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Shallow acceptor states in undoped GaSb
S o l l d S t a t e Communications, Vol. 74, No. 6, pp. 429-432, 1990. Printed in Great Britain.
SHALLOW
ACCEPTOR
STATES
A . N . B a r a n o v t, P . E . D y s h l o v e n k o $ 0
0038-1098/9053.00+.00 Pergamon Press plc
IN U N D O P E D
GaSb
A . A . K o p y l o v ~, V . V . S h e r s t n y e v t
~l.F.Yoffe Physico-Technlcal Institute L e n i r ~ r a d , 194021, U S S R ~V.I.Ulyanov
(Lenin) E l e c t r i c a l E n g i n e e r i n g L e n i n g r a d , 197022, U S S R
( R e c e { u e d 22
J~tu~
Institute
fQQO b~ M . O a # d m ~ )
Photoexcitation s p e c t r a of s e v e r a l a c c e p t e r states in G a S b h a v e b e e n o b s e r v e d f o r the f i r s t t i m e b y F I R a b s o r p t i o n measurements. In Czochralski 6Town bulk crystals the a c c e p t e r l e v e l w i t h the i o n i z a t i o n e n e r g y of 3 6 ± 2 m e V w a s f o u n d to d o m i n a t e . The accepter l e v e l s 13±I a n d 16±I m e V have been detected in epitaxial layers grown from Ga-Sb-Pb s o l u t i o n s . A t h e o r e t i c a l e v a l u a t i o n of the d o u b l e a c c e p t e r & m o u n d s t a t e e n e r g i e s i n G a S b is p e r f o r m e d .
Gallium antlmonide has been studied for more then thirty years, however, little is known about impurity and defect states in this semiconductor [I]. For example, experimental values of ionization energies for the most frequently mentioned native double a c c e p t e r [2] r a n g e 24 to 35 m e V f o r the n e u t r a l s t a t e a n d 56 to 1 2 0 m e V f o r the single charged. For shallower levels no unambiguous information is available. The few papers on IR optical properties of p - G a S b k n o w n [3,4] w e r e p u b l i s h e d i n the 60's, and only deal with the spectral region ~60 meV. I n the p r e s e n t p a p e r w e r e p o r t d a t a on FIR impurity absorption measurements in undoped p-GaSb grown by Czochralski and I~E techniques. The Czochralski grown samples had room temperature hole c o n c e n t r a t i o n s ~ 1 0 1 7 c m -3. T h e e p i t a x i a l layers were obtained from Ga-Sb-Pb solutions, and their characteristics are given in Table I. Measurements were
cazu'ied o u t f o r p h o t o n e n e r g i e s i n the rar~ge 4 - 6 0 m e V u s i n g a F o u r i e r t r a n s f o r m spectrometer LFS-IOOO and a helium cold finger cryostat. Samples were mechanically polished and then c h e m i c a l l y e t c h e d in o r d e r to e l i m i n a t e e f f e c t s of s u r f a c e s t r a i n s . T h e s a m p l e thickness varied from 30 to 150 ~m depending o n the a b s o r p t i o n magnitude. In the case of epitaxial samples substrates were completely removed. I n the C z o c h r a l s k i 6 T o w n b u l k G a S b a s t r o n g a b s o r p t i o n b a n d p e a k i n g at 33 m e V with a well defined low-energy threshold was observed at low temperatures, as s h o w n i n F i g . 1 . O n h e a t i n g f r o m 10 to 80 K the absorption strength reduced n e a r l y twlce, h o w e v e r , at 8 0 K the b a n d remained pronounced and disappeared at higher temperatures. The shape and temperature dependence of the band are characteristic of the impurity absorption. Thus, we attribute it to photolonization o f the a c c e p t e r l e v e l s ,
T a b l e 1. C h a r a c t e r i s t i c of the i n v e s t i g a t e d e p i t a x i a l p-GaSh samples grown from Ga-Sb-Pb solutions.
Hole Sample
#
concentration
(1017
c m -3)
300 K 61114-1 61114-4 61119-1 61119-3
78 K
1.1 0.8 1.2 0.5
0.7 0.5 0.4 0.2
429
Solution
composition
(mass f r a c t i o n )
Ga
Sb
0.11 0.12 0.49 0.225
0.59 0.38 0.21 0.225
430
SHALLOW ACCEPTOR STATES IN UNDOPED GaSb
I000
Vol. 74, No. 6
I000
Ti 80O o
u 600
600--
E
o 400
2OO
0
I0
20 30 40 50 Photon energy (meV)
Fig.1. Absorption Czochralski grown
spectra p-GaSh.
60
70
80
5OO TO
I
I
I
I
I
60
70
I
20
{
{
30 40 50 60 Photon energy (meV)
{
{
{
70
Pig.2. A b s o r p t i o n s p e c t r a o f the ~pitaxial samples grown from Ga-rich ~ t o c h i o m e t r i c m e l t s . T ~ I O K.
80
s p e c t r a o f the @~rown f r o m S b - r i c h
1S3/2~2P5/2(FS)_
should
be
the
most
strong for acceptors in GaSh. T h i s is r e a s o n a b l e d u e to the s i m i l a r i t y b e t w e e n the valence band parameters of GaSb (V1=11.80: 72=4.03; 73=5.26) and Oe 72=4.25:
73=5.69)
[7]. the binding a n d 2 P 5 / 2 ( F 8)
a c c e p t o r s t a t e s in G a S b a r e 2 . 6 a n d 3 . 6 meV, r e s p e c t i v e l y . A s the s p l i t t i n g is small compared with the observed linewldth, individual photoexcitation lines can not be resolved experimentally. These two t r a n s i t i o n s , mainly composing the photoexcitation peak, h a v e a p p r o x i m a t e l y e q u a l s t r e n g t h . Therefore, to estimate the acceptor ionization energy from the photoexcitation peak position, it is reasonable to e m p l o y the a v e r a g e of the 2 P 5 / 2 ( F 7) a n d 2 P 5 / 2 ( F 8) b i n d i n g energy
I0(3
I0
I
According to [6], e n e r g i e s of the 2 P 5 / 2 ( P 7)
1
0
I
20 SO 40 50 Photon energy (me V)
impurity band characteristic of the Czochralski grown GaSb crystals is substantially reduced in a l l e p l t a x i a l samples investigated. Thus, t h r e e t y p e s of a c c e p t o r l e v e l s h a v e b e e n d e t e c t e d in d i f f e r e n t u n d o p e d p-GaSb crystals. A quantitative i n t e r p r e t a t i o n o f the a b s o r p t i o n s p e c t r a may be based on the effective mass t h e o r y (I~T) of s h a l l o w a c c e p t o r s t a t e s in cubic semiconductors developed by Baldereschi a n d L i p a r i [5,6]. S i m i l a r l y to germanium (see the experimental spectra reproduced in [6]), the transitions 1S3/2~2P5/2(F7) and
(71=13.35;
2P5/2
j_ 3o0
I I0
Fig.3. Absorption epitaxial samples m e l t s . T ~ I O K.
of the T ~ I O K.
while the peak at 33 meV is due to the correspondin~ photoexcitation t r a n s i t i o n s . T h e s h a r p p e a k at 2 8 m e V is o b v i o u s l y r e l a t e d to the T O - p h o n o n . Absorption spectra far the LPE samples strongly differ from those 3bserved for the Czochralski ones. T h e gamples grown from Ga-rich or stochiometric, relatively to Sb, m e l t s 3how s t r o n g i m p u r i t y a b s o r p t i o n e x t e n d e d In e n e r g y d o w n to h ~ 1 0 m e V (Fig.2). T h e ) h o t o e x c i t a t i o n p e a k c l e a r l y a p p e a r s at 13 meV. For the samples grown from ]b-rich melts the photoexcitation ~ t r u o t u r e is l e s s p r o n o u n c e d a n d a p p e a r s ks a s t e p n e a r 10 m e V (Fig.3). I n b o t h ~ases photoexcitation features are ~hermally quenched at temperatures below 30 K. It s h o u l d b e n o t e d that the 33 m e V
" 400 =.
I 0
80
and
values, in G a S b p r e c i s e l y 3 . 1 ± 0 . 5 meV. The results of the estimation are p r e s e n t e d in T a b l e 2. P r e s u m a b l y , the two s h a l l o w e r l e v e l s , 13 a n d 16 meV, b e l o n g to s l n ~ l e a c c e p t o r s , i n a c c o r d a n c e w i t h the ~ 4 T v a l u e o f the
Vol.
Table 2. I o n i z a t i o n e n e r g l e s of the a c c e p t o r levels d e t e c t e d in the i n v e s t i g a t e d u n d o p e d GaRb crystals.
Sample origination
Photoexcitation peak (meV)
Czochralski LPE G a - r i c h LPE Sb-rich
33±I 13±0.5 10±0.5
acceptor EA=12.56
A p p r o p r i a t e s y m m e t r y r e q u i r e m e n t s have b e e n regarded. The p a r a m e t e r s ~ , p ,C O and
Ionization energy (meV)
with the first ionization the n a t i v e double a c c e p t o r
[2]. At present, no r e a l i s t i c t h e o r e t i c a l model of double acceptors in cubic s e m i c o n d u c t o r s is known. We h a v e c a r r i e d out an ~ c a l c u l a t i o n of the double a c c e p t o r states t a k i n g into account the d e g e n e r a t e n a t u r e of the v a l e n c e band. The t w o - p a r t i c l e H a m i l t o n i a n i n c l u d l n g the h o l e - h o l e C o u l o m b i n t e r a c t i o n is H(rhl.rh2)
= H(rhl ) + H(rh2J e
2
C2
are
supposed
to
be
determined
a l o n g w i t h the c o r r e s p o n d i n g eigenvalues u s i n g a v a r i a t i o n a l procedure. The b i n d i n g e n e r g i e s of the o n e - h o l e a n d two-hole g r o u n d states, E I and E 2 respectively, have b e e n calculated. In Table 3 the results of the c a l c u l a t i o n for Ge and GaRb are presented. The first and second ionization energies are II d e t e r m i n e d as E ~ = E 2 - E I and E A =E I . The
36!2 16!I 13±1
ionization energy in GaRb meV [6]. The level 36 meV
correlates e n e r E y of
431
SHALLOW ACCEPTOR STATES IN UNDOPED GaRb
74, No. 6
(1)
exchange splitting of the two-hole E r o u n d state, f o u n d to be
+ 4~s01rhl-rh21 where 2 Ph 5 7 H(r h) = ~ 0 ( 7 1 + 2--7) - ) mo(Ph'J 40--
[2)
/
2e 2 a~SSOr h is the o n e - p a r t i c l e H a m i l t o n i a n for the d o u b l e - c h a r g e d a c c e p t o r centre in the s p h e r i c a l a p p r o x i m a t i o n of B a l d e r e s c h i and L i p a r i [5]. In the e x p r e s s i o n s above e is the c r y s t a l d i e l e c t r i c constant; m0 is the free electron mass; 7=(272+373)/5, where 7 1 , 72 a n d 73 are the L u t t i n g e r v a l e n c e b a n d parameters: Ph is the h o l e linear m o m e n t u m operator. and J is the ~ l a r momentum operator c o r r e s p o n d l n ~ to spin 3/2. The t w o - p a r t l c l e w a v e f u n c t i o n s for H a m i l t o n l a n (I) were c o n s t r u c t e d u s i n g the g r o u n d - s t a t e - l i k e o n e - p a r t l c l e wave functions in the form
2o
z~ Be •
0
I
5
I
20
I
25
Fig.4. R e l a t i o n b e t w e e n the first and s e c o n d i o n i z a t i o n energies of the group II double a c c e p t o r s in gez~nanium. The e x p e r i m e n t a l data are taken from [ 1 ] , R O = 4 . 3 2 meV.
ml=2 ~ Y(2)(e,~)Is=3/2,mj-ml> ml=-2 ml
x
I
15
EIA/Ro
l~312>mj = CO e-at y ~ O ) ( e , ~ ) i s = 3 1 2 . m j >
+ C2r2e-~r
I
10
(3)
432
Vol. 74
SHALLOW ACCEPTOR STATES IN UNDOPED GaSb Table used
3. T h e
~4T
double
in the c a l c u l a t i o n ;
7
~
acceptor ~=27/71,
e
I
ground
state
energies
a n d pare~neters
Ro=e4mo/2h2(a~SeO)271.
EI -RO
E2 -R0
RO
EA
(meV)
(meV)
(meV)
Ge
13.35
0.766
15.36
8.44
12.14
4.32
16.0
36.5
GaSb
11.8 11.0 a
0.808 0,70 a
15.7
9.70 7.10
13.98 10.19
4.68 5.02
20.0 15.5
45.4 35.6
These parameters are deduced from the experimental o f R e f . 8 , the r e s t a r e the s a m e as in R e f . 6 .
empirical approach may be appreciated. The most representative set of double acceptors experimentally studied is k n o w n f o r g e r m a n i u m [I]. T h e r e l e v a n t data are plotted in Fig.5, showing a good correlation between the f i r s t a n d second ionization energies of the double acceptor centres. Assumln~ that the i n t e r p o l a t e d c u r v e is v a l i d f o r G a S b , w e may speculate o n the p r o p e r t d e s of the 36 m e V a c c e p t o r l e v e l . If the l a t t e r is related conventionally to the first ionization energy of a double acceptor, then the corresponding value of the
No. 6
data
s e c o n d i o n i z a t i o n e n e r g y is e x p e c t e d to l l e i n the r a n g e 9 3 - 1 0 6 meV. T h e r e a r e several experimental indications of acceptor levels with the binding e n e r g i e s ~ 1 0 0 m e V i n G a S b (see [2] a n d references therein). But to prove reliably a direct connection between these two levels, further investigations are required.
Acknowledgements - The authors would l l k e to t h a n k Dr. Y u . P . Y a k o v l e v f o r m a n y helpful discussions.
References I. L a n d o l t - B ~ r n s t e i n , Numerical Data and Functional Relationship in Science and Technolo~. New Series, Group III, Vo1.17, Subvol.a, Physics of Group IV Elements and III-V Compounds (Edited by O.Madeltuag). Sprir~erV e r l a g (1982). ~. K . N a k a c h i m a , Japanese Journal of A p p l i e d P h y s i c s ~0, 1085 (1981). 3. E . J . J o h n s o n , I.Fillnskl, H.Y.Fan, Proc. 6th Inter~lat. Conf. Ph,Ts. S e m i c o n d . , p . 3 7 5 , E x e t e r (1962).
4. E . J . J o h n s o n , H . Y . F a n , P h y s i c a l R e v i e w 139, A 1 9 9 1 (1965). 5. A . B a l d e r e s c h i , N.O.Lipari, Physical R e v i e w B S, 2 6 9 7 (1973). 6. A . B a l d e r e s c h l , N.O.Lipari, Physical R e v i e w B g, 1525 (197A). 7. P . L a w a e t z , P h y s i c a l R e v i e w B 4, 3460 (1971). 8. R . A . S t r a d l i n ~ , Physics Letters 20, 2 1 7 (1966).
SHALLOW
ACCEPTOR
STATES
A . N . B a r a n o v t, P . E . D y s h l o v e n k o $ 0
0038-1098/9053.00+.00 Pergamon Press plc
IN U N D O P E D
GaSb
A . A . K o p y l o v ~, V . V . S h e r s t n y e v t
~l.F.Yoffe Physico-Technlcal Institute L e n i r ~ r a d , 194021, U S S R ~V.I.Ulyanov
(Lenin) E l e c t r i c a l E n g i n e e r i n g L e n i n g r a d , 197022, U S S R
( R e c e { u e d 22
J~tu~
Institute
fQQO b~ M . O a # d m ~ )
Photoexcitation s p e c t r a of s e v e r a l a c c e p t e r states in G a S b h a v e b e e n o b s e r v e d f o r the f i r s t t i m e b y F I R a b s o r p t i o n measurements. In Czochralski 6Town bulk crystals the a c c e p t e r l e v e l w i t h the i o n i z a t i o n e n e r g y of 3 6 ± 2 m e V w a s f o u n d to d o m i n a t e . The accepter l e v e l s 13±I a n d 16±I m e V have been detected in epitaxial layers grown from Ga-Sb-Pb s o l u t i o n s . A t h e o r e t i c a l e v a l u a t i o n of the d o u b l e a c c e p t e r & m o u n d s t a t e e n e r g i e s i n G a S b is p e r f o r m e d .
Gallium antlmonide has been studied for more then thirty years, however, little is known about impurity and defect states in this semiconductor [I]. For example, experimental values of ionization energies for the most frequently mentioned native double a c c e p t e r [2] r a n g e 24 to 35 m e V f o r the n e u t r a l s t a t e a n d 56 to 1 2 0 m e V f o r the single charged. For shallower levels no unambiguous information is available. The few papers on IR optical properties of p - G a S b k n o w n [3,4] w e r e p u b l i s h e d i n the 60's, and only deal with the spectral region ~60 meV. I n the p r e s e n t p a p e r w e r e p o r t d a t a on FIR impurity absorption measurements in undoped p-GaSb grown by Czochralski and I~E techniques. The Czochralski grown samples had room temperature hole c o n c e n t r a t i o n s ~ 1 0 1 7 c m -3. T h e e p i t a x i a l layers were obtained from Ga-Sb-Pb solutions, and their characteristics are given in Table I. Measurements were
cazu'ied o u t f o r p h o t o n e n e r g i e s i n the rar~ge 4 - 6 0 m e V u s i n g a F o u r i e r t r a n s f o r m spectrometer LFS-IOOO and a helium cold finger cryostat. Samples were mechanically polished and then c h e m i c a l l y e t c h e d in o r d e r to e l i m i n a t e e f f e c t s of s u r f a c e s t r a i n s . T h e s a m p l e thickness varied from 30 to 150 ~m depending o n the a b s o r p t i o n magnitude. In the case of epitaxial samples substrates were completely removed. I n the C z o c h r a l s k i 6 T o w n b u l k G a S b a s t r o n g a b s o r p t i o n b a n d p e a k i n g at 33 m e V with a well defined low-energy threshold was observed at low temperatures, as s h o w n i n F i g . 1 . O n h e a t i n g f r o m 10 to 80 K the absorption strength reduced n e a r l y twlce, h o w e v e r , at 8 0 K the b a n d remained pronounced and disappeared at higher temperatures. The shape and temperature dependence of the band are characteristic of the impurity absorption. Thus, we attribute it to photolonization o f the a c c e p t e r l e v e l s ,
T a b l e 1. C h a r a c t e r i s t i c of the i n v e s t i g a t e d e p i t a x i a l p-GaSh samples grown from Ga-Sb-Pb solutions.
Hole Sample
#
concentration
(1017
c m -3)
300 K 61114-1 61114-4 61119-1 61119-3
78 K
1.1 0.8 1.2 0.5
0.7 0.5 0.4 0.2
429
Solution
composition
(mass f r a c t i o n )
Ga
Sb
0.11 0.12 0.49 0.225
0.59 0.38 0.21 0.225
430
SHALLOW ACCEPTOR STATES IN UNDOPED GaSb
I000
Vol. 74, No. 6
I000
Ti 80O o
u 600
600--
E
o 400
2OO
0
I0
20 30 40 50 Photon energy (meV)
Fig.1. Absorption Czochralski grown
spectra p-GaSh.
60
70
80
5OO TO
I
I
I
I
I
60
70
I
20
{
{
30 40 50 60 Photon energy (meV)
{
{
{
70
Pig.2. A b s o r p t i o n s p e c t r a o f the ~pitaxial samples grown from Ga-rich ~ t o c h i o m e t r i c m e l t s . T ~ I O K.
80
s p e c t r a o f the @~rown f r o m S b - r i c h
1S3/2~2P5/2(FS)_
should
be
the
most
strong for acceptors in GaSh. T h i s is r e a s o n a b l e d u e to the s i m i l a r i t y b e t w e e n the valence band parameters of GaSb (V1=11.80: 72=4.03; 73=5.26) and Oe 72=4.25:
73=5.69)
[7]. the binding a n d 2 P 5 / 2 ( F 8)
a c c e p t o r s t a t e s in G a S b a r e 2 . 6 a n d 3 . 6 meV, r e s p e c t i v e l y . A s the s p l i t t i n g is small compared with the observed linewldth, individual photoexcitation lines can not be resolved experimentally. These two t r a n s i t i o n s , mainly composing the photoexcitation peak, h a v e a p p r o x i m a t e l y e q u a l s t r e n g t h . Therefore, to estimate the acceptor ionization energy from the photoexcitation peak position, it is reasonable to e m p l o y the a v e r a g e of the 2 P 5 / 2 ( F 7) a n d 2 P 5 / 2 ( F 8) b i n d i n g energy
I0(3
I0
I
According to [6], e n e r g i e s of the 2 P 5 / 2 ( P 7)
1
0
I
20 SO 40 50 Photon energy (me V)
impurity band characteristic of the Czochralski grown GaSb crystals is substantially reduced in a l l e p l t a x i a l samples investigated. Thus, t h r e e t y p e s of a c c e p t o r l e v e l s h a v e b e e n d e t e c t e d in d i f f e r e n t u n d o p e d p-GaSb crystals. A quantitative i n t e r p r e t a t i o n o f the a b s o r p t i o n s p e c t r a may be based on the effective mass t h e o r y (I~T) of s h a l l o w a c c e p t o r s t a t e s in cubic semiconductors developed by Baldereschi a n d L i p a r i [5,6]. S i m i l a r l y to germanium (see the experimental spectra reproduced in [6]), the transitions 1S3/2~2P5/2(F7) and
(71=13.35;
2P5/2
j_ 3o0
I I0
Fig.3. Absorption epitaxial samples m e l t s . T ~ I O K.
of the T ~ I O K.
while the peak at 33 meV is due to the correspondin~ photoexcitation t r a n s i t i o n s . T h e s h a r p p e a k at 2 8 m e V is o b v i o u s l y r e l a t e d to the T O - p h o n o n . Absorption spectra far the LPE samples strongly differ from those 3bserved for the Czochralski ones. T h e gamples grown from Ga-rich or stochiometric, relatively to Sb, m e l t s 3how s t r o n g i m p u r i t y a b s o r p t i o n e x t e n d e d In e n e r g y d o w n to h ~ 1 0 m e V (Fig.2). T h e ) h o t o e x c i t a t i o n p e a k c l e a r l y a p p e a r s at 13 meV. For the samples grown from ]b-rich melts the photoexcitation ~ t r u o t u r e is l e s s p r o n o u n c e d a n d a p p e a r s ks a s t e p n e a r 10 m e V (Fig.3). I n b o t h ~ases photoexcitation features are ~hermally quenched at temperatures below 30 K. It s h o u l d b e n o t e d that the 33 m e V
" 400 =.
I 0
80
and
values, in G a S b p r e c i s e l y 3 . 1 ± 0 . 5 meV. The results of the estimation are p r e s e n t e d in T a b l e 2. P r e s u m a b l y , the two s h a l l o w e r l e v e l s , 13 a n d 16 meV, b e l o n g to s l n ~ l e a c c e p t o r s , i n a c c o r d a n c e w i t h the ~ 4 T v a l u e o f the
Vol.
Table 2. I o n i z a t i o n e n e r g l e s of the a c c e p t o r levels d e t e c t e d in the i n v e s t i g a t e d u n d o p e d GaRb crystals.
Sample origination
Photoexcitation peak (meV)
Czochralski LPE G a - r i c h LPE Sb-rich
33±I 13±0.5 10±0.5
acceptor EA=12.56
A p p r o p r i a t e s y m m e t r y r e q u i r e m e n t s have b e e n regarded. The p a r a m e t e r s ~ , p ,C O and
Ionization energy (meV)
with the first ionization the n a t i v e double a c c e p t o r
[2]. At present, no r e a l i s t i c t h e o r e t i c a l model of double acceptors in cubic s e m i c o n d u c t o r s is known. We h a v e c a r r i e d out an ~ c a l c u l a t i o n of the double a c c e p t o r states t a k i n g into account the d e g e n e r a t e n a t u r e of the v a l e n c e band. The t w o - p a r t i c l e H a m i l t o n i a n i n c l u d l n g the h o l e - h o l e C o u l o m b i n t e r a c t i o n is H(rhl.rh2)
= H(rhl ) + H(rh2J e
2
C2
are
supposed
to
be
determined
a l o n g w i t h the c o r r e s p o n d i n g eigenvalues u s i n g a v a r i a t i o n a l procedure. The b i n d i n g e n e r g i e s of the o n e - h o l e a n d two-hole g r o u n d states, E I and E 2 respectively, have b e e n calculated. In Table 3 the results of the c a l c u l a t i o n for Ge and GaRb are presented. The first and second ionization energies are II d e t e r m i n e d as E ~ = E 2 - E I and E A =E I . The
36!2 16!I 13±1
ionization energy in GaRb meV [6]. The level 36 meV
correlates e n e r E y of
431
SHALLOW ACCEPTOR STATES IN UNDOPED GaRb
74, No. 6
(1)
exchange splitting of the two-hole E r o u n d state, f o u n d to be
+ 4~s01rhl-rh21 where 2 Ph 5 7 H(r h) = ~ 0 ( 7 1 + 2--7) - ) mo(Ph'J 40--
[2)
/
2e 2 a~SSOr h is the o n e - p a r t i c l e H a m i l t o n i a n for the d o u b l e - c h a r g e d a c c e p t o r centre in the s p h e r i c a l a p p r o x i m a t i o n of B a l d e r e s c h i and L i p a r i [5]. In the e x p r e s s i o n s above e is the c r y s t a l d i e l e c t r i c constant; m0 is the free electron mass; 7=(272+373)/5, where 7 1 , 72 a n d 73 are the L u t t i n g e r v a l e n c e b a n d parameters: Ph is the h o l e linear m o m e n t u m operator. and J is the ~ l a r momentum operator c o r r e s p o n d l n ~ to spin 3/2. The t w o - p a r t l c l e w a v e f u n c t i o n s for H a m i l t o n l a n (I) were c o n s t r u c t e d u s i n g the g r o u n d - s t a t e - l i k e o n e - p a r t l c l e wave functions in the form
2o
z~ Be •
0
I
5
I
20
I
25
Fig.4. R e l a t i o n b e t w e e n the first and s e c o n d i o n i z a t i o n energies of the group II double a c c e p t o r s in gez~nanium. The e x p e r i m e n t a l data are taken from [ 1 ] , R O = 4 . 3 2 meV.
ml=2 ~ Y(2)(e,~)Is=3/2,mj-ml> ml=-2 ml
x
I
15
EIA/Ro
l~312>mj = CO e-at y ~ O ) ( e , ~ ) i s = 3 1 2 . m j >
+ C2r2e-~r
I
10
(3)
432
Vol. 74
SHALLOW ACCEPTOR STATES IN UNDOPED GaSb Table used
3. T h e
~4T
double
in the c a l c u l a t i o n ;
7
~
acceptor ~=27/71,
e
I
ground
state
energies
a n d pare~neters
Ro=e4mo/2h2(a~SeO)271.
EI -RO
E2 -R0
RO
EA
(meV)
(meV)
(meV)
Ge
13.35
0.766
15.36
8.44
12.14
4.32
16.0
36.5
GaSb
11.8 11.0 a
0.808 0,70 a
15.7
9.70 7.10
13.98 10.19
4.68 5.02
20.0 15.5
45.4 35.6
These parameters are deduced from the experimental o f R e f . 8 , the r e s t a r e the s a m e as in R e f . 6 .
empirical approach may be appreciated. The most representative set of double acceptors experimentally studied is k n o w n f o r g e r m a n i u m [I]. T h e r e l e v a n t data are plotted in Fig.5, showing a good correlation between the f i r s t a n d second ionization energies of the double acceptor centres. Assumln~ that the i n t e r p o l a t e d c u r v e is v a l i d f o r G a S b , w e may speculate o n the p r o p e r t d e s of the 36 m e V a c c e p t o r l e v e l . If the l a t t e r is related conventionally to the first ionization energy of a double acceptor, then the corresponding value of the
No. 6
data
s e c o n d i o n i z a t i o n e n e r g y is e x p e c t e d to l l e i n the r a n g e 9 3 - 1 0 6 meV. T h e r e a r e several experimental indications of acceptor levels with the binding e n e r g i e s ~ 1 0 0 m e V i n G a S b (see [2] a n d references therein). But to prove reliably a direct connection between these two levels, further investigations are required.
Acknowledgements - The authors would l l k e to t h a n k Dr. Y u . P . Y a k o v l e v f o r m a n y helpful discussions.
References I. L a n d o l t - B ~ r n s t e i n , Numerical Data and Functional Relationship in Science and Technolo~. New Series, Group III, Vo1.17, Subvol.a, Physics of Group IV Elements and III-V Compounds (Edited by O.Madeltuag). Sprir~erV e r l a g (1982). ~. K . N a k a c h i m a , Japanese Journal of A p p l i e d P h y s i c s ~0, 1085 (1981). 3. E . J . J o h n s o n , I.Fillnskl, H.Y.Fan, Proc. 6th Inter~lat. Conf. Ph,Ts. S e m i c o n d . , p . 3 7 5 , E x e t e r (1962).
4. E . J . J o h n s o n , H . Y . F a n , P h y s i c a l R e v i e w 139, A 1 9 9 1 (1965). 5. A . B a l d e r e s c h i , N.O.Lipari, Physical R e v i e w B S, 2 6 9 7 (1973). 6. A . B a l d e r e s c h l , N.O.Lipari, Physical R e v i e w B g, 1525 (197A). 7. P . L a w a e t z , P h y s i c a l R e v i e w B 4, 3460 (1971). 8. R . A . S t r a d l i n ~ , Physics Letters 20, 2 1 7 (1966).