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
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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.
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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.
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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.
ACKNOWLEDGMENT
This wo k has been suppo ed by CICYT unde P ojec
No. ESP-98 1340.
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TABLE III. Haasen pa ame e s o Mn-doped 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
6.5⫻10-5 2.6 2.6 5.9
4828 J. Appl. Phys., Vol. 90, No. 9, 1 No embe 2001 Plaza
e al.
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