Energy spectrum of transition metal impurity in a semiconductor with an ideal surface
Energy spectrum of the transition metal impurity which substitutes a cation in a zink-blende structure semiconductor with an ideal surface is investigated theoretically. Model Hamiltonian of the semiconductor is treated by the semi-empirical tight-binding method, and energy of deep 3d-levels is d...
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Інститут фізики конденсованих систем НАН України
1999
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| Цитувати: | Energy spectrum of transition metal impurity in a semiconductor with an ideal surface / S.V. Melnychuk, I.M. Yurijchuk // Condensed Matter Physics. — 1999. — Т. 2, № 1(17). — С. 133-142. — Бібліогр.: 15 назв. — англ. |
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irk-123456789-1199182017-06-11T03:03:10Z Energy spectrum of transition metal impurity in a semiconductor with an ideal surface Melnychuk, S.V. Yurijchuk, I.M. Energy spectrum of the transition metal impurity which substitutes a cation in a zink-blende structure semiconductor with an ideal surface is investigated theoretically. Model Hamiltonian of the semiconductor is treated by the semi-empirical tight-binding method, and energy of deep 3d-levels is determined by the Green function method within the framework of the Kikoin-Flerov model. Numerical calculations are performed for Cr impurity atoms in a CdTe semiconductor with an [100] ideal surface. It is shown that in the case when the impurity substitutes an atom near the surface, essential reconstruction of its energy spectrum takes place. One-electron t₂ - and e -levels occurring from 3d -volume states for the crystal with an ideal surface due to the lowering of the system symmetry split up. The magnitude of the splitting is rather small, when impurity is situated near but at some distance from the surface, and strongly increases when impurity substitutes an atom directly on an ideal surface. Main mechanisms of one-electron deep level formation in the forbidden gap of a semiconductor with ideal anion and cation surfaces are determined. Теоретично досліджується енергетичний спектр домішки з незаповненою 3d -оболонкою, що заміщує катіон в напівпровіднику з структурою цинкової обманки у випадку наявності в кристалі ідеальної поверхні. Модельний гамільтоніан напівпровідника будувався в моделі напівемпіричного сильного зв’язку, а енергії глибоких 3d -рівнів визначалися методом функцій Гріна в рамках моделі Кікоєна-Флерова. Числові розрахунки виконані для домішки Cr в напівпровіднику CdTe з ідеальною поверхнею [100]. Показано, що у випадку розташування домішки поблизу поверхні відбувається суттєва перебудова її енергетичного спектру. Одноелектронні t₂- i e -рiвнi, що обумовленi 3d - центрами в об’ємному напiвпровiднику для системи, обмеженої iдеальною поверхнею, внаслiдок пониження симетрiї розщеплюються. Величина розщеплення різко зростає для домішки, розташованої безпосередньо на атомнiй площинi, що утворює ідеальну поверхню. Внаслідок полярності поверхні [100] напівпровідника CdTe можливе iснування двох типiв поверхнi, якi по рiзному впливають на енергетичний спектр 3d -домiшок. Встановлено основні механiзми формування одноелектронних глибоких рiвнiв в забороненiй зонi напiвпровiдника для двох типів поверхнi. 1999 Article Energy spectrum of transition metal impurity in a semiconductor with an ideal surface / S.V. Melnychuk, I.M. Yurijchuk // Condensed Matter Physics. — 1999. — Т. 2, № 1(17). — С. 133-142. — Бібліогр.: 15 назв. — англ. 1607-324X DOI:10.5488/CMP.2.1.133 PACS: 73.20 http://dspace.nbuv.gov.ua/handle/123456789/119918 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Energy spectrum of the transition metal impurity which substitutes a cation
in a zink-blende structure semiconductor with an ideal surface is investigated theoretically. Model Hamiltonian of the semiconductor is treated
by the semi-empirical tight-binding method, and energy of deep 3d-levels
is determined by the Green function method within the framework of the
Kikoin-Flerov model. Numerical calculations are performed for Cr impurity
atoms in a CdTe semiconductor with an [100] ideal surface. It is shown
that in the case when the impurity substitutes an atom near the surface,
essential reconstruction of its energy spectrum takes place. One-electron
t₂ - and e -levels occurring from 3d -volume states for the crystal with an
ideal surface due to the lowering of the system symmetry split up. The
magnitude of the splitting is rather small, when impurity is situated near but
at some distance from the surface, and strongly increases when impurity
substitutes an atom directly on an ideal surface. Main mechanisms of one-electron deep level formation in the forbidden gap of a semiconductor with
ideal anion and cation surfaces are determined. |
| format |
Article |
| author |
Melnychuk, S.V. Yurijchuk, I.M. |
| spellingShingle |
Melnychuk, S.V. Yurijchuk, I.M. Energy spectrum of transition metal impurity in a semiconductor with an ideal surface Condensed Matter Physics |
| author_facet |
Melnychuk, S.V. Yurijchuk, I.M. |
| author_sort |
Melnychuk, S.V. |
| title |
Energy spectrum of transition metal impurity in a semiconductor with an ideal surface |
| title_short |
Energy spectrum of transition metal impurity in a semiconductor with an ideal surface |
| title_full |
Energy spectrum of transition metal impurity in a semiconductor with an ideal surface |
| title_fullStr |
Energy spectrum of transition metal impurity in a semiconductor with an ideal surface |
| title_full_unstemmed |
Energy spectrum of transition metal impurity in a semiconductor with an ideal surface |
| title_sort |
energy spectrum of transition metal impurity in a semiconductor with an ideal surface |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
1999 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119918 |
| citation_txt |
Energy spectrum of transition metal impurity in a semiconductor with an ideal surface / S.V. Melnychuk, I.M. Yurijchuk // Condensed Matter Physics. — 1999. — Т. 2, № 1(17). — С. 133-142. — Бібліогр.: 15 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT melnychuksv energyspectrumoftransitionmetalimpurityinasemiconductorwithanidealsurface AT yurijchukim energyspectrumoftransitionmetalimpurityinasemiconductorwithanidealsurface |
| first_indexed |
2025-07-08T16:54:31Z |
| last_indexed |
2025-07-08T16:54:31Z |
| _version_ |
1837098520698421248 |
| fulltext |
Condensed Matter Physics, 1999, Vol. 2, No. 1(17), p. 133–142
Energy spectrum of transition metal
impurity in a semiconductor with an
ideal surface
S.V.Melnychuk, I.M.Yurijchuk
Chernivtsi State University,
2 Kotsiubynsky Str., 274012 Chernivtsi, Ukraine
Received February 19, 1999
Energy spectrum of the transition metal impurity which substitutes a cation
in a zink-blende structure semiconductor with an ideal surface is inves-
tigated theoretically. Model Hamiltonian of the semiconductor is treated
by the semi-empirical tight-binding method, and energy of deep 3d -levels
is determined by the Green function method within the framework of the
Kikoin-Flerov model. Numerical calculations are performed for Cr impurity
atoms in a CdTe semiconductor with an [100] ideal surface. It is shown
that in the case when the impurity substitutes an atom near the surface,
essential reconstruction of its energy spectrum takes place. One-electron
t2 - and e -levels occurring from 3d -volume states for the crystal with an
ideal surface due to the lowering of the system symmetry split up. The
magnitude of the splitting is rather small, when impurity is situated near but
at some distance from the surface, and strongly increases when impurity
substitutes an atom directly on an ideal surface. Main mechanisms of one-
electron deep level formation in the forbidden gap of a semiconductor with
ideal anion and cation surfaces are determined.
Key words: semiconductor, 3d-impurity, surface, energy spectrum
PACS: 73.20
Semiconductor heterostructures, due to their wide use in modern electronics,
have recently aroused much scientific interest [1]. The properties of defects in such
systems have not been investigated enough as compared with the case of defects in
bulk materials. The main interest was focused on the studies of charged impurities
which give shallow levels in the forbidden gap. As to the defects which create deep
levels there are to our knowledge only investigations of vacancies and impurities of
6 groups in GaAs/GaAlAs superlattices [2]. The purpose of this paper is to study
transition metal impurities in a semiconductor with an ideal surface. Transition
elements give deep levels practically in all bulk A2V6 semiconductors. Substitution
impurities in A2V6 semiconductors are neutral, therefore, perturbation induced
c© S.V.Melnychuk, I.M.Yurijchuk 133
S.V.Melnychuk, I.M.Yurijchuk
by an impurity is short-range and almost completely defined by the difference
of core potentials of the impurity and the matrix. Nowadays the theory of deep
levels created by 3d-elements in bulk semiconductors has achieved a high level of
development [3–5]. It is proved that one-particle states, which form deep levels in
the forbidden gap of these semiconductors, emerge due to the resonance scattering
of band electrons on unfilled 3d-states [6,7] and not to the potential scattering on
the impurity potential as in the case of a usual isoelectron impurity. As a result,
deep levels have d- and not s- or p-symmetry, while eigen-d-levels are repulsed
into the forbidden gap and influence the matrix results in a covalent mixing that
distorts the atomic function but does not change its point symmetry. The fact that
the position of 3d-levels in the forbidden gap is defined mainly by the nature of
the impurity and not by the semiconductor matrix sets forth an idea to consider
impurities as universal levels which are reference points when an interface between
two semiconductors is created and give the possibility to define a valence band
offset in heterostructure [8]. In paper [9] the opposite approach is proposed: namely,
to investigate energy position of 3d-levels in a heterostructure in comparison with
their position in initial bulk semiconductors. In [9,10] the theory of deep levels
created by transition metal impurities in semiconductor superlattices is developed.
This approach is based on a theoretical model which was successfully used for the
investigation of chemical trends in A2V6 semiconductors and appears to be very
clear for understanding the 3d-levels nature [3]. As it was mentioned above, the
main features of the impurity behaviour are determined by 3d-orbitals and not by
the matrix. But there are specific situations when the matrix essentially influences
the energy spectrum of the impurity. As it will be shown further, this is when the
impurity changes its position in the crystal towards the interface. In this paper we
consider the case of a sharp interface of a semiconductor with vacuum, i.e. an ideal
surface. Fundamental peculiarities of the behaviour of 3d-levels on an ideal surface
should also be present in the case of other hererostructures. A crystal with an ideal
surface can be treated as a semi-infinite set of crystallographic planes parallel to
the plane which forms an interface of the crystal with vacuum. For a zink-blende
semiconductor with an ideal surface perpendicular to the [100] direction, each
atomic plane comprises only identical atoms (cations or anions) and is sandwiched
between unlike atomic planes. We chose a coordinate system such that the OZ
axis is parallel to the [100] direction and axes OX, OY are directed along the basis
vectors a1, a2 of a two-dimensional lattice. The equilibrium position of the atom
in the superlattice is defined by the vector
R(nNplk) = l1a1 + l2a2 + τ
pk
⊥ + τ
pk
‖ .
Here Np is the number of the atomic plane 1 6 Np 6 ∞; l1, l2 are integers; vector
τ
pk
⊥ specifies the position of the atomic plane Np and the position of k-th atom
in the atomic plane Np inside an elementary two-dimensional cell is given by τ
pk
‖
(k = 1, 2).
The characteristic feature of impurities with a semi-filled 3d-shell consist in
the fact that the impurity potential leads to the appearance of 3d-levels in the
134
Transition metal impurity in a semiconductor
forbidden gap or in its vicinity. Therefore, as the basis for the system we choose
[6]:
Φi = {Ψka,Ψdµ}, (1)
where Ψka is a wave function of band electrons and Ψdµ –one of d-electrons; k is a
vector in the Brillouin zone.
We suggest that the impurity substitute an atom in a cation atomic plane of the
crystal with an ideal surface. The impurity has four nearest neighbour anion atoms
from the adjacent planes. One-electron Schrodinger equation for a semiconductor
with an impurity is given by [6]
[
−
~
2∇2
2m
+
∑
j 6=0
Uh(r −Rj) + Us(r −R0)− E
]
Ψi(r) = 0, (2)
where
∑
j 6=0 Uh(r−Rj) is a ligand crystal field, Us(r−R0) is a substitution impurity
potential
Us(r −R0) = Ud(r −R0)− Uh(r −R0) + U1{∆̺(r)}.
Here Ud, Uh are core potentials of the impurity and the ion, U1{∆̺(r)} is a change
of the valency electron potential induced by a redistribution of the electron den-
sity; the self-consistent potential Ud(r−R0) for d-electrons enters the Schrodinger
equation for eigen-d-functions ψdm
[
−
~
2∇2
2m
+ Ud(r −R0)− εd
]
ψdm(r −R0) = 0,
where m is a projection of the orbital moment l = 2. The solution of equation (2)
can be presented as an expansion on the basis (1)
Ψiγµ(r) = A−1/2
γ [Ψdγµ(r) + Ψbγµ(r)] . (3)
In (3), µ numbers the rows of irreducible representation γ, Aµ is a scale factor;
Ψdγµ(r) are functions localized near the impurity centre and are a linear combina-
tion of the atomic orbitals φm(r)
Ψdγµ(r) = F
γµ
d
∑
m
uγµm φm(r) = F
γµ
d ϕγµ(r); (4)
and
Ψdγµ(r) =
∑
ka
F
γµ
ka ϕ̃ka(r,R0) (5)
is a linear superposition of Bloch states of a pure crystal.
Inserting (3) in (2), taking into account (4) and (5) and considering the ap-
proximation when the contribution from the potential scattering can be omitted as
compared with the contribution from resonance scattering we obtain an equation
for deep energy levels:
Eiγ − εγ =Mγ(E), (6)
135
S.V.Melnychuk, I.M.Yurijchuk
where
εγ = εd +∆εd + 〈γµ|W |γµ〉, (7)
Mγ(E) =
∑
ka
〈γµ|W |ka〉〈ka|W |γµ〉
E − εka
= 〈γµ|WG0(E)|γµ〉. (8)
Here W is a crystal field, e.g., the total potential of matrix ions and valency
electrons, which splits d-states into t2- and e-levels; G0(E) is a Green function
of a pure crystal with an ideal surface; εka is a band spectrum of the crystal.
For the numerical analysis we use a semi-empirical tight-binding model [12,13]
which is comparatively simple in practical implementation but gives a clear and
comprehensive picture of chemical tendencies in the system. In the tight-binding
method a wave function of the crystal is presented as a linear combination of
atomic orbitals centred in different atoms. For A2V6 semiconductors it is sufficient
to include in the basis s- and p-orbitals and to take into account an interaction
with the nearest neighbours only. Thus, a one-electron wave function of the crystal
is given as a linear combination of s- and p- tight-binding orbitals centred on sites
R(nNplk)
φnka(r) =
∑
iNp
CiNp
(nka)ϕiNp
(r). (9)
In the basis (9), we obtain a secular matrix for the energy band spectrum of the
crystal with the surface
∣
∣
∣
H
(0)
iNp,jNp
(n,k‖ + k⊥, a)−Eδij
∣
∣
∣
= 0. (10)
The Hamiltonian matrix H
(0)
iNp,jNp
(n,k‖+k⊥, a) is constructed with the use of a
set of parameters deduced from the available experimental data of bulk materials
[13].
Projection of the Green functions G0(E) on the tight-binding orbitals has the
form:
G
(0)
iNp,jNp
(E) =
1
N
∑
ka
CjN ′
p
(nka)C∗
iNp
(nka)
ε− εnka
. (11)
For the calculation of matrix elements 〈ka|W |γµ〉 in (8), the following relation
was used [14]:
〈ka|W |γµ〉 = 〈ka|Vd − Vh|γµ〉+ (εka − εd)〈ka|γµ〉. (12)
Here Us = (Vd − Vh) is an impurity potential which we treat in the Hartree-Fock-
Slater approximation:
Us(r) = V 2+
d (r −R0)− V 2+
h (r −R0);
V (r) =
2Z0
r
−
2
r
∫ r
0
σ(t)dt− 6
(
3
8
̺(r)
)1/3
,
where Z0 is an atomic number, ̺(r) = (4πr2)−1σ(r) is the averaged electron density.
With the obtained potential two-centre integrals entering (12) were defined. We
136
Transition metal impurity in a semiconductor
choose atomic functions [15] as eigen-functions of 3d-electrons. Equation (6) for
the evaluation of deep level energies was solved numerically. Energy dependencies
Mγ(E) were defined from relation (8) where eigenvalues εka and the eigenfunctions
of a pure crystal entering G(0)(E) were obtained by diagonalizing the Hamiltonian
matrix (10). Intersections of E − εγ with Mγ(E) give one-electron energy of 3d-
levels of transition metal impurities in the forbidden gap of semiconductors.
Figure 1. Band structure of semiconduc-
tor CdTe [100] ideal surface. Bound sur-
face states are denoted by Ci (for cation
surface) and Ai (for anion surface). A
set of tight-binding parameters used for
the band structure calculations is given
in [13].
Relations (6)–(8) are similar to
those of bulk materials [6,7]. But there
are essential differences. An expression
for Mγ(E) contains a Green function
whose projection on the local basis de-
pends on index Np. Thus, the energy of
deep levels Eiγ also depends on this in-
dex, e.g., on whose atomic plane Np an
impurity substitutes a host atom. Fur-
thermore, the presence of an ideal sur-
face lowers the system symmetry. In the
case of an [100] ideal surface, the point
symmetry of a zink-blende crystal low-
ers from Td to C2v. Degenerated t2- and
e-levels split up in the C2v crystal field
to t2 = a1 + b1 + b2, e = a1 + a2. There-
fore, index γ in (6)–(8) enumerates irre-
ducible representation of the C2v group:
a1, a2, b1, b2.
Generally speaking, the Hamilto-
nian matrix of a crystal with an ideal
surface is of an infinite dimension.
Therefore, in numerical calculations for
surface modelling a slab method is used
[10,11], in which a semi-infinite crystal
is confined by the second surface identical to the first. The system is modelled
by a slab with a finite width but infinite in the direction parallel to the surface.
For the surface band structure calculation typically 12–15 layers are enough to be
taken into consideration. The slab of this width simulates the bulk, as well as the
surface band structure. Wave functions on the opposite surfaces do not intersect
with each other and the energy spectrum practically does not change when more
layers are added to the slab.
Let us consider in more detail the peculiarities of the formation of an [100]
ideal surface in a zink-blende crystal. When a surface is formed, the surface crystal
bonds are broken and an atom on the surface lacks one or more neighbours. Each
atom in an [100] ideal surface has two bulk and two broken bonds. Interaction
between neighbour atoms and the existence of a translation symmetry parallel to
the surface result in the splitting of dehybridized states into the bands of surface
137
S.V.Melnychuk, I.M.Yurijchuk
states. These states are localized near the surface when their energies lie in the
gaps of the energy spectrum of the crystal (bound surface states).
Figure 2. Densities of electron states of
semiconductor CdTe projected on ideal
anion and cation surfaces.
The calculated band structure of a
[100] surface along some high symme-
try directions of the Brillouin zone for
the semiconductor crystal CdTe is pre-
sented in figure 1. The [100] surface is
polar, therefore it is necessary to distin-
guish two cases depending on whether
the surface consists of cations (Cd[100])
or anions (Te[100]), respectively. Bound
surface states for the both ideal sur-
faces are presented in the same figure
and denoted as Si and Ai, respectively.
As it follows from figure 1, as the re-
sult of surface creation, groups of sur-
face states emerge on the background of
the bulk energy spectrum. In the case
of an anion surface there are five sur-
face bands. A1-states split up from s-
orbitals, and A2, A3 – from p-orbitals
of the valency band. In the case of a
cation surface there are also five sur-
face bands. C1-, C2- states split up from
cation s-orbitals.
Analyzing partial densities of elec-
tron states projected on each atomic
plane (figure 2), the origin of surface
states and their localization have been found out. Projected densities were ob-
tained as an imaginary part of Green functions (11) at Np = N ′
p. As follows from
figure 2, peaks responsible for surface bands are absent in the bulk density, hence
these states are almost completely localized on the surfaces which form an ideal
surface. Here it is important to note the presence of three bands situated in the
forbidden gap: C2 are states which lie slightly below the conduction band, and A2
and A3 are states which lie near the valency band edge.
The energy of deep levels caused by Cr impurity in CdTe is found as the solution
of equation (6). Calculating matrix elements (8), we assume that the impurity
potential does not change essentially compared with that of the bulk material. In
figures 3,4 we present the results of the solution of equation (6) in the case when
the impurity is situated near the cation (figure 3) or the anion (figure 4) ideal
surface. Index Np numbers atomic planes in an ascending order of the distance
from the surface. Np = 1 denotes an atomic plane which forms an ideal surface:
for an anion surface 3d-impurity substitutes an atom in atomic planes with odd
Np, and for a cation one – with even Np. Values Mγ(E) calculated for an impurity
138
Transition metal impurity in a semiconductor
substituting an atom far enough from the surface are represented in figures 3,4 by
bold curves. It should be noted that the results for the impurity located in the
volume of the crystal (Np > 12) coincide with the calculations for bulk CdTe [7].
The values Mγ(E) for different irreducible representations γ, when approaching
the surface (from Np = 7, 8), differ among themselves. It means that accidentally
degenerate, (t2-threefold, e-twofold) deep levels split up and their energy positions
move. In figure 5 we present the energies of deep levels for impurity Cr in CdTe
depending on the number of atomic plane Np.
Figure 3. Graphic solution of equa-
tion (9) for the system CdTe:Cr in the
case of a cation ideal surface: a – t2-
level, b – e-level. Bold curves denoted
by M(E) are calculated for an impu-
rity substituting an atom in the vol-
ume of the crystal.
Figure 4. Graphic solution of equa-
tion (9) for the system CdTe:Cr in the
case of an anion ideal surface: a – t2-
level, b – e-level. Bold curves denoted
by M(E) are calculated for an impu-
rity substituting an atom in the vol-
ume of the crystal.
Analyzing figures 3,4 several features common for two different surfaces should
be noted. A cation surface, as well as an anion surface influence t2-states stronger
than e-states. For the both surfaces a2-states, which split up from volume e-states
139
S.V.Melnychuk, I.M.Yurijchuk
Figure 5. Deep level energies of the sys-
tem CdTe:Cr depending on the distance
from a-cation and b-anion ideal surfaces.
when approaching the surface, practi-
cally do not change their energy po-
sition, and a1-states give two addi-
tional levels situated at almost equal
distances from the original state. The
influence of the surface on renormaliza-
tion of Mt2(E) is much stronger and is
especially significant for a cation sur-
face (figure 5a). It is evident, since in
this case the impurity is situated di-
rectly on an ideal surface. Energy de-
pendencies Mγ(E) for γ = b1 splitting
up from volume t2-states are practi-
cally the same (they change the sign in
the forbidden gap), whereas Mγ(E) for
γ = a1, b2 differ for two different sur-
faces: they move to lower energies for a
cation surface and vice versa for an an-
ion surface. A1-, b2-levels move in dif-
ferent directions from the volume level
depending on the type of the surface.
Such behaviour is caused by two sur-
face bands which are situated near the
valency band edge (A2, A3 in figure 1).
These bands occur as the result of de-
hybridization of anion bonds and are
located slightly above the hybridized
p-states responsible for valency band
mixing. Besides, as can be shown from
figure 2, these bands give the greatest
contribution to the projected densities of states. It results in a shift of deep t2-levels
to high energies: the mixing of t2-levels with surface bands adds to the mechanism
of the covalent mixing of t2-levels with valency electrons, the latter is responsible
for the formation of 3d-deep levels in the volume of the crystal. The density of an-
ion surface states for a cation surface is rather small and, therefore, the respective
hybridization is negligible.
Numerical calculations of deep level energies of Cr impurity in CdTe, when
the impurity substitutes an atom near an [100] ideal surface and in the volume
of the crystal allow us to draw such conclusions. Deep t2- and e-levels occurring
from 3d-volume states for a crystal with an ideal surface due to the lowering of the
system symmetry split up. The magnitude of splitting is rather small, when the
impurity is situated near but at some distance (about 3–5 atomic planes) from the
surface, and strongly increases when the impurity substitutes an atom directly on
an ideal surface (up to 1 eV). The second important conclusion is the possibility
140
Transition metal impurity in a semiconductor
of the situation when the levels occurring from t2-states as the result of splitting
and the energy shift appear to be situated below the levels occurring from e-states.
Thus, an inversion of deep levels as compared with the volume crystal is possible.
An ideal surface [100] of zink-blende semiconductors is polar. Therefore, there
are two types of surfaces which influence the energy spectrum of 3d-impurity in
different ways. Reconstruction of the impurity energy spectrum is much stronger
for states occurring from t2-levels and also when the impurity is situated directly
on an ideal surface (the case of a cation surface). Function Mγ(E) reveals in these
cases a sharper behaviour and, accordingly, the amount of splitting increases. The
main feature of t2-level behaviour near an anion ideal surface is its splitting and the
energy shift to high energies in the forbidden gap (even the repulsion of levels to
the conduction band). For a cation surface the inverse situation takes place. These
differences are due to the existence on an anion ideal surface of the bands emerging
as the result of dehybridization of valency band p-states. The covalent mixing of 3d-
states with anion surface bands is the main mechanism of the creation of deep levels
in the forbidden gap in a semiconductor with an ideal anion surface. One-electron
deep-levels calculated in the present paper are the basis for the construction of
multiplet terms of transition metal impurities in the forbidden gap of a crystal
with an ideal surface and the determination of their ionization energies.
References
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Спектр домішки перехідного металу в
нaпівпровіднику з ідеальною поверхнею
С.В.Мельничук, І.М.Юрійчук
Чернівецький державний університет,
274012 Чернівці, вул. Коцюбинського, 6
Отримано 19 лютого 1999 р.
Теоретично досліджується енергетичний спектр домішки з незапов-
неною 3d -оболонкою, що заміщує катіон в напівпровіднику з струк-
турою цинкової обманки у випадку наявності в кристалі ідеальної по-
верхні. Модельний гамільтоніан напівпровідника будувався в моделі
напівемпіричного сильного зв’язку, а енергії глибоких 3d -рівнів ви-
значалися методом функцій Гріна в рамках моделі Кікоєна-Флерова.
Числові розрахунки виконані для домішки Cr в напівпровіднику CdTe
з ідеальною поверхнею [100]. Показано, що у випадку розташування
домішки поблизу поверхні відбувається суттєва перебудова її енер-
гетичного спектру. Одноелектронні t2 - i e -рiвнi, що обумовленi 3d -
центрами в об’ємному напiвпровiднику для системи, обмеженої iде-
альною поверхнею, внаслiдок пониження симетрiї розщеплюються.
Величина розщеплення різко зростає для домішки, розташованої
безпосередньо на атомнiй площинi, що утворює ідеальну поверхню.
Внаслідок полярності поверхні [100] напівпровідника CdTe можли-
ве iснування двох типiв поверхнi, якi по рiзному впливають на енер-
гетичний спектр 3d -домiшок. Встановлено основні механiзми фор-
мування одноелектронних глибоких рiвнiв в забороненiй зонi напiв-
провiдника для двох типів поверхнi.
Ключові слова: нaпівпровідник, 3d-домішкa, поверхня,
енергетичний спектр
PACS: 73.20
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