Amphoteric native defects in semiconductors
W. Walukiewicz
Citation: Appl. Phys. Lett. 54, 2094 (1989); doi: 10.1063/1.101174
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Amphoteric native defects in semiconductors
w. Walukiewicz
Center for Advanced Materials, Materials and Chemical Sciences Ditlisioll, Lawrence Berkeley LaboratOlY,
1 Cyclotron Road, Berkeley, Cafijbmia 94720
(Received 6 January 1989; accepted for publication 17 March 1989)
We show that a new concept of amphoteric native defects with strongly Fermi level dependent
defect formation energy provides the basis for a unified explanation of a large variety of
phenomena in semiconductors. Formation of Schottky barriers, particle irradiation induced
compensation, doping-induced superlattice intermixing, and limits of free-carrier
concentration find for the first time a common simple explanation.
Identification of the processes controlling the incorporation of native (or intrinsic) defects during semiconductor
material preparation and/or processing is of primary importance since so many electronic and structural properties critically depend on the presence of such defects.! In this letter
we present a simple and general theory which provides a
unified understanding of the factors affecting the abundances and reactions of simple native defects in semiconductors. The theory is based on a recently introduced concept of
amphoteric native defects. 2,3 Within this fundamental concept a large multiplicity of apparently unrelated phenomena
such as Schottky barrier formation, compensation of electrical activity in particle-irradiated semiconductors, dopinginduced superlattice intermixing, and limits of free-carrier
concentration can be, for the first time, understood in terms
of a single unifying theme.
Let us first recall the major aspects of the amphoteric
defect concept. It is based on the discovery that the introduction oflarge-enough concentrations of native defects always
leads to the same ultimate position of the Fermi energy,
E Fs .2,3 It has been shown in a detailed analysis of the GaAs
case that a new class of defects "amphoteric native defects"
with Fermi energy-controlled formation energy and defect
reaction rates are responsible for the stabilization of the Fermi level? The stable Fermi energy corresponds to the equilibrium condition for the following reactions:
for the explanation of several previously poorly understood
phenomena in semiconductors. Thus, it has been shown previously6 that the Fermi level dependent defect formation energy accounts for a slow dependence of the Fermi level pinning observed upon metal deposition on semiconductor
surfaces. 7 Here we show that the same concept can be used to
understand doping-induced superlattice intermixing and
limitations offree-carrier concentrations in semiconductors.
Doping-induced superlattice intermixing is a phenomenon which has been very extensively studied in the last few
years. g.9 It has been found that !Hype doping to the level
exceeding ~3X lOiS cm<> dramatically enhances interdiffusion in GaAslAlAs superlattices. lO Also, it has been demonstrated that the intermixing does not depend on the chemical identity of the site occupied by the donors and that it can
be suppressed by p-type codoping. II This phenomenon finds
a straightforward explanation in terms of the amphoteric
native defect model.
As is seen in Fig. 1, the formation energy of VGa is greatly reduced in heavily doped n-type GaAs. This leads to high
equilibrium concentration of the vacancies at elevated temperatures. Since the diffusion of Ga is proportional to the
gallium vacancy concentration [~ja 1 it also leads to enhanced interdiffusion of Ga and Al in GaAsl AlAs superlattices. The equilibrium concentration of triply ionized V~,~ is
(Ia)
and
(lb)
Here, we have neglected interstitials which are fast diffusing
species and do not play any role in the phenomena considered in the present letter. The total energies of the defects
participating in reactions (la) and (lb) are shown in Fig. 1.
The diagrams were obtained using reported total defect energy calculations. 4 •5 As is seen in Fig. 1, in n-(p-) type GaAs
acceptor- (donor) like defects are predominantly formed,
leading to a shift of the Fermi energy away from the band
edges. Eventually the Fermi level will be stabilized when the
formation rates for both types of defects are the same. For
reactions (la) and (lb) it occurs for EF~E" + 0.6 eV and
EF~E" + 0.8 eV, respectively. Also, as is seen in Fig. 1 the
reduction of the defect of the defect formation energy depends on the energy separation IEF - E FS I. The Eps dependent reduction of the defect formation energy is the very
property of the amphoteric native defects which is essential
2094
Appl. Phys. Lett. 54 (21). 22 May 1989
:;:-2.
8.0
7.0
2- GaAS + VGa
>-
OJ ~
0
Ci3 o.
c
Q) 5.0
-
"!
I
AS Ga +
oQ)
W
o
VAS
I
I
I
4.0
I
o
Ga:
3-
....,..3-
"-
,
!
I
I
I
3.0
2.0
"'-,
IV:
I
I
I
~
I
0.5
I
I ~--L-._<1"-'--L-'---'---'
1.0
1.5
Fermi energy (eV)
FIG. 1. Defect formation energies of simple vacancies V,;". V~, and related
As,;" + VA" Ga", + v,;" defects. The numbers at the curves represent the
net charge transfers from the Fermi sea to the defects. Maximum of the
diagram corresponds to the stabilization energy, E,-s, for a given defect system.
0003-6951/89/212094-03$01.00
@ 1989 American Institute of Physics
2094
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given by [Vba J = C exp(3EF lkT). In n-type GaAs, VGa
compensates intentionally introduced donors and the freeelectron concentration is
T _
n = IV
D
-
3 -- ]
3 [V Cia
,
= NJ;] 12
(13 1n [Vct}a J) ' (2)
where N [i is the total donor concentration and PI/2(?]) is
the Fermi-Dirac integral. Equation (2) has been solved for
Nc = 6x lO t8 cm\ corresponding to T',;;;f 1000 K and for
C = 3 X 10 18 em -3. The diffusion constant D (D~ [ VGa ] )
is shown in Fig. 2 as a function of the donor concentration.
We find that for N I) < C, D~ (N ; )l. This third power
dependence is in very good agreement with the experimental
data on interdiftusion in Si-doped GaAslAlAs. t2 Calculations show that for N [j > C, a much weaker D ~ N J dependence should be observed. The very efficient intermixing
in n-type GaAs stems from the large value of IEp - E FS I
=0.6 eV for n=3XlO 18 cm-<l. This means that at
n = 3 X 10 18 cm 3 the formation energy of [ VUa ] is reduced
by ~ 1.3 eV compared to the formation energy in the intrinsic GaAs. This reduction leads to about a six order magnitude increase of [ VG • ].
The situation is entirely different in p-type GaAs, where
the condition lEE - E,s I = 0.6 eV is achieved for the freehole concentration exceeding 1020 cm - \ and the stable defects are VAs and AS Ga + VAS' which do not enhance Ga
diffusion. Therefore, we can conclude that the Fermi energy
induced intermixing will not be efficient in p-type GaAsl
AlAs superlattices. This finding is in agreement with experiments which indicate that there is no universal intermixing
in the p-type superlattices. Doping with Be to concentration
levels greater than 2 X 10 19 cm- 3 does not lead to any interdiffusion. 11 On the other hand, very fast low-temperature
intermixing caused by the Zn diffusion finds another explanation related to the uncommonly fast diffusion of Zn in
GaAs. R• Li A similar mechanism of doping or Fermi level
induced intermixing has been suggested previously.I.~ However, the lack of the intrinsic reference level for the defect
8
' ~---.-----------..-~-
~
C'
"
1017
1Q18
1019
------
e--
.~-'-'--'----'----'---"--L:' 10 17
102C
10 21
Donor concentration (cm-~
FIG. 2. Diffusion constant Din Il-type GaAs/ AlAs and electron concentration in GaAs as functions of donor concentrations. Experimental data from
Si-doped (hAs/AlAs superlattice intermixing ( 0 ) (Ref- 12) and from
Hall measurements of dectron concentration in Se-doped GaAs ( • ) (Ref.
15)_
2095
Appl. Phys. Lett., VoL 54, No. 21,22 May 1989
formation energy led the authors to the conclusion that all
types of doping in all types of semiconductor systems will
induce such intermixing. It is shown here that this is not the
case and that the information on the location of E FS with
respect to the band edges is essential for understanding of the
intermixing process.
As we have argued above, intentional doping reduces
the formation energies of compensating native defects. For
heavily doped semiconductors with large values of
IEFs - Ec [ or ~E,s - E" I the reduction can be quite significant leading to large concentrations of the compensating defects. This in turn will reduce the concentration of free carders. In n-type GaAs the concentration offree carriers is given
by Eq. (2). The results for the calculated free-electron concentration as a function of the donor concentration N Ii are
shown in Fig. 2. Experimental data on Se doping of GaAs 15
are also given in this figure. An excellent agreement between
the calculations and the experiment is observed for the donor
concentration extending over three orders of magnitude. We
find from Eq. (2) that to a good approximation
n- [VGa] 113, which means that n-N /; for N.t < C and
n ~ N jj 1/3 for N Ii > C. This very characteristic cube root
dependence for N Ii , as well as third power dependence for
the gallium diffusion constant D-N .t, for N i; < C, are related to the fact that triply ionized VOu acceptor is involved
in both phenomena. Previously, this limitation of the free~
carrier concentration bas been interpreted as due to the formation of Se 3 complexes. ,5 However, since practically the
same dependence n-Nj/I has been recently found in heavily Te-doped GaAs l6 and also since the saturation level of
free-electron concentration of about 2 X 10 19 cm -3 is practically the same for Se, Te, Si!7 and Sn lX donors, it is very
unlikely that the chemical identity of the donor species could
be of any significance in limitation ofthe free-carrier concentration in GaAs. 19 In accordance with the above considerations, higher limits for electron (hole) concentration are
predicted in a semiconductor with Eps located closer to the
conduction (valence) band edge. Excellent support for this
argumentation is provided by two most extensively studied
group III-V semiconductors: GaAs and InP. The intrinsic
properties of those two semiconductors, such as cohesive
energy and thus also the structural part of the defect formation energy, as wen as the energy gap, are very similar. An
important characteristic which is much different is the position of E FS with respect to the band edges. At room temperature E FS is located at ~E" + 0.6 eV in GaAs and at
-Eu + 1.0 eV in Inp.3 In GaAs doped with Si at temperatures of about 900 K the limit of n max = 1.8 X lOt q cm - 3 for
the conduction~band electron concentration has been found.
This concentration corresponds to EF - E"s ',;;;fO.S eV. Applying this value of E[o' - E FS to lnP we obtain a free-electron concentration limit n;nax = 8 X 10 19 em " which is in
very good agreement with the highest electron concentration of9 X lOt'! cm- 3 reported for Sn-doped InP.20 Similarly
good agreement is obtained for p-type GaAs and InP. The
experimentally found, very different values for the maximum hole concentrations Pmax = 1.4 X 10 20 cm- :1 in GaAs 2 i
andpma, = 4X 101~ cm- 3 in InP211 correspond to almost the
same value of IEp - E FS I ~O.6 eV in both semiconductors.
W. Walukiewicz
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2095
This is a quite remarkable agreement if one bears in mind the
approximate nature of such estimates.
In summary, we have demonstrated that the Fermi level
stabilization energy plays the role of an intrinsic energy reference level for the evaluation of the formation energy of
amphoteric native defects. The strong dependence of the defect formation energy on the Fermi level position allows for
quantitative understanding of a multitude of phenomena in
semiconductors. Detailed accounts for doping-induced superlattice intermixing, and limits of free-carrier concentrations in semiconductors, are given. It shows that these phenomena, as well as the peviously considered formation of
Schottky barriers and irradiation-induced compensation,
are different manifestations of the same fundamental concept.
The author wishes to acknowledge stimulating discussions with E. E. HaUer. This work was supported by the
Director, Office of Energy Research, Office of Basic Energy
Sciences, Materials Sciences Division of the U. S. Department of Energy under contract No. DE-AC03-76SF00098.
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Appl. Phys. Lett., Vol. 54, No. 21, 22 May 1989
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