Plastic deformation at high temperatures of pure and Mn-doped GaSb

Plas ic de o ma ion a high empe a u es o pu e and Mn-doped GaSb J. L. Plazaa) and E. Die ´guez Depa amen o de Fı ´sica de Ma e iales, Facul ad de Ciencias, Uni e sidad Au o ´noma de Mad id, Can oblanco, 28049, Mad id, Spain M. Jime ´nez-Melendo and A. Domı ´nguez-Rod ı ´guez Depa amen o de Fı ´sica de la Ma e ia Condensada, Uni e sidad de Se illa, Apa ado 1065, 41080 Se illa, Spain 共Recei ed 1 Feb ua y 2001; accep ed o publica ion 1 Augus 2001兲 In his wo k he plas ic beha io o GaSb and Mn-doped GaSb a high empe a u e has been analyzed. Se e al expe imen s a di e en cons an load and empe a u es a ound 500°C we e ca ied ou . The pa ame e s used in he Haasen model ha e been ob ained expe imen ally and compa ed wi h he ones ob ained om simula ions. © 2001 Ame ican Ins i u e o Physics. 关DOI: 10.1063/1.1406970兴 I. INTRODUCTION The na ow-band-gap III–V semiconduc o s a e p omis- ing ma e ials ega ding he de elopmen o high quali y op- ical modula o s and he e os uc u e lase s, which can ope - a e in he midin a ed 共2–5 ␮ m兲 egion.1Mic owa e and op ical de ices ha e been de eloped.2–4 In his sense, GaSb is one o he mos impo an III–V semiconduc o com- pounds because a wide ange o elec onic and elec o-op ic de ices a e based on his ma e ial including esonan unnel- ing de ices,5mid in a ed lase s6and pho odiodes,7long wa eleng h in a ed de ec o s,8and he mopho o ol aic cells.9 Mn occupies an impo an ole as a dopan in GaSb. I o e s an oppo uni y o s udy chemical ends ela ed o he in e ac ion be ween ca ie s and magne ic spins in a di e en hos wi hou he need o addi ional doping because o he shallow accep o le els o Mn in GaSb.10–12 These ea u es make i necessa y o p epa e homoge- neous ma e ials wi h low disloca ion densi ies in o de o sa is y he equi emen s o he elec onic and op oelec onic indus ies. I is well known ha , du ing he g ow h p ocess, he mal s esses can induce he gene a ion and p opaga ion o dislo- ca ions, which a e di ec ly ela ed o he plas ic de o ma ion o he ma e ial. The quan i a i e knowledge o de o ma ion phenomena gi es insigh abou he op imal condi ions unde which GaSb c ys als can be g own wi h low disloca ion den- si ies. Fo his pu pose i is e y use ul o use he Haasen model13 which explains he plas ic de o ma ion in e ahe- d ally coo dina ed semiconduc o s such as GaSb. This model depends on se e al pa ame e s, which s ill a e no known o se e al ma e ials. The knowledge o hese pa ame e s is needed in o de o ca y ou ull g ow h p ocess simula ions om which he condi ions o lowe ing he disloca ion den- si y may be ob ained. In his wo k, se e al uniaxial de o ma ion expe imen s a cons an load, o di e en s esses and empe a u es, ha e been conduc ed in o de o ob ain he Haasen pa ame e s o he case o pu e and Mn-doped GaSb. II. THEORY The Haasen model is he mos success ul model ega d- ing he plas ic de o ma ion a high empe a u e in e ahe- d ally coo dina ed semiconduc o s.13 This model is based on he O owan equa ion,14 which ela es he mac oscopic de o - ma ion o he mic oscopic p ocesses associa ed wi h he dis- loca ion mo emen and gene a ion. The Haasen model is ep esen ed ma hema ically by he ollowing equa ions: d␧ d ⫽bNB0e⫺E/kT共 ␶ ⫺A 冑 N兲m,共1a兲 dN d ⫽KNB0e⫺E/kT共 ␶ ⫺A 冑 N兲m⫹1,共1b兲 whe e ␧is he s ain, Nis he disloca ion densi y, bis he Bu ge s ec o , ␶ is he applied s ess, Eis he disloca ion ac i a ion ene gy, Kis a cons an aking in o accoun dislo- ca ion mul iplica ion, kis he Bol zman cons an , Tis he empe a u e, Ais a cons an which is associa ed wi h he disloca ions mic os uc u e o he ma e ial, mis he s ess exponen which lies in he ange be ween 1 and 2.5 o e - ahed ally coo dina ed semiconduc o s, and B0is a cons an ela ed o he disloca ion eloci y. III. EXPERIMENTAL DETAILS In o de o ca y ou he de o ma ion expe imen s, wo pu e and Mn-doped GaSb ingo s we e g own by he B idg- man me hod. High pu i y Ga and Sb 共99.9999%兲and Mn 共99.9%兲we e used as s a ing ma e ials. These wo ingo s we e 60 mm long, 12 mm in diame e , and 40 g in weigh . Two single c ys als wi h p isma ic geome y we e cu om he ingo s. The dimensions o he samples we e 4.4 ⫻3⫻3mm 3 o pu e GaSb and 5.4⫻3⫻3mm 3 o Mn-doped GaSb. The o al Mn concen a ion in his case was ob ained by means o a omic abso p ion analysis and ound a兲Elec onic mail: [email p o ec ed] JOURNAL OF APPLIED PHYSICS VOLUME 90, NUMBER 9 1 NOVEMBER 2001 48250021-8979/2001/90(9)/4825/4/$18.00 © 2001 Ame ican Ins i u e o Physics [This a icle is copy igh ed as indica ed in he a icle. Reuse o AIP con en is subjec o he e ms a : h p://sci a ion.aip.o g/ e mscondi ions. Downloaded o ] IP: 150.214.182.92 On: Tue, 25 Aug 2015 08:25:57 o be 1.8⫻1019 cm⫺3. In o de o e eal he disloca ion den- si y, he samples we e mechanically polished wi h 5 and 1 ␮ m alumina powde and chemically e ched wi h HNO3: HF: CH3COOH: H2O共5:3:3:11兲. The e ching p o- cess e ealed a disloca ion pi densi y o 105cm⫺3. The comp ession aces o he samples we e o ien ed by Laue back- e lec ion X- ay echniques,15 cu wi h a diamond saw, and polished successi ely wi h 5 and 1 ␮ m alumina powde s o emo e he damage gene a ed du ing cu ing. The o ien a ion chosen o he comp ession samples was 关111兴. The samples we e moun ed in a comp ession appa a us which allows he execu ion o expe imen s a high empe a- u e. A schema ic o his sys em is shown in Fig. 1. The expe imen s we e ca ied ou o comp ession a cons an load a empe a u es a ound 500°C 共0.7 TM兲in an ine A a mosphe e con aining 100 ppM o oxygen. The s ess is ansmi ed o he sample h ough a mobile pis on, which is placed below he sample. The sample is de o med and he mobile pis on mo es upwa ds pushing a piezoelec- ic ansduce , which is connec ed o a displacemen mea- su ing appa a us. The whole sys em 共pis ons, sample, and alumina he me ic ube兲is loca ed inside a high empe a u e u nace, which, o sake o simplici y, is no shown in Fig. 1. The empe a u e is con olled by a he mocouple 共⫾1°C兲. IV. RESULTS AND DISCUSSION The samples we e de o med in comp ession a cons an load and he collec ed da a o ⌬l e sus a e plo ed as ln␧ ˙ e sus ␧, whe e ␧⫽关ln(l/l0兲兴 wi h ␧ ˙ he s ain a e. This ep- esen a ion allows us o know when he s a iona y s a e is eached and i any i egula i y in plas ic low occu s. A high empe a u es he s ain is cha ac e ized by a s a- iona y s a e whe e he s ain a e is kep cons an . Because hese expe imen s a e ca ied ou a cons an comp ession load, he s ain a e a he s a iona y s a e decays linea ly wi h ime. This beha io is due o he ac ha he sample c oss sec ion inc eases and he e o e he s ess dec eases. This ypical beha io is desc ibed in Fig. 2. We ha e applied he Haasen model gi en by Eqs. 共1a兲 and 共1b兲 o he s a iona y s a e in di e en uniaxial comp es- sion expe imen s a cons an load o di e en empe a u es and s esses. The special so wa e de eloped by ou g oup can simula e he e olu ion as a unc ion o ime, o s ain, and o disloca ion densi y by sol ing nume ically he Eqs. 共1兲. This makes i necessa y o exp ess he expe imen al poin s as de o ma ion e sus ime ins ead o s ain a e e - sus s ain. In o de o sol e Eqs. 共1兲, each s ain un has been con- side ed as independen om he p e ious ones. In his case, wo pa ame e s a e equi ed; he ini ial s ain and he ini ial densi y o disloca ions. The o me is ob ained om he inal FIG. 2. Typical beha io o a s ain cu e a high empe a u e a cons an s ess. FIG. 3. Expe imen al esul s o he s ain a e s s ain, om he comp es- sion expe imen s a high empe a u e o pu e GaSb. The do s include he e o ma gins. FIG. 4. Expe imen al 共poin s兲and simula ed 共con inuous lines兲 esul s o he s ain s ime o pu e GaSb single c ys als a di e en s esses and em- pe a u es: 共a兲18 MPa, 500 °C; 共b兲21.5 MPa, 500 °C; 共c兲25.8 MPa, 500 °C; 共d兲31.0 MPa, 500 °C; 共e兲37.4 MPa, 500 °C; 共 兲37.4 MPa, 535 °C; 共g兲37.4 MPa, 500 °C; and 共h兲43.8 MPa, 500 °C. The open ci cles include he e o ma gins. FIG. 1. Schema ic o he sys em used o he measu emen s o comp ession a high empe a u e. 4826 J. Appl. Phys., Vol. 90, No. 9, 1 No embe 2001 Plaza e al. [This a icle is copy igh ed as indica ed in he a icle. Reuse o AIP con en is subjec o he e ms a : h p://sci a ion.aip.o g/ e mscondi ions. Downloaded o ] IP: 150.214.182.92 On: Tue, 25 Aug 2015 08:25:57 s ain eached in he p e ious ou ine, which can be expe i- men ally measu ed. Because he la e is di icul o know om he expe imen s, i is ob ained om he simula ions gi en by he inal alue p esen ed by he e olu ion o he disloca ion densi y wi h ime in he p e ious un. Al hough his alue is di icul o compa e wi h he eal ones, i is aken o be sa is ac o y because o he easonable esul s ob- ained, as i will be shown. Howe e , he ini ial disloca ion densi y was measu ed p e ious o he s a o he comp es- sion expe imen s. We ound 105cm⫺2 o bo h samples. Di e en comp ession uns ha e been ca ied ou o s esses anging om 18 o 43.8 MPa and o empe a u es be ween 500 and 535°C on pu e and Mn-doped GaSb samples. Du ing each ou ine bo h he empe a u e and he applied s ess we e kep cons an . A. Pu e GaSb In his case, eigh di e en consecu i e comp ession uns we e ca ied ou . The samples we e de o med un il ac- cele a ion in he s ain a e was obse ed as shown in Fig. 3, indica ing ha ano he mechanism s a s o be ac i a ed. The s aigh lines indica e he s a iona y s a e o di e en ou- ines. I is clea ha only a ew poin s depa om he s a- iona y s a e. I can also be seen ha he slope p og essi ely inc eases in he s a iona y s a e wi h inc easing s ess. This could be due o he ha dening o he ma e ial as a conse- quence o he inc easing disloca ion densi y.13 This beha io is aken in o accoun by he e m A冑Nin he Haasen model 关Eqs. 共1兲兴 and known as a backs ess e m.13 Ano he indica- ion o his ha denning e ec is ha he slope o he cu es a he s a iona y s a e is a ound 15 highe han he s ess expo- nen o he Haasen model 共a ound 2.5 as i will be shown la e 兲. No mally his slope coincides wi h he s ess expo- nen . This disc epancy is a clea indica ion o he ha dening e ec due o he accumula ion o disloca ions. These expe imen al esul s ha e been plo ed as s ain s ime and simula ed by using ou so wa e based on he Haasen model. These esul s and he nume ical simula ions a e shown in Fig. 4. Good ag eemen is ob ained be ween he expe imen al poin s and he simula ions. The la ges depa - u es om he simula ions a e coming om hose expe imen- al poin s associa ed wi h he ansien s a e. The basic inpu pa ame e s used o hese simula ions a e gi en in Table I. These ini ial ial alues o he known pa ame e s ha e been aken om he li e a u e.15 The Haasen pa ame e s o pu e GaSb, ob ained om he i o hese simula ions o he expe imen al esul s, a e gi en in Table II. We no ice ha he alues ob ained in his wo k a e in good ag eemen wi h hose epo ed p e iously and shown in Table I.15 To ou knowledge, he pa ame e K, ha is ela ed o he disloca ion mul iplica ion, was unknown.16 I is in e es ing ha he alue o Kp esen ed he e o GaSb and ob ained om he bes i is o he same o de o magni ude as he one ela ed o GaAs, being 8.8 ⫻10⫺5m/N.15,16 B. GaSb:Mn The expe imen al esul s in e ms o s ain a e s s ain o Mn-doped GaSb a e shown in Fig. 5. In his case, he slope o he s aigh line, which ep esen s he s a iona y s a e, emains almos cons an o he di e en uns. I mus be poin ed ou ha he maximum s ess is lowe han in he FIG. 5. Expe imen al esul s o he s ain a e s s ain, om he comp es- sion expe imen s a high empe a u e o Mn-doped GaSb. The expe imen al poin s include he e o ma gins. FIG. 6. Expe imen al 共poin s兲and simula ed 共con inuous lines兲 esul s o he s ain s ime o Mn-doped GaSb single c ys als a di e en s esses and empe a u es: 共a兲24.0 MPa, 500 °C; 共b兲24.0 MPa, 535 °C; 共c兲24.0 MPa, 500 °C; 共d兲28.8 MPa, 500 °C; 共e兲28.8 MPa, 535 °C; 共 兲28.8 MPa, 500 °C; and 共g兲36.0 MPa, 500 °C. The expe imen al poin s include he e o ma - gins. The open ci cles include he e o ma gins. TABLE I. Ini ial inpu pa ame e s used o ca y ou he simula ions based in he Haasen model. Bu ge s ec o 4.3⫻10⫺10 m Ha dening cons an A3.1 N/m S ess exponen m2.2 Pa ame e B02.5⫻10⫺10 seg3.2 m⫺1.1/K g2.2 Ac i a ion ene gy E1.6 eV Ini ial de o ma ion 0 Ini ial disloca ion densi y N01⫻109m⫺2 TABLE II. Haasen pa ame e s o pu e GaSb. Mul iplica ion cons an , K 共m/N兲 S ess exponen , mAc i a ion ene gy E共eV兲 Ha dening cons an A共N/m兲 3.8⫻10⫺52.70 2.8 8.5 4827J. Appl. Phys., Vol. 90, No. 9, 1 No embe 2001 Plaza e al. [This a icle is copy igh ed as indica ed in he a icle. Reuse o AIP con en is subjec o he e ms a : h p://sci a ion.aip.o g/ e mscondi ions. Downloaded o ] IP: 150.214.182.92 On: Tue, 25 Aug 2015 08:25:57 case o pu e GaSb 共43.8 MPa兲. This could be he eason why no a ia ions in he slope a he s a iona y s a e we e obse ed in he case o Mn-doped GaSb. The expe imen al da a ha e been eplo ed as s ain s ime in o de o es ablish he compa ison wi h he heo e ical esul s ob ained om he Haasen model. These simula ions and he expe imen al esul s a e shown in Fig. 6. I can be obse ed ha he e exis s good ag eemen be ween he ex- pe imen al and he heo e ical esul s. The pa ame e s ap- pea ing in he Haasen model equa ions 关Eqs. 共1兲兴, shown in Table III, we e ob ained om hese esul s. Compa ing Tables I and III we no ice ha all he alues a e sligh ly lowe in he case o GaSb:Mn han o pu e GaSb. Howe e , he di e ences a e small. A lowe disloca- ion ac i a ion ene gy could indica e ha Mn sligh ly en- hances he disloca ion gene a ion and p opaga ion, which co esponds o a lowe ene gy o hei mo emen ac oss he c ys alline la ice han in he case o pu e GaSb. I is in e - es ing o no e ha , a he doping le el used in his wo k, he plas ic p ope ies a e mo e sensi i e han o he GaSb me- chanical p ope ies like Young’s modulus and ha dness, which emain unmodi ied.17 V. CONCLUSIONS In his wo k uniaxial comp ession expe imen s a con- s an load and high empe a u e ha e been ca ied ou wi h pu e and Mn-doped GaSb. The simula ion o hese expe imen s by means o he Haasen model and he compa ison wi h he expe imen s p o- ided he alues o he Haasen pa ame e s. These pa ame e s will be use ul o he simula ion o gene a ion and mo ion o disloca ions induced by he mal s esses du ing he eal g ow h p ocess. The good ag eemen be ween he expe imen s and he heo y alida e he Haasen model o he p ope desc ip ion o plas ic de o ma ion in GaSb. 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Phys., Vol. 90, No. 9, 1 No embe 2001 Plaza e al. [This a icle is copy igh ed as indica ed in he a icle. Reuse o AIP con en is subjec o he e ms a : h p://sci a ion.aip.o g/ e mscondi ions. Downloaded o ] IP: 150.214.182.92 On: Tue, 25 Aug 2015 08:25:57