Simulation of the electronic states in the band gap for ZnS: Cu, Cl crystallophosphors
The results of calculations of the valence band top, conduction band bottom, optical band gap, gap states formed by the homopolar bonds and clusters in ZnS: Cu, Cl crystallophosphors have been presented. The calculation procedure has been based on the linear combination of atomic orbitals and pseudo...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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irk-123456789-1181572017-05-29T03:03:55Z Simulation of the electronic states in the band gap for ZnS: Cu, Cl crystallophosphors Savchenko, N.D. Shchurova, T.N. Popovych, K.O. Rubish, I.D. Leising, G. The results of calculations of the valence band top, conduction band bottom, optical band gap, gap states formed by the homopolar bonds and clusters in ZnS: Cu, Cl crystallophosphors have been presented. The calculation procedure has been based on the linear combination of atomic orbitals and pseudo-potential methods. The energy values have been determined in the centre of the Brillouin zone. The atomic terms determined within Herman-Skillman and Hartree-Fock approximations have been used in the calculations. The quantitative agreement between theoretical and experimental data on the band gap and photoemission threshold for this type of materials has been shown. The energy values for the optical transitions have been determined (1.77; 2.41; 2.65 and 2.95 eV) and correlated with the experimental emission spectra for the samples processed under different conditions. 2004 Article Simulation of the electronic states in the band gap for ZnS: Cu, Cl crystallophosphors / N.D. Savchenko, T.N. Shchurova, K.O. Popovych, I.D. Rubish, G. Leising // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 2. — С. 133-137. — Бібліогр.: 24 назв. — англ. 1560-8034 PACS: 78.60.Fi, 71.15.Fv, 71.55.Gs http://dspace.nbuv.gov.ua/handle/123456789/118157 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The results of calculations of the valence band top, conduction band bottom, optical band gap, gap states formed by the homopolar bonds and clusters in ZnS: Cu, Cl crystallophosphors have been presented. The calculation procedure has been based on the linear combination of atomic orbitals and pseudo-potential methods. The energy values have been determined in the centre of the Brillouin zone. The atomic terms determined within Herman-Skillman and Hartree-Fock approximations have been used in the calculations. The quantitative agreement between theoretical and experimental data on the band gap and photoemission threshold for this type of materials has been shown. The energy values for the optical transitions have been determined (1.77; 2.41; 2.65 and 2.95 eV) and correlated with the experimental emission spectra for the samples processed under different conditions. |
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Savchenko, N.D. Shchurova, T.N. Popovych, K.O. Rubish, I.D. Leising, G. |
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Savchenko, N.D. Shchurova, T.N. Popovych, K.O. Rubish, I.D. Leising, G. Simulation of the electronic states in the band gap for ZnS: Cu, Cl crystallophosphors Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Savchenko, N.D. Shchurova, T.N. Popovych, K.O. Rubish, I.D. Leising, G. |
| author_sort |
Savchenko, N.D. |
| title |
Simulation of the electronic states in the band gap for ZnS: Cu, Cl crystallophosphors |
| title_short |
Simulation of the electronic states in the band gap for ZnS: Cu, Cl crystallophosphors |
| title_full |
Simulation of the electronic states in the band gap for ZnS: Cu, Cl crystallophosphors |
| title_fullStr |
Simulation of the electronic states in the band gap for ZnS: Cu, Cl crystallophosphors |
| title_full_unstemmed |
Simulation of the electronic states in the band gap for ZnS: Cu, Cl crystallophosphors |
| title_sort |
simulation of the electronic states in the band gap for zns: cu, cl crystallophosphors |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2004 |
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http://dspace.nbuv.gov.ua/handle/123456789/118157 |
| citation_txt |
Simulation of the electronic states in the band gap for ZnS: Cu, Cl crystallophosphors / N.D. Savchenko, T.N. Shchurova, K.O. Popovych, I.D. Rubish, G. Leising // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 2. — С. 133-137. — Бібліогр.: 24 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-07-08T13:28:11Z |
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133© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 2. P. 133-137.
PACS: 78.60.Fi, 71.15.Fv, 71.55.Gs
Simulation of electronic states in the band gap
of ZnS: Cu, Cl crystallophosphors
N.D. Savchenko1, T.N. Shchurova1, K.O. Popovych2, I.D. Rubish2, G. Leising3
1Department of Electronic Systems, Faculty of Engineering, Uzhgorod National University
13, Kapitulna St., 88000 Uzhgorod, Ukraine, Phone (fax): +380 (3122) 30656, E-mail: root@tv.uzhgorod.ua
2Department of Solid State Electronics, Faculty of Physics, Uzhgorod National University,
54, Voloshyn St., 88000 Uzhgorod, Ukraine, Phone: +380 (312) 614312, E-mail: sva3@univ.uzhgorod.ua
3Institute for Solid State Physics, Technical University Graz
16, Petersgasse, 8010 Graz, Austria, Fax +43 316873-8478, E-mail: g.leising@tugraz.at
Abstract. The results of calculations of the valence band top, conduction band bottom, optical band
gap, gap states formed by the homopolar bonds and clusters in ZnS: Cu, Cl crystallophosphors have
been presented. The calculation procedure has been based on the linear combination of atomic orbitals
and pseudo-potential methods. The energy values have been determined in the centre of the Brillouin
zone. The atomic terms determined within Herman-Skillman and Hartree-Fock approximations have
been used in the calculations. The quantitative agreement between theoretical and experimental data on
the band gap and photoemission threshold for this type of materials has been shown. The energy
values for the optical transitions have been determined (1.77; 2.41; 2.65 and 2.95 eV) and correlated
with the experimental emission spectra for the samples processed under different conditions.
Keywords: photoemission threshold, LCAO, gap states, ZnS: Cu, Cl crystallophosphor,
electroluminescence
Paper received 04.02.04; accepted for publication 17.06.04.
1. Introduction
The use of reliable theories giving insight into the basic
fundamental physical properties of solids gives possibil-
ity to predict the band gap structure and properties for
the novel materials, and to make correct interpretation
of the effect of preparation techniques and external fac-
tors on these properties.
The methods of the linear combination of atomic or-
bitals and pseudo-potential are known to be used for the
calculation of physical parameters of solids [1]. This
method now is being used for the calculations of the band
gap structure and properties for a number of materials
[2�7]. The calculations have also been carried out for
ZnS crystals. Bearing in mind that this method being still
under development (see, [8�9]) enables the calculation of
the radiative transitions from the electronic structure of
the solid. It can be used for the simulation of electronic
states in the band gap and the fundamental properties of
ZnS: Cu, Cl phosphors within the same model. In this
method of calculations, the intratomic parameters
(terms), determined within the Hartree-Fock approxima-
tion are applicable. In this work, the calculations have
been performed for different approximations, since the
results of the calculations in different specified cases can
coincide or differ. The interatomic distance dependence
of the matrix element characterising the covalent bond-
ing energy requires the detailed analysis of the correla-
tion of solid body properties with this parameter. For the
analysis, the compounds of AIIBVI type (ZnS, ZnSe, and
ZnTe) have been chosen.
Zinc sulphide doped with Cu and/or Cl manifests the
electronic states inherent to Cu2S and CuCl compounds.
These electronic states are responsible for the changes in
the luminescence spectra and physical properties of the
doped ZnS. Thus, the calculations should be done for
these compounds as well.
This work is devoted to the simulation of the elec-
tronic structure for ZnS: Cu, Cl crystallophosphors and
its correlation with the known experimental results.
2. Simulation of optical properties for
chalcogenides of zinc and activator and
co-activator based compounds
To calculate the positions of the electronic states in the
band gap for semiconductors, it is necessary to know
134
SQO, 7(2), 2004
N.D. Savchenko et al.: Simulation of the electronic states in the band gap of�
the energy position of the upper part of the valence band
(Ev) and the bottom of the conduction band (Ec) with
respect to the vacuum level. These values can be calcu-
lated following the formulae given in the works by W.A.
Harrison [1, 10�13]:
relax
a
p
c
p
v EV.VVE +++−
+
= 1
2
3
2
2 111
2
εε
, (1)
2
2
UE
a
p
c
p
c +
+
=
εε
, (2)
where c
pε and a
pε are the atomic terms of the cation (Zn,
Cu) and anion (S, Cl) p-states. The metallic bond energy
(V1) and ionic bond energy (V3) have been found from the
equations:
82
11
1
c
s
c
p
a
s
a
p
ac VV
V
εεεε −+−
=+= , (3)
23
a
p
c
pV
εε −
= , (4)
where c
sε and a
sε are the atomic terms of the anion and
cation s-states. The values for the atomic terms have been
taken from Ref. [1].
The covalent bonding energy (V2) has been determined
from the equation:
22
md
ç
V
h= , (5)
where η = 2.16 is the dimensionless coefficient that derives
the approximate values of the interatomic interaction matrix
elements for the Γ-point, the centre of the Brillouin zone,
ðh 2=h is the Planck constant, m is the electronic mass.
The relaxation energy Erelax has been calculated from
Eq. (13):
ε
ε
2
)1( −= U
Erelax (6)
where ε is the dielectric constant. In the calculations, the
following values for this magnitude have been used [14]:
for ZnS � ε = 5.3, for ZnSe � ε = 6.3, for ZnTe � ε = 7.8,
and for CuCl � ε = 5.7. For Cu2S the calculated value of
ε = 3.7 has been used.
The intratomic Coulomb repulsion U has been calcu-
lated following Eq. (13):
2121
2
2
2
2
2
4
5
/a
p
c
p
/
h
m
eU
+
=
εεπ
(7)
where e is the electronic charge.
The photoemission threshold (Φ) corresponds to the
energy of Ev, that is Φ = Ev, and the band gap is Eg = |Ec � Ev|.
The procedure of going from the atomic p-orbitals to
the energy bands for ZnS crystals has been illustrated in
Fig. 1. The following designations have been made there:
V1* = 1.11V1; Epπ is the energy corresponding to the non-
bonding π-states S 3p of sulphur atoms in ZnS band gap.
The latter has been derived from the formula:
.SUE pp )(2+= επ (8)
When going from the atomic terms to the energy bands
in solids non-bonding states have been splitted into a nar-
row (near ±0.2 eV) band [15] the lower part of which is
occupied with electrons.
The energy parameters V1, V2, V3, U and Erelax, calcu-
lated within Herman-Skillman and Hartree-Fock approxima-
tions, and experimental d, Eg and Φ values for ZnS, ZnSe,
ZnTe, Cu2S and CuCl compounds are given in the Table.
Simulation of the internuclear distance d has been performed
using the data on the covalent atomic radii by Pauling and
Haggins [16]. From this Table, it is seen that the experimen-
tal and calculated d values are in agreement within the
accuracy of ±0.001 nm.
Theoretical and experimental dependences of the band
gap and photoemission threshold for AIIBVI compounds
on the internuclear distance d are presented in Fig. 2 and
Fig. 3. From Fig. 2 it is seen that for ZnS the experimental Eg
values closest to the calculated ones have been obtained
with the terms, calculated within the Herman-Skillman ap-
proximation. Thus, in simulation of the electronic states in
ZnS band gap, this approximation is applicable. The varia-
tion of the photoemission threshold with the internuclear
distance in the compounds of AIIBVI type (Fig. 3) is in quali-
tative agreement with theoretical data. As it has been shown
in examination, for the experimental Φ and d values the
magnitude of dlnΦ/dlnd equals to �2, while for those cal-
culated within Herman-Skillman and Hartree-Fock ap-
proximations, these magnitudes are �3.0 and �2.5, re-
spectively.
3. Simulation of the electronic states in zinc
sulphide band gap
The energy diagram illustrating the formation of the elec-
tronic states in the band gap for ZnS (a), ZnS: Cu (b), ZnS:
Cl (c) and ZnS: Cu, Cl (d) is given in Fig. 4. In this figure, the
(ep
Z n + ep
S )/2
pp
0
�5
�10
Z n 4p
S 3p
U /2 (S )
U /2 (Z nS )
E v
E c
E pp
3 .9 1 eV
(V 2
2 +V3
2 )1/2
V1
*
Erelax
Fig. 1. Illustration to the procedure of using LCAO method to
proceed from the atomic p-orbitals to the energy bands in zinc
sulphide.
N.D. Savchenko et al.: Simulation of the electronic states in the band gap of �
135SQO, 7(2), 2004
4
3
2
2.3 2.4 2.5 2.6 2.7
E
,
eV
Z n S1
2
Z n Se
Z n Te
d, Å
g
2.3
5
6
7
8
2.4 2.5 2.6 2.7
Ô
, e
V
Z n S
1
2
Z n Se
Z n Te
d, Å
Table. Parameters of the semiconductors along with the calculated and experimental values for the internuclear distances,
band gaps and photoemission thresholds. The values predicted within the Hartree-Fock approximation are given in parentheses
ZnS ZnSe ZnTe Cu2S CuCl Reference
d, nm (theory) 0.235 0.245 0.263 0.239 0.234
d, nm (exper.) 0.234�0.236* 0.245 0.264 � 0.234 [1], [18]
V1, eV 1.95 1.98 1.70 1.95 2.18
(2.06) (2.03) (1.70) (1.57) (2.33)
V2, eV 2.96 2.74 2.36 2.88 3.01
V3, eV 3.45 3.08 2.61 4.21 5.24
(3.81) (3.35) (2.78) (4.15) (5.24)
U/2, eV 3.46 3.42 3.31 2.70 3.37
(4.33) (4.23) (3.96) (3.93) (4.34)
Erelax, eV 2.80 2.87 2.88 1.97** 2.78
(3.51) (3.55) (3.45) (2.87**) (3.58)
Eg, eV 3.91 2.51 2.06 3.91 4.45
(theory) (3.36) (2.76) (2.26) (3.08) (4.47)
Eg, eV 3.80 2.82 2.39 � � [1]
(exper.) � 2.67 2.26 � � [18]
3.6 2.6 2.2 � � [17]
Φ, eV 6.41 5.55 4.74 7.26 7.13
(theory) (6.82) (5.86) (5.06) (7.84) (8.68)
Φ, eV 7.5 6.8 5.8 � � [1]
(exper.) � 6.76 5.76 � � [18]
Notes: *) The value of d = 0.236 nm corresponding to sphalerite structure has been used in the simulation of the parameters
**) The calculated value for the dielectric constant ε = 3.7 has been used in the simulation of Erelax
Fig. 2. Band gap (Eg) versus internuclear distance (d) for ZnS,
ZnSe and ZnTe semiconductors. Curves 1 and 2 correspond to
theoretical dependences constructed using the atomic terms
within Herman-Skillman (1) and Hartree-Fock (2) approxima-
tions. Symbols (�), (∆) and (×) show the experimental Eg values
taken from Refs [1], [18] and [17].
Fig. 3. Photoemission threshold (Φ) versus internuclear distance
(d) for ZnS, ZnSe and ZnTe semiconductors. Curves 1 and 2 corre-
spond to theoretical dependences constructed using the atomic terms
within Herman-Skillman and Hartree-Fock approximations, respec-
tively. Experimental values are designated similarly to those in
Fig. 2.
136
SQO, 7(2), 2004
N.D. Savchenko et al.: Simulation of the electronic states in the band gap of�
arrows show the possible optical radiative transitions and
corresponding energy values. Experimental energy val-
ues related to the peak in the emission spectrum are given
along with these values in parentheses [19, 20].
Electronic states with the energies of E1 and E2 corre-
spond to Zn 4p and Zn sp3 atomic terms. Electronic states
with the energy of E3 are formed by the bonding Zn 4p
states of Zn-Zn homopolar bonds. For these states, the
splitting value can be found from Eq. (5) and is V2 = 2.35 eV.
The internuclear distance d for Zn-Zn bond equals to
0.266 nm [21]. E4 electronic states correspond to the en-
ergy of the bottom of the non-bonding p-band.
In ZnS: Cu phosphors (Fig. 4,b) additional E5 elec-
tronic states corresponding to the hybridized states of
copper atoms (Cu sp3) can be formed in the band gap.
The electronic states forming the bottom of the conduc-
tion band in Cu2S fall into the band gap of these materi-
als too. They are denoted as Ev* in Fig. 4, b.
In ZnS: Cl phosphors (Fig. 4, c) no new electronic
states are formed in the band gap. One can suppose that
Cl atoms compensate Zn sp3 electronic states, and thus
the red emission band in these phosphors fades out.
Doping of ZnS with Cu and Cl atoms results in blue
(2.8 eV) and green (2.4 eV) emission of these phosphors
only (Fig. 4, d). The shift of the blue band towards lower
energies is liable to stem from the occupation of the lower
part of p-band by the electrons. The shift of the green band
�10
�10 �10
�10
�5
�5
�5
�5
0
0 0
0
E n erg y, eV
a
c d
b
Z n 4p
Ev
E c
1 .7 7 (1 .77 )
Z n 4s
Z n sp3
E 1
E 2
E 3
E 4
0 .6 2, 0 .8 8 (0 .6 9, 0 .8 4)
2 .6 5 (2 .66 )
Z n 4p
E v
E c
2 .4 1 (2 .4)
Z n 4s
Z n sp3
E 1 , E c
*
E 2
E 3
E 4 , E 6
C u sp3
C u 4p- S 3p
E 5
1 .7 7 (1 .77 )
2 .9 3, 2 .9 5 (2 .8 , 2 .9 )
E nergy, eV
Z n 4p
E v
E c
2.41 (2 .4)
Z n 4s
E1
E 3
E 4
2 .65 (2 .6-2.7)
Z n 4p
Ev
E
c
2 .4 1 (2 .4)
Z n 4s
E 1 , E c
*
E 3
E 4
C u sp3
E 5
2 .9 3 (2 .8)
Fig. 4. Tentative electronic states in the band gap for ZnS (a), ZnS: Cu (b), ZnS: Cl (c) and ZnS: Cu, Cl (d). Arrows show the optical radiative
transitions and corresponding energy values (in electron-volts). Experimental energy values related to the peak in emission spectrum are
given in parentheses.
N.D. Savchenko et al.: Simulation of the electronic states in the band gap of �
137SQO, 7(2), 2004
can originate from the reduction of the Cu-S bonds number
due to formation of more efficient Cu-Cl bonds.
Fig. 5 shows emission spectra of photoluminescence,
electroluminescence and cathodoluminescence for pure and
doped ZnS single crystals reported by different authors
[20�24] and powders doped with copper and chlorine (cur-
ve 7) obtained in these studies. The arrows in this figure
show the energy values corresponding to the optical tran-
sitions in visible spectral range given in Fig. 4. As seen,
these energy values (1.77; 2.41; 2.65 and 2.95 eV) are in
good agreement with positions of the peaks in emission
spectra observed experimentally.
4. Conclusions
The energy band diagram for ZnS: Cu, Cl phosphors has
been calculated. The applicability of the modified LCAO
method for the calculation of the electronic states in the
band gap has been demonstrated.
The quantitative agreement between theoretical and
experimental data on the band gap and photoemission
threshold has been shown. The possible optical transitions
responsible for the position of the peaks in experimental
emission spectra have been determined.
The method can be used as a new approach to the mod-
elling of the luminescence centres and thus understanding
of the nature of degradation processes.
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24. Yu.Yu. Bacherikov, M.S. Golovina, N.V. Kytsiuk, M.A. Mukhlyo
and V.E. Rodionov, Some peculiarities of ZnS: Cu, Cl crystal-
lophosphors annealing, in Int. Conf. Papers Structural Relaxa-
tion in Solids, pp.180-182, Vinnitsya (Ukraine) (2003).
1.5 2 2.5 3
E n erg y, eV
R
el
at
iv
e
in
te
ns
ity
, a
.u
.
0
0.2
0.4
0.6
0.8
1 7
15
2
3 '
6
3
4
E 5 → E4E 1 → E4E 1, Ec
∗ → E3E 2 → E v
Fig. 5. Emission spectra for 1 � pure ZnS treated in zinc during
30 hours [22]; 2 � hexagonal ZnS: Cl at 80 K [20]; 3, 3' � hexagonal
ZnS: 10�3 Cu at 80 K and 300 K [20]; 4 � hexagonal ZnS: 1.5×10�4
Cu: 10�4 Cl at 80 K (heating at 1473 K in H2S with subsequent
annealing during 74 hours at 448 K in air) [20]; 5 � cathodolumi-
nescence spectrum at 83 K (15 kWt, 10�8 A cm�2) for ZnS: 2×10�3
Cu annealed with MgCl2, NaCl at 1223 K [23]; 6 � electrolumi-
nescence spectrum for ZnS: Cu, Cl powder annealed during 6 hours
at 1073 K with CuCl (1.25 %) and CuCl2 (1.25 %) [24]; 7 � ZnS: Cu,
Cl powder phosphor (sample No. 1579a).
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