Double-crystal spectrometer measurements of lattice parameters and X-ray topography on heterojunctions GaAs-AlxGa1-xAs

627 Ac a C ys . (1976). A32, 627 Double-C ys al Spec ome e Measu emen s o La ice Pa ame e s and X- ay Topog aphy on He e ojunc ions GaAs-AlxGal - xAs BY E. ESTOP*, A. IZRAEL AND M. SAUVAGE Labo a oi e de Min~ alogie C is allog aphie, associd au CNRS, Uni e si O P. e M. Cu ie, 4 place Jussieu, 75230 Pa is Cedex 05, F ance (Recei ed 2 Decembe 1975; accep ed 4 Feb ua y 1976) He e ojunc ions GaAs-AlxGa~_~As in ol ed in he elabo a ion o IR lase diodes ha e been s udied. The di e ence in la ice pa ame e be ween he GaAs subs a e and he aluminum-subs i u ed epi axic laye AlxGa~_~As has been measu ed accu a ely on a double-c ys al spec ome e o a se ies o com- posi ions. These da a coupled wi h adius o cu a u e de e mina ion ha e pe mi ed calcula ion o he s ess in he laye and he bulk la ice pa ame e o AI~Ga~_~As. Cha ac e iza ion o he de ec s in o- duced du ing he liquid-phase epi axy has been pe o med by X- ay opog aphy. In oduc ion The elabo a ion o mul iple he e ojunc ions o in a- ed lase semiconduc o de ices in ol es as a i s s ep he deposi ion o a laye o aluminum-subs i u ed gallium a senide AlxGa~_xAs on a gallium a senide subs a e by liquid-phase epi axy (LPE). Since bo h c ys als ha e di e en pa ame e s a oom empe a u e, he ma ching o he wo la ices along he in e ace is no pe ec and elas ic s ains o plas ic de o ma ion may occu in he sample. The p esence o such de ec s signi ican ly dec eases he li e ime o he de ices and nume ous s udies ha e been pe o med o imp o e he unde s anding o de ec gene a ion. The pu pose o he p esen wo k is o measu e accu a ely he di e ence in la ice pa ame e be ween he epi axic laye and he subs a e and he esul ing cu a u e o he sample. Such measu emen s ha e al eady been pe o med by Rozgonyi, Pe o & Panish (1974) and D uzhinina e al. (1975). Howe e he esul s ob ained by he wo g oups we e con- adic o y and i was hough wo hwhile o make addi- ional expe imen s. Ac ually, he esul s o he p esen wo k show ha he disag eemen be ween p e ious da a is only appa en and is due o a lack o de ailed analysis. Sample cha ac e is ics The samples we e p o ided by he C. G.E. Resea ch Labo a o ies who pe o med he liquid-phase epi axy on Monsan o Labo a o y gallium a senide subs a es hea ily doped wi h silicon (mo e han 10 TM a oms pe cma). The epi axy was ollowed by accu a e measu e- men s o he laye hickness and composi ion. Al- hough he mic op obe analysis is subjec o many unce ain ies, one can be a he con iden in he assigned composi ion alues since hey ha e been con- olled by an independen echnique, namely he meas- u emen o he ene gy gap in AlxGal_~As as a unc ion * P esen add ess: Facul ad de Ciencias, Depa amen o de C is alog a ia y Mine alogia, A da. J. An onio 585, Ba celona 7, Spain. o x by Ba b6 (1974). The accu acy in composi ion o he epilaye is hen be e han a ew pe cen . P io o epi axy, he samples had been e ched in a mix u e H2SOa-H202-H20 (4:1:1). The in es iga ed c ys als a e ec angula (100) wa e s (6x 12x0.25 mm) wi h clea ed edges along [011] and [01T]. The epi axic laye is a ew/ m hick (see Table 1 a) and as a esul o he deposi ion echnique, he concen a ion in A1 dec eases om he in e ace o he ex e nal su ace a a a e o 0.5% /zm -~ (Ba b6, 1974). Table 1. Expe imen al da a (a) Measu ed K~I peak shi ('), adius o cu a u e o he wa e Q (m) and a e age s ess in he epilaye a (x 10 a dyn cm -2) as unc ions o aluminum con en x and laye hickness h(/ m). x z ,40x Q l 0 2"30 0 c~ 0 0-12 3"66 44 15"8 2"26 0.24 4"15 82 6-8 4"64 0"39 3"66 144 3"9 9"2 0"54 3"05 204 4"0 10"7 0"68 2"80 236 4"0 11"7 0-79 2"44 285 3"3 16"3 (b) Rela i e pa ame e di e ence be ween laye and subs a e in he s ained s a e (Aa~/a)~ (x 10-4), s ains in he laye dada (× 10 -4) and subs a e ,dada (x 10-5), ela i e pa - ame e di e ence in he s ain- ee s a e (da~/a)s (x 10 -4) as unc ions o x. a /o a a a /0 0 0 0 0 0 0" 12 3"28 1 "36 0"79 1 "84 ___ 0"25 0-24 6.12 2-78 1-85 3"16+_0"35 0"39 10"7 5"52 3"23 4"86 +_ 0"55 0"54 15"2 6"42 3"13 8.47+_0.62 0"68 17"6 7"02 3"14 10"27 _+ 0"66 0"79 21"3 9"78 3"80 11"14+_0"86 1 Debye-Sche e measu emen 14.8 +_ 2-5 Expe imen al echniques (a) Measu emen o he pa ame e o AlxGa~_xAs A double-c ys al spec ome e was used o measu e he shi AOx o he K~I e lexion peak be ween he A C 32A - 7* 628 LATTICE PARAMETERS AND X-RAY TOPOGRAPHY ON HETEROJUNCTIONS GaAs subs a e and he epi axic laye AlxGal_~As. The i s c ys al is a pe ec GaAs single c ys al ad- jus ed o he 400 e lexion o Cu K~I in he symme - ical Laue case ( ansmission se ing). In o de o p e en he simul aneous e lexion o Cu Kc~2, a ~o ° di e gence sli is inse ed be o e he i s c ys al. The sample unde in es iga ion is aken as second c ys al and adjus ed in he symme ical B agg case ( e- lexion se ing). I has been checked ha when he sample is la o only sligh ly cu ed, he ull wid h a hal maximum (FWHM) o he ocking cu e is close o he heo e ical alue o 8.5" bu ha i inc eases wi h inc easing cu a u e (see Fig. 1). Wi h such na ow p o iles, he e is no peak o e lap as was he case in he expe imen al de e mina ion by Rozgonyi e al. (1974) and he alue o he Ka, peak shi AO~ is ob ained wi h an absolu e e o o +2". Since he co esponding alue (Aa/a):, o he measu ed ela i e la ice pa ame e a ia ion is gi en by = co n 0 (,, Resul s and discussion (a) La ice pa ame e o Al~Gal_xAs as a unc ion o x Since he samples a e cu ed, he measu emen s o he Kcq peak shi dOx be ween he laye and subs a e (Fig. 1) gi e he alue o he ela i e pa ame e di - e ence (Aa~/a)s when bo h he epilaye and he sub- s a e a e in a s ained s a e. I Aa /a and AaJa ep- esen he s ains no mal o he e lec ing plane in he laye and subs a e espec i ely, one has he ollowing ela ion: (Aa~] Aa, (AaZsi Aa~ - + (2) a /s a a /0 a Hence, in o de o each he co esponding (Aa~/a)o o s ain- ee ma e ials, i is necessa y o de e mine he mean alue o he s esses wi hin a dep h equi alen o he pene a ion dis ance o he X- ay beam. In he p esen case o he 400 e lexion wi h Cu Kcq his dis ance is o he o de o 3 pm. he absolu e e o on (Aa/a)x is abou + 1.5 × 10 -s. The measu ed peak shi s ha e been co ec ed o a possible pu e o a ion componen . (b) Di ec measu emen o he pa ame e o pu e AlAs Ve y pu e AlAs (Ce ac/Pu e inc. 99.999 %) was used o powde measu emen s on a 19 cm diame e Debye-Sche e came a. Since he ine-g ained powde is apidly des oyed in ai he samples we e g ound and loaded in capilla y qua z ubes unde a ni ogen a mosphe e. (c) E alua ion o he adius o cu a u e The measu emen s we e pe o med on a classical X- ay opog Nghy se ing, he di e gence o he in- ciden beam being o he o de o one minu e o a c. The me hod, al hough manually con olled, is equi - alen o he ABAC echnique (au oma ic B agg-angle con ol) desc ibed by Rozgonyi e al. (1974). The sample is mo ed in s eps o 1.5 mm, each s ep being measu ed wi h an accu acy o 10/ m. The FWHM o he e lexion p o ile is abou 60" and since he peak posi ion can be loca ed wi hin + 5", he e o on he peak shi be ween wo posi ions on he samples is _+ 10". As a consequence, he homogenei y o he cu a u e is con olled wi hin 20 % whils he cu a u e i sel is measu ed wi h an accu acy o 10 % making use o he la ges in e al, 4.5 mm. The exac geome y o he cu a u e has been analysed wi h he help o ou di e en e lexions: 022, 022, 040, 004. (d) Cha ac e iza io.n o c ys al pe ec ion T ansmission X- ay opog aphy was used p io o epi axy o image he de ec s in he subs a e. A e epi axy, he newly c ea ed de ec s we e obse ed by bo h e lexion and ansmission opog aphy. 8,5 '¸ Aloa 2 6acLee As AIo.79 G ao.2~ As Fig. 1. 400 e lexion p o iles eco ded on a double spec o- g aph in he pa allel se ing wi h Cu K~I adia ion. Uppe cu e: supe imposed p o iles o he GaAs subs a e and epilaye ; mid cu e: shi ed p o iles o he subs a e (le ) and he AlxGal_xAs epilaye ( igh ) o x=0.12; lowe cu e: shi ed p o iles o x = 0.79. E. ESTOP, A. IZRAEL AND M. SAUVAGE 629 I can be shown (Reinha & Logan, 1973; Rozgonyi & Ciesielka, 1973) ha when he hickness h o he epilaye is negligible wi h espec o he hickness , o he subs a e, he exp ession o he a e age s ess a in he epilaye akes he o m -e (3) a - 64(1- ) whe e E is Young's modulus (E=1012 dyne/cm2), is Poisson's a io ( =0-3) and Q is he adius o cu a u e o he sample. In he same app oxima ion he s ess o's in he i s /zm o he subs a e close o he in e ace is gi en by , = - 4 ~- a . (4) O's Then he s ains can be eadily calcula ed h ough he elas ici y ela ion Aa (s) _ 2 a E (,) , (5) a (s~ being de e mined by he measu emen o he adius o cu a u e Q desc ibed in he p e ious sec ion. In he whole cou se o hese calcula ions, he elas ic cons an s o he laye and subs a e a e assumed o be equal; he alidi y o his assump ion will be discussed la e . The expe imen al da a Q, AOx and (Aa~/a)s a e lis ed in Table 1 oge he wi h he calcula ed alues o he s esses and s ains; he esul ing s ain- ee ela i e pa ame e di e ences (Aa~/a)o a e lis ed in he las column o a se ies o samples wi h inc easing AI con en in he epilaye . I is wo h no icing ha in he i s sample conce ning he homoepi axy o pu e GaAs on a hea ily doped GaAs subs a e, he adius 15~6' 10.1~ 4 5.10 4 Aa~ A B i i i i i , i 0,12 0,24 0,39 0,54 0,68 0,79 1 Fig. 2. Measu ed ela i e la ice pa ame e di e ence be ween GaAs and a s ain- ee solid solu ion AlxGal_xAs as a unc ion o x. Debye-Sche e da a o x=l" A p esen de e mina ion; B esul s o E enbe g & Pa (1970); he solid line ep esen s he p edic ion o Vega d's law. o cu a u e was ound o be in ini e and no Ke~ peak shi could be de ec ed. The a ia ion o (Aa~/a)o as a unc ion o x, plo ed in Fig. 2 is qui e consis en wi h he linea beha iou p edic ed by Vega d's law, a esul al eady ob ained by Rozgonyi e al. (1974). The non-physical case o x= 1 (epi axy o pu e AlAs on GaAs) has been cal- cula ed on he basis o he p esen Debye-Sche e measu emen s* o he la ice pa ame e s o pu e GaAs and AlAs powde s: a(A1As) = 5.6612 _+ 0.0008, a(GaAs) = 5.6528 + 0.0006 A. A ough check o he consis ency o he me hod is ob ained by compa ing he measu ed adius o cu a- u e 0 wi h he alue calcula ed on he basis o he ela i e pa ame e di e ences (Aa~/a)o lis ed in Table l(b) acco ding o he o mula gi en by Reinha e al. (1973)" c Q = (_A_~)6h' (6) 0 which is only alid i h is much smalle han s and whe e C deno es a unc ion o he elas ic cons an s o bo h compounds equal o one when hese cons an s a e assumed o be iden ical. In Table 2 he alues cal- cula ed in he hypo hesis C= 1 oge he wi h he bes i ob ained by leas -squa es analysis and co e- sponding o C=0.93 a e compa ed wi h he expe - imen al da a. The compa ison is a he sa is ac o y since he cu a u e was no pe ec ly homogenous al hough sphe ical, as was demons a ed by use o ou di e en e lexions. Table 2. Compa P~on be ween measu ed and calcula ed adius o cu a u e (m) as a unc ion o x O 0 calcula ed wi h x measu ed C= 1 C= 0.93 0.12 15.8 15.5 14.4 0.24 6.8 7.9 7.3 0.39 3.9 5.8 5-4 0-54 4.0 4-0 3.7 0-68 4.0 3.6 3-4 0.79 3-3 3-8 3-5 I should be no iced ha he esul s ound in he p esen wo k ag ee wi h he da a p e iously published independen ly by Rozgonyi e al. (1974) and by D uzhinina e al. (1975), al hough he wo pape s appea con adic o y a i s sigh . The eason migh be ha Rozgonyi e al. p oduce ela i e pa ame e di e ences p esumably co ec ed o s ain con ibu- ions while D uzhinina e al. publish he (Aa~/a)s in he he s ained s a e as measu ed di ec ly by he Kcq peak shi . * The powde diag ams we e aken by B. K inzle a he Labo a oi e de C is allog aphie aux Rayons X, Uni e si y o Gene a. ACTA CRYSTALLOGRAPHICA, VOL. A32, 1976--EsTo ', IZRAEL AND SAUVAGE PLATE 27 -, ~i :~,...: :, .:~..,:.. .... , , . ,i,.~ " 1 .. ~ . • ...,,. " --."'4" ,< i , D ,...: (a) (b) ,.,) ., • .2:. Fig. 3. T ansmission opog aph, 02~ e lexion, Mo K~I. (a) Disloca ion- ee c ys al p io o epi axy, (b) same c ys al a e epi axy o a 4 pm hick laye o AlxGal_xAs wi h x=0-3. No ice he newly c ea ed linea de ec s. [To ace p. 630 ACTA CRYSTALLOGRAPHICA, VOL. A32, 1976---ESTOl', IZRAEL AND SAUVAGE PLATE 28 °.. " • " ~Q . .-.. ~:: ,~.,~ • ? ( .. • ,.~ °.. • ,L.'. (a) (b) Fig. 4. Bo mann ansmission opog aph, 02~ e lexion, Mo K~, GaAs subs a e showing a la ge a ie y o disloca- ions. (c) Fig. 5. Mis i disloca ions. (a) Re lexion opog aph, 402 e- lexion on he epi axic laye only, Cu K~I, he disloca ions a e isible, (b) ansmission opog aph, Mo K~I, 022 e- lexion, (c) e lexion opog aph, Cu K~I, 444 e lexion on he epi axic laye . The disloca ions a e ou o con as in (b) and (c). 630 LATTICE PARAMETERS AND X-RAY TOPOGRAPHY ON HETEROJUNCTIONS Making use o o mulae (3), (4), (5) and (6) i is possible o exp ess he s ain componen s in e ms o he s ain- ee alue (AaI/a)o. Hence, exp ession (2) akes he o m: (Aa~i = (1+ 2 8 h) (_A~) x (7) a /, -]-Z- +]- }] 0 Since in he cases o in e es he e, h/ s lies be ween 10 -2 and 1.6 x 10 -2, o mula (7) leads o s 0 This simple esul explains why he measu ed alue ela ed o he K~ peak shi is abou wice as la ge as he alue gi en by Vega d's law. On his poin i can be summa ized ha he p esen measu emen s ag ee wi h D uzhinina e al. (1975) and lead o co ec ed alues con i ming hose o Rozgonyi e al. (1974). (b) De ec s ela ed wi h liquid-phase epi axy As was de eloped in he p e ious sec ion, GaAs and AlxGal_~,As ha e di e en la ice pa ame e s a oom empe a u e. Howe e , because o he di e ence in he mal expansion coe icien s, he misma ch anishes o any alue o x a ound 900 °C, which is nea o he empe a u e chosen o he LPE (845 °C) (E enbe g & Pa , 1970; Pie on, Pa ke & McNeely, 1966). This p ope y was co obo a ed by ollowing he p o- g essi e o e lap o he e lexion peaks om he laye and subs a e on inc easing he empe a u e om 25 o 850°C (Ba aul , 1975). The epi axic laye hus g ows s ain ee, bu s esses appea on cooling esul ing in he elas ic sphe ical cu a u e o he sample al eady desc ibed in his pape . Howe e , i he h eshold o mis i disloca ion gene a ion is su passed, some disloca ions may appea in he in e ace be ween laye and subs a e. In o de o ha e mo e in o ma ion on his phenomenon, X- ay opog aphs o he same sample we e aken be o e and a e LPE. Mos sub- s a es show no g own-in disloca ions bu only b oad bands due o an i egula dopan dis ibu ion (Fig. 3a). In some samples disloca ion pile-up in {111} glide planes, o mo e complica ed disloca ion angles p esumably in oduced du ing handling o clea ing, we e obse ed (Fig. 4). I should be no iced ha in such a highly abso ban sample (~ =8.7) he con as is pu ely dynamical and disloca ions appea as whi e lines on a da k g ey backg ound. A e epi axy, newly c ea ed linea de ec s pa allel o he [011] di ec ion a e some imes obse ed as is shown in a ansmission opog aph (Fig. 3b)* and in a e lexion opog aph as well (Fig. 5a). In he ansmission se ing, he majo con ibu ion o he image comes * Mo phological su ace de ec s due o gallium d ople s (Small e al., 1975) a e also isible on his opog aph, such de ec s a e now elimina ed by a be e con ol o he g ow h p ocess. om he subs a e since he ays belonging o he e- lexion domain o he epilaye ha e been abso bed ou be o e eaching i . As a consequence, he p esence in Fig. 3(b) o whi e dynamical images o he linea disloca ions p o ides e idence o hei belonging o he subs a e. On he o he hand, Fig. 5(a) ep esen s a e lexion opog aph aken wi h he 402 e lexion. Since such e exions (h + k + l# 4n) ha e a anishingly small s uc u e ac o in GaAs one can be su e ha he opog aph is only due o he epilaye A10.3Ga0.TAs. Hence he p esence o he linea disloca ions in Fig. 5(a) indica es ha hey belong also o he epilaye and a e hus loca ed in he in e ace. The disloca ions a e pu e edge wi h Bu ge s ec o ½[01T], as can be seen om Fig. 5(b) and (e) whe e hey a e ou o con as . They a e mos likely mis i disloca ions gene a ed on local s ess concen a ions, bu hei densi y is a oo low o accomoda e he la ice misma ch which is p ope ly accoun ed o by he cu a u e. Conclusion The p esen measu emen s ha e pe mi ed elucida ion o he misunde s andings be ween independen g oups wo king in he ield o he e ojunc ions on GaAs. The esul s p o ide con i ma ion o he o de o magni ude o he s esses in he epi axic laye s and es ablish he compa ibili y o he pa ame e a ia ion in s ess- ee AlxGal_xAs wi h he p edic ion o Ve- ga d's law. Fu he wo k on mul iple he e ojunc ions wi h phospho us addi ion is in p og ess. The au ho s a e g ea ly indeb ed owa ds J. Benoi and his co-wo ke s om he C.G.E. esea ch labo - a o ies who p o ided hem wi h he samples and pe o med all he measu emen s on he epi axic laye cha ac e is ics. One o us (E.E.) wishes o hank he F ench go e nmen o a CROUS esea ch g an . This wo k has been pa ly suppo ed by a con ac wi h he DGRST (No. 74.7.0420). Re e ences BARB~, M. (1974). Th~se de 3eme cycle, Pa is (unpublished). BARRAULT, J. V. (1975). P i a e communica ion. DRUZHININA, L. V., BUBLIK, V. T., DOLGINOV, L. M., ELISEEV, P. G., KERBELEV, M. P., OSVENSKII, V. B., PINSKER, I. Z. ~ SHUMSKII, M. G. (1975). Soy. Phys. Tech. Phys. 7, 935-939. ETTENBERG, M. & PAFF, R. J. (1970). J. AppL Phys. 41, 3926-3927. PIERRON, E. n., PARKER, D. L. & McNE'ELY, J. B. (1966). Ac a C ys . 21,290. REINHARDT, F. K. ~; LOGAN, m. A. (1973). J. Appl. Phys. 44, 3171-3175. ROZGONYI, G. A. & CIESIELKA, T. J. (1973). Re . Sci. Ins um. 44, 1053-1057. ROZGONYI, G. A., PETROFF, P. M. & PANISH, M. B. (1974). J. C ys . G ow h. 27, 106-117. SMALL, M. B., BLAKESLEE, A. E., SHIH, K. K. & POTEMSKI, R. M. (1975). J. C ys . G ow h, 30, 257-266.