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4.1 Introduction
The group III-V and II-VI semiconductors are having great technological
importance. In group III-V compounds, Boron compounds have wide-gap make
them of great technological interest for high temperatures, electronic and optical
applications [1]. The zinc-blende boron compounds BN, BP and BAs have wide
band gaps, excellent physical hardness, extremely large heterojunction offsets,
high thermal conductivity and high melting temperature. Furthermore, these
compounds possess some peculiar characteristics such as the inverse role
between the cation and the anion in terms of charge transfer and the new high-
pressure phase transitions [2, 3]. According to the Phillips scale of ionicity, BP (fi =
0.006) and BAs (fi = 0.002) are the most covalent of the III–V semiconductors [4],
and there are interesting consequences of this property. BSb (like BAs and BP)
shows strong covalent character and exhibits an unusual behavior due to small
core and absence of “p” electrons in boron atom compared to other III-V
compounds. It makes this compound a potential material for high temperature
electronic and optical applications. BN is not concerned with the first anomalous
point, because it can be viewed less as a boron compound than a nitride [3]. BN
has chemical stability over a wide range of pressures and temperatures [5]. The
properties of cubic BN thus far determined indicate that it is an excellent
candidate for pressure calibration in simultaneous high-temperature high-
pressure experiments using the diamond-anvil cell [5]. BN, AlN and GaN have
wide band gap ranging from the ultraviolet (UV) to the visible regions of the
spectrum, strong interatomic bonds, high thermal conductivity, a high melting
temperature, high bulk modulus and a low dielectric constant [6-9], which make
them to be an ideal materials for optoelectronic and high-temperature and high-
power devices, short-wavelength light-emitting diodes (LEDs), laser diodes and
optical detectors as well as for high-frequency electronic devices [9]. AlN films
are utilized in SAW devices, rugate filters and have potential for applications in
blue-violet light emitting diodes, lasers, and ultraviolet light detectors [10]. At
ambient conditions, the ground state structure of GaN is the wurtzite phase.
However, the meta-stable zinc-blende phase is also possible to synthesize. GaN-
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based LEDs have recently attracted considerable interest for use in outdoor full-
color displays, traffic signals, backlight units in liquid crystal display, solid-state
lighting and solar cells [11, 12]. InSb has received a great deal of attention due to
its high electron mobility and the narrowest band-gap as a unique III–V
compound semiconductor for 3–5 μm infrared device applications. InSb is an
attractive material because of its potential application for large area detector
arrays, high frequency devices and magnetorsistive sensors for position sensing,
etc [13]. Among compound III–V semiconductors, GaSb is particularly interesting
as a substrate material because its lattice parameter matches solid solutions of
various ternary and quaternary III–V compounds whose band gaps cover a wide
spectral range from 0.3 to 1.58 eV, i.e. 0.8–4.3 μm, also, detection of longer
wavelengths, 8–14 μm [14, 15]. The binary compound semiconductors AlSb,
GaSb, InSb, and InAs along with their related alloys are candidates for high-
speed, low-power electronic devices. Applications could include high-speed
analog and digital systems used for data processing, communications, imaging
and sensing, particularly in portable equipment such as hand-held devices and
satellites. The development of Sb-based transistors for use in low-noise high-
frequency amplifiers, digital circuits, and mixed-signal circuits could provide the
enabling technology needed to address these rapidly expanding needs [16]. The
antimonide–arsenide materials are used in the fabrication of high electron
mobility transistors (HEMTs), resonant tunneling diodes (RTDs), and
heterojunction bipolar transistors (HBTs) [16], rechargeable lithium batteries as
anode materials [17]. BSb is a potential material for high temperature electronic
and optical applications. GaSb is a good candidate for thermo-photovoltaic cells
for systems with low radiator temperature, as its cell technology is rather
straightforward resulting in higher efficiency than Si thermo-photovoltaic cells
[17]. Antimonide compounds, due to their high mobility, are therefore well-
known for advanced device applications [17]. III–V materials exhibit many
interesting electrical and optical properties that make them very good
candidates for nanowire applications in several fields. Their high mobility can be
used in vertical field effect transistors, where the electrostatic coupling with the
wrap gates is optimal [18]. Among compound semiconductor materials, GaAs is
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commonly preferred for space applications, near-IR LEDs, solar cells because of
its advanced technology [19]. GaAs is the second most common in use after
silicon, commonly used as substrate for other III-V semiconductors, e.g. InGaAs
and GaInNAs.
Group II-VI compounds were the first semiconductors to be studied and used as
phosphors for applications in cathode ray tube (CRT) displays [22]. The wide-gap
II-VI semiconductors, well known anisotropic materials used in high technology,
have received much attention in the past decades since they have important
applications in short-wavelength light emitting diodes (LEDs), laser diodes and
optical detectors. The ZnS, ZnSe, and ZnTe compounds have a high melting point,
high thermal conductivity, and large bulk modulus. The hardness and large bulk
modulus of these anisotropic materials make them ideal protective coating
materials in photovoltaic applications. These materials can, therefore, be used
for optoelectric devices in which the availability of light sources in the mid-
infrared spectral region is crucial for many applications, i.e. molecular
spectroscopy and gas-sensor systems for environmental monitoring or medical
diagnostics [23]. CdTe, ZnTe and HgTe compounds with energy gaps covering the
whole spectral range from IR to UV are compatible candidates for optoelectronic
devices. In fact, telluride materials have shown remarkable results on micro-
cavities, diluted magnetic semiconductors and hybrid structures. CdTe and its
ternary alloy Cd1−xZnxTe are the important semiconductor materials used in solar
cells, x-ray detectors and other optoelectronic devices [24]. Due to their chemical
and structural compatibility, they are also the best candidates as substrates for
growing epitaxial layers of HgCdTe, a useful IR detecting material in the 8–12 mm
infrared range [24]. Experimentally, MgTe, ZnTe, and CdTe are found to have
room-temperature direct band gaps of 3.5, 2.4, and 1.5 eV, respectively. This
makes them excellent candidates for low-cost thin film or high efficiency multi-
junction solar cell materials [25]. Due to their large band gaps and low dielectric
constants, Mg compounds, particularly Mg chalcogenides can be used in blue
and ultraviolet-wavelength optics and high-temperature electronics. These Mg-
based semiconductors are also preferable to use for protective coatings due to
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their hardness, large bulk modulus, high melting point and high thermal
conductivity. The II-VI semiconducting materials cover a large range of bandgap
energies from 0 (some of these compounds are semimetals like HgTe and HgSe)
to more than 4 eV. In addition they all have a direct bandgap suited to light
emission or absorption. This is the reason why these materials have been used
for many years as luminophors [26]. CdTe exhibits many interesting features like
a band gap in the middle of the solar spectrum, a high atomic weight for x-ray
detection, and an electro-optic coefficient, which is about a factor of 4 higher
than in GaAs. In addition, CdTe is the base material for the related ternary alloys
Hg1-xCdxTe and Cd1-xMnxTe. Hg1-xCdxTe is an important infrared detector material,
and CdMnTe as a dilute magnetic semiconductor exhibits unique features such
as, e.g., a giant Faraday rotation and magnetic polaron formation [27]. Cadmium
sulphide (CdS) is a wide gap semiconductor with bulk bandgap energy of 2.41 eV,
corresponding to an optical cut-off of 515 nm, with exciton Bohr radius (rB) of 3
nm. CdS has been used in photodetectors and for solar cell applications [28].
Recently, magnetic semiconductors have been extensively studied due to their
possible applications in silicon technology. When doped with transition metal
elements, compound semiconductors often exhibit magnetic properties in
addition to typical semiconductor properties. Moreover, the possibility of half-
metallicity, i.e., metallic in one spin direction and insulating in the other spin
direction, has also been noted for these materials [29].
Due to their wide energy gap, group II-VI compounds and their alloys are
applicable to optical devices in the blue to the near-ultraviolet region. While
group III-V compounds are useful to fabricate optical devices operating in the
visible to infrared region. These materials are very sensitive to the external
influence such as temperature, external fields and strains, which make them
strong candidates for sensors operating in the infrared, visible and ultraviolet
regions of the spectrum. We can fabricate the material having required lattice
constant and band gap for any optoelectronic application by taking proper
combination of the suitable semiconductor compounds for ternary and
quaternary alloys.
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The higher order perturbation theory is successfully employed to compute
various physical properties of group IV semiconductors and their solid solutions
in the previous chapter. We have extended the application of the higher order
perturbation theory with our proposed model potential to group III-V and group
II-VI semiconductor compounds in the present chapter. It is seen that the
contribution of the higher order terms to the total energy is negligible in simple
metals. But in covalent crystals these higher order terms, which include in the
covalent correction terms, are essential to take account for computing any
physical property.
In the present chapter we have employed our model potential along with six
screening functions to compute total energy, energy-volume relations, pressure-
volume relations, bulk modulus, bulk modulus-volume and bulk modulus-
pressure relations, pressure derivatives of bulk modulus, elastic properties,
energy band gap at Jones-zone face, variation of energy band gap at Jones-zone
face with volume and pressure for group III-V in the section 4.2 and for group II-
VI in section 4.3 respectively. The Nagy’s local field correction function [32] has
been first time incorporated to such a study of various physical properties of
group III-V and group II-VI semiconductors. In the present work, computations of
all physical properties are in zinc-blende phase.
4.2 Group III-V semiconductors
In the present study, we have selected B, Al, Ga and In based 16 compounds to
predict certain physical properties of interest. The presentation of all physical
properties in the Tables and Figures are arranged from lighter to heavier
element, i.e. from B → Al → Ga → In, for group III and from N → P → As → Sb for
group V respectively.
4.2.1 Total Energy
The total energy per electron for BX, AlX, GaX and InX semiconductor compounds
(with X = N, P, As and Sb) computed using equation (3.1) with our proposed
potential and local field correction functions due to N [32], H [30], T [33], I [34],
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F [35] and S [36] are shown in Table 4.1 with available experimental data and
other such theoretical findings.
Table 4.1 Total energy (-ET) (Rydberg/electron) of group III-V semiconductors.
Comp
ound
Present results using different screening functions
f(q) Expt. Others
N [32] H [30] T [33] I [34] F [35] S [36]
BN 3.299 3.095 3.330 3.372 3.372 3.256 - -
BP 2.679 2.449 2.701 2.757 2.757 2.635 - -
BAs 2.550 2.318 2.570 2.629 2.629 2.505 - -
BSb 2.383 2.151 2.398 2.462 2.462 2.336 - -
AlN 2.776 2.550 2.801 2.854 2.854 2.733 3.388-3.393 [43] 2.550-2.855,
2.549-4.368 [43]
AlP 2.238 2.010 2.247 2.316 2.315 2.190 2.196 [41] 2.010-2.318,
1.425-2.584 [43]
AlAs 2.152 1.930 2.158 2.230 2.229 2.104 2.131 [41] 1.930-2.232,
1.225-2.497 [43]
AlSb 1.978 1.771 1.976 2.051 2.050 1.930 1.935-1.939 [37] 1.772-2.055 [43],
1.953-1.990 [37]
GaN 2.700 2.471 2.723 2.778 2.778 2.656 2.634, 2.635 [43] 2.471-2.780,
2.426-3.644 [43]
GaP 2.237 2.010 2.246 2.316 2.315 2.190 2.221-2.223 [37]
2.229-2.271 [37],
2.207-2.281 [39],
2.010-2.320 [40],
2.010-2.318 [43]
GaAs 2.155 1.932 2.161 2.233 2.232 2.107 2.157-2.159 [37, 38]
2.151-2.194 [37],
2.148-2.190 [38],
2.056-2.115 [39],
1.933-2.232 [40],
1.933-2.235 [43]
GaSb 1.984 1.776 1.982 2.057 2.056 1.936 1.965 [37]
1.977-2.019 [37],
1.975-2.016 [38],
1.908-1.964 [39],
1.777-2.039 [40],
1.777-2.061 [43]
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Table 4.1 Total energy (-ET) (Rydberg/electron) of group III-V semiconductors. (Cont.)
Comp
ound
Present results using different screening functions
f(q) Expt. Others
N [32] H [30] T [33] I [34] F [35] S [36]
InN 2.449 2.216 2.466 2.528 2.528 2.403 2.269, 2.271 [43] 2.217-2.530,
2.015-3.435 [43]
InP 2.073 1.857 2.075 2.149 2.148 2.025 2.176 [37]
2.186-2.222 [37],
2.006-2.070 [39],
1.857-2.152 [43]
InAs 2.012 1.802 2.011 2.086 2.085 1.964 2.112 [37, 38],
2.108 [43]
2.135-2.176 [37],
2.128-2.168 [38],
1.976-2.041 [39],
1.802-2.090 [43]
InSb 1.865 1.673 1.857 1.932 1.931 1.818 1.919 [37, 38]
1.929-1.972 [37],
1.925-1.967 [38],
1.848-1.913 [39],
1.673-1.937 [43]
From Table 4.1 it is seen that total energy computed by employing local field
correction functions due to N [32], H [30], T [33], I [34], F [35] and S [36] for all 16
group III-V compounds are found in good agreement with the experimental
results with acceptable deviations. H [30] generates higher values of total energy
while I [34] and F [35] give lower values of total energy among all six screening
functions. The total energy computed using S [36] for Al-based compounds, N
[32] for Ga-based and In-based compounds are found in excellent agreement
with the experimental data. No such experimental data are available for B-based
compounds to make comparison. I [34] and F [35] generate almost same total
energy. The percentage deviation observed from the experimental findings is
upto 2% for Al-based and Ga-based compounds, 2% to 5% for In-based
compounds in the computed total energy for N [32]. It is seen from 2% to 8% for
T [33], I [34], F [35] and S [36], while large deviation about 7% to 18% seen for H
[30]. As static local field correction function H [30] does not include any exchange
and correlation effects, it is necessary to take account of exchange and
correlation effects in energy computation to get proper results. In nitride
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compounds, highest deviation 18% to 32% is observed in AlN. As nitride
compound are generally preferred to grow in wurtzite structure in place of zinc-
blende structure at equilibrium conditions, some large deviation found in the
present findings of total energy from the experimental findings.
4.2.2 Energy-Volume Relations
The total energy of any crystal depends on its atomic volume. It is seen in group
IV semiconductors that the total energy of the system increases on compression
or expansion from its equilibrium volume or normal pressure. It is also found that
the total energy depends upon the selection of the local field correction function.
On changing the screening function, the minimum value of the total energy at
equilibrium volume (normal pressure) also gets changed.
In group III-V semiconductor compounds, same nature of inclusion of screening
function is visualized. Therefore we have take GaAs to study energy-volume
relations of group III-V semiconductor compounds for different local field
correction functions under consideration. The variations of total energy per
electron with different atomic volume using local field correction functions due
to N [32], H [30], T [33], I [34], F [35] and S [36] for GaAs are shown in Figure 4.1.
Figure 4.1 Total energy-volume relations for GaAs.
-2.3
-2.1
-1.9
-1.7
0.4 0.6 0.8 1 1.2 1.4 1.6
E T(R
ydbe
rg)
Ω/Ω0
GaAsNHTIFS
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It is seen from Figure 4.1 that for all six local field correction functions, total
energy of GaAs show same trend. Total energy becomes minimum at equilibrium
volume and increases on compression or expansion of volume. H [30] gives
higher values of energy, while I [34] and F [35] give lower values of total energy
at any volume during compression or expansion. N [32] and T [33] generate
almost same energy for a given volume. S [36] generates higher value of total
energy compared to N [32], T [33], I [34] and F [35]. As H [30] does not include
any exchange or correlation effects, the inclusion of the local field correction
function suppresses the total energy.
The total energy-volume relations for B-based, Al-based, Ga-based and In-based
compounds using Nagy’s local field correction function [32] are shown in Figures
4.2 to 4.5 respectively.
From Figures 4.2 to 4.5 it is seen that the antimonide compounds generate
higher values of total energy, while nitride compounds generate lower values of
total energy.
It is seen from Figures 4.1 to 4.5 that all curves of total energy are not symmetric
around mid point, at equilibrium volume. So we predict that the effect of
compression is more than the effect of expansion of volume on total energy.
Figure 4.2 Total energy-volume relations for boron based compounds.
-3.4
-3.2
-3
-2.8
-2.6
-2.4
-2.2
-2
0.4 0.6 0.8 1 1.2 1.4 1.6
E T(R
ydbe
rg)
Ω/Ω0
BNBPBAsBSb
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Figure 4.3 Total energy-volume relations for aluminium based compounds.
Figure 4.4 Total energy-volume relations for gallium based compounds.
-2.8
-2.6
-2.4
-2.2
-2
-1.8
0.4 0.6 0.8 1 1.2 1.4 1.6E T
(Ryd
berg
)
Ω/Ω0
AlNAlPAlAsAlSb
-2.8
-2.6
-2.4
-2.2
-2
-1.8
0.4 0.6 0.8 1 1.2 1.4 1.6
E T(R
ydbe
rg)
Ω/Ω0
GaNGaPGaAsGaSb
Chapter 4 Ph D (Thesis) 115
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Figure 4.5 Total energy-volume relations for indium based compounds.
4.2.3 Pressure-Volume Relations
The most remarkable aspect of group III-V compounds of tetrahedral coordinate
structures is their low density. Therefore, under pressure, a tetrahedral
coordinated semiconductor can be transformed to a structure with high density.
The development of the diamond anvil cell and its inherent ruby fluorescence
monometer are used to study electronic and vibrational properties of
semiconductors under very high hydrostatic pressure [44].
The pressure-volume relations for GaAs using all six local field correction
functions are shown in the Figure 4.6. It is seen from Figure 4.6 that the static
dielectric function H [30] generates very high pressure compared to other
screening functions, while I [34] and F [35] generate lower pressure in all six local
field correction functions. H [30] generates 64% higher pressure than pressure
generated by I [34] at 60% compression. The influence of screening effect
increases as compression is increased. The influence of the local field correction
functions is found identical in nature for all 16 group III-V compounds. We have
compared present findings of equation of states with those computed by using
Murnaghan equation of state [45] and Vinet equation of state [46]. At low
pressure regions, overall good agreement between present results with those
obtained from Murnaghan and Vinet equations of state [45, 46] is seen. At large
-2.5
-2.3
-2.1
-1.9
-1.7
0.4 0.6 0.8 1 1.2 1.4 1.6
E T(R
ydbe
rg)
Ω/Ω0
InNInPInAsInSb
Chapter 4 Ph D (Thesis) 116
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compression Murnaghan equation of state and Vinet equation of state [45, 46]
are not valid. It is seen that the pressures obtained using I [34] and F [35] at a
given volume are identical in values.
Figure 4.6 Pressure-volume relations for GaAs.
The pressure-volume relations for B-based, Al-based, Ga-based and In-based
compounds using Nagy’s local field correction function [32] are shown in Figures
4.7 to 4.10 respectively.
Figure 4.7 Pressure-volume relations for boron based compounds.
0
100
200
300
400
500
0.4 0.5 0.6 0.7 0.8 0.9 1
P (G
Pa)
Ω/Ω0
GaAsNHTIFSMurnaghanVinet
0
400
800
1200
1600
2000
2400
0.4 0.5 0.6 0.7 0.8 0.9 1
P (G
Pa)
Ω/Ω0
BNBPBAsBSb
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Figure 4.8 Pressure-volume relations for aluminium based compounds.
Figure 4.9 Pressure-volume relations for gallium based compounds.
0
200
400
600
800
1000
0.4 0.5 0.6 0.7 0.8 0.9 1
P (G
Pa)
Ω/Ω0
AlNAlPAlAsAlSb
0
200
400
600
800
1000
0.4 0.5 0.6 0.7 0.8 0.9 1
P (G
Pa)
Ω/Ω0
GaNGaPGaAsGaSb
Chapter 4 Ph D (Thesis) 118
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Figure 4.10 Pressure-volume relations for indium based compounds.
From Figures 4.7 to 4.10 we predict that all nitride compounds generate very
large pressures, while all antimonide compounds generate low pressures in all
four groups of semiconductors. The pressure difference between BN and BSb is
1701 GPa, between AlN and AlSb is 691 GPa, between GaN and GaSb is 576 GPa
and between InN and InSb is 331 GPa at 60% compression than the equilibrium
volume. From this result, we predict that all antimonide compounds are more
compressible than the nitride compounds of the same element of group III and
compressibility increase from higher to lower element of group III i.e. from In →
Ga → Al → B.
4.2.4 Bulk Modulus
The bulk modulus computed in the present investigations for sixteen group III-V
semiconducting compounds with six local field correction functions due to N
[32], H [30], T [33], I [34], F [35] and S [36] along with experimental findings and
other such theoretical findings are shown in Table 4.2.
0
100
200
300
400
500
600
0.4 0.5 0.6 0.7 0.8 0.9 1
P (G
Pa)
Ω/Ω0
InNInPInAsInSb
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Table 4.2 Bulk modulus (GPa) of group III-V semiconductors.
Comp
ound
Present results using different screening functions f(q)
Expt. Others
N [32] H [30] T [33] I [34] F [35] S [36]
BN 610.38 651.38 595.67 587.54 586.58 590.50 372.3 [42],
369 [97]
382, 400, 412 [49], 403 [50], 401 [51],
397 [52, 53], 395 [54], 367 [55],
368-403.6 [96], 395.7, 408.9 [97]
BP 206.96 238.82 199.00 194.03 193.67 202.02 152 [42],
165 [96]
152 [56], 173 [57], 267 [58], 165 [59],
166 [60], 162.6-177 [96]
BAs 161.51 192.91 154.62 149.80 149.53 158.48 138 [42] 148 [61], 145 [60], 132.1-174.8 [96]
BSb 115.59 146.16 110.08 105.23 105.08 114.62 - 96-116 [17], 89.2, 103.0, 112.0,
115.0 [96]
AlN 248.39 280.65 239.57 234.37 233.94 241.78 202, 208,
216 [43]
191-212 [9], 232.41-281.02 [43],
206 [47], 203 [48], 220 [62], 218 [51],
216 [52], 203 [48], 228 [63], 208 [64],
214 [54], 193.1-214.1 [96]
AlP 85.73 115.06 81.44 76.39 76.33 86.17
185 [42],
86 [96],
86.5 [43]
76.61-114. 9 [43], 86 [65, 66], 90
[67], 87.5 [68], 86.5 [69], 84.5 [70],
82.5-90.9 [96]
AlAs 71.68 100.02 68.13 62.91 62.91 72.81 74.1 [43],
82 [96]
63.09-99.91 [43], 74 [71, 72], 77 [65],
77.3 [66], 75 [67], 74.1 [69], 71 [70],
66.8-76.5 [96]
AlSb 49.69 75.37 47.71 42.07 42.18 51.89
58 [17, 96],
59.3 [37],
55.1 [42]
49-65 [17], 48.0-60.2 [37],
42.1-75.4 [43], 58 [67, 71], 59.3 [66],
54.3 [70], 49.8-58.1 [96]
GaN 215.48 247.42 207.34 202.32 201.95 210.19
190, 188 [8],
207, 210
[43]
175.4-239 [7], 173.6, 184.3 [8],
156-254 [9], 201.03-247.78 [43],
225 [47], 201 [48], 202 [52, 73],
203 [52, 64], 174.8-207.1 [96]
GaP 85.63 114.96 81.34 76.29 76.24 86.08
88.7 [37],
87.4 [42],
88 [96]
68.4-87.2 [37], 73.6-89.8 [39],
65.7-114.8 [40, 43], 77.2-88.7 [44],
88.7 [66, 76], 89.7 [69], 86.8 [70],
88.1 [74], 88.5 [75], 87.4 [77], 88.19
[78], 91.1 [79], 88.8 [80, 81], 89.8
[82], 89.1 [83], 77.3-91.9 [96]
GaAs 72.12 100.50 68.55 63.33 63.33 73.23
75.4
[37, 38],
74.8 [42],
77 [96]
62.2-82.3 [37], 71.2-91.0 [38],
68.6-80.0 [39], 52.1-100.4 [40, 43],
60.2-74.8 [44], 74.8 [66, 76], 72.5
[69], 70.8 [70], 74.7 [84, 85], 75.4
[86],
86 [87], 60.2-77.1 [96],
Chapter 4 Ph D (Thesis) 120
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Table 4.2 Bulk modulus (GPa) of group III-V semiconductors. (Cont.)
Comp
ound
Present results using different screening functions f(q) Expt. Others
N [32] H [30] T [33] I [34] F [35] S [36]
GaSb 50.26 76.05 48.23 42.61 42.72 52.44
56 [17, 96],
56.3
[37, 38],
56.1 [42]
45-80 [17], 43.4-57.6 [37], 49.0-63.0
[38], 49.7-58 [39], 31.0-76.1 [40, 43],
45.9-57 [44], 56.3 [66], 55.7 [70],
56.35 [88], 56.1 [89], 45.9-60.0 [96],
InN 132.07 163.02 126.02 121.20 121.01 130.34 126, 137
[43]
116-159 [9], 121.01-162.84 [43], 137
[47], 139 [48], 126a, 139a, 165a,
170b [49] , 121.6-148.4 [96],
127.7, 155.4 [97], 133-146 [97]
InP 60.70 87.94 57.86 52.45 52.50 62.37
72.5 [37],
71 [43],
72 [96]
58.7-71.3 [37], 64.1-74.9 [39],
52.5-87.9 [43], 72.5 [66], 70 [70],
76 [90], 71.1 [91], 60.1-73.4 [96]
InAs 53.37 79.64 51.08 45.52 45.61 55.40
57.9
[37, 38],
58.0 [96]
44.9-58.4 [37], 55.6-68.9 [38],
49.3-59.5 [39], 45.58-79.69 [43],
58 [66], 58.1 [70], 49.1-63.4 [96]
InSb 39.20 62.71 38.28 32.41 32.59 41.87
46 [17, 96],
46.5
[37, 38],
45.6 [42]
37-58 [17], 38.4-49.2 [37],
44.4-55.0 [38], 40.0-47.7 [39],
32.3-62.9 [43], 46.6 [66], 47.0 [70],
45.7 [92], 46.5 [93], 44.3 [94], 44.6
[95], 37.9-51.1 [96]
It is seen from Table 4.2 that local field correction function H [30] produces very
high value of bulk modulus, N [32] and S [36] produce results of bulk modulus
with very small deviation with the experimental findings, while some
underestimation of the present results has been seen for T [33], I [34] and F [35].
It is to be noted that all group III-nitride compounds have higher values of bulk
modulus. Similarly boron-based compounds have higher values of bulk modulus.
Present results of the boron-based semiconductor compounds having large
deviations from the experimental results. This is due to the fact that growth of
boron-based compounds in zinc-blende structure at normal conditions is very
difficult. Hence very little experimental work has been reported for different
properties of boron-based semiconductors. Some theoretical results are
reported but the method of computing bulk modulus is not uniform and in favor
of these theoretical results, no experimentally matching results are reported till
today. Therefore by considering experimental limitations we have take liberty to
predict theoretical results of bulk modulus of boron-based compounds.
Chapter 4 Ph D (Thesis) 121
Paresh Vyas Sardar Patel University January 2012
4.2.5 Bulk Modulus-Volume and Pressure Relations
The bulk modulus-volume relations for GaAs using six different local field
correction functions due to H [30], N [32], T [33], I [34], F [35] and S [36] are
shown in Figure 4.11.
Figure 4.11 Bulk modulus-volume relations for GaAs.
From Figure 4.11, it is seen that H [30] gives larger value of bulk modulus, while I
[34] and F [35] give lower value of bulk modulus at a given volume on
compression. The bulk modulus computed using N [32] and T [33] are same in
values but S [36] generates some higher values of bulk modulus than N [32],
T [33], I [34] and F [35]. As compression increases, the difference in the
computed value of bulk modulus from different screening functions also gets
increased. H [30] produces 62% higher value than I [34] at 60% compression. It
clearly indicates that the inclusion of the exchange and correlation effects
through local field correction function suppresses the bulk modulus at any given
volume.
0
300
600
900
1200
1500
0.4 0.5 0.6 0.7 0.8 0.9 1
B (G
Pa)
Ω/Ω0
GaAs
NHTIFS
Chapter 4 Ph D (Thesis) 122
Paresh Vyas Sardar Patel University January 2012
The bulk modulus-pressure relations for B-based, Al-based, Ga-based and In-
based compounds using Nagy’s local field correction function [32] are shown in
Figures 4.12 to 4.15 respectively.
Figure 4.12 Bulk modulus-pressure relations for boron based compounds.
Figure 4.13 Bulk modulus-pressure relations for aluminium based compounds.
0
200
400
600
800
1000
0 20 40 60 80 100
B (G
Pa)
P (GPa)
BNBPBAsBSb
0
150
300
450
600
0 20 40 60 80 100
B (G
Pa)
P (GPa)
AlNAlPAlAsAlSb
Chapter 4 Ph D (Thesis) 123
Paresh Vyas Sardar Patel University January 2012
Figure 4.14 Bulk modulus-pressure relations for gallium based compounds.
Figure 4.15 Bulk modulus-pressure relations for indium based compounds.
Following points are narrated from the bulk modulus- pressure relations
The curves of bulk modulus-pressure show same trend and linear in nature.
As the pressure increases the bulk modulus also increases.
All nitride compounds have higher values of bulk modulus compared to other
compounds of the same group.
At large pressure, the values of bulk modulus of phosphide, arsenide and
antimonide compounds are closer in comparison of small pressure.
0
150
300
450
600
0 20 40 60 80 100
B (G
Pa)
P (GPa)
GaNGaPGaAsGaSb
0
100
200
300
400
500
0 20 40 60 80 100
B (G
Pa)
P (GPa)
InNInPInAsInSb
Chapter 4 Ph D (Thesis) 124
Paresh Vyas Sardar Patel University January 2012
4.2.6 Pressure Derivative of Bulk Modulus
Table 4.3 Pressure derivative of bulk modulus of group III-V semiconductors.
Compound Present results using different screening functions f(q)
Expt. Others N [32] H [30] T [33] I [34] F [35] S [36]
BN 2.91 2.90 2.91 2.91 2.91 2.91 3.0- 4.1
[97]
3.32- 3.81 [96], 3.94,
3.6, 2.91–3.97 [97]
BP 2.94 3.06 2.95 2.92 2.92 2.98 4.3 [20]
3.07- 3.89 [96], 3.97,
4.77 [20], 3.07-4.3
[20]
BAs 2.98 3.12 2.99 2.94 2.95 3.03 - 3.49- 4.29 [96]
BSb 3.05 3.21 3.08 3.00 3.01 3.13 - 3.89- 5.28 [17],
4.13- 5.28 [96]
AlN 2.92 3.02 2.93 2.90 2.91 2.95 5.2, 5.7,
6.3 [43]
3.2- 4.06 [9],
3.80- 4.01 [43],
3.30- 4.60 [43],
3.54- 4.23 [96]
AlP 3.13 3.30 3.20 3.09 3.10 3.23 -
4.08- 4.31 [43],
4.04, 4.18, 4.40 [43],
3.70- 4.24 [96]
AlAs 3.20 3.36 3.28 3.16 3.17 3.31 5 [43]
4.14- 4.37 [43],
3.26, 4.18, 4.40 [43],
4.13- 4.47 [96],
AlSb 3.36 3.47 3.49 3.36 3.37 3.48 4.2, 4.6
[43]
4.28- 4.52 [17],
4.33- 4.49 [43], 4.01,
4.36, 4.40 [43],
3.96- 4.77 [96],
GaN 2.94 3.05 2.94 2.91 2.92 2.98 4.3 [6, 8],
3.2 [43]
3.57- 4.68 [6],
3.6- 4.29 [9],
3.93- 4.04 [43],
4.38- 4.88 [96]
GaP 3.13 3.30 3.20 3.09 3.10 3.23 4.5, 4.8
[43]
4.29- 5.30 [7],
4.08- 4.31 [43],
4.00- 4.88 [44],
4.34- 4.58 [96]
Chapter 4 Ph D (Thesis) 125
Paresh Vyas Sardar Patel University January 2012
Table 4.3 Pressure derivative of bulk modulus of group III-V semiconductors. (Cont.)
Compound Present results using different screening functions f(q)
Expt. Others N [32] H [30] T [33] I [34] F [35] S [36]
GaAs 3.19 3.35 3.28 3.16 3.17 3.30 4.49, 4.67
[43]
4.14- 4.36 [43],
4.30- 5.20 [96],
3.36- 5.20 [44]
GaSb 3.35 3.47 3.48 3.35 3.36 3.47 4.75, 4.78
[43]
4.02- 4.66 [17],
4.32- 4.49 [43],
3.83- 5.16 [44],
4.16- 4.80 [96]
InN 3.02 3.18 3.04 2.98 2.98 3.09 4.1 [43]
4.38- 4.64 [9],
3.98- 4.17 [43],
4.02- 4.06 [43],
4.42- 4.63 [96],
3.36- 4.48 [97]
InP 3.26 3.41 3.37 3.24 3.25 3.38 4.00- 4.67
[43]
4.22- 4.42 [43],
4.20- 4.93 [43],
4.58- 5.31 [96]
InAs 3.32 3.45 3.45 3.31 3.33 3.44 4.79, 6.80
[43]
4.28- 4.47 [43],
3.60- 4.72 [43],
4.57- 5.02 [96]
InSb 3.49 3.55 3.66 3.54 3.55 3.61 3.65- 4.90
[43]
4.43- 4.69 [17],
4.49- 4.66 [43],
4.61- 5.21 [43],
4.33- 5.04 [96]
The pressure derivative of bulk modulus at equilibrium for group III-V
semiconductor compounds are shown in Table 4.3. The present results of the
pressure derivative of bulk modulus are found much lower than the experimental
findings for all group III-V semiconductors. Good agreement between present
results with the experimental data is seen for GaN and InSb. We would like to
mention here that we have found constant difference nearly equal to one in the
present findings of pressure derivative of bulk modulus and those reported by
Jivani [43] for some screening functions.
Chapter 4 Ph D (Thesis) 126
Paresh Vyas Sardar Patel University January 2012
4.2.7 Elastic Properties
By following procedure shown in section 3.7, we have computed elastic
constants c11, c12 and c44 for group III-V semiconductor compounds. The
computed elastic constants c11, c12 and c44 with available experimental findings
and other theoretical results for sixteen group III-V semiconductor compounds
are given in Table 4.4.
Table 4.4 Elastic constants (in GPa) of group III-V semiconductors.
Comp
ound
c11 c12 c44
Present Expt. Others Present Expt. Others Present Expt. Others
BN 1246.0 798.4-820
[5] 605-1204 [5] 537.2
172-190
[5] 179-493 [5] 577.6
469-480
[5] 433-502 [5]
BP 400.0 315 311, 316.9 [20],
329-360 [20] 172.5 100
60.8, 104 [20],
78-155 [20] 184.9 160
114.3, 117 [20],
146-202 [20]
BAs 309.5 279 - 133.5 120 - 143.1 113 -
BSb 218.9 - - 94.4 - 101.1 - -
AlN 483.2 315, 410
[43]
374.0- 491.0
[43], 278 [47],
298 [48],
294- 360 [43]
208.3 149 [43],
150
158.6- 176.0
[43], 171 [47],
164 [48],
119- 168 [43]
223.8 125 [43],
185
116.3- 179.9
[43], 159 [47],
187 [48],
135- 237 [43]
AlP 160.1 124.9 [43],
150
130.7- 204.7
[43],
120.2- 136.5 [43]
69.0 54.7 [43],
64.2
49.4- 70.0 [43],
57.0- 108.0 [43] 74.3
58.9 [43],
61.1
64.4- 108.8
[43],
52.0- 70.0 [43]
AlAs 132.4 119.3,
120.2 [43]
109.6- 177.1 [43]
116- 129 [43] 57.1
57.5 [43],
57.2
39.6- 61.3 [43],
48.9- 98.6 [43] 61.5
56.6, 58.9
[43]
59.3- 99.0 [43],
51.4- 57.3 [43]
AlSb 88.7 89.4 [43],
87.69
76.3- 131.2 [43],
84.4- 98.9[43] 38.2
44.3 [43],
43.41
24.7- 47.6 [43],
31.7- 80.1 [43] 41.1
41.6 [43],
40.76
51.0- 80.2 [43],
37.4- 43.0 [43]
GaN 417.0 291 [43]
324.8- 435.5
[43], 307 [47],
282 [48],
285- 314 [43]
179.8 148 [43]
137.0- 153.9
[43], 185 [47],
159 [48],
108- 161 [43]
193.3 158 [43]
106.2- 168.3
[43], 176 [47],
142 [48],
149- 225 [43]
GaP 159.9 141.2 [43],
140.5
130.6- 204.5
[43],
129- 147 [43]
68.9 62.5 [43],
62.03
49.3- 69.9 [43],
57.8- 62.0 [43] 74.1
70.5 [43],
70.33,
64.4- 108.7
[43],
55.6- 79.0 [43]
GaAs 133.2
118.8 [38],
118, 119
[43]
117.1- 127.2
[38],
110.2- 178.0
[43],
116- 125 [43]
57.4
53.7 [38],
53.2, 53.8,
57.1 [43]
82.8- 96.1 [38],
39.9- 61.6 [43],
50.7- 56.6 [43]
61.6
59.4 [38],
59.2, 59.5
[43]
25.3- 28.5 [38],
59.4- 99.3 [43],
50.7- 62.0 [43]
Chapter 4 Ph D (Thesis) 127
Paresh Vyas Sardar Patel University January 2012
Table 4.4 Elastic constants (in GPa) of group III-V semiconductors. (Cont.)
Comp
ound
c11 c12 c44
Present Expt. Others Present Expt. Others Present Expt. Others
GaSb 89.8 88.4 [38],
88.3 [43]
79.0- 88.2 [38],
77.2- 132.5 [43],
86.8- 99.1 [43]
38.7
40.3 [38],
40.2 [43],
40.27
68.1- 74.8 [38],
25.1- 47.9 [43],
33.5- 44.1 [43]
41.5 43.2 [38]
9.7- 21.8 [38],
50.7- 80.8 [43],
36.5- 45.2 [43]
InN 251.3 192 [43]
200.7- 290.3
[43], 204 [47],
182 [48], 190-
297 [43]
108.4 73 [43]
81.5- 99.1 [43],
102 [47], 125
[48], 81- 135 [43]
116.6 93.5 [43]
80.0- 134.2
[43], 103 [47],
79 [48], 46- 105
[43]
InP 110.6 102.2 [43] 93.0- 154.7 [43],
87.6- 102.0 [43] 47.7
57.3, 57.6
[43]
32.1- 54.5 [43],
41.1- 83.4 [43] 51.2
44.2, 46.0
[43]
55.0- 90.3 [43],
37.5- 48.4 [43]
InAs 96.0 83.3 [38],
83.29 [43]
80.1- 89.5 [38],
81.9- 139.2 [43],
80.8- 89.0 [43]
41.4 45.3 [38],
45.26 [43]
62.9- 71.2 [38],
18.1- 40.7 [43],
35.2- 45.1 [43]
44.4 39.6 [38],
39.59 [43]
16.5- 19.1 [38],
45.7- 68.6 [43],
32.5- 41.9 [43]
InSb 67.5 66.7 [38],
67.2 [43]
56.0- 64.6 [38],
60.3- 107.2 [43],
59.1- 72.5 [43]
29.1 36.4 [38],
36.7 [43]
47.8- 53.9 [38],
18.1- 40.7 [43],
25.3- 37.4[43]
31.2 30.2 [38],
30.27 [43]
13.4- 16.6 [38],
45.7- 68.6 [43],
24.0- 33.5 [43]
From Table 4.4, it is seen that except nitride compounds, present results of c11,
c12 and c44 for all III-V compounds are found to be in agreement with the
experimental findings and other such theoretical findings, but some large
deviation is seen in nitride compounds. For elastic constant c11, we have
achieved excellent agreement between present results and experimental data
for AlSb, GaSb, InSb. For c12, we have found good matching for AlP, AlAs, AlSb,
GaP, GaAs, GaSb and InAs; and for c44, such a good agreement is seen for AlAs,
AlSb, GaP, GaAs, GaSb, InP, InAs and InSb between present results and
experimental findings. As large discrepancy is visualized between theoretical
findings of elastic constants, and present results are also in the range of other
such theoretical findings, justifies the validity of the present approach.
The Young’s modulus, shear modulus and Poisson’s ratio computed using
equations (3.35) to (3.37) for group III-V semiconductor compounds. The Young
modulus, shear modulus and Poisson’s ratio for group III-V semiconductors are
summarized in Table 4.5 along with available experimental and similar
theoretical findings.
Chapter 4 Ph D (Thesis) 128
Paresh Vyas Sardar Patel University January 2012
Table 4.5 Young modulus, shear modulus, Poisson’s ratio of group III-V
semiconductors.
Comp
ound
Y (GPa) c’ (GPa) σ
Present Expt. [43] Others [43] Present Expt. [38] Others [38] Present Expt. [43] Others
BN 922.12 - - 354.31 - - 0.301 - -
BP 296.06 - - 113.76 - - 0.301 - -
BAs 229.11 - - 88.03 - - 0.301 - -
BSb 162.00 - - 62.25 - - 0.301 - -
AlN 357.62 - 276.3-398.1 137.41 - - 0.301 - 0.264-0.303
AlP 118.48 - 103.5-169.0 45.52 - - 0.301 - 0.252-0.275
AlAs 82.17 - 88.2-145.6 37.64 - - 0.301 - 0.249-0.257
AlSb 65.63 - 63.6-105.8 25.22 - - 0.301 - 0.237-0.266
GaN 308.68 - 241.3-355.1 118.60 - - 0.301 - 0.261-0.301
GaP 118.33 103 103.4-168.9 45.47 - - 0.301 0.31 0.255-0.275
GaAs 98.61 86 88.7-146.3 37.89 32.5 15.5-20.7 0.301 0.31 0.250-0.268
GaSb 66.48 - 64.3-107.0 25.55 24.0 7.3-9.6 0.301 - 0.238-0.266
InN 186.04 - 152.8-239.9 71.48 - - 0.301 - 0.254-0.290
InP 81.88 61 76.1-126.3 31.46 - - 0.301 0.36 0.244-0.261
InAs 71.08 51 67.9-112.9 27.31 19.0 6.9-11.2 0.301 0.35 0.239-0.264
InSb 49.97 - 51.3-84.8 19.20 15.1 3.6-7.3 0.301 - 0.230-0.275
The present results of Young modulus and shear modulus for group III-V
compounds are found in good agreement with the theoretical results of Jivani
[43].
The present findings of wave speed of longitudinal waves in [100], [110] and
[111] directions for group III-V semiconductor compounds are summarized in
Table 4.6 and those of transverse waves are summarized in Table 4.7 along with
the experimental data and other such theoretical findings.
Chapter 4 Ph D (Thesis) 129
Paresh Vyas Sardar Patel University January 2012
Table 4.6 Wave speed (in 105 cm/s) of longitudinal acoustic waves in group III-V
semiconductors.
Comp
ound
vL[100] vL[110] vL[111]
Present Expt. [43] Others [43] Present Expt. [43] Others [43] Present Expt. [43] Others [43]
BN 18.90 - - 20.53 - - 21.04 - -
BP 11.74 - - 12.75 - - 13.06 - -
BAs 7.70 - - 8.36 - - 8.57 - -
BSb - - - - - - - - -
AlN 12.18 - 10.71-12.27 13.23 - 10.86-12.55 13.56 - 10.91-12.64
AlP 8.17 - 7.42-9.28 8.87 - 8.06-10.18 9.09 - 8.27-10.46
AlAs 5.93 - 5.42-6.89 6.45 - 6.00-7.65 6.61 - 6.17-7.89
AlSb 4.56 - 4.22-5.54 4.95 - 4.87-6.30 5.08 - 5.06-6.53
GaN 8.29 - 7.30-8.45 9.00 - 7.45-8.71 9.23 - 7.50-8.80
GaP 6.22 5.83 5.63-7.04 6.75 6.43 6.12-7.72 6.92 6.63 6.27-7.93
GaAs 5.01 4.73 4.56-5.79 5.43 5.24 5.04-6.42 5.57 5.4 5.19-6.62
GaSb 4.00 - 3.73-4.88 4.34 - 4.29-5.55 4.45 - 4.46-5.75
InN 6.09 - 5.37-6.48 6.61 - 5.65-6.89 6.78 - 5.74-7.03
InP 4.80 4.58 4.41-5.68 5.21 5.08 4.96-6.38 5.34 5.23 5.13-6.60
InAs 4.12 3.83 3.78-4.93 4.47 4.41 4.32-5.58 4.58 4.28 4.49-5.78
InSb 3.42 - 3.23-4.31 3.71 - 3.84-4.97 3.80 - 4.03-5.17
Chapter 4 Ph D (Thesis) 130
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Table 4.7 Wave speed (in 105 cm/s) of transverse acoustic waves in group III-V
semiconductors.
Comp
ound
vT[100] = vT1[110] vT2[110] vT[111]
Present Expt. [43] Others [43] Present Expt. [43] Others [43] Present Expt. [43] Others [43]
BN 12.87 - - 10.08 - - 11.09 - -
BP 7.98 - - 6.26 - - 6.89 - -
BAs 5.24 - - 4.11 - - 4.52 - -
BSb - - - - - - - - -
AlN 8.29 - 5.97-7.43 6.50 - 5.70-6.95 7.15 - 6.74-8.31
AlP 5.57 - 5.21-6.77 4.36 - 4.13-5.32 4.79 - 5.43-7.03
AlAs 4.04 - 3.99-5.15 3.16 - 3.06-3.94 3.48 - 4.10-5.30
AlSb 3.11 - 3.44-4.33 2.43 - 2.44-3.13 2.68 - 3.44-4.36
GaN 5.64 - 4.17-5.25 4.42 - 3.90-4.80 4.86 - 4.67-5.81
GaP 4.23 4.12 3.95-5.13 3.32 3.08 3.14-4.04 3.65 3.46 4.12-5.33
GaAs 3.41 3.35 3.34-4.33 2.67 3.35 2.57-3.31 2.94 2.8 3.44-4.45
GaSb 2.72 - 3.02-3.81 2.13 - 2.15-2.75 2.34 - 3.03-3.84
InN 4.15 - 3.40-4.40 3.25 - 2.93-3.72 3.57 - 3.66-4.70
InP 3.26 3.08 3.39-4.34 2.56 2.16 2.51-3.23 2.81 2.51 3.44-4.42
InAs 2.80 2.64 3.01-3.82 2.20 2.64 2.17-2.79 2.41 2.13 3.03-3.87
InSb 2.32 - 2.81-3.45 1.82 - 1.89-2.40 2.00 - 2.77-3.42
The present results of wave speed are found in good agreement with the
available experimental data in comparison of other such theoretical findings [43].
It confirms the validity of the present approach. Due to limited experimental
results and other such theoretical results of wave velocities are available; we
hope that the present results of wave velocities for group III-V compounds would
be useful to refer for theoretical and experimental study.
Chapter 4 Ph D (Thesis) 131
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4.2.8 Energy Band Gap at point X on the Jones-Zone Face Eg(X)
Table 4.8 Energy band gap at point X at Jones-zone face Eg(X) (eV) of group III-V
semiconductors.
Comp
ound
Present results using different screening functions
f(q) Expt. Others
Eg(X)0
[37] N [32] H [30] T [33] I [34] F [35] S [36]
BN 5.40 3.59 5.35 5.71 5.70 4.55 6.1- 6.4 5.37, 4.41 [96] -
BP 4.53 3.03 4.52 4.86 4.86 3.99 - 1.96, 1.35 [96] -
BAs 4.30 2.88 4.30 4.65 4.64 3.81 - 2.01, 1.43 [96] -
BSb 3.99 2.68 4.01 4.34 4.34 3.57 - 1.29, 0.71 [96] -
AlN 4.69 3.13 4.67 5.02 5.01 4.11 5.34 [96] 4.13, 3.28 [96], 3.16 [105] -
AlP 3.71 2.50 3.73 4.07 4.06 3.33 2.52 [96] 2.49, 1.54 [96] -
AlAs 3.55 2.39 3.57 3.90 3.89 3.19 2.24 [96], 2.16 [108] 2.33, 1.43 [96], 2.07 [108] -
AlSb 3.19 2.18 3.23 3.54 3.54 2.89 4.2 [37], 1.69 [96],
1.61 [108]
4.96 [37], 1.87, 1.29 [96],
1.61 [108] 0.54
GaN 4.56 3.05 4.55 4.90 4.89 4.01 4.52 [96] 4.15, 3.33 [96], 3.2, 4.57,
4.7 [98], 3.2 [105] -
GaP 3.71 2.50 3.73 4.07 4.06 3.33 5.1 [37], 2.35 [96]
5.55 [37], 5.46 [39],
5.41 [39], 4.99 [40],
2.55, 1.68 [96]
0.65,
0.82
GaAs 3.55 2.40 3.57 3.90 3.90 3.20 4.6 [37], 1.98 [96],
1.90 [108]
4.89 [37], 4.91 [39],
4.82 [39], 4.79 [40],
2.32, 1.49 [96], 1.90 [108]
0.14,
0.27
GaSb 3.20 2.19 3.24 3.55 3.55 2.90 4.1 [37], 1.14 [96],
1.05 [108]
5.22 [37], 4.58 [39],
4.79 [39], 4.37 [40],
1.46, 0.94 [96], 1.03 [108]
0.0,
0.41
InN 4.12 2.76 4.13 4.47 4.46 3.67 - 3.45, 2.84 [96], 2.51, 2.8,
4.60 [98], 1.56 [105] -
InP 3.39 2.30 3.41 3.74 3.73 3.06 4.8 [37], 2.38 [96],
2.19 [108]
5.17 [37], 5.01 [39], 2.68,
1.82 [96], 2.19 [108] 0.27
InAs 3.26 2.22 3.29 3.61 3.61 2.95 4.5, 1.43 [96],
1.37 [108]
4.83 [39], 4.91 [39], 2.36,
1.65 [96], 1.37 [108] 0.0
InSb 2.96 2.04 3.00 3.30 3.30 2.70 4.0, 0.63 [96],
0.83 [108]
4.56 [39], 4.50 [39], 1.96, 1.35
[96], 1.0 [108] 0.0
Chapter 4 Ph D (Thesis) 132
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The energy band gap at point X on the Jones-zone face Eg(X) computed in the
present investigations by using equation (3.39) for group III-V semiconductor
compounds are shown in Table 4.8. Here we have incorporated six screening
functions [30, 32-36] and the results are compared with the experimental
findings along with other such theoretical findings. It is seen that H [30]
generates lower values and I [34] gives higher values of energy band gap Eg(X) at
point X on the Jones-zone face. It is seen that the computed band gap Eg(X) using
H [30] are close to the experimental findings and other such results. Some large
underestimation is seen in the computed values of energy band gap of GaAs,
GaSb, InAs and InSb.
4.2.9 Energy Band Gap-Volume and Pressure Relations
The variations of energy band gap at point X on the Jones-zone face Eg(X) with
volume using six different screening functions for GaAs are shown in the Figure
4.16.
Figure 4.16 Energy band gap Eg(X)-volume relations for GaAs.
It is seen from Figure 4.16 that I [34] and F [35] give higher values of energy band
gap Eg(X) and H [30] gives lower value of Eg(X), while N [32], T [33] and S [36]
generate energy band gap Eg(X) in the intermediate range for any volume in the
2
2.5
3
3.5
4
4.5
0.4 0.6 0.8 1 1.2 1.4 1.6
E g(X
) (eV
)
Ω/Ω0
GaAs
NHTIFS
Chapter 4 Ph D (Thesis) 133
Paresh Vyas Sardar Patel University January 2012
compression and expansion of volume upto 60%. From Figure 4.16, it is seen that
Eg(X) computed by H [30], T [33], I [34], F [35] and S [36] continuously increases on
compression of volume upto 60% from its equilibrium volume. But Eg(X)
computed by N [32] decreases upto 10% compression (0.9 times of its
equilibrium volume) thereafter it increases upto 60% compression. On expansion
it is seen that Eg(X) computed by N [32] continuously increases upto 60%
expansion (1.6 times of its equilibrium volume), while Eg(X) computed by other
screening functions decreases upto 60% expansion. Out of all six screening
functions, only N [32] gives minimum value of Eg(X) in the total volume range, i.e.
from 60% compression to 60 % expansion for GaAs. The large change in Eg(X) of
1.45 eV is seen for GaAs from 60% compression to 60 % expansion for H [30]. The
change in the energy band gap seen 0.30 eV for N [32], 0.33 eV for I [34], 0.35 eV
for F [35], 0.48 eV for S [36] and 0.59 eV for T [33] from 60% compression to 60 %
expansion. As the energy band gap generates by N [32] has totally different
characteristics, and it is first time introduced in such type of computation in the
present work, we have shown the variations of Eg(X) with different pressure
computed by using only N [32]. The energy band gap-pressure relations for B-
based, Al-based, Ga-based and In-based compounds using Nagy’s local field
correction function [32] are shown in Figures 4.17 to 4.20 respectively.
Figure 4.17 Energy band gap Eg(X)-pressure relations for B-based compounds.
3.9
4.3
4.7
5.1
5.5
0 20 40 60 80 100
E g(X
) (eV
)
P (GPa)
BNBPBAsBSb
Chapter 4 Ph D (Thesis) 134
Paresh Vyas Sardar Patel University January 2012
Figure 4.18 Energy band gap Eg(X)-pressure relations for Al-based compounds.
Figure 4.19 Energy band gap Eg(X)-pressure relations for Ga-based compounds.
3
3.4
3.8
4.2
4.6
5
0 20 40 60 80 100
E g(X
) (eV
)
P (GPa)
AlNAlPAlAsAlSb
3.1
3.4
3.7
4
4.3
4.6
0 20 40 60 80 100
E g(X
) (eV
)
P (GPa)
GaNGaPGaAsGaSb
Chapter 4 Ph D (Thesis) 135
Paresh Vyas Sardar Patel University January 2012
Figure 4.20 Energy band gap Eg(X)-pressure relations for In-based compounds.
From Figures 4.17 to 4.20 following points are remarkable.
For BN, Eg(X) is continuously decreases with the pressure, while for BP, BAs
and BSb; Eg(X) decreases upto pressure 50 GPa and thereafter increases with
pressure upto 100 GPa.
For AlN Eg(X) decreases upto 150 GPa pressure (not shown in the graph) after
that Eg(X) continuously increases. But for AlP, AlAs and AlSb Eg(X) decreases
upto 10 GPa pressure and thereafter increases with pressure upto 100 GPa.
For GaN Eg(X) decreases upto 66 GPa pressure after that Eg(X) continuously
increases. But for GaP, GaAs and GaSb, Eg(X) decreases upto 10 GPa pressure
and thereafter increases with pressure upto 100 GPa.
For InN Eg(X) decreases upto 16 GPa pressure after that Eg(X) continuously
increases. But for InP and InAs Eg(X) decreases upto 6 GPa pressure and for
InSb Eg(X) decreases upto 1 GPa pressure thereafter increases with pressure
upto 100 GPa.
In nitride compounds Eg(X) decreases upto large pressure in comparison of
phosphide, arsenide and antimonide compounds.
The decrement in Eg(X) also decreases from B → Al → Ga → In.
2.8
3.1
3.4
3.7
4
4.3
0 20 40 60 80 100
E g(X
) (eV
)
P (GPa)
InNInPInAsInSb
Chapter 4 Ph D (Thesis) 136
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The sensitivity and slow variation in the band gap with pressure suggest that
nitride compounds are applicable as sensors and other switching circuits in
the optoelectronics which are used in wide operating range of pressure.
4.2.10 Optical Properties
We have calculated refractive index for group III-V semiconductors following
different approaches [109-129] discussed in the previous chapter. The computed
refractive index for group III-V semiconductors using six local field correction
functions [30, 32-36] are shown in Tables 4.9 to 4.12 for boron based, aluminium
based, gallium based and indium based semiconductors along with experimental
results and other such theoretical results.
As the results of refractive index computed by Gupta and Ravindra [114] relation
are very low and for some materials they become negative and due to
inconsistent results of refractive index for group III-V semiconductors, we have
not shown them in Table 4.9 to 4.12 for comparison.
The fruitful outcome from the present results shown in Tables 4.9 to 4.12 is
described below.
For BN, refractive index computed by Ravindra and Srivastava [112] using
N [32], T [33], I [34], F [35]; and refractive index computed by S [36] using
relations [109], [116], [119], [128] strongly agree with the experimental
results [131].
For BP and BAs, in all approaches the results of Reddy [120] with H [30]
are closer to other such theoretical results [135].
For BSb, a good agreement with other theoretical findings [135] is seen
for H [30]. Also good agreement is seen for results computed from the
relation given by Reddy [120] using all screening functions.
For Al-based semiconductors, good agreement with the experimental
results is seen. Except for AlN, the results computed using Reddy’s
Chapter 4 Ph D (Thesis) 137
Paresh Vyas Sardar Patel University January 2012
relation [120] with H [30] are consistently matching with experimental
and other theoretical findings.
For GaN, considerable matching is obtained for the computed values of
refractive index using relations given in [109], [112], [116], [120], [128]
with other theoretical and experimental findings.
For GaP, good matching with the experimental findings is seen for Reddy
[120] with H [30].
For GaAs and GaSb, refractive index computed by Reddy [120] along with
H[30] are closer to the experimental findings compared to other findings.
But we have found very good matching between refractive index
computed from bulk modulus-plasmon energy relation [99], which is
shown in the next section.
For InN, H [30] gives good results compared to other results and give
better agreement with the experimental findings.
For InP, we have obtained good matching for the values computed using
relation given by Reddy [120] combined with H [30].
For InAs and InSb, the results of refractive index computed from bulk
modulus-plasmon energy relations are extremely good.
Compared to large discrepancy, which is observed between the values of
refractive index computed by different theoretical methods for group III-V
semiconductors, the present results are found in close agreement with
available experimental data.
The refractive index computations using different local field correction
functions have been first time reported in this thesis. We hope that the
present results are useful to the researchers working in the same field.
Chapter 4 Ph D (Thesis) 138
Paresh Vyas Sardar Patel University January 2012
Table 4.9 Refractive Index for boron-based semiconductors.
Comp ounds
Using formula of Ref.
Present results using screening functions f(q) Expt Others
N [32] H [30] T [33] I [34] F [35] S [36]
BN
[109] 2.05 2.27 2.05 2.02 2.02 2.14
2.12 [128], 2.10 [131] 1.23-2.45 [128]
[112] 2.11 2.34 2.12 2.09 2.09 2.21
[113] 0.74 1.86 0.77 0.54 0.55 1.26
[115] 1.84 2.19 1.85 1.80 1.80 1.98
[116] 2.00 2.26 2.00 1.96 1.96 2.10
[119] 1.90 2.31 1.91 1.85 1.85 2.07
[120] 2.35 2.63 2.36 2.32 2.32 2.46
[128] 1.95 2.23 1.96 1.92 1.92 2.07
[99] 0.05 -0.04 0.08 0.10 0.10 0.09
BP
[109] 2.14 2.37 2.14 2.10 2.10 2.21
3.1, 3.25 [135]
[112] 2.21 2.44 2.21 2.17 2.17 2.28
[113] 1.28 2.21 1.28 1.07 1.07 1.61
[115] 1.99 2.34 1.99 1.93 1.93 2.09
[116] 2.11 2.36 2.11 2.06 2.06 2.19
[119] 2.08 2.48 2.08 2.01 2.01 2.21
[120] 2.47 2.76 2.47 2.42 2.42 2.55
[128] 2.07 2.36 2.07 2.02 2.02 2.16
[99] 1.57 1.37 1.63 1.66 1.67 1.61
BAs
[109] 2.17 2.40 2.17 2.13 2.13 2.23
3.35 [135]
[112] 2.24 2.47 2.24 2.20 2.20 2.31
[113] 1.42 2.30 1.42 1.20 1.21 1.72
[115] 2.03 2.39 2.03 1.96 1.97 2.13
[116] 2.14 2.40 2.14 2.09 2.09 2.22
[119] 2.13 2.53 2.13 2.05 2.06 2.25
[120] 2.50 2.80 2.50 2.45 2.45 2.59
[128] 2.10 2.39 2.10 2.05 2.05 2.19
[99] 1.92 1.67 1.98 2.03 2.03 1.95
BSb
[109] 2.21 2.44 2.21 2.16 2.16 2.27
2.52 [135]
[112] 2.28 2.52 2.28 2.23 2.23 2.35
[113] 1.61 2.42 1.60 1.39 1.39 1.87
[115] 2.09 2.45 2.09 2.02 2.02 2.19
[116] 2.19 2.44 2.18 2.13 2.13 2.26
[119] 2.21 2.60 2.20 2.12 2.12 2.32
[120] 2.55 2.86 2.55 2.49 2.49 2.63
[128] 2.16 2.45 2.15 2.10 2.10 2.23
[99] 2.39 2.06 2.46 2.53 2.53 2.41
Chapter 4 Ph D (Thesis) 139
Paresh Vyas Sardar Patel University January 2012
Table 4.10 Refractive Index for aluminium-based semiconductors.
Comp ounds
Using formula of Ref.
Present results using screening functions f(q) Expt Others
N [32] H [30] T [33] I [34] F [35] S [36]
AlN
[109] 2.12 2.35 2.12 2.09 2.09 2.19
2.20 [123],
2.16 [128],
[131]
2.20 [123], 1.73-
2.25 [123], 1.67
[125], 1.73-2.27
[128], 2.11, 2.14
[129]
[112] 2.19 2.42 2.19 2.15 2.15 2.26
[113] 1.18 2.14 1.19 0.97 0.98 1.54
[115] 1.96 2.31 1.96 1.90 1.90 2.07
[116] 2.08 2.34 2.09 2.04 2.04 2.17
[119] 2.04 2.45 2.05 1.98 1.98 2.18
[120] 2.44 2.73 2.45 2.40 2.40 2.53
[128] 2.05 2.33 2.05 2.00 2.00 2.13
[99] 1.32 1.14 1.37 1.40 1.40 1.35
AlP
[109] 2.25 2.48 2.25 2.20 2.20 2.31
2.75 [123],
[131]
2.72 [123], 2.22-
2.49 [123], 2.58
[125], 2.22-2.77
[128], 2.88, 2.85
[129]
[112] 2.32 2.56 2.32 2.27 2.27 2.39
[113] 1.78 2.53 1.77 1.56 1.57 2.02
[115] 2.16 2.51 2.15 2.08 2.08 2.25
[116] 2.23 2.49 2.23 2.17 2.18 2.30
[119] 2.28 2.67 2.27 2.19 2.19 2.39
[120] 2.60 2.91 2.60 2.54 2.54 2.68
[128] 2.21 2.51 2.20 2.14 2.14 2.28
[99] 2.82 2.40 2.89 2.98 2.98 2.81
AlAs
[109] 2.27 2.51 2.27 2.22 2.22 2.34
2.92 [123],
2.87 [128],
3.00 [131]
2.88 [123], 2.74-
2.86 [123], 2.83
[125], 2.58-3.04
[128], 3.06, 3.10
[129]
[112] 2.35 2.59 2.35 2.29 2.30 2.41
[113] 1.88 2.60 1.87 1.67 1.67 2.11
[115] 2.20 2.55 2.19 2.11 2.12 2.29
[116] 2.26 2.52 2.26 2.20 2.20 2.33
[119] 2.32 2.72 2.32 2.23 2.23 2.43
[120] 2.64 2.95 2.63 2.57 2.57 2.72
[128] 2.24 2.54 2.23 2.17 2.17 2.32
[99] 3.07 2.60 3.14 3.25 3.25 3.05
AlSb
[109] 2.34 2.57 2.33 2.28 2.28 2.39
3.19 [123],
[131]
3.19 [123], 3.09-
3.18 [123], 3.16
[125], 2.60-3.22
[128], 3.40, 3.51
[129]
[112] 2.41 2.65 2.40 2.35 2.35 2.47
[113] 2.11 2.73 2.08 1.89 1.89 2.29
[115] 2.29 2.63 2.28 2.20 2.20 2.38
[116] 2.33 2.57 2.32 2.26 2.26 2.40
[119] 2.43 2.81 2.42 2.33 2.33 2.53
[120] 2.72 3.04 2.71 2.64 2.64 2.79
[128] 2.32 2.62 2.31 2.24 2.24 2.39
[99] 3.59 3.00 3.64 3.82 3.82 3.52
Chapter 4 Ph D (Thesis) 140
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Table 4.11 Refractive Index for gallium-based semiconductors.
Comp ounds
Using formula of Ref.
Present results using screening functions f(q) Expt Others
N [32] H [30] T [33] I [34] F [35] S [36]
GaN
[109] 2.14 2.36 2.14 2.10 2.10 2.21
2.24
[123],
2.40
[128],
[131]
2.21 [123], 2.07-
2.41 [123], (-
2.29)-2.41 [121],
2.10-2.41 [136],
1.69 [125], 1.91-
2.65 [128], 2.23,
2.39 [129]
[112] 2.21 2.44 2.21 2.17 2.17 2.28
[113] 1.26 2.19 1.26 1.05 1.05 1.60
[115] 1.98 2.33 1.98 1.92 1.92 2.09
[116] 2.10 2.36 2.10 2.06 2.06 2.18
[119] 2.07 2.47 2.07 2.00 2.00 2.20
[120] 2.46 2.75 2.46 2.41 2.42 2.55
[128] 2.06 2.35 2.07 2.02 2.02 2.15
[99] 1.52 1.32 1.57 1.61 1.61 1.55
GaP
[109] 2.25 2.48 2.25 2.20 2.20 2.31
2.90
[123],
[131],
3.2, 3.35
[128]
2.96 [123], 2.70-
2.82 [123], 2.83
[125], 2.55-3.01
[128], 3.16, 3.23
[129]
[112] 2.32 2.56 2.32 2.27 2.27 2.39
[113] 1.78 2.53 1.77 1.56 1.57 2.02
[115] 2.16 2.51 2.15 2.08 2.08 2.25
[116] 2.23 2.49 2.23 2.17 2.18 2.30
[119] 2.28 2.67 2.27 2.19 2.19 2.39
[120] 2.60 2.91 2.60 2.54 2.54 2.68
[128] 2.21 2.51 2.20 2.14 2.14 2.28
[99] 2.82 2.40 2.89 2.98 2.98 2.81
GaAs
[109] 2.27 2.51 2.27 2.22 2.22 2.33
3.30
[123],
[131],
4.02
[128]
3.27 [123], 3.24-
3.36 [123], 3.29
[125], 2.86-3.47
[128], 3.5, 3.85
[129]
[112] 2.35 2.59 2.35 2.29 2.29 2.41
[113] 1.88 2.60 1.87 1.67 1.67 2.10
[115] 2.20 2.55 2.19 2.11 2.11 2.29
[116] 2.26 2.51 2.26 2.20 2.20 2.33
[119] 2.32 2.71 2.32 2.23 2.23 2.43
[120] 2.64 2.95 2.63 2.57 2.57 2.71
[128] 2.24 2.54 2.23 2.17 2.17 2.31
[99] 3.06 2.59 3.13 3.24 3.24 3.04
GaSb
[109] 2.33 2.57 2.33 2.27 2.27 2.39
3.75
[123],
3.82
[128],
3.79
[131]
3.86 [123], 3.58-
3.84 [123], 4.08
[125], 3.29-4.31
[128], 4.04, 4.74
[129]
[112] 2.41 2.65 2.40 2.35 2.35 2.47
[113] 2.10 2.73 2.08 1.88 1.88 2.29
[115] 2.29 2.63 2.28 2.20 2.20 2.38
[116] 2.33 2.57 2.32 2.26 2.26 2.39
[119] 2.43 2.81 2.41 2.32 2.32 2.53
[120] 2.71 3.03 2.71 2.64 2.64 2.79
[128] 2.31 2.62 2.30 2.24 2.24 2.39
[99] 3.57 2.98 3.63 3.80 3.80 3.51
Chapter 4 Ph D (Thesis) 141
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Table 4.12 Refractive Index for indium-based semiconductors.
Comp ounds
Using formula of Ref.
Present results using screening functions f(q) Expt Others
N [32] H [30] T [33] I [34] F [35] S [36]
InN
[109] 2.19 2.42 2.19 2.15 2.15 2.26
2.35 [123]
2.27 [123], 2.84-
2.94 [123], 1.78
[125], 3.47, 3.79
[129]
[112] 2.26 2.50 2.26 2.22 2.22 2.33
[113] 1.53 2.37 1.52 1.31 1.32 1.81
[115] 2.07 2.42 2.06 2.00 2.00 2.17
[116] 2.17 2.42 2.16 2.11 2.12 2.24
[119] 2.17 2.57 2.17 2.09 2.09 2.29
[120] 2.53 2.83 2.53 2.47 2.48 2.61
[128] 2.13 2.43 2.13 2.08 2.08 2.21
[99] 2.21 1.91 2.27 2.33 2.33 2.23
InP
[109] 2.30 2.54 2.30 2.24 2.25 2.36
3.10
[123],
[131]
3.16 [123], 3.30-
3.42 [123], 3.12
[125], 3.36, 3.40
[129]
[112] 2.38 2.62 2.37 2.32 2.32 2.44
[113] 1.98 2.66 1.97 1.77 1.77 2.19
[115] 2.24 2.59 2.23 2.15 2.15 2.33
[116] 2.29 2.54 2.29 2.23 2.23 2.36
[119] 2.37 2.76 2.36 2.27 2.27 2.47
[120] 2.67 2.99 2.67 2.60 2.60 2.75
[128] 2.27 2.57 2.27 2.20 2.20 2.35
[99] 3.30 2.78 3.37 3.51 3.51 3.26
InAs
[109] 2.32 2.56 2.32 2.26 2.26 2.38
3.51
[123], 4.1
[128],
3.50 [131]
3.53 [123], 3.86-
4.61 [123], 3.65
[125], 3.75-5.37
[128], 4.17, 4.51
[129]
[112] 2.40 2.64 2.39 2.34 2.34 2.46
[113] 2.06 2.71 2.04 1.85 1.85 2.26
[115] 2.27 2.62 2.27 2.18 2.18 2.36
[116] 2.32 2.56 2.31 2.25 2.25 2.38
[119] 2.41 2.79 2.40 2.31 2.31 2.51
[120] 2.70 3.02 2.69 2.62 2.62 2.78
[128] 2.30 2.60 2.29 2.23 2.23 2.38
[99] 3.48 2.92 3.55 3.71 3.71 3.43
InSb
[109] 2.38 2.61 2.37 2.32 2.32 2.44
3.96
[123],
5.13
[128],
3.95 [131]
3.93 [123], 3.97-
5.30 [123], 3.96,
4.17 [125], 3.92-
6.19 [128], 4.48,
5.06 [129]
[112] 2.46 2.70 2.45 2.39 2.39 2.51
[113] 2.25 2.82 2.22 2.04 2.04 2.41
[115] 2.36 2.69 2.35 2.26 2.26 2.44
[116] 2.38 2.61 2.37 2.31 2.31 2.44
[119] 2.50 2.88 2.49 2.40 2.40 2.60
[120] 2.78 3.10 2.76 2.69 2.69 2.85
[128] 2.37 2.68 2.36 2.29 2.29 2.44
[99] 3.92 3.26 3.95 4.19 4.18 3.83
Chapter 4 Ph D (Thesis) 142
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We have obtained a large number of data for refractive index computied by
different relations proposed by several authors [109-129] on strong physical
ground. Out of all results we have used results of refractive index computed
using Reddy and Ahammed relation [120] for further computation. As Kumar and
Singh [128] have used lower values of band gap for InSb and InAs in
computation, which generates imaginary number therefore they have not
quoted any results of refractive index for InAs and InSb using their relation [120].
As we have used relation given by Reddy and Ahammed [120] in the further
study of optical properties, we have used results of refractive index computed
from bulk modulus-plasmon energy relation [99] for InAs and InSb along with
GaP, GaAs and GaSb.
Certain optical properties, which can be derived from refractive index, are
described as follows.
The high-frequency dielectric constant [130] is calculated using relation given by
2ε n=∞ (4.1)
The computed high-frequency dielectric constants for group III-V semiconductors
using screening functions of N [32] along with H [30], T [33], I [34], F [35] and S
[36] are shown in Table 4.13.
It is observed from Table 4.13 that the present results of high frequency
dielectric constant are found in good agreement with the experimental results
for BN, BP, AlP, AlAs, GaP, GaAs, GaSb, InAs and InSb. All screening functions [30,
32-36] produce results of high frequency dielectric constants for group III-V
semiconductors with acceptable deviations. Schowalter et al. [129] used LDA and
GGA as the exchange and correlation part of the potential and a large
discrepancy between the results obtained by the both approaches [129] is
observed. We have found large difference between present results and those of
Schowalter et al. [129].
Chapter 4 Ph D (Thesis) 143
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Table 4.13 The high-frequency dielectric constants for group III-V semiconductors.
Compound Present results using screening functions f(q)
Expt [42] Others [129] N [32] H [30] T [33] I [34] F [35] S [36]
BN 5.53 6.91 5.56 5.37 5.37 6.07 4.5, 7.1 -
BP 6.08 7.60 6.09 5.85 5.85 6.52 7.8 -
BAs 6.26 7.83 6.26 5.99 6.00 6.69 - -
BSb 6.52 8.16 6.50 6.22 6.22 6.93 - -
AlN 5.97 7.46 5.98 5.75 5.76 6.41 4.71, 4.93 4.47, 4.59
AlP 6.79 8.49 6.77 6.45 6.46 7.21 7.5 8.31, 8.14
AlAs 6.95 8.72 6.93 6.60 6.61 7.38 8.2 9.38, 9.63
AlSb 7.38 9.21 7.33 6.96 6.96 7.81 10.24 11.62, 12.29
GaN 6.06 7.57 6.07 5.83 5.83 6.50 4.86 4.97, 5.69
GaP 7.94 5.77 8.35 8.88 8.89 7.90 9.11 10.01, 10.44
GaAs 9.36 6.72 9.81 10.52 10.52 9.23 10.86 12.25, 14.83
GaSb 12.74 8.91 13.15 14.45 14.43 12.31 14.5 16.36, 22.47
InN 6.40 8.02 6.40 6.12 6.13 6.83 8.4 12.04, 14.37
InP 7.14 8.92 7.11 6.75 6.77 7.56 10.9 11.32, 11.54
InAs 12.14 8.53 12.57 13.75 13.73 11.78 12.37 17.39, 20.33
InSb 15.36 10.61 15.62 17.54 17.47 14.64 15.68 20.07, 25.57
For plasmon energy, Reddy et al. [131] proposed a relation between refractive
index and the plasmon energy as,
( )bnexpmp ⋅=ω (4.2)
The plasmon energy computed using equation (4.2) and screening functions due
to H [30], N [32], T [33], I [34], F [35] and S [36] for group III-V semiconductors
are shown in Table 4.14 with available experimental results and other such
theoretical results.
Chapter 4 Ph D (Thesis) 144
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Table 4.14 The plasmon energy (eV) for group III-V semiconductors.
Comp- ound
Present results using screening functions f(q) Expt Others
N [32] H [30] T [33] I [34] F [35] S [36]
BN 20.82 18.87 20.77 21.07 21.07 20.01 24.53 [131] 22.75 [131]
BP 19.99 18.03 19.98 20.32 20.32 19.38 - -
BAs 19.74 17.77 19.74 20.11 20.10 19.16 - -
BSb 19.38 17.41 19.41 19.79 19.79 18.84 - -
AlN 20.15 18.19 20.13 20.47 20.47 19.52 22.97 [131] 22.28 [131]
AlP 19.03 17.05 19.05 19.48 19.47 18.50 16.65 [131] 18.07 [131]
AlAs 18.81 16.82 18.84 19.27 19.26 18.29 15.75 [131] 16.54 [131]
AlSb 18.29 16.34 18.35 18.80 18.80 17.79 13.72 [131] 15.46 [131]
GaN 20.02 18.06 20.01 20.36 20.35 19.41 21.98 [131] 20.46 [131]
GaP 17.65 20.45 17.20 16.66 16.65 17.69 16.50 [131] 17.14 [131]
GaAs 16.19 19.12 15.79 15.18 15.18 16.32 15.35 [131] 14.87 [131]
GaSb 13.52 16.63 13.24 12.45 12.46 13.81 13.38 [131] 12.50 [131]
InN 19.54 17.56 19.55 19.93 19.92 18.98 - -
InP 18.59 16.62 18.62 19.07 19.05 18.08 14.76 [131] 15.96 [131]
InAs 13.93 17.02 13.63 12.87 12.88 14.19 14.07 [131] 13.85 [131]
InSb 11.94 15.10 11.80 10.86 10.89 12.34 12.73 [131] 11.81 [131]
It is seen from Table 4.14 that present results of plasmon energy for group III-V
semiconductor compounds are satisfactorily agree with the experimental results
and theoretical results. Some underestimation is seen for BN and AlN, while
some overestimation is found for AlSb. H [30] gives lower but I [34] and F [35]
generate higher values of plasmon energy except GaP, GaAs, GaSb, InAs and
InSb.
Singh et al. [99] derived an empirical relation between bulk modulus and
Plasmon energy as
( ) 'ApAB ω= (4.3)
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Where A = 0.275 for zinc-blende crystals and 0.115 for diamond crystals; A΄ = 2
for zinc-blende and 2.4 for diamond crystals respectively as per Singh et al. [99].
Kumar [138] has proposed a relationship between bond length and Plasmon
energy. Based on it, Reddy et al. [122] has proposed a relation for estimation of
bond length d (Å) using refractive index of the material given by
( ) ( )nKexpKÅd 21= (4.4)
Here K1 = 1.159 and 1.944; K2 = 0.2364 and 0.1186 for group III-V and II-VI
respectively.
The bond length computed using six local field correction functions [30, 32-36]
for group III-V semiconductors are shown in Table 4.15.
Table 4.15 The bond length (Å) for group III-V semiconductors.
Comp- ound
Present results using screening functions f(q) Expt Others
N [32] H [30] T [33] I [34] F [35] S [36]
BN 2.02 2.16 2.02 2.00 2.00 2.07 1.56 [131] 1.91 [131]
BP 2.08 2.22 2.08 2.05 2.05 2.12 - -
BAs 2.09 2.25 2.09 2.07 2.07 2.14 - -
BSb 2.12 2.28 2.12 2.09 2.09 2.16 - -
AlN 2.06 2.21 2.07 2.04 2.04 2.11 1.86 [131] 1.93 [131]
AlP 2.15 2.31 2.14 2.11 2.11 2.19 2.35 [131] 2.22 [131]
AlAs 2.16 2.33 2.16 2.13 2.13 2.20 2.43 [131] 2.36 [131]
AlSb 2.20 2.38 2.20 2.16 2.16 2.24 2.66 [131] 2.47 [131]
GaN 2.07 2.22 2.07 2.05 2.05 2.12 1.94 [131] 2.05 [131]
GaP 2.26 2.05 2.30 2.34 2.35 2.25 2.36 [131] 2.30 [131]
GaAs 2.39 2.14 2.43 2.49 2.49 2.38 2.43 [131] 2.53 [131]
GaSb 2.69 2.35 2.73 2.85 2.84 2.66 2.65 [131] 2.84 [131]
InN 2.11 2.26 2.11 2.08 2.08 2.15 - -
InP 2.18 2.35 2.18 2.14 2.14 2.22 2.54 [131] 2.41 [131]
InAs 2.64 2.31 2.68 2.78 2.78 2.61 2.59 [131] 2.65 [131]
InSb 2.93 2.50 2.95 3.12 3.11 2.86 2.80 [131] 2.95 [131]
Chapter 4 Ph D (Thesis) 146
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It is seen from Table 4.15 that the present results of bond length of group III-V
semiconductor compounds computed by using screening functions [30, 32-36]
are found in good matching with the available experimental and theoretical
results. The excellent agreement is observed between present results and
experimental results is observed for BN, AlP, AlAs, GaN, GaP, GaAs, GaSb, InAs
and InSb.
Reddy et al. [122] has proposed a relationship for microhardness and refractive
index of the material as
( ) ( ) 321 AnAexpAGPaH −= (4.5)
As per Reddy et al., A1 = 104.953 and 9.273; A2 = -0.3546 and -0.1779 and
A3 = 26.82 and 4.97 for group III-V and II-VI respectively.
The microhardness computed in the present investigations by using equation
(4.5) for group III-V semiconductor compounds are shown in Table 4.16. Here we
have incorporated six screening functions due to H [30], N [32], T [33], I [34],
F [35] and S [36] and the results are compared with the experimental findings
along with other such theoretical findings. It is seen that H [30] generates lower
values and I [34] gives higher values of microhardness except for GaP, GaAs,
GaSb and InAs. It is seen that the computed microhardness using I [34] and F [35]
are close to the experimental findings and other such results for GaN and GaP.
Some large deviation is seen in the computed values of microhardness for other
group III-V semiconductors.
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Table 4.16 The microhardness H (GPa) for group III-V semiconductors.
Comp- ound
Present results using screening functions f(q) Expt Others
N [32] H [30] T [33] I [34] F [35] S [36]
BN 18.77 14.50 18.67 19.33 19.32 17.00 26.90, 34.3-73 [131] 23.02 [131]
BP 16.96 12.66 16.93 17.69 17.69 15.63 - -
BAs 16.41 12.10 16.41 17.23 17.21 15.14 - -
BSb 15.63 11.30 15.68 16.51 16.51 14.44 - -
AlN 17.32 13.02 17.27 18.02 18.00 15.94 12.30, 23.48 [131] 21.97 [131]
AlP 14.85 10.52 14.91 15.83 15.81 13.69 5.50, 9.64 [131] 12.76 [131]
AlAs 14.38 10.01 14.44 15.38 15.36 13.22 4.8-5, 7.67 [131] 9.40 [131]
AlSb 13.22 8.96 13.36 14.35 14.35 12.14 4, 4.43 [131] 7.04 [131]
GaN 17.03 12.73 17.00 17.77 17.75 15.68 21.32 [131] 17.99 [131]
GaP 11.83 17.96 10.85 9.66 9.64 11.93 9.32, 9.45 [131] 10.71 [131]
GaAs 8.65 15.05 7.76 6.41 6.41 8.92 6.79, 7.50 [131] 5.75 [131]
GaSb 2.79 9.60 2.18 0.44 0.47 3.42 2.48, 4.48 [131] 0.55 [131]
InN 15.96 11.63 15.99 16.82 16.79 14.74 - -
InP 13.88 9.57 13.95 14.94 14.91 12.77 4.1, 5.5 [131] 8.14 [131]
InAs 3.69 10.45 3.03 1.36 1.38 4.26 3.30, 3.99 [131] 3.52 [131]
InSb - - - - - - - -
As per Salem [123], the electronic polarizability αe can be calculated using
Lorentz-Lorentz formula [123] as
252
2
1095321α −⋅
⋅
+−
= X.dM
nn
e (4.6)
Where M is the molecular weight and d is the density.
The computed electronic polarizability for group III-V semiconductors are shown
in Table 4.17. Here we have incorporated six screening functions due to H [30], N
[32], T [33], I [34], F [35] and S [36] and the results are compared with the
experimental findings along with other such theoretical findings. It is seen that H
Chapter 4 Ph D (Thesis) 148
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[30] generates higher values and I [34] give lower values of electronic
polarizability except for GaP, GaAs, GaSb, InAs and InSb.
Table 4.17 The electronic polarizability (10-24 cm3) for group III-V semiconductors.
Comp- ound
Present results using screening functions f(q) Expt Others
N [32] H [30] T [33] I [34] F [35] S [36]
BN 1.69 1.87 1.70 1.67 1.67 1.77 2.45 [131] 2.11-2.75 [131]
BP 3.58 3.91 3.58 3.52 3.52 3.69 - -
BAs 4.13 4.51 4.13 4.05 4.06 4.25 - -
BSb 5.17 5.63 5.17 5.07 5.07 5.30 - -
AlN 3.10 3.40 3.10 3.05 3.05 3.20 2.74 [131] 1.86, 2.79 [125], 2.51-3.22 [131]
AlP 6.28 6.81 6.27 6.15 6.15 6.43 6.50 [131] 5.25, 5.51 [125], 5.92-7.08 [131]
AlAs 7.12 7.71 7.11 6.97 6.98 7.28 8.16 [131] 7.40, 7.55 [125], 7.42-8.33 [131]
AlSb 9.38 10.10 9.36 9.18 9.18 9.57 10.10 [131] 10.44, 10.49 [125],
9.59-10.75 [131]
GaN 3.42 3.74 3.42 3.36 3.36 3.53 3.80 [131] 2.07, 3.10 [125], 3.18-3.58 [131]
GaP 6.71 5.90 6.83 6.96 6.96 6.70 6.87 [131] 6.74, 6.85 [125], 6.24-7.03 [131]
GaAs 7.91 7.05 8.02 8.17 8.17 7.88 8.27 [131] 8.22, 8.24 [125], 7.66-8.31 [131]
GaSb 10.73 9.77 10.81 11.02 11.01 10.65 10.72 [131] 11.29, 10.94 [125], 10.34-11.38 [131]
InN 4.83 5.26 4.82 4.73 4.74 4.95 - 3.11, 4.45 [125]
InP 8.04 8.68 8.03 7.87 7.87 8.22 8.94 [131] 8.95, 8.92 [125], 8.64-9.09 [131]
InAs 10.42 9.46 10.50 10.71 10.70 10.35 10.48 [131] 10.65, 10.47 [125],
9.53-10.21 [131]
InSb 13.39 12.33 13.43 13.70 13.69 13.26 13.46 [131] 13.67, 13.42 [125], 12.74-14.27 [131]
The refractive index, high frequency dielectric constant, plasmon energy, bond
length, microhardness and electronic polarizability computations using different
local field correction functions have been first time reported in this thesis. We
hope that present results of above mentioned properties of group III-V
semiconductors will be considered as reference for future.
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4.3 Group II-VI semiconductors
In the present study, we have selected Zn, Cd, Hg and Mg based 16 compounds
and one magnetic semiconductor compound MnTe to predict certain physical
properties of interest. In the present investigations we have considered only zinc-
blende phase of the above said semiconductors.
4.3.1 Total Energy
The total energy for selected thirteen group II-VI semiconductor compounds
having zinc-blende structures using equation (3.1) and six local field correction
functions [30, 32-36] are shown in Table 4.18 with available experimental data
and other such theoretical findings.
From Table 4.18 it is seen that total energy computed with employing six
screening functions for all thirteen group II-VI compounds are found in good
agreement with the experimental results with reasonable deviations. H [30]
generates higher values of total energy while I [34] and F [35] give lower values
of total energy among all six screening functions. The total energy computed
using I [34] and F [35] are comparatively found closer to experimental findings
for all group II-VI semiconductor compounds. No such experimental data are
available for Hg-based, Mg-based and MnTe compounds to make comparison. I
[34] and F [35] generate almost same values of total energy for all compounds.
The percentage deviation upto 5% from the experimental findings is seen for
total energy obtained using I [34] and F [35]. It is observed 4% to 10% for N [32]
and T [33] and 8% to 16% for S [36]. As static local field correction function H [30]
does not include any exchange and correlation effects, the large deviation about
21% to 30% seen for H [30].
Finally we suggest that to get proper results of total energy for semiconductors it
is necessary to take account of exchange and correlation effects in energy
computation. It is also necessary to consider covalent correction term which
includes third and fourth order perturbation terms in total energy calculations as
it is seen from Table 3.1 for group IV semiconductors.
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Table 4.18 Total energy (-ET) (Rydberg/electron) of group II-VI semiconductors.
Compound
Present results using different screening functions f(q)
Expt. Others
N [32] H [30] T [33] I [34] F [35] S [36]
ZnS 2.5783 2.2376 2.5969 2.7194 2.7182 2.4967 2.851, 2.852 [37],
3.724 [43]
2.803-2.920 [37],
2.238-2.723 [43]
ZnSe 2.4572 2.1238 2.4702 2.6042 2.6027 2.3726 2.698 [37],
2.576 [43]
2.695-2.756 [37],
2.124-2.609 [43]
ZnTe 2.2769 1.9639 2.2793 2.4337 2.4314 2.1888 2.396, 2.397 [37],
2.835 [43]
2.344-2.404 [37],
1.965-2.440 [43]
CdS 2.3838 2.0573 2.3929 2.5347 2.5329 2.2976 - 2.058-2.540 [43]
CdSe 2.2924 1.9772 2.2958 2.4483 2.4461 2.2045 - 1.978-2.455 [43]
CdTe 2.1221 1.8372 2.1133 2.2871 2.2838 2.0342 2.379, 2.380 [37] 2.358-2.440 [37],
1.838-2.296 [43]
HgS 2.3763 2.0506 2.3850 2.5276 2.5258 2.2899 - -
HgSe 2.2783 1.9651 2.2808 2.4350 2.4328 2.1903 - -
HgTe 2.1290 1.8426 2.1206 2.2937 2.2905 2.0410 - -
MgS 2.4866 2.1510 2.5011 2.6321 2.6306 2.4027 - -
MgSe 2.3596 2.0357 2.3672 2.5118 2.5099 2.2729 - -
MgTe 2.1560 1.8641 2.1497 2.3194 2.3164 2.0677 - -
MnTe 2.2133 1.9107 2.2113 2.3737 2.3711 2.1248 - -
4.3.2 Energy-Volume Relations
The energy computed using any local field correction function show the same
trend for all group II-VI semiconductors; we have selected MnTe to study effect
of local field correction function on total energy at different volume. The total
energy-volume relations using six local field correction functions for MnTe are
shown in Figure 4.21.
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Figure 4.21 Total energy-volume relations for MnTe.
It is seen from Figure 4.21 that for all six local field correction functions, total
energy of MnTe show same trend. Total energy becomes minimum at
equilibrium volume and increases on compression or expansion of volume. As H
[30] does not include any exchange or correlation effects, H [30] gives higher
values of total energy.
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