of their etch ratewas not stated.Another piece of information gleaned from a hydrogen plasma cleaning ofGaAs publication is the formation of the stable Ga203 at temperatures less than150 °C 44. Mikhailov et al." found through X-ray Photoelectron Spectroscopy ()CPS)studies that this oxide may well be responsible for the inhibition of etches at12temperatures less than 150 °C. However they proposed that the decomposition ofGa203 and 2H yielding desorbed Ga90 and water at higher temperatures can resultin the removal of the oxide.13SECTION 2: EXPERIMENTAL2.1 REACTION VESSELGaAs was exposed to large fluxes (— 5 mTorr) of atomic hydrogendownstream from a low pressure (0.4 Torr) H2 plasma resulting in a chemicalreaction between the gas phase H atoms and the solid phase GaAs. The reactor,including valve bodies, was entirely Pyrex (see Figure 2-1). This "fast" flow systemwas driven with a Welch Duo-Seal model 1402 45 1/min (at 0.5 Torr) rotary pumpwhich provided an H2 flow from a standard cylinder of 40 sccm over the sample.The pressure in the flow system is measured with an Edwards capacitance typemanometer. A microwave discharge was created 15 cm upstream from the sample.The sample temperature was measured by a thermocouple mounted within thesample holder.The reaction tube was 20 mm in diameter in the region of the gas - solidreaction. Since the reaction was found to only proceed above 180° C, the walls ofthe reactor and hence the gas and sample were heated by wrapping a heating tapearound the outside of the reactor leaving as small an apperture as possible in orderto permit the passage of the incident and reflected laser light neccesary to monitorthe etch in-situ. The heater "tape" was across the output of a Variac. Adjusting theac voltage output of the Variac controls the power the heater "tape" delivers to thereactor and hence the reactor, sample and gas temperature. It is presumed thewalls, sample and gas are in thermal equilibrium under any given etchant gas flowconditions.The room temperature gases, carried by copper tubing, that were admittedinto the flow system through needle valves were prepurified H2 and N2 suppliedby Linde and according to supplier's specifications were 99.99 and 99.998 % purerespectively. The H2 flow rate was measured with a Sierra Top-Track mass flow14Figure 2-1. Schematic layout of flow system for H atom generation, detection andetching of (100) GaAs15meter. The N2 flow rate was determined relative to the H2 flow. To estimate theN2 flow the flow of H2 was remeasured by feeding the output voltage of thepressure guage to a chart recorder while bleeding the H2 gas into the sealed reactorand recording the increase of pressure with time. The slope (=dP/dt) of theresulting plot is proportional to the flow of H2. After pumping out the H2 andrepeating, the same prodedure is carried out flowing only N2 gas. During anexperimental run, the smaller N2 flow is mixed with the larger H2 flow. The highpressure side of the N2 needle valve is - 1 atm overpressure, so the differencebetween the flow of N2 in the absence of H2 and in the presence of less than 1 Torrof 1-12 is negligible. The resulting slope for the N2 dP/dt tests was consistently - 10-3of the H2 slope. This indicates N2 was - 0.1% of the total flow. This fraction wasnot particularly intended. It was merely the smallest measureable nonzero flowthat could be obtained from the needle valve used to admit the N2.Care was taken to preserve gas purity during regulator installation by leavingregulator valves open during initial opening of the gas cylinder valves.The H2 gaseous flow in these experiments is on the order of 40 scan andtotal pressures were just above 400 mTorr.Vibration isolation is not elaborate in this experimental arrangement. Aflexible rubber hose coupling the low pressure side of the vacuum pump to thereaction vessel is the only hint of vibration isolation. The etching of GaAs isfollowed in-situ by observing interference fringes produced by reflections off of thesample of visible red laser light which traverses a total path length of about onemetre. The reflected laser light impinges on a photoconductor changing itselectrical conductivity. This photoconductor is one element of a voltage divider.The dc voltage appearing across the constant resistance element of the voltagedivider is fed to the input of a chart recorder. The periodicity of the interferogram(on the order of one hour) is much larger than that of conceivable vibrations from16the building or the system vacuum pump. However, vibratory motion of thesample holder will move the specular reflection off the sample such that it partiallyor completely misses the photoconductor. Clearly this can lead to fluctuations inthe intensity of detected light which could be miscontrued as the manifestation ofsurface roughening. The two sample surfaces responsible for the laser reflection,the silicon nitride mask and the GaAs surface being etched, do not move relative toone another in the absence of etching (or growth) when the temperature of thesample is constant in time. Since the reflections from these surfaces are assumedsolely responsible for the interference, the sample can undergo limiteddisplacements without adversely affecting the resulting interferogram. Providedthe specular reflection does not miss the photoconductor, vibratory motion of thesample holder and the sample does not result in substantial photoconductorvoltage swings. Therefore, small variations of the sample holder about itsequilibrium position result in no noticeable intensity flucuations.Indeed, the Pyrex sample holder's thinness did lead to erroneousfluctuations in the detected light intensity which were correlated with sample andholder temperature variations. If the temperature is raised from 300 °C to 325 °Cfor example, the Pyrex sample holder may move due to thermal stress. Thedisplacement associated with this could result in a total loss of the specular beamfor the room temperature detector has not experienced a complimentarydisplacement. Some samples were etched at two temperatures. Data acquisitionrequiring a range of temperatures necessitated readjustment of system optics foreach temperature and confidence thermal equilibrium has been established.Celophane tape was used to scatter the light incident on the photoconductor in aneffort to reduce the detector's directionality making it less vulnerable to intensityshifts due to sample holder displacements.17To minimize noise from ambient light sources a red narrow pass filter wasused (see Figure 2-1 for placement) resulting in the selection of primarily theneighboring wavelengths around the lasing transistion wavelength at 632.8 nm. Ablue filter was also used to avoid saturation of the photoconductor.2.2 SAMPLE HOLDER AND THERMOMETRYThe functionality of the sample holder draws on its ability to keep thesample in a fixed position, conduct heat away from the sample, allow interaction ofthe sample with the etchant, H, permit the measurement of the sampletemperature and allow quick loading of the sample into the reactor. Sampleholders were blown from 4" straight sections of 0.25 " OD Pyrex tubing (see Figure 2-2). The first step of sample holder fabrication is to close the tube at one end, thenblow, stretch and flatten the glass under flame such that the wall thickness at thisend of the tube is less than 0.1mm. A small area on this end of the sample holderis heated locally and a 1800 bend is created resulting in a spring-like configuration.This spring depresses the GaAs sample against the aforementioned thin-walledsection of the Pyrex tube. Within this tube, not in direct contact with the sample orthe etchant gas flow, is a point contact Chromel Alumel J-type thermocoupleconnected to a Fluke readout displaying the sample temperature to the nearest 0.1°C. Confidence in the absolute sample temperature estimate is based largely on thefact that independent measurements of the temperature dependence of thisreaction, made in this laboratory45 with the thermocouple in direct contact withthe sample yielded consistent results. Hydrogen atoms recombining to form H2 onthe thermocouple itself eliminate the possibility of direct exposure of thethermocouple to the hydrogen atom flow.18GaAs Sample0.25 " OD Pyrex^ Thermocouple4"Figure 2-2. 0.25 "OD pyrex tubing sample holder with GaAs sample andthermocouple192.3 GALLIUM ARSENIDE SAMPLES AND SILICON NITRIDE MASKUndoped, semi-insulating single crystal LEC GaAs was grown by JohnsonMatthey. The wafer was 2" diameter 0.5 mm thick mechanical grade (100) GaAsoriented 2° off axis. In order to follow the etching reaction, it was neccesary topattern the wafer with an array of thin stripes which essentially transform the flatGaAs surface into a multislit optical interference device (see Figure 2-3). The maskused in this process consisted of two orthogonal 1 cm2 areas of 15 ;.ttn wide straightlines separated by a distance of 15 gm. Several 2 cm2 pieces were cleaved from thewafer and patterned seperately. This was achieved by firstly depositing a 950 Asilcon nitride film on our wafer. Then, half the silicon nitride was removed duringthis preparatory treatment through standard photolithography and etchingtechniques45 resulting in 50% of the surface covered with nonreactive siliconnitride stripes. The processed wafer had silicon nitride (Si3N4) stripes 15 gm wideand 15 gm apart aligned on half of the total wafer area parallel to the <011>direction and on the other half perpendicular to it. Rectangular GaAs chips werecleaved from these 2 cm2 pieces resulting in sample surfaces of - 0.2 cm2 andsample volumes of - 0.01 cm3. Other details of the nitride preparation can befound in the above reference.Just prior to each experiment, the masked and cleaved (100) GaAs sampleswere immersed in a few millilitres of room temperature concentrated hydrochloricacid for about a minute to remove any native oxide layer. The samples thenexperienced an agitated dip in distilled water.Before acquiring data, the samples were loaded onto the sample holder byslipping them under the glass spring in an N2 ambient. Then the holder withsample is inserted into the heated, He back-filled reactor toward the center of flow.20<100>4)------0<011><011>Figure 2-3. (100) GaAs with equally spaced silicon nitride stripes (a = 30 iim, b = 15—gm). Mask alignment along each the <01-1> and <011> were used.212.4 HYDROGEN ATOM PRODUCTIONAtomic hydrogen is obtained by dissociation of molecular hydrogen. This isachieved by passing a short length of the reactor (cross sectional area - 1 cm2) withits flowing H2 / N2 gas mixture (H2 and N2 are mixed several centimetersupstreamfrom the discharge) through a coaxial cable fed quarter wave microwavecavity with 50 W at 2.45 GHz = 12.2 cm) incident upon it from an E.M.I.Microtron 200 microwave power generator. The cavity is equipped with a port forcooling air which provides for heat removal from the hot walls containing theresulting plasma.No "wall poisons" are employed in the present configuration of thisapparatus. Wall poisons such as phosphoric acid are often intentionally used toincrease the hydrogen atom concentration46 for the products that can be withdrawnfrom a pure H2 plasma in a clean pyrex tube contain very few H atoms. Thereaction rates which we investigate in this experiment commonly necessitateconstant hydrogen atom concentrations over periods of one to three hours. Thedecay in time of the effectiveness of these "poisons" lead the author to try othermeans of sustaining a constant concentration. Certainly, a constant and generoussupply of H is required for a kinetic study of this kind.An alternative to wall poisons is to "trickle" pre-purified nitrogen gas intothe predischarge flow of H2. Similarly, other researchers have added traceamounts, 0.1 - 0.3 %47, of H2O or 02 to reduce recombination of H in H2 plasmas.This provides the long term stability necessary for these protracted reaction ratemeasurements. Purified H2 gas flows through the reactor with 0.1 % purified N2added to stabilize the hydrogen atom concentration over periods of several hours.Larger flows of nitrogen were found to substantially retard the etch rate.222.5 HYDROGEN ATOM DETECTIONThe hydrogen atom concentration was determined with an isothermalcalorimetric probe" which uses the heat of recombination of the atoms on aplatinum wire to measure the hydrogen atom flow. A comparison of the absoluteH concentration determined via the platinum wire with that determined via a H +NOC1 titration found agreement within 1 %49 . A 15 cm length of platinum wire(AWG #30) was coiled to occupy as much of the reactor's flow cross-section aspossible (as in Figure 2-4). The biased coil (and its leads) behaves as a resistivebranch of a Wheatstone bridge configured in a 1: 1 ratio (see Figure 2-5).A ten turn potentiometer adjusts the current and another ten turnpotentiometer adjusts the opposite variable branch of the bridge. A digitalvoltmeter is the null detector measuring the "null" voltage to the nearest 100 laV.The isothermal calorimeter is comparable to that of E.L. Tollefson and D.J.LeRoy in their pioneering experiments of hydrogen with acetylene" The platinumwire was wound and spot welded to two stainless steel lead-in rods 3 mm indiameter. The vacuum seals between the glass and rods are made of Torr Seal®epoxy. The stainless steel rods are exposed to the hydrogen flow with no adverseeffects upon the quantitative hydrogen atom concentration for they aredownstream from the detector, where all the atoms have been removed.The purpose of the bridge is to monitor as accurately as possible thetemperature dependent dc resistance of the Pt wire. Keeping the detector inequilibrium with the walls of the reaction tube is the "name of the game" for theisothermal calorimeter. What it does best is utilize the Wheatstone bridge tomeasure changes in the resistance of the wire corresponding to temperaturechanges in the wire. The hydrogen atoms available for the reaction underinvestigation recombine on the Pt wire to form hydrogen molecules. The heat ofrecombination of the hydrogen atoms tends to warm the Pt wire increasing its dc23(a)EINUTOIAWMOIMUMMIIR(b)(a)^(d)Figure 2-4. Winding process for Pt wire H atom detector (a) straight AWG #30 Ptwire, (b) wind Pt wire around 0.125 " OD glass tubing, (c) use 0.4 " glasstube as a form to shape Pt wire into spiral from already coiled wire, (d)final Pt wire configuration, as in the reactor24Figure 2-5. 1: 1 Wheatstone bridge configuration for H atom detection withcurrent regulator, Is, null detector voltmeter, Vo. Pt wire detector, R, andvoltmeter, V, to imply coil current25resistance and destroying the sensitive balance of the bridge. Immediate decreaseof the bridge current upon ignition of the discharge from its initial value 'off tosome final value Ion where 'off (> Ion) rebalances the bridge due to the resultingrestoration of its temperature and resistance.An actual experimental determination of the hydrogen atom concentrationin the flow system consists of a measurement of Ion with the H2/N2 discharge on inthe steady state (i.e. dT/dt = 0) followed by a measurement of Ioff with the dischargeextinguished. The thermal conductivity of the flowing gas remains constantregardless of the status of the discharge. Only H2 should be carrying heat away fromthe Pt wire. Since the dissociation of H2 in the region of interest of this experiment(downstream from the discharge) doesn't exceed 3% (see Section 3) the Pt wire'sthermal link to the walls of the reaction vessel, remains constant, eliminatingperturbations to thermal equilibrium due to discharge status dependent variationsin the thermal conductivity between the detector wire and the vessel wall.Knowing one experimental parameter other than the difference in coilcurrent with the discharge off and on, namely the dc resistance of the Pt wire at itsoperating temperature, an absolute determination of the heat added to the Pt wireper second and hence the total heat of recombination per second can be found fromthe relation between power, current and resistance:P = A(I2) x RPtwhere A(I2) = Ioff2 - Ion2 and Rpt = Pt wire dc resistance. This heat per secondadded to the wire has been shown to be49 directly proportional to the absolutenumber of hydrogen atoms per second (assuming the detector's efficiency is unity)in the reactor's flow. If one divides P by the heat given off by the exothermic26p^H atom flow [mol/sec]^x total pressureH - H2 flow [mot/sec.'recombination reaction of H+H---> H2 (218 kj/mol of H) one is left with the numberof moles of atomic hydrogen per second:P 1J/sec] H atom flow [mol/sec] = 218 kJimolTo calculate PH we can use the measured H atom flow, H2 flow and totalreactor pressure,where the mol/sec of H2 are found simply by multiplying the flow of H2 from theflow meter by its density . The STP molar volume of H2 can be used in thiscalculation to determine the flow of H2 in moles per second because the H2 sourceflow is measured in standard cubic centimeters per minute (sccm).STP Molar volume of H2 = 22.43 l/mol = 2.243 x 104 cm3/molDensity of 112 = 1/molar volume = 4.458 x 10-5 mol/cm3mol/sec of H2 =#sccm of 112 x 4.458 x 10-5 mol/cm360 sec/minThe H2 flows in this study, on the order of 40 sccm, correspond to approximately3x10-5 mol/sec.2.6 INTERFEROMETERThe probe for material removal observation is a 10 mW 632.8 nm He-Nelaser operating in continuous mode and shone upon the effective multislit27aperture created by the sample's silicon nitride stripes (as in Figure 2-3). Thereceding surface from which material is removed reflects part of the beam ofphotons from the laser while the silicon nitride, unaffected by the hydrogen atometchant, reflects the remaining fraction of the beam. In the limit of a perfectlyconstant etch rate this configuration is a small scale Lamellar GratingInterferometer. Invented in the 1950's by Strong and Vanasse at Johns HopkinsUniversity50, the full scale version is more commonly used in Fourier TransformSpectroscopy.Unlike reflected photons from the silicon nitride, those from the GaAsexperience a rather continuous change in optical path length. Etching of the GaAsleads to an oscillation in the reflected light intensity at a point far from the sample.The periodicity of this oscillation can be predicted by the relationnX— = 2dsin0 I 0=.1t/211where r is the refractive index of air at 632.8 nm (assumed unity) and 0 is the angleof incidence relative to the (100) GaAs surface and dsine is the added optical pathlength a photon reflected off the GaAs surface experiences relative to a photonreflected off the silicon nitride. Due to the fact that the detector and light source cannot occupy the same place in space, there is some error associated with theapproximation that 0 = /c/2. With our detector and light source geometry (one ontop of the other) the angle of incidence is closer to n/2 - 0.035 rad (88 °) which resultsin less than a 0.2 % error in sine.Constructive interference of the beams reflected off the different surfaces willoccur for the zeroth order reflection whenever 2d = nX, or equivalently, anytimethe depth of the etch is a multiple of X/2.A light intensity dependent voltage from a biased silicon photoconductor issent to a chart recorder which simply plots the intensity of the reflected specular28beam from the sample versus time (see Figure 2-6). The resulting interferogramhas a periodicity corresponding to half of the He-Ne's wavelength (i.e. two cycles ofthe interferrogram depict the removal of approximately 633 nm of material fromthe GaAs surface). The geometry of the silicon nitride stripes turns out to be ofsome consequence to the signal-to-noise ratio of the interferometer. One simplesilicon nitride step is sufficient to give interference as described above. However,experimentors in this laboratory have found the smallest stripe width, b, and thesmallest center to center stripe separation, a, yields the most discernibleinterferogram on the chart recorder paper.When the He-Ne laser is shone onto the striped sample, the reflected lightintensity has the same angular dependence as a diffraction grating. When light isincident normal to a diffraction grating the first (not zeroth) principal maximumoccurs at an angle (measured from the surface normal), 01, where 01 satisfiesasinOi 1X,where a is defined as above and X, is the He-Ne wavelength (632.8 nm). So eldepends on a and A, via,01 = sin-1 (X/a).This angular separation of the zeroth and first principal maxima in thediffraction pattern corresponds to a separation in space, As, at the detector (-0.5 mfrom the surface)As=rx0= 0.5mx0i.Silicon nitride stripes on (100) GaAs from 15 i.tm widths (=b) separated by 15 grri(=a/2) to 100 gm widths separated by 100 p.m have been used in this laboratory.Evaluating 01 (i.e. the angular separation between the zeroth and first principalmaxima) using the above expression and these two values of a,/632.8 x 10-9 m\01(a=30jam) = sin-1 k^)30 x 10-6 m^= 2.1x10-2 rad [15^stripes]99Time [minutes]1 division = 5 minutesFigure 2-6. Photoconductor's output as a function of time. One 1.5 hour period,corresponding to H atom etching of 316 nm of (100) GaAs at 281 °C.30/632.8 x 10-9 m 3.2x10-3 rad [100 .t.m stripes].01(a=200gm) = sin-1 k 200 x 10-6 m )These angular separations lead to a spatial separation, As, between the zeroth andfirst principal maxima at the detector (0.5 m away),As = 0.5 m x 2.1x10-2 rad = 1.1 cm [15 gm stripes]As = 0.5 m x 3.2x10-3 rad = 1.6 mm [100 p.m stripes].With the He-Ne laser light close to normal incidence in the presence ofetching, all the diffraction orders51 are modulated, due to the aforementionedphase difference, by an order dependent cos28 term, i.e. the angle dependentintensity is:1i92^0 {sinNa 1I(0) = -^sinc2^j cos28N2 sina 2nb^nawhere 13 -E —X sine and a ..,7-. j- sine and 0, a, b and X are defined as above.So,Reo cos28where 8 is given by,52= nm + —27cd2^xwhere m is the order of interest, X is the He-Ne wavelength and d (a function oftime) is the difference in height between the silicon nitride and the GaAs. Due tothe form of the 8 order dependence, the intensity oscillations of the zeroth and firstorder are IC out of phase with respect to each other (see Figure 2-7). This can be seenby examining 8 for both the zeroth and first order (i.e. m=0, ±1) evaluated also atthe height differences corresponding to both constructive (d=X/2) and destructive(d=X /4) interference for the zeroth order.8(m=0, d=2/2) = IC; COS28 = 18(m=±1, d=X/ 2) = -±n/2; cos28 = 031Figure 2-7. Angular dependence of irradiance from a Lamellar GratingInterferometer with a = 2b at an etch depth, d, of (a) X/2 and (b) X/4328(m=0, d=X/4) = n/2; cos28 = 05(m=±1, d=X/ 4) = 0, it; cos28 = 1Since the intensity is proportioal to cos26 one can see that constructive interferencein the zeroth order coincides with destructive interference in the first order (theconverse is also true).It is found upon substitution of the above values of cos28 into the intensityexpression and setting a = 2b that,I(m=0, d=X/2) = I(0)I(m=0, d=X/4) =0I(m=±1, d=X/2) = 0I(m=±1, d=X/4) = 0.586 I(0)This phase dependent modulation of the orders neccesitates spatialseparation of the orders if one desires to observe maximum modulation of thereflected light amplitude. It is apparent from the above calculation that the zerothorder maximum and the first (actually all odd) order maxima vary sinusoidally inrelative phase as well as in amplitude as the etch progresses. If, neglectingcontributions from higher orders, both zeroth and first orders are "seen" by thephotoconductor (i.e. the orders nearly overlap in space), in this case of 15 gm siliconnitride stripes, the light intensity will be the sum of the two "out of phase" beamswhich leaves'net = [2 x 0.586 -1] I(0)where one factor of 0.586 comes from each of the m=±1 orders'net = 0.17 I(0).Whereas if the zeroth order only is "seen" by the phototconductor a total swing inlight intensity equal to I(0) is possible. Therefore, best results are obtained when thezeroth order maximum can be separated from the others.33Since our detector diameter is of the order 5 mm, it is clear that the 15 gmstriped samples (As = 1.1 cm) would lead to an enhanced signal to noise ratio overthat of the 100 p.m striped samples (As = 1.6 mm) since the zeroth order maximumfrom the 15 gm striped sample alone will be incident upon the detector.A blue filter was used to prevent saturation of the phoconductor from theHe-Ne's specular reflection off of the GaAs and to minimise the laser enhancementof the etching. A simple transmission experiment was performed to determine theextent to which the filter attenuated the light. At the wavelength of interest, 632.8nm, the filter was found to reduce the laser's intensity 23%. Also of relevance isthe attenuation of the light from a single pass through Pyrex into the reactor. Thetransmission coefficient for pyrex at 630 nm is — 0.9. The sum of the attenuations is—33%, hence the power of the laser light incident on the GaAs is about 6.7 mW,corresponding to 2x1017 photons/sec.The etching reaction yielded such textured surfaces that a fraction of thereflected light that makes it to the detector could conceivably come from subsurfacereflections of the incident light from extended defects or other related abruptrefractive index changes. Owing to the different index of refraction for GaAsrelative to air, a single interference fringe resulting from superposition of asubsurface reflection with a surface reflection would then correspond to removal ofless material then would be expected under the assumption the two interferingwaves are of the same wavelength (632.8 nm). The possibility of sytematic error inthe etch depths, and hence the etch rates, was eliminated by comparison of theinterferometry etch depth measurements with post-etch depth measurementsmade with both a scanning electron microscope and a Tencor Alpha Step 200profilometer.34SECTION 3: RESULTS3.1 MEASUREMENT OF THE ATOMIC HYDROGEN CONCENTRATIONA determination of the rate constants for the H atom etching of (100) GaAs isonly possible when the reaction (etch) rate as well as the absolute hydrogen atomconcentration are known. The atomic hydrogen partial pressures were measuredjust below the GaAs samples downstream from the microwave H2 discharge. Thereactor pressure was on the order of 400 mTorr (1 - 2 % atomic H) and hydrogenatom partial pressures were measured in the 200 - 360 °C range.The rate at which heat is added, P, to the platinum wire from H atomrecombination is obtained from the product of the platinum wire's electricalresistance at its operating temperature and the difference of the squares of theplatinum wire's current neccesary to maintain a constant temperature in thepresence (Ion) and absence (Ioff) of H atoms. While etching at 360 °C, for example,the power the atoms contributed to the platinum wire was,P = 0.0420 A2 x 2.06 f2 = 86.4 mW.The measured H2 flow rate, along with the STP density of 1-12 gas and the knownenergy released in H recombination (217.9 kJ/mol), now permits the computationof the partial pressure of atomic hydrogen.H2 flow =42 sccmtotal pressure = 0.431 Torr0.0864 W / 218 x 103 j/mol PH —^ x 60 sec/min x 0.431 Torr42 sccm x 4.458 x10-5 mol/cm335These values lead to a hydrogen atom partial pressure, PHPH = 5.46 mTorr.The measured hydrogen atom concentrations in this study varied from 3 - 10mTorr (see Table 3-3 below).3.2 MEASUREMENT OF THE ORDER OF THE REACTION WITH RESPECT TOTHE CONCENTRATION OF ATOMIC HYDROGENFrom a compilation of the author's acquired data and independentlyacquired data of another experimentor in this laboratory43 (Tables 3-1 and 3-2) twoestimates of the order of the reaction of the (100) GaAs surface with respect to thehydrogen atom concentration are made. The order can only be tested byexperiment. One needs to etch at one temperature over a range of etchantconcentrations. The etch rate at a given temperature, r, in general should beproportional to the atom concentration to some power, x, i.e.r = kfPF-dxwhere x is the order of the reaction which can take on positive or negativefractional or integer values or even zero. A plot of the natural log of the etch rate atsome temperature vs. the natural log of the partial pressure of H atoms yields aslope equal to the order of the reaction with respect to atomic hydrogen.ln r = xln [PH] + In kFigure 3-la and Figure 3-lb are plots of the log - log data in Tables 3-1 and 3-2.The slopes are found to be 0.90±0.06 and 0.8±0.1 at 250 °C and 280 °C, respectively36Table 3-1Etch Rate, r(nm/min)H Partial Pressure(mTorr)ln r ln PH3.20 4.68 1.16 -5.374.52 7.74 1.51 -4.8626.4 51.0 3.273 -2.98Table 3-2Etch Rate, r(nm/min)H Partial Pressure(mTorr)In r In PH5.70 4.72 1.74 -5.363.37 3.27 1.22 -5.7215.1 2.66 2.72 -3.6321.7 26.7 3.08 -3.62Tabulated data for estimation of the order, x, of the GaAs etching reaction withrespect to the atomic hydrogen concentration, PH at 250 °C (Table 3-1) and 280 °C(Table 3-2).37-6^-5^-4^-3In (H[l / mTord )(b)Figure 3-1. Plot of GaAs ln(etch rate) vs. ln(H atom partial pressure) at (a) 250 °Cand (b) 280 °C to estimate the order of the reaction with respect to the Hatom concentration.38(quoted errors are derived in the Appendix 1). Taking into account the fact that theH atom partial pressure uncertainty is suspected to be of order 25 %, theimplications of the smaller, graphically determined errors associated with thereaction order determination can not be seriously considered. The more realistic 25% uncertainty in the H atom partial pressure measurement brings the reactionorder to unity within experimental error, or at least it is not evident the order ofthe reaction with respect to the hydrogen atom concentration differs from unity .Reaction orders are frequently temperature dependent. In this narrowtemperature range (between 250 °C and 280 °C) the two experimentally determinedvalues of the order are the same, namely: unity.To follow is a rate constant calculation which assumes the etching reaction isfirst order with respect to hydrogen atoms.3.3 MEASUREMENT OF THE ABSOLUTE RATE CONSTANTS ANDACTIVATION ENERGY FOR ETCHING GALLIUM ARSENIDE WITH ATOMICHYDROGENAssuming from the above discussion the reaction rate is first order withrespect to H, the rate coefficeints (or constants) are related to the etch rate, r, via:r = kr[H]1 = kr[H]where kT is the rate coefficient at temperature T. kT can also be related to theactivation energy and the absolute temperature by the Arrhenius equation,kT = A exp(-Ea/RT),where the preexponential constant, A, and its uncertainty were found from theArrhenius plot (see Appendix 2) to be,A = 105.710.7 nm min-1 Torr-1.The preexponential factor can be represented as a frequency factor, Z, through asimple conversion39n m ^cm  min^moleculesZ A min Torr 107 nm^S x 2.21x1022 cm3molecules Z = 1.96x1019 cm2 s Torr •If the rate coefficient represents a simple elementary rate controlling reactionbetween a gas phase hydrogen atom and some unidentified surface species (perhapsGaH2) to produce gaseous products, the preexponential cannot exceed the collisionfrequency of H atoms with the surface. In other words, the H atom supply rate atthe surface must exceed the possible GaAs removal rate.For atomic hydrogen at 360 °C, the limiting frequency factor per Torr ofhydrogen atom pressure can be obtained from the relation,Z = 3.513x1022 avf T)-1/2 an-2 s4where T is the absolute temperature (633 K) and M is the atomic mass of hydrogen(1.008 g/mol). Upon substitution, we find,Z = 1.39x1021 collisions cm-2 s' 1 Torr-1which is two orders of magnitude larger than than the "removal frequency"satisfying the aforementioned constraint leading us to conclude the rate constantthat we measure is for a rate controlling elementary reaction of atomic hydrogen.Hence the empirical temperature and activation energy dependence of therate coefficient, kr, for atomic hydrogen etching of (100) GaAs in the temperaturerange of this experiment (200 °C - 400 °C) is:kT = 105.7±0.7 nm min-1 Torr-1 exp(-29±7 kJ/mop/RT.The most direct way of experimentally determining the temperaturedependent rate coefficients is to, assuming the reaction is first order in H, simplydivide the etch rate at a temperature by the partial pressure of atomic hydrogenresponsible for the etch. For example, an etch rate of 9.04 nm min-1 was observed at360 °C while exposed to 5.46 mTorr of atomic hydrogen leading to:409.04 nm min-1 k3600 = 5.46 mTorr - 1650 nm min-1 Torr.Table 3-3 contains all of the acquired GaAs temperatures, etch rates, H partialpressures and the corresponding rate constants. Not included in the table is thelowest temperature (180 °C) etch during which no measurement of the H atomconcentration could be obtained. As the table infers the reaction rate increases withincreasing temperature. An Arrhenius plot of the etch rate data (Figure 3-2) yieldsan activation energy for the etching of (100) GaAs with thermalised atomichydrogen of 29±7 kj/mol = 0.31±0.07 eV. This activation energy is slightly higherthan that of Kishimoto et al. 43 but is difficult to compare directly for they quote nouncertainty.3.4 POST-ETCH SURFACE DESCRIPTIONUpon discovery of a substantial reflectivity reduction at 632.8 nm during Hatom etching of GaAs, it seemed a close look at the surfaces after etching may proveinteresting. Subsequently, scanning electron microscopy was performed on some ofthe etched GaAs. In fact surfaces etched at the lowest temperatures, were unusuallytextured (Figure 3-3, below). Smoothness of the resulting surfaces seems to increasewith temperature, as does the reflectivity at 632.8 nm relative to the reflectivity at632.8 nm of the lower temperature, texturising etches.The "dry" etching of GaAs with atomic hydrogen in the lowest temperaturerange (- 200 °C) tends to culminate in gross surface texturisation presumablyaccompanied by enhanced optical absorbtion. As previouly described, aphotoconductor was monitoring the specular reflection of a 632.8 nm helium neonlaser off of the GaAs surface. Increased sample temperature during etching lead tolower levels of texturisation or the texturisation occured on a smaller scale. The41Kinetic DataTemperature(°C)Etch Rate(nm/min)PH(mTorr)Rate Coefficient kT(nm/min Torr)229 4.3 9.79 439235 3.2 7.79 405250 4.5 7.74 584250 3.2 4.68 684278 3.4 3.27 1030281 5.7 4.72 1210360 9.0 5.46 1650Table 3 -3. The measured quantities: GaAs temperature, GaAs etch rate with atomichydrogen, atomic hydrogen partial pressure during the reaction andcomputed rate coefficients.42I 1_In k= 13.185 - 3.5319/ir5.5Ea = (29±7)kJ/mol = (0.31±0.07)eV1.5^1.6^1.7^1.8^1.9^2.01000/T [1/K]Figure 3-2 Arrhenius plot with standard error shown yielding determination of theactivation energy for etching (100) GaAs with hydrogen atoms.43higher temperature etches (— 300 °C) resulted in a smaller loss in reflectivity at632.8 nm.Scanning electron micrographs of the H atom etched surfaces have beenstudied in the 200 - 360 °C range. The micrographs clearly demonstrate thatcrystallographic etching is more pronounced at lower temperatures.Of particular interest are the 180 and 205 °C micrographs of the etched (100)GaAs imaged from directly above the etched surface. Figure 3-3a and 3-3b are twoperspectives of the same GaAs surface H atom etched at 205 °C. The axis ofsymmetry is apparent in both micrographs.Figure 3-4a and 3-4b shows a reduction in the scale of the texturisation for 280°C H atom etched GaAs relative to those etched in the 180 - 200 °C range.Figure 3-5a and 3-5b demonstrate how smoothness improves for the mid tohigh temperature etches.3.5 X-RAY PHOTOELECTRON SPECTROSCOPY RESULTAlthough no gallium droplets were visible with the scanning electronmicroscope, results of X-ray Photoelectron Spectroscopy experiments performed atSurface Science Western, Ontario suggest the etched surfaces were Ga-rich. For asample etched at 200 °C an As 3d to Ga 3d ratio of 0.31was obtained. This ratio ofAs to Ga on the surface, which would be unity if the surface was stoichiometric,indicated the etched sample surface was —70 % gallium.44(a)(b)Figure 3-3. Scanning electron micrographs of H atom etched (100) GaAs at 205 °Cas viewed from (a) the side and (b) the top.45x3.0(a)(b)Figure 3-4. Scanning electron micrographs of (100) GaAs H atom etched at (a) 180 °Cand (b) 205 °C as viewed from above.46(a) (b)Figure 3-5. Scanning electron micrographs of (100) GaAs H atom etched in the midto high temperature range: (a) 280°C and (b) 360 °C.47SECTION 4: DISCUSSION4.1 ATOMIC HYDROGEN ADSORPTION ON SILICON AND GALLIUMARSENIDEAtomic H adsorption is known to occur on Si and GaAs53. According torecent band structure calculations31 the presumably unreconstructed (100) GaAssurface turns out to be a metal without H adsorption. Both the gallium and arsenicsurface dimers (considering the 2x4 reconstruction) are believed to be preserved31,although buckled slightly, upon H adsorption. The added electron, in the case ofGaAs, from the H effectively pushes some charge density down toward theadsorbate's bonds to the bulk.Yamaguchi and Horikoshi54 have in fact measured different activationenergies for the desorption of arsenic from (100) GaAs depending on thereconstruction.Unlike (100) GaAs, (100) Si is believed to break its dimer upon adsorption ofatomic hydrogen55 . The effect of the H adsorption on the Si-Si bonds (other thanthe broken dimers) should be much smaller (because the surface Si is againtetrahedrally coordinated) than the distortion imposed by H on GaAs resulting inlittle change of the energy needed to dissociate the Si.Surface adsorbed H atoms may be diffusing into the bulk and bulk H atomssegregating to the surface26.4.2 ATOMIC HYDROGEN PLATELETS IN GALLIUM ARSENIDEPlatelets in GaAs exposed to atomic hydrogen may form due to the H - Hinteraction potential between bond center sites within the crysta156 . It turns out theH - H interaction is repulsive for nearest neighbor H bond center sites and attractivefor next nearest neighbor sites, repulsive , attractive,  and so on leading to a48condensed cluster of H oriented parallel to the (111) planes. These planes areassumed not to be of monolayer thickness but rather several planes coexist one,two, three or perhaps four next nearest neighbor bond lengths apart. So plateletthicknesses should be of order 15 - 50 A and as mentioned previously hundreds ofangstrOms in diameter.4.3 ATOMIC HYDROGEN INDUCED CRYSTALLOGRAPHIC ETCHINGIt has been well known for some time that different crystal planes havedifferent formation energies associated with them. Covalent bonded solid surfaces,like GaAs, are considered to have free chemical or dangling bonds. Ge forexample57 has 1.25, 0.88 and 0.72 x 1019 dangling bonds per square meter on the(100), (110) and (111) surfaces, respectively. The relative etch rates of these planes inacid has been found to be 1.00, 0.89 and 0.62 respectively. This shows the (1111planes of Ge etch at 62% of the rate at which the (1001 etch.It is also worth noting that the work needed to create a unit area of surfaceunder constant temperature and pressure is lower for more closely packed planes57The f111) are the most closely packed of the low index planes in GaAs, so one mightexpect this plane to form most easily.Here we account for the anisotropy of the (100) surface etched with thermalH atoms. Upon examination of Figures 3-3 and 3-458 it is readily apparent that theprotruding structures have symmetry along the trench (i.e. they are elongated alongthe trench, whereas they have little extent across the trench). We believe thesefigures, representing our lowest temperature etches achieveable, are of particularrelevance since higher temperature etches lead to a loss of resolution of thecrystallographic features. Perhaps low temperature (-200 °C) hydrogen atometching of the (100) GaAs surface results in exposing either primarily (111)A or(111)B GaAs planes due to their different relative etch rates.49The planes exposed in the figures appear to be primarily (111). Surface andextended bulk defects, due to their spatially enlarged charge distributions are oftenthought to be initiation "centres" for etching. Surface terminations of planar orline defects may provide initiation centres for etching and may feed H atoms intoGaAs creating platelets along which etching may occur. Hence, platelet formationis a plausible explanation of the origin of the apparent texturisation of the H etched(100) GaAs surfaces.50SECTION 5: CONCLUSIONThermalised atomic hydrogen continuously etches the (100) GaAs surfacefrom temperatures as low as 180 °C with an activation energy of 0.31± 0.07 eV. Therate coefficient for the etching reaction over the 230 °C - 360 °C range can bedescribed by,kT = 105.7±0.7 nm min-1 Torr-1 exp(-29±7 kJ/mol)/RT.The rate constants were found to vary from 439 nm/min Torr at 229 °C to 1650nm/min Torr at 360 °C and the reaction is close to first order in H. The lowesttempertaure etches left the (100) surface highly textured, exposing what appear to bemostly Ga-rich (111) planes.51SUGGESTIONS FOR FURTHER WORKThis study demonstrated etching (100) GaAs with atomic hydrogen in thelowest temperature range (- 200 °C) leads to textured (100) surfaces possessingmarked losses in optical reflectivity. Presently, solar cells are being fabricated fromGaAs with the help of an antireflection coatings to minimize loss of incident lightto reflection. Since H is the smallest of atoms which may be capable of creating thesmallest of optically lossy voids in the near surface region of the GaAs, study of theextent to which the optical absorption increases after a low temperature H atometch might be fruitful.It also remains unknown to what degree the post-etched surface remainscrystalline. Perhaps Raman scattering experiments could elucidate details ofstructural damage59 or electron channeling experiments could be performed usinga scanning electron microscope6Oto probe the crystallinity of the resulting surface.Enquiry into the validity of the assumption that diffused atomic H iscontributing to the etching reaction would certainly prove interesting. One couldcoat all but one surface with silicon nitride to presumably reduce the absorbed Hatom flux. Alternatively, one could try saturating bulk GaAs at high temperaturewith atomic H and observe whether or not the etch continues after the source of His removed.The resulting surface morphology is sure to be strongly influenced by theatomic hydrogen concentration if etching is a result of H diffusion and subsequentplatelet formation. Study of the H atom partial pressure dependence of the post-etched surface morphology may help solidify the interrelationship of theseprocesses (i.e. etch over as wide a range of measurable H atom concentrations aspossible).52Etching while simultaneously monitoring several of the diffraction maximafrom the interferometer separately would help to determine the relevance of any"shadowing" contribution (i.e. a reduction in the intensity as the etch progressesdue to reflection from the etched walls) to the interferogram arising from the finitedepth of the etch trenches.53References1 S. j. Pearton, F. Ren, C. R. Abernathy, W. S. Hobson, T. R. Fullowan, R. Esagui, J.R. Lothian, Appl. Phys. Lett. 61 586 (1992) and references therein2 N. M. Johnson, C. Doland, F. Ponce, J. Walker and G. Anderson, Physica B 170 3(1991)3 Paul C. Weakliem, Christine J. Wu and Emily A. Carter, Phys. Rev. Lett. 69 200(1992)4 S. J. Pearton, J. W. Corbett and M. Stavola, Hydrogen in CrystallineSemiconductors, p. 325, Springer-Verlag, 1992 and references therein5 see for example J. N. Heyman, J. W. Ager III, E. E. Haller, N. M. Johnson, J. Walkerand C. M. Doland, Phys. Rev. B 45 13 363 (1992)6 J. W. Corbett, J. L. LindstrOm and S. J. Pearton Mat. Res. Soc. Symp. Proc. 104 229(1988)7 A. Van Wieringen and N. Warmoltz, Physica 22 849 (1956) in J. W. Corbett, J. L.LindstrOm and S. J. Pearton Mat. Res. Soc. Symp. Proc. 104 229 (1988)8 N. M. Johnson, F. A. Ponce, R. A. Street and R. J. Nemanich Phys. Rev. B 35 4166(1987)9 J. Weber, Physica B 170 201 (1991)10 w. B. Jackson and S. B. Zhang Physica B 170 197 (1991)11 J. B. Boyce, N. M. Johnson, S. E. Ready and J. Walker, Phys. Rev. B 46 4308 (1992)12 S. J. Feng and G. S. Oehrlein, Appl. Phys. Lett. 50 1912 (1987)13 F. Lu, J. W. Corbett and L. C. Snyder, Physics Lett. A 133 249 (1988)14 S. Nanarone, C. Astaldi, L. Sorba, E. Colavita and C. Colandra, J. Vac. Sci. Tech. A5 619 (1987)15 B. Clerjaud, F. Gendron, M. Krause and W. Ulrici, Phys. Rev. Lett. 65 1800 (1990)16 R Rahbi, D. Mathiot, J. Chevallier, C. Grattepain and M. Razeghi, Physica B 170135 (1991)17N. M. Johnson, Physica B 170 3 (1991)5418 L. Pavesi, Solid St. Comm. 83 317 (1992)19 L. Pavesi and P. Giannozzi, Phys. Rev. B 46 4621 (1992)20 L. Pavesi, P. Giannozzi and F. K. Reinhart, Phys. Rev. B 42 1864 (1990)21 L. Pavesi and P. Giannozzi, Physica B 170 392 (1991)22 R. G. Wilson et al. in J. H. Neethling, Physica B 170 285 (1991)23 j. Chevallier, B. Machayekhi, C. M. Grattepain, R. Rahbi and B. Theys, Phys. Rev.B 45 8803 (1992)24 E. M. Omeljanovsky et al. in S. J. Pearton, J. W. Corbett and J. T. Borenstein,Physica B 170 85 (1991)25 J. M. Zavada et al. in S. J. Pearton, J. W. Corbett and T. S. Shi, Appl. Phys. A 43 153(1987)26 W. C. Dautremont-Smith, Mat. Res. Soc. Proc. 104 313 (1988)27 K.C. Hsieh, M.S. Feng, G.E. Stillman, N. Holonyak, Jr., C.R. Ito and M. Feng, ApplPhys Lett. 54 341 (1989)28N. Caglio, E. Constant, J. C. Peasant and J. Chevallier, J. Appl. Phys. 69 1345 (1991)29J. H. Neethling, Physica B 170 285 (1991)30 M. Stutzmann, J. -B. Chevrier, C. P. Herrero and A. Breitschwerdt, Appl. Phys. A53 47 (1991)31 Y. Miyamoto and S. Nonoyama, Phys. Rev. B 46 6915 199232 S. Nonoyama, Y. Aoyagi and S. Namba, Jpn. J. Appl. Phys. 31 1298 (1992)33 G. Smolinsky, R. P. H. Chang and T. M. Mayer, J. Vac. Sci. Tech. 18 12 (1981)34 R. P. H. Chang and S. Darack, Appl. Phys. Lett. 38 898 (1981)35 R. P. H. Chang, C. C. Chang and S. Darack, J. Vac. Sci. Tech. 20 45 (1982)36 A. Okubora, J Kasahara, M. Arai and N. Watanabe, J. Appl. Phys. 60 1501(1986)37 S. Sugata, A. Takamori, N. Takado, K. Asakawa, E. Miyauchi and H55Hashimoto, J. Vac. Sci. Tech. B 6 1087 (1988)38M. -C. Chuang, J. W. Coburn, J. Appl. Phys. 67 4372 (1990)39J Suemune, A. Kishimoto, K. Hamaoka, Y. Honda, Y. Kan and M.Yamanishi, Appl. Phys. Lett. 56 2393 (1990)40 j. R. Creighton, J. Vac. Sci. Tech. A 8 3984 (1990)41 j. A. Schaefer, V. Persch, S. Stock, Th. Allinger and A. Goldman, Euorophys.Lett. 12 563 (1990)42 j. A. Schaefer, Th. Allinger, Ch. Stuhlmann, U. Beckers and H. Ibach, Surf.Sci. 251/252 1000 (1991)43 A. Kishimoto, I. Suemune, K. Hamaoka, T. Koui, Y. Honda and M. Yamanishi,Jpn. J. Appl. Phys. 29 2273 (1990)44 G. M. Mikhailov, P. V. Bulkin, S. A. Khudobin, A. A. Chumakov and S. Yu.Shapoval, Vacuum 43 199 (1992)45 P. F. A. Meharg, Ph.D. Thesis, Dept. of Chemistry, University of BritishColumbia (1992), unpublished46 E. A. Ogryzlo, J. Phys. Chem. 65 191 (1961)47 S. J. Pearton, J. W. Corbett and M. Stavola, Hydrogen in CrystallineSemiconductors, p. 8, Springer-Verlag, 1992 and references therein48 E. L. Tollefson and D. J. Le Roy, J. Chem. Phys. 16 1057 (1948)49 Daniel W. Trainor, David 0. Ham and Frederick Kaufman, J. Chem. Phys. 58 4599(1973)50 j. D. Strong and G. A. Vanasse, J. Phys. Radium 19 192 (1958)51 Since the center to center spacing , a, of the nitride stripes is equal to twice thestripe width, b, all nonzero even orders vanish. Hence, due to our particular stripegeometry, the diffraction pattern consists of zero and odd order maxima only.52 R. J. Bell, Introductory Fourier Transform Spectroscopy, p. 208, Academic Press,19725653 For an introduction see S. J. Pearton, J. W. Corbett and T. S. Shi, Appl. Phys. A 43153 (1987)54 H. Yamaguchi and Y. Horikoshi, J. Appl. Phys. 71 1752 (1992)55 Z. Jing and J. L. Whitten Phys. Rev. B 46 9544 (1992)56 S.R. Kreitzman, private communication.57 Richard A. Swalin Thermodynamics of Solids, p. 225, Wiley, 1972 and referencestherein58 Figure 3-6 has the same symmetry, however the mask orientation isperpendicular to that of Figure 3-3 and 3 -4.59 see for example J.E. Maslar, S. R. Kisting, P. W. Bohn, I. Adesida, D. G. Ballegeer,C. Caneau and R. Bhat, Phys. Rev. B 46 1820 (1992)60 D. C. Joy in SEM Microcharacterization of Semiconductors, p.69, ed. D. B. Holtand D. C. Joy, Academic Press, 1989.57APPENDIX 1: SLOPE UNCERTAINTY CALCULATIONSThe uncertainties in the estimated activation energy and reaction orderswere calculated using the simple, conventional "Delta Y" method. The magnitudeof both the activation energy, Ea, and the reaction order, x, are obtained graphicallyfrom slopes of logarithm plots since both parameters are exponents. The basicpurpose of the "Delta Y" method is to approximate the error in the slopes of theplots and hence the uncertainty in the measurements of the physical quantities.The name "Delta Y" presumably comes from the fact that this analysis8mproposes the fractional error in the slope, —m , is proportional to the averagedeviation of the data from the "best fit" line, 6y, and inversely proportional to therange of the acquired data :8m 26y m Y2 - Y1where m is the slope, 8m is the uncertainty in the slope.The quoted uncertainty in the activation energy will be computed here,using the above method. The quoted uncertainties in the reaction order withrespect to the atomic hydrogen concentration can obtained similarly.Since the technique is graphical one only needs a plot with a best fit (obtainedhere by Cricket Graphe) line to begin (see Figure A-1). Sy is obtained by finding theaverage deviation of the data from the line along the ordinate (y-axis). In thisexample the average deviation, 8y, of the data points parallel to the In k - axis (seeFigure A-1) is approximately 6.57 mm. The range of the data points, y2 - yi, in thesame units is measured to be approximately 55 mm. The last quantity needed toestimate the uncertainty in the slope is the slope itself, m, obtained from the CurveFitting program in Cricket Graph®. Using the above expression for the fractionalerror in the slope,58Ea = (29±7)kJimol = (0.31±0.07)eV7.55.51 5^1.6^1.7^1.81000/T [1/1C]2.0Figure A-1. Illustration of "Delta Y" method used for estimating the uncertainty inthe activation energy associated with the reaction of hydrogen atomswith GaAs.59(2)(6.57 mm)(3532 5m 55 mm6m --- 841 KNow the slope with its uncertainty can be written as,m-Arn = (3532±841) K.Next one needs the relationship between the slope and the activation energy.Assuming the rate constant, k, is related to the activation energy, Ea, viak = A exp(-Ea/RT)where A is the preexponential related to the attempt frequency, R is the gasconstant 8.314 J/mol K and T is the absolute temperature. Taking the natural log ofboth sides leads to an expression,Ea 1in k = In A -which displays clearly that the relationship between the slope of a plot of ln k vs.1/T and the activation energy is,Solving for Ea,so,SEa = -8m R.Finally, using the above value of the slope and its uncertainty for the hydrogenatom etching of GaAs,Ea ± 8Ea = R(m ± 8m)Ea ± 8Ea = (8.314 J/mol K)(3532 K ± 841 K)Ea -±8Ea = 29 ±7 kJ/mol.Eam = REa = -m R.60APPENDIX 2: PREEXPONENTIAL UNCERTAINTY ESTIMATEThe slope of the Arrhenius plot and its uncertainty for the etching of (100)GaAs with atomic hydrogen was obtained in Appendix 1. This slope and itsuncertainty can aid in the determination of the preexponential factor, A and itsassociated error, 8A.The slope was found to be 3532 ± 841 K. The maximum and minimum slopewould then be 4373 K and 2691 K respectively. These slopes were used to createlinear functions enabling extrapolation of the upper and lower bounds for theexperimentally determined preexponential factor (see Figure A-2).For 1/T approaching zero the best-fit value of the natural logarithm of therate coefficient (i.e. the y-intercept) was determined by Cricket Graph® polynomialCurve Fitting to be 13.2. This impliesIn k (as T tends to .) = In A - 13.2 ,andA =exp(13.2) - 5.32 x 105 nm min-1 Torr-1.The y-intercept for the maximum slope was found to be -14.7 which leads to Amax- 2.39 x 106 nm min-1 Torrl. Similarly, the y-intercept for the minimum slope wasfound to be -11.3 which leads to Amin - 8.40 x 104 nm min-1 Torr-1.To express this preexponential and its uncertainty in conventional notationwe want to write it as 107 nm min-1 Torr-1,exp[(ln k)ma xi^e14.688= 1 oiaxandexp[(ln k)min] e11339 = 1 Orninwhich yields ymax = 6.38 and ymin = 4.92.The preexponential with its associated uncertainty will be written61Pregponentiat Uncertainty Estimate0.00^ 1.00^ 2.001000/TFigure A-2. Extrapolation to large T and resulting Arrhehnius preexponential withuncertainty determined by the maximum and minimum slopes of theArrhenius plot for H atom etching of (100) GaAs.62where,10(7167) nm min-1 Torr-1,87_ Ymax - 7min2= 0.73.Finally, the preexponential can be written:A = 105.710.7 nm min-1 Torr-1.


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