Systematic approach to distinguishing a perturbed host state from an impurity state in a
supercell calculation for a doped semiconductor: Using GaP:N as an example
Yong Zhang,
1,
* A. Mascarenhas,
1
and L.-W. Wang
2
1
National Renewable Energy Laboratory, 1617 Cole Blvd., Golden, Colorado 80401, USA
2
Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
Received 23 December 2005; revised manuscript received 10 March 2006; published 21 July 2006
We illustrate a systematic approach for distinguishing a perturbed host state from an impurity state in a
supercell calculation for a doped semiconductor, using GaP:N as an example and employing a charge-patching
technique based on a first-principles pseudopotential method. For GaP:N, we 1 identify an impuritylike state
that is resonant with the conduction band minimum in the dilute doping limit, which provides a qualitative
explanation for the peculiar behavior of the A
x
transition; 2 provide an alternative explanation of a recent
finding of the existence of multiple impurity states resonant within the conduction band up to the energy of the
point; and 3 show that there exists no impurity state caused by a valley-orbit interaction within a few
hundred meV proximity of the N bound state, in contrast to the decades long speculation of the existence of
such a state.
DOI: 10.1103/PhysRevB.74.041201 PACS numbers: 71.55.Eq
The impurity potential introduced by an isoelectronic im-
purity in a semiconductor is generally considered highly lo-
calized, and thus can only give rise to a very limited number
of impurity states.
1,2
In perhaps the best-studied isoelectronic
impurity system, GaP:N, an isolated N center was consis-
tently found to have only one impurity state IS, a bound
state with a
1
symmetry of T
d
, near the conduction band CB
minimum CBM in theoretical calculations using either the
empirical pseudopotential or Koster-Slater model, when a
highly localized impurity potential was assumed.
2–4
Only
when a “long-range” component was artificially introduced
into the impurity potential to simulate the effects of lattice
relaxation and electronic polarization, was it possible to gen-
erate an excited state with e symmetry lying close to the a
1
state, resembling the valley-orbit coupling for a Columbic
impurity, because the valley-orbit coupling is expected to be
very large for the short-range potential.
2
Experimentally, the
existence of such an e symmetry excited state for the bound
electron was speculated for the isolated N center to be
24 meV above a
1
i.e., above the CBM,
5
as well as for NN
1
the nitrogen pair center with the deepest bound state
80 meV below the CBM.
6
Although the early studies were
only concerned with the existence of one excited state caused
by the valley-orbit coupling effect,
2,5,6
a recent empirical
pseudopotential EP calculation using a supercell approach
has concluded that the isolated N, as well as N pairs, may
introduce multiple additional IS’s the so-called “N cluster
states” between the CBM and the CB point CB.
7
Such
a finding is rather surprising, because for an impurity with a
highly localized potential, if it has already produced a bound
IS, as in the case of GaP:N, usually there will not be another
resonance IS, according to a scattering theory for solids.
1
Besides its significance for the above mentioned issues, un-
derstanding the electronic structure of GaP:N in the dilute
limit should lay the groundwork for understanding the highly
interesting nonconventional GaPN alloys, which is currently
a field of major controversy.
7–9
A supercell approach is frequently adopted for investigat-
ing impurity or defect states in semiconductors. One typi-
cally needs to use a sufficiently large supercell to ensure the
convergence of the impurity level
10
and track the origin of
the state of interest to the dilute doping limit.
11
However, the
use of a supercell inevitably causes a folding effect in k
space, i.e., one typically gets a large number of states in each
k point of the supercell Brillouin zone. Such a folding effect
makes it nontrivial to identify an IS that happens to be reso-
nant with the host conduction or valence band and to differ-
entiate a genuine IS from a folded but perturbed host state
PHS. Thus, it is an issue of general interest how to distin-
guish an IS from a PHS in the supercell approach.
Because of the above-mentioned controversy and specu-
lations involving GaP:N, we will use this system to illustrate
a systematic approach for categorizing the electronic states
obtained in a large supercell calculation. For an isolated N in
GaP:N, we show that no excited state can be formed within
the energy window of CBM-CB. However, we identify one
additional a
1
impuritylike state that extrapolates to the CBM
in the dilute N limit. This state could be responsible for the
so-called A
x
transition induced by N doping, which has been
observed for decades
12
but not well understood.
9
The electronic band structure of GaP:N is calculated using
a charge-patching method i.e., reassembling of charge
motifs.
13
This method is based on a self-consistent first-
principles pseudopotential approach in the framework of
density functional theory within a local density approxima-
tion LDA. The band structure calculated with the reas-
sembled charge density is typically accurate to within a few
meV of the direct self-consistent calculation with or without
the impurity. This method has been shown to describe accu-
rately for GaAs:N the shift of the GaAs host bandgap in the
dilute N doping region that is typically not accessible to the
direct self-consistent calculation.
14
The Ga pseudopotential is
generated with a nonlocal core correction and the 3d states
are not included in the valence electrons. The energy cutoff
for the plane wave basis is 35 Ry. The valence force field
method is used to relax the atomic positions. Empirical cor-
rections to the nonlocal pseudopotentials of Ga, P, and N
atoms are introduced to fix the LDA errors in the band gap as
well as the intervalley separations e.g., -L and -X.
15
Other computational details can be found in previous
PHYSICAL REVIEW B 74, 041201R2006
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