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).
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ELISEEV, P.
G.,
KERBELEV, M.
P.,
OSVENSKII, V. B.,
PINSKER, I. Z. ~ SHUMSKII, M. G. (1975).
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Phys.
7, 935-939.
ETTENBERG, M. & PAFF, R. J. (1970).
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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.
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J. C ys . G ow h.
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SMALL, M. B., BLAKESLEE, A. E., SHIH, K. K. & POTEMSKI,
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