New shodhganga.inflibnet.ac.inshodhganga.inflibnet.ac.in/bitstream/10603/7350/12/12... · 2015. 12. 4. · Chapter 4 Ph D (Thesis) 105 Paresh Vyas Sardar Patel University January

Chapter 4 Ph D (Thesis) 105

Paresh Vyas Sardar Patel University January 2012

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-



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



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



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.



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],



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]



Table 4.1 Total energy (-ET) (Rydberg/electron) of group III-V semiconductors. (Cont.)

Comp

ound


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



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



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



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



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



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



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



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



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],



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.



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



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



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



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]



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.



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]



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.



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.



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



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.



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


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



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



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



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



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



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



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.



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



Table 4.10 Refractive Index for aluminium-based semiconductors.

Comp ounds



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



Table 4.11 Refractive Index for gallium-based semiconductors.

Comp ounds



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



Table 4.12 Refractive Index for indium-based semiconductors.

Comp ounds



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



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].



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.



Table 4.14 The plasmon energy (eV) for group III-V semiconductors.

Comp- ound


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)



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


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]



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.



Table 4.16 The microhardness H (GPa) for group III-V semiconductors.

Comp- ound


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



[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


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.



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.



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.



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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