Electronic structure of HgTe nanocrystals: An observation of p-d weakening

Article abstract of DOI:10.1016/j.susc.2006.02.037

Photoemission studies to identify the electronic structure of the HgTe nanocrystals revealed a new phenomenon of p-d weakening, as a consequence of size quantization effect associated with the mean crystalline size, 5.35 ± 0.83 nm. The weakening of the p-d hybridization by a factor of 0.33, to that of the bulk HgTe suggests the valence band maxima and core level shifts toward higher binding energy. The widening of the band gap due to size quantization is confirmed from optical absorption and photoluminescence measurements. The upward and downward shift of the conduction band minima and the valence band maxima with respect to the bulk value of HgTe are found to be 1.6 eV and 0.54 eV respectively.

Full text of DOI:10.1016/j.susc.2006.02.037

Surface Science 600 (2006) L110–L115
www.elsevier.com/locate/susc
Surface Science Letters
Electronic structure of HgTe nanocrystals:
An observation of p–d weakening
S. Rath, S.N. Sahu *
Institute of Physics, Cluster and Nanostructure Laboratory, Sachivalaya Marg, Bhubaneswar 751 005, India
Received 17 August 2005; accepted for publication 23 February 2006
Available online 20 March 2006
Abstract
Photoemission studies to identify the electronic structure of the HgTe nanocrystals revealed a new phenomenon of p–d weakening, as
a consequence of size quantization effect associated with the mean crystalline size, 5.35 ± 0.83 nm. The weakening of the p–d hybridiza-
tion by a factor of 0.33, to that of the bulk HgTe suggests the valence band maxima and core level shifts toward higher binding energy.
The widening of the band gap due to size quantization is confirmed from optical absorption and photoluminescence measurements. The
upward and downward shift of the conduction band minima and the valence band maxima with respect to the bulk value of HgTe are
found to be 1.6 eV and 0.54 eV respectively.
ꢀ
2006 Elsevier B.V. All rights reserved.
Keywords: Electronic structure; Nanocrystals; Semiconductor; Quantum confinement effect
1
. Introduction
the valence p–d orbital interactions between the central
atom, mercury, d states and the ligand, tellurium, p states
are permitted [6]. For conventional symmetry representa-
Mercury–telluride (HgTe) belongings to the II–VI group
have been studied considerably over the past decade [1,2].
However, the electronic structural study of the nanocrys-
talline Hg-VI semiconductor which is distinguished by a
cation d-band inside the main valence band is important
for its wide applications in optoelectronic [3], spintronic
tion, the anion p state has t symmetry and the cation d
2
state has t and e symmetry. The above is shown schemat-
2
ically in Fig. 1(a). The details of Fig. 1(b–f) is to be dis-
cussed in a later section. From the symmetry point of
view, the hybridization between t symmetry of the p state
2
[
4] and quantum devices [5]. Bulk HgTe is an inverted nar-
and t symmetry of the d state is allowed which results in
2
ꢀ
row band gap semiconductor. At the gap, the fully occu-
pied valence band maximum (VBM) has C15 symmetry
and the empty conduction band minimum (CBM) has C1
symmetry. Taking spin degree of freedom into account,
the symmetry of the band can be described within the dou-
ble-group representation such as the C15 level splitting into
a fourfold degenerate, C level and a twofold C , with the
the shift of C level. However, the C
6
level remains un-
8
changed due to the symmetry forbidden nature of hybrid-
ization between t symmetry state of the p orbital and e
2
symmetry state of the d orbital [6]. This results in an in-
ꢀ
verted narrow band gap feature of HgTe with E
g
¼ C
6
ꢀ
C ¼ ꢀ0:15 eV at room temperature [7–9] (300 K). The
8
negative band gap is due to the large partial delocalization
8
7
C level above the C of the p states. Similarly, the C level
of the Hg d state which is attributed to the attractive poten-
8
7
1
ꢀ
splits into a twofold degenerate C level of the s state.
tial of Hg ion and pertains to the C
6
level below C [10,11].
6
8
Since, bulk HgTe has tetrahedral symmetry, T , hence,
Notably, the band gap of Hg-VI compound is based on
three factors: (1) the chalcogen (Te) p spin–orbit (SO) split-
ting, (2) the Hg d SO splitting and (3) the strength of the p–
d hybridization [4]. Since p-SO and d-SO splittings are an
atomic properties, hence, the nature of band gap is solely
d
*
Corresponding author. Tel.: +91 674 2301058; fax: +91 674 2300142.
E-mail address: sahu@iopb.res.in (S.N. Sahu).
0
039-6028/$ - see front matter ꢀ 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2006.02.037

S. Rath, S.N. Sahu / Surface Science 600 (2006) L110–L115
L111
Γ
Γ8 ,
c
6
(
t )
d
2
Cation, d
Cation, s
Γ
εc
6
c
εc
Γ
a
ε
Γ
6
f
d (e)
p
6
(
t )
2
ε
ε
Γ8
HHV
f
ε
Γ8
HHV
Anion, p
εLHV
εLHV
Γ
6
Γ7
a
κ
Γ
κ
6
b
c
Γ
6
c
(
t )
d
Γ8
2
Cation, d
Cation, s
c
a
Γ
6
d (e)
εC
p
(
t )
2
1
.6 eV
Hg
Te
εf
Anion, p
0
.54 eV
Γ7
εHHV
d
e
f
Fig. 1. Schematic representation of the p–d hybridization occurring during HgTe crystal formation and resulted the band gap as E
temperature is shown in (a) and (b) respectively. The quantum size effect attributing the band gap opening and observation of the p–d weakening are
shown in (c) and (d) respectively. The downward and upward arrow indicated in (e) represents the shifting of the levels towards higher binding energy side.
g
= ꢀ0.15 eV, at room
c
The shift of conduction band (e ) and valence band (eHHV) with respect to the Fermi energy is illustrated in (f).
depends upon p–d hybridization [12]. As a result of which
ꢀ
the C level exhibits both p and d character whereas C
6
8
exhibits the s character (schematic is shown in Fig. 1(a))
6]. With the above consideration, the present work de-
[
scribes the studies on the electronic structure of the HgTe
nanocrystals and their associated unique optical properties
through X-ray photoelectron spectroscopy (XPS), optical
absorption and photoluminescence (PL) measurements.
2
. Experimental
HgTe nanocrystalline thin films have been synthesized
under galvanostatic condition with an electro-deposition
2
current density, 1.5 mA/cm for a period of 2 min using a
solution containing HgCl (0.028 M) and TeCl (0.052 M)
2
4
at temperature, 278 K and at pH 0.6. The substrates were
indium tin oxide (ITO) coated glass, carbon coated Cu grid
and titanium (Ti) used respectively as cathode and plati-
num as anode for sample synthesis. Near stoichiometric
HgTe nanocrystals (NCs) could be obtained by the above
mentioned electro-deposition parameters [13]. The stoichio-
metry, and size of the NCs deposited on three different sub-
strate were tested through Rutherford back scattering and
optical absorption studies. The measurements reveal the
composition and/or absorption spectrum do not vary
appreciably which suggests that the results are independent
of substrates under consideration. Shown in Fig. 2(a) is the
transmission electron microscopy (TEM) (Jeol 2010 TEM
machine operated at 200 keV) micrograph of the HgTe
NCs. The NCs appeared as black points in the micrograph
have the mean crystalline size as 5.35 ± 0.83 nm. Fig. 2(b)
shows the high resolution TEM (HRTEM) image of a typ-
Fig. 2. TEM micrograph (a), high resolution image (b) and the electron
diffraction pattern (c) of the HgTe NCs.

L112
S. Rath, S.N. Sahu / Surface Science 600 (2006) L110–L115
ical HgTe NC (black point). It should be noted that in the
HRTEM image (Fig. 2(b)), the boundary of the NC is not
resolvable. Further, there is a small size distribution in
deposited NCs. Hence, a typical NC was chosen for
HRTEM image for getting the structure (lattice spacing)
of the NC. The lattice spacing, d (difference between two
consecutive bright or dark fringes) calculated from
HRTEM is found to be 0.62 nm which corresponds to
the cubic phase of the HgTe as compared to standard
JCPDS data with 3% lattice contraction. The cubic phase
of the HgTe NCs have been verified with different NCs
the energy band diagram of the bulk HgTe (Fig. 1(b)), the
energy difference between heavy hole valence (HHV) band
to light hole valence (LHV) band is around 0.15 eV at
temperature, T = 300 K and the conduction band (CB)
touches the HHV band because of the relativistic effect
[9] (i.e., strong valence electron–nucleus interaction). As a
result, the band gap of the bulk HgTe is considered as
ꢀ0.15 eV [8,9] and such inverted narrow band gap nature
of bulk HgTe has been verified from magnetoreflection,
optical absorption, photoluminescence and photovoltaic
studies by several groups [1,2,14–17] since decade. Hence,
bulk HgTe is known as infrared sensitive material. Further,
the characteristic optical absorption of the HgTe NCs in
the visible regime (shown in Fig. 3) reveals the widening
of the band gap by shifting the CB, HHV and LHV bands
due to the quantum-confinement effect (QCE) and is sche-
matically shown in Fig. 1(c). Hence, the peaks, A and A
(
(
black points). As to the selected area electron diffraction
SAD) measurements, shown in Fig. 2(c), the exposed
sample diameter under electron beam is around 150 nm.
Whereas the mean size of the NCs is 5.35 nm. Hence,
the SAD is the contribution from all the NCs under
the beam giving the ring patterns. The ring like SAD pat-
terns (Fig. 2(c)) corresponding to the crystallographic
planes, (220), (311) and (222) reveal the polycrystalline
cubic phase character of the deposit. The structure of the
HgTe NC is also verified using grazing angle X-ray diffrac-
tion (GXRD) measurements (figure is not shown) and
shows consistent results (cubic phase) as observed from
TEM [13].
1
2
are attributed to the HHV band–conduction band (CB)
and LHV band–CB transitions respectively. Such strong
QCE (i.e., shifting of VBM and CBM) is expected as the
mean crystalline size, 5.35 nm is much less than the Bohr
exciton radius, a = 40 nm. A similar type of excitonic fea-
b
tures have also been observed from CdS passivated HgTe
NCs by Rogach et al. [18]. It should be noted that the pro-
nounced well resolved absorption spectrum predicts good
crystallinity in the sample. Photoluminescence (PL) mea-
surements were carried out at room temperature (300 K)
using Oriel PL set up with wavelength, k = 369 nm as an
exciting radiation available from a Hg–Xe lamp and the
spectrum is shown in Fig. 3 (marked by the right arrow).
The PL spectrum in the wavelength range 500–700 nm,
shows a broad peak with a small shoulder towards lower
wavelength. Deconvoluting the PL spectrum using Gauss-
ian function, we get two bands, P and P at 579.5 nm
3
. Results and discussion
Fig. 3 shows the optical absorption spectrum (left ar-
row) and photoluminescence spectrum (right arrow) of
the HgTe NCs prepared on ITO substrate. Note that both
the spectra are normalized to the same scale. Optical
absorption measurements of the HgTe NCs were carried
out using a dual beam Shimadzu UV-3101PC spectropho-
tometer. The absorption spectrum shows the striking exci-
tonic features around 578.5 nm and 550 nm marked by A1
1
2
and 588 nm respectively. Since, the energy difference be-
and A respectively, in the optical absorption. According to
tween P and P is around 30 meV which can be considered
2
1
2
as the localization energy of exciton and the energy corre-
sponding to the room temperature is 26 meV, hence, some
of the excitons are thermally released from the bound
state as free exciton. Thus, peak P and P are ascribed
to the luminescence corresponding to the free-exciton and
bound-exciton transition [19] respectively. Further, as the
4
3
2
1
4
3
2
1
1
2
PL peak, P position is very close to the first excitonic tran-
1
sition, A in the absorption spectrum (Fig. 3) hence, the
1
origin of P can be ascribed to the band edge luminescence
1
providing the band gap as E = 2.14 eV and confirms the
P2
g
P1
semiconducting nature of the HgTe NCs. One possibility
of such large band gap opening (2.14 eV) can be ascribed
to the change in the electronic structure and discretization
of energy levels as the crystalline size approaches to the
quantum limit. It may be noted that the hybridization is
a ground state property. However, as the surface to volume
ratio is very large, the majority of the atoms on the HgTe
NCs do not experience a true bulk-like environment. As a
result, the impact of atomic-coordination number imper-
fection provides the change in crystal potential of the
nano-solid which is given by [20]
A2
A1
0
5
0
700
00
550
600
Wavelength (nm)
650
Fig. 3. Optical absorption (left arrow) and photoluminescence (right
arrow) spectra of the HgTe NCs.

S. Rath, S.N. Sahu / Surface Science 600 (2006) L110–L115
L113
V ðD Þ ¼ V atomðrÞ þ V crystalðrÞ½1 þ Dlꢁ
ð1Þ
tively. The results suggest a significant weakening of p–d
hybridization in the HgTe NCs. The magnitude of the p–
l
where Vatom(r) is the intra-atomic trapping potential,
Vcrystal(r) is the crystal potential and
d hybridization (DE ) can be estimated perturbatively
pd
[
6], as
X
2
pd
D
l
¼
c D
i
V
ij
DEpd ꢂ ꢀc
ð3Þ
i63
a
p
ꢀ ꢀ
d
s
s
in;i
D
ꢀ D
sci
Kj
out;i
c
a
p
cij ¼
ꢂ
;
K
j
¼ D
j
=2d
0
ð2Þ
where V , ꢀ and ꢀ are p–d orbital interaction potential,
s
j
pd
d
D
cation, d orbital energy and anion, p orbital energy respec-
tively in the valence level.
Comparing the experimental DEpd value with bulk and
that of nano we get
2
c
i
i
ðz Þ ¼ d
i
=d
0
¼ 1
þ exp½ð12 ꢀ z
i
Þ=8z
i
ꢁ
The parameters, D , s, D , d and z are the contribution
i
j
0
i
N
pd
c
d
B
a
p
B
from interlayer bond contraction, dimensionality of the
nano-solid (e.g., s = 1, 2 and 3 correspond to the dimen-
sionality of a thin plate, a rod, and a spherical dot respec-
tively), diameter of the nano-solid in jth layer, bulk bond
length, atomic coordination number of the ith layer respec-
tively. This leads to the localization of the charge in relaxed
surface region and helps to modify the bond formation
during hybridization and is reflected on the electronic
structure by shifting of the valence and core levels [21].
In pursuit of the change in the electronic structure and
the band opening phenomena associated with HgTe NCs,
DE
DE
ðꢀ Þ ꢀ ðꢀ Þ
¼
¼ 0:33
ð4Þ
B
pd
c
d
N
N
a
p
ðꢀ Þ ꢀ ðꢀ Þ
Hence, the p–d hybridization in case of the HgTe NCs is
weakened by a factor of 0.33 to that of the bulk (schemat-
ically it has been illustrated in Fig. 1(d)). The weakening of
p–d hybridization is consistent with the transfer of non –
d electrons from Hg to Te [11]. Note that in explaining
the above behavior, we have assumed that the background
contribution to the valence band spectrum is negligible.
However, in order to quantify the results one need to
record the XPS spectrum at resonance X-ray photon
energy for which the work is in progress. From the valence
level XPS analysis, we have observed that there is a shift in
VBM to higher BE. The shift of VBM can be determined
from a linear extrapolation of the leading valence band
edge [23] as marked by an arrow shown in the inset of
Fig. 4 and found to be 1.13 eV. The possible explanation
of the VBM shifting of the HgTe NCs can be due to the
rearrangement of the DOS leading to a change in electronic
structure because of size quantization where the crystal (in
nanoform), does not exhibit true bulk like behavior [24].
Fig. 4(b) shows the Te core level spectrum of the HgTe
NCs. It consists of four peaks namely s , s , s and s .
ꢀ9
XPS measurements were carried out at 2 · 10 mbar pres-
sure using VG Microtech XPS setup incorporated with
3
00 W Mg/Al X-ray source and a hemispherical analyzer
with a channeltron detector (resolution 0.9 eV) at room
temperature. The exciting radiation was 1256.4 eV Mg Ka
X-ray source. After removal of few mono-layers of the
adsorbed impurities and surface oxides by Ar ion sput-
tering, the XPS scan has been made for the HgTe NC sam-
ple. The valence and core level spectra were calibrated
against the C 1s peak and the background (due to inelastic
scattering of the secondary electrons) corrections have been
carried out by a polynomial fitting of experimental data
using VG Microtech software. The valence band spectrum
of the HgTe NC as shown in Fig. 4(a) consists of six peaks,
r1 (4.40 eV), r (6.42 eV), r (8.41 eV), r (10.27 eV), r
5
1
2
3
4
The peaks, s and s represent the 4d and 4d3/2 respec-
2
3
5/2
tively of 4d level. For the HgTe NCs, we have observed
that the 4d5/2 level is at 40.79 eV with a BE shift of
2
3
4
(
12.89 eV) and r6 (14.87 eV) where r3 and r4 represent
the Hg 5d
and 5d3/2 levels with BE shift, DE5d5=2
¼
1.11 eV from its bulk value. Similarly, the peak, s appear-
ing at 42.25 eV shows the BE shift of 1.13 eV from its bulk
5
/2
3
N
B
N
B
E5 ꢀ E
¼ 0:88 eV and DE5d3=2 ¼ E
ꢀ E
¼ 0:83
d5=2
5d5=2
5d3=2
5d3=2
respectively. Note that the full width of half maxima
counter part. The prominent peaks s and s appeared at
1
4
(
FWHM) of Hg 5d3/2 is large compared to Hg 5d5/2 and
BE, 37.32 eV and 45.81 eV can be accounted to the Te
4d5/2–O and 4d3/2–O hybrid levels respectively. Similarly,
the spectrum in the range 570–595 eV illustrated in
Fig. 4(c) is the Te 3d core level spectrum which consists
of four peaks t , t , t and t . The peaks, t and t appearing
is due to the effect of orbital-hybridization leading rear-
rangement of density of states (DOS) as a result of the size
quantization. Peaks, r and r corresponds to the Te 5p
1
2
derived DOS and a hybrid, Hg 6s–Te 5p derived DOS
1
2
3
4
1
3
respectively [22]. Similarly, peaks, r and r are due to the
at 573.27 eV and 583.59 eV are the 3d5/2 and 3d3/2 core lev-
els of Te with BE shift of 0.57 eV and 0.55 eV respectively
5
6
Hg 5d–Te 5s derived DOS and Te 5s state respectively.
Since, the band position and the width reflect the degree
of overlapping and the strength of the hybridization [11],
to that of bulk Te. The appearance of the peak, t at
2
578.21 eV can be ascribed to the contribution from Te
NꢀB
N
p
B
p
hence, the values of
E
¼ E ꢀ E ¼ 0:71 eV and
3d5/2–O derived DOS. Similarly, the peak, t appearing at
p
4
NꢀB
N
B
E
¼ E ꢀ E ¼ 0:91 eV suggests that the d level of Hg
588.56 eV is due to Te 3d3/2–O. The Hg core 4f level has
been observed in the BE range 94–114 eV as shown in
Fig. 4(d). The SO splitting of 4f level (4f7/2 and 4f5/2) is
illustrated by the peaks, u (100.75 eV) and u (105.21 eV)
d
d
d
is shifting more towards higher BE with narrow line width
compared to the low shift and long tail of Te 5p state. The
superscript N and B stand for nanocrystal and bulk respec-
2
3

L114
S. Rath, S.N. Sahu / Surface Science 600 (2006) L110–L115
3
000
000
000
0
8000
(
a)
(c)
t1
t3
6
4
2
000
000
000
0
2
1
0
2
4
6
B. E. (eV)
t2
t4
570
575
580
585
590
595
0
2
4
6
8
10
12
14
16
18
B. E. (eV)
B. E. (eV)
2
1
1
000
500
000
10000
8000
(
b)
(d)
u3
u2
s2
s3
6
4
2
000
000
000
0
s1
s4
u4
500
u1
0
3
5
40
45
B. E. (eV)
50
55
94
99
104
109
114
B. E. (eV)
Fig. 4. (a) Valence band XPS spectrum of the HgTe NCs and the inset is the linear extrapolation of valence band edge to evaluate the valence band
maxima as indicated by the downward arrow. Core level spectrum of Te 4d state (b), Te 3d state (c) and Hg 4f state (d) of the HgTe NCs.
with BE shift of 1.05 eV and 1.40 eV respectively. Apart
the Hg metal where the effect of Hg nucleus on the valence
electrons is stronger than the core electrons [6]. However,
for Te, the case is reversed. This is because of the core level
electrons are highly attracted by the nucleus than valence
electrons. Since, the cationic core levels stay nearly constant
[25], thus, the measured cation core level shifts must have
resulted from the movement of the VBM. For the sake of
from u and u , two other peaks, u and u are also appear-
2
3
1
4
ing at BE, 96.50 eV and 109.79 eV respectively. Moreover,
the intensity of 4f7/2 should be higher than 4f5/2 whereas the
intensities of the above two (u and u ) are approximately
2
3
same here. It indicates that the satellite feature of Hg 4f
at lower binding energy side namely, u can be due to the
1
transformation of DOS to ligand, Te [11]. The peak u ap-
clarity, the BE scale is referred to the Fermi energy, E . In
4
f
pear in the higher energy side can be ascribed to the Hg–O
hybrid level.
case of bulk HgTe, the E is lying at 0.59 ± 0.05 eV above
f
the VBM [22] at room temperature. However, the E posi-
f
Analysis of valence and core level spectra of the HgTe
NCs shows that the BE of the Hg 5d5/2, Hg 4f7/2, Te 4d5/2
and Te 3d5/2 levels are shifted by 0.88, 1.05, 1.11 and
tion would change if the spectra recorded at low temperature
(40 K) [7]. As we have recorded the spectra at room temper-
ature, the E is assumed to be 0.59 eV above the VBM.
f
0
.57 eV respectively with respect to their bulk counter part.
Further, the optical absorption and PL measurements
Further, it can be noted that in case of Hg cation, the core
level shift is more compared to the valence level (shown in
Fig. 1(e) which is due to the (n ꢀ 1)d configuration of
estimated the E of HgTe NCs as 2.14 eV. Considering both
the XPS, optical absorption and PL measurements, carried
out at room temperature, we found that the conduction
g
1
0

S. Rath, S.N. Sahu / Surface Science 600 (2006) L110–L115
L115
band is shifting up by 1.6 eV and the valence band is shifted
Acknowledgements
down by 0.54 eV from the Fermi level as shown in Fig. 1(f).
This is due to weakening of the p–d hybridization and the
discretization of the electronic energy level as a result of size
quantization effect. The particle size estimated using effec-
tive mass approximation [26] from the band edge lumines-
cence is about 5.2 nm which does not agree with the
value, 5.35 nm obtained from TEM measurement. The
above discrepancy can be accounted to the p–d interaction
weakening and particle in a finite potential well. Hence, for
the good agreement of the experimental result to that of the
theory, the semi empirical relation [26] (i.e. effective mass
approximation) of the confinement energy for HgTe NCs
can be given by
Thanks are due to Prof. S.N. Behera, Dr. R.K. Choudh-
ury, Institute of Physics, Bhubaneswar, India, for their
helpful discussion and constant encouragement. Dr. P.V.
Satyam and Dr. Shikha Varma, Institute of Physics,
Bhubaneswar, India are acknowledged for helping in
TEM and XPS measurements. The author would like to
acknowledge Mr. S.N. Sarangi for his help during the
experiments.
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2
2
2
L. Sosnowski, Phys. Status Solidi B 8 (1965) K135.
ꢁ
h p
1:86e
ꢀr
E
c
¼ dE
where dE
g
þ 2
ꢀ
ꢀ epol
[2] G.L. Hansen, J.L. Schmit, T.N. Casselman, J. Appl. Phys. 53 (1982)
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m r2
¼ E
ꢃ
ð5Þ
7
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g
g
þ DEpd
*
Taking m = 0.029m , ꢀ = 21, e = 0.674 meV of HgTe,
0
pol
particle size = 5.35 nm (from TEM result), E = 2.14 eV
[5] T.C. McGill, D.A. Collins, Semicond. Sci. Technol. 8 (1993) S1.
c
[
[
6] S.-H. Wei, Alex Zunger, Phys. Rev. B 37 (1988) 8958.
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(
from optical absorption data), the DEpd value is estimated
as 0.23 eV. Comparing the result with theoretical calcula-
tion, DEpd = 0.68 eV for bulk HgTe [6], we observed that
[8] Donald Long, Joseph L. Schmit, Semicond. Semimetal 5 (1970)
190.
N
pd
B
pd
DE ’ 0:33DE
ð6Þ
[9] Isaak M. Tsidikovski, Electron Spectroscopy of Gapless Semicon-
ductor, 116, Springer, 1997, p. 85.
From the above observation, it can be concluded that the
widening of the band gap in HgTe NCs is associated with
the weakening of p–d hybridization leading to minimiza-
tion of the relativistic effect (i.e. the correction of the poten-
tial energy between the valence electron and nucleus
interaction due to localization of d orbital, during hybrid-
ization decreases as a result, the conduction band moves
up) and the discretization of the energy levels due to QCE.
[
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[
[
[
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4
. Conclusions
In conclusion, HgTe nanocrystals with mean size as
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5
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(
1) weakening of the p–d hybridization and (2) quantiza-
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of 0.33 to that of the bulk value. It further reveals that
the conduction band is shifted up by 1.6 eV and valence
band is moved down by 0.54 eV from the Fermi level.
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