Nonlinear Optics and Quantum Optics, Vol. 41, pp. 179–200
Reprints available directly from the publisher
Photocopying permitted by license only
©2010 Old City Publishing, Inc.
Published by license under the OCP Science imprint, a member of the Old City Publishing Group
Shruti Dutta Roy
Physics Department, Burdwan University, Burdwan 713104, India
E-mail: bwn_lord@yahoo.co.in
Received: September 10, 2009. Accepted: October 25, 2009.
Studies about some quaternary compounds showing lattice matching condition on various substrates suitable for device design in various wavelength regions are reported here. The compositional dependence of lowest energy band gap, dielectric constant, coefficient of thermal expansion, temperature and pressure dependence of lowest band gap energy, etc. of these compounds are presented and finally proper concentrations suitable for device design under lattice matching condition is given.
Keywords: Band gap, dielectric constant, electro-optical properties, quaternaries.
PACS Nos: 85.60Bt, 78.20.-e, 42.70.-a, 81.05.Zx.
INTRODUCTION
Technical interest in alloys arises for possibilities to develop semiconductors of adjustable energy gap and dielectric constant. The wavelength region
1–2
µ m [1–3] is very useful for optoelectronic devices particularly for optical communication because of the presence of minimum loss at 1.5
µ m [4, 5] and minimum dispersion at 1.3
µ m [6] in optical fiber. The spectral region
2–4
µ m is drawing considerable attention because of recent development of low loss fluoride glass fibers in this spectral region and λ
=
800 nm is useful for communication, entertainment and medical applications. And around this wavelength high powered devices have been built [7, 8]. Not only the single crystal, the mixed compound semiconductors are coming out as important materials as the design parameters like lowest energy band gap, lattice parameter, thermal expansion coefficient and band structure parameter can be
179
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180
S. D. Roy tailored to the desired values by changing the concentration of the constituent components of the crystal. As the material selection for device applications
[9, 10] is limited within III–V compounds, several kinds of ternary and quaternary compounds are being considered. But the selection of the materials depends among other factors, on the quality of the crystals and easiness of the crystal growth. Thus growth, characterization and investigation of physical properties of ternary and multinary compounds play an important role in the field of material research and their applications. In this context we have studied quaternary compounds like AlGaPSb, AlGaAsSb, AlInPSb, AlInAsSb,
GaInPSb, GaInAsSb. The parameters [12, 13] studied here are dielectric constant, band gap energy, coefficient of linear expansion, temperature dependence of lowest energy band gap, pressure dependence of lowest energy band gap, effective mass and some correlation among them. Among these parameters the band gap energy controls the operating wavelength of optoelectronic devices while refractive index has a useful role in design of heterostructure laser [14]. The knowledge of thermal expansion coefficient for different materials is very useful as it gives information about strain and dislocation that may be produced in the material. Further the temperature and pressure dependence of band gap energy give valuable informations regarding the operating wavelength of the devices (tunable laser). Effective mass is also an important parameter as it is related to carrier mobility hence it is useful for obtaining the knowledge of transport properties in this type of mixed quaternary compounds.
Phillip’s ionicity, Fröhlich coupling parameters and bond bending and bond stretching force constants are also important as they have correlation with different material properties.
The working of the devices like LED, photo detector and transport devices like high speed transistor using the said quaternaries are limited due to lack of knowledge of various material parameters as stated above. Our work will definitely give some important useful informations about these parameters of the quaternary compounds. Again choice of suitable substrate to grow the crystals is very important. In this respect, we have studied the lattice matching condition of different substrates for different quaternaries and this would help to choose the right substrate for growing of crystal for a definite purpose. So our detailed study for the control of various design parameters of these quaternary compounds with proper lattice matching conditions will be very helpful to select the proper crystal with appropriate band gap, dielectric constant, lattice parameter etc. for the design of wide variety of optoelectronic devices.
METHOD OF EVALUATION
Quaternary III–V semiconductor alloys are important in the field of communication industry because the lowest energy band gap can be tuned with composition over the spectral range suitable for low loss and low dispersion for
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Quaternary Compounds Relevant to Optoelectronic Device Design 181 the optical fibers. But there is lack of knowledge of many material parameters which are very useful for the design of optoelectronic devices. Again there is no exact formulation which can be used to describe the change of these parameters with composition. In this paper we have used interpolation schemes as a tool to estimate parameters of the quaternary compounds represented by
A x
B
1
− x
C
1
− y
D y where A & B are group III elements (between A and B , A has lower atomic number) and C & D are group V elements (between C and
D , C has lower atomic number). A quaternary alloy parameter is described by Q(x, y) over x, y composition (0
≤ x
≤
1, 0
≤ y
≤
1) which along with x and y forms a three dimensional surface with values of the parameter for different compositions. The four corners of the surface gives the value of the parameter for four binaries AC ( x
=
1 , y
=
0), AD ( x
=
1 , y
=
1),
BC ( x
=
0 , y
=
0) and BD ( x
=
0 , y
=
1). Similarly the four boundaries of the surface give the variation of the parameter with composition for the ternaries AC
A x
B
1
− x
1
− y
D(y
=
1 ) .
D y
(x
=
1 ) , BC
1
− y
D y
(x
=
0 ) , A x
B
1
− x
C(y
=
0 ) and
Lattice matching conditions using different substrates are obtained by considering that the lattice parameter has a linear dependence with the composition
[15, 16]. If the parameter of the four constituent binaries of a quaternary compound are known, we can use the well known interpolation scheme
Q(x, y)
=
( 1
− x)
[ yB
AC
+
( 1
− y)B
AD
] + x
[ yB
BC
+
( 1
− y)B
BD
]
.
(1)
If compositional relationship for the four ternaries mentioned above are available then we can write Q(x, y) as
Q(x, y)
= x( 1
− x)
[
( 1
− y)T
ABD
+ yT
ABC
] + y( 1
− y) x( 1
− x)
+ y( 1
− y)
[
( 1
− x)T
ACD
+ xT
BCD
]
(2)
The ternary alloy parameters are obtainable by interpolation from those of the binary constituents using T ij
= xB j
+
( 1
− x)B i
C ij are bowing parameters and reduces to T ij
= xB j
−
C ij x( 1
− x) where
+
( 1
− x)B i for linear dependence. We have used another type of interpolation scheme used by Moon
et al. [17] for calculating the band gap energy as
Q(x, y)
=
( 1
− x)T
14
(y)
+ xT
23
(y)
−
(3) where
= x( 1
− x)
[
( 1
− y)C
12
+ yC
43
] + y( 1
− y)
[
( 1
− x)C
14
+ xC
23
]
.
Data used for the evaluation for the necessary parameters as discussed in this paper have been taken using the references [18, 19].
RESULTS AND DISCUSSION
Different combinations of III–V quaternaries have been studied for their applications in various optoelectronic devices and also to match different
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182
S. D. Roy transmission properties through optical fibers. Since the performance of the optoelectronic devices depends not only on the band gap, refractive index etc.
but also on the structural quality of the heterojunction interface and epitaxial layers grown. But the quality of the crystals gets deteriorated due to the lattice mismatch between the crystal and substrate. At the growth temperature, the close lattice matching of the semiconductors gives a high quality heteroepitaxial layer. As the choice of the substrate depends on the operating wavelength region, refractive index etc. we have studied in detail the lattice matching conditions of different quaternary crystals using different substrates and these results on the lattice matching conditions for different alloys on different substrates are shown in the Table 1. In Figure 1 the compositional variation of lowest band gap energy of AlInPSb and GaInAsSb is plotted for
Al
1
Compound
− x
Ga x
P y
Sb
Al
1
− x
Ga x
As y
Sb
1
− y
Al
Al
1
Ga
Ga
1
− x
1
− x
1
− x
− x
In
In x
P x
As y
In x
P y
In x
As y y
Sb
Sb
1
1
− y
Sb
1
− y
Sb
1
− y
1
−
− y y
Substrates
GaAs
InP
InP
InAs
GaAs
InAs
GaSb
InP
GaAs
InP
InAs
AlSb
GaSb
InAs
Lattice matching condition y y y
=
=
=
0 .
4817
−
1 .
04x
0 .
673
−
1 .
0292x
0 .
2662
−
1 .
04x
0 .
673
−
1 .
0292x
0 .
2662
−
0 .
04x
0 .
475
+
0 .
0333x y y
=
=
0 .
0766
−
0 .
04x
0 .
475
+
0 .
0333x
0 .
4817
+
0 .
3437x
0 .
673
−
0 .
0631x y
= y
=
0 .
0766
+
0 .
3437x
0 .
673
−
0 .
0631x
0 .
04
+
0 .
3437x
0 .
475
−
0 .
0543x y
= y
=
0 .
2662
+
0 .
3437x
0 .
475
−
0 .
0543x
0 .
452
+
0 .
3847x
0 .
6445
−
0 .
0344x y
= y y
=
=
0 .
225
+
0 .
3847x
0 .
6445
−
0 .
0344x
0 .
0356
+
0 .
3847x
0 .
6445
−
0 .
0344x
0 .
3847x
−
0 .
041
0 .
6445
−
0 .
0344x y y
=
=
0 .
3847x
0 .
452
−
0 .
0317x
0 .
0356
+
0 .
3847x
0 .
452
−
0 .
0317x
Compositional range
0
≤ y
≤
0 .
715
0
≤ x
≤
0 .
463
0
≤ y
≤
0 .
395
0
≤ x
≤
0 .
25
0 .
445
≤ y
≤
0 .
56
0
≤ x
≤
1
0 .
072
≤ y
≤
0 .
16
0
≤ x
≤
1
0 .
715
≤ y
≤
1
0
≤ x
≤
0 .
47
0 .
114
≤ y
≤
0 .
689
0
≤ x
≤
1
0 .
085
≤ y
≤
0 .
91
0
≤ x
≤
1
0 .
56
≤ y
≤
1
0
≤ x
≤
0 .
52
0 .
7
≤ y
≤
1
0
≤ x
≤
0 .
458
0 .
349
≤ y
≤
1
0
≤ x
≤
1
0 .
05
≤ y
≤
0 .
689
0
≤ x
≤
1
0
≤ y
≤
0 .
563
0 .
1
≤ x
≤
1
0
≤ y
≤
0 .
91
0
≤ x
≤
1
0 .
078
≤ y
≤
1
0
≤ x
≤
1
Wavelength region in
µ m
0.832–0.416
0.673–0.492
1.425–0.499
1.722–0.539
0.488–0.416
1.722–0.534
4.275–0.541
0.843–0.499
0.666–0.619
1.078–0.925
1.937–1.530
2.695–1.907
4.939–1.738
3.415–1.802
TABLE 1
Comparison of the lattice matching conditions of different quaternary crystals using different substrates
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Quaternary Compounds Relevant to Optoelectronic Device Design 183
4
3
2
1
0
1
AlInPSb on GaSb
0.5
y
0 0
0.2
0.4
x
0.6
0.8
1
1.5
1
0.5
GaInAsSb on GaSb
0
1
1
0.5
0.6
0.8
0.4
0.2
y
0 0 x
FIGURE 1
Plot of E g vs. compositional variation for the region 0
≤ x
≤
1, 0
≤ y
≤
1 of AlInPSb and
GaInAsSb on GaSb (black solid line) substrate.
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184
S. D. Roy the region 0
≤ x
≤
1, 0
≤ y
≤
1 along with the variation of the same under lattice matching condition (black solid line) using GaSb substrate. Also the compositional dependence of lowest band gap energy have been evaluated by the three interpolation methods as stated earlier and plot of these results for the quaternaries AlGaAsSb and AlInAsSb is shown in Figure 2.
THERMAL EXPANSION COEFFICIENTS
There are some point defects and extended defects in the crystals and the presence of these defects [20] have enormous importance on the efficiency and performance of the electronic devices, because of the difference in the thermal expansion coefficient between the crystal and the substrate, the lattice may be strained and which in turn affects the performance of the material. In this light, we have evaluated here the variation of thermal expansion coefficient with composition of various quaternary alloys with lattice matching condition for finding out the region of composition on different substrates to have better performance of material in the devices. For example from the variation of thermal expansion coefficient with y composition in our calculation, it may be concluded that for lower y value InP is a good substrate for Al x
Ga
1
− x
P
1
− y
Sb y for lower value of y, GaAs and for higher value of y InAs is suitable
; for Ga x
Al x
In
1
− x
As
1
− y
Sb y
Ga
1
− x
P
1
− y
Sb y
. The variation on thermal expansion coefficient for and Ga x
In
1
− x
As
1
− y
Sb y has been shown in Figure 3.
PRESSURE AND TEMPERATURE DEPENDENCE OF LOWEST
BAND GAP ENERGY
The study with regard to the change in the energy band structure with pressure and temperature is very important for device design. The knowledge of the pressure dependence of energy gap (dEg/dP) is useful as it helps to calculate the deformation potential for the valence-conduction band separation.
The temperature dependence of band gap (dEg/dT) arises due to the combined effect of the thermal expansion of the lattice and electron-phonon interaction
[21]. The contribution of temperature coefficient of thermal expansion is probably positive while due to electron-phonon interaction has been expected to be negative. Here temperature and pressure dependence of lowest energy band gap of different quaternaries with composition have been evaluated by interpolation technique and the results have been plotted and shown in Figure 4 for AlInPSb and GaInAsSb, respectively.
EFFECTIVE MASS
Effective mass is one of the most important device parameter [22] for the design of optoelectronic devices as it has direct effect on the carrier mobility
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Quaternary Compounds Relevant to Optoelectronic Device Design
3
2.5
AlGaAsSb on InP
[ by eqn (1)]
[- - - by eqn(2)]
[ . . by eqn(3)]
2
185
1.5
1
0.5
0.44
0.46
0.48
0.5
0.52
y
0.54
0.56
0.58
0.6
2.5
2
AlInAsSb on InP
[ by eqn (1)]
[- - - by eqn(2)]
[ . . by eqn(3)]
1.5
1
0.5
0
0 0.1
0.2
0.3
0.4
0.5
y
0.6
FIGURE 2
Plot of E g vs.
y composition of AlGaAsSb and AlInAsSb.
0.7
0.8
0.9
1 and many investigations have been done on the compositional dependence of different alloys. And we have here evaluated the values of effective mass of different quaternary compounds for various compositions by interpolation method. The effective mass is related with the lowest band gap energy through the relation m
∗ = −
0 .
020
+
0 .
112 E g
−
0 .
018 E
2 g
, obtained from the best fit
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186
6
AlGaPSb
[ on GaAs]
[- - - on Inp]
5.5
S. D. Roy
5
0 0.1
0.2
0.3
0.4
y
0.5
0.6
0.7
7
6.8
6.6
6.4
6.2
GaInAsSb
[ on GaSb]
[ - - - on InAs]
6
5.8
5.6
5.4
5.2
5
0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
y
FIGURE 3
Plot of dEg/dT vs.
y composition of Al x
Ga
1
− x
P
1
− y
Sb y and Ga x
In
1
− x
As
1
− y
Sb y
.
1
0.8
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Quaternary Compounds Relevant to Optoelectronic Device Design 187
-3
AlInPSb
[ on GaAs]
[- - - on InAs]
[.... on GaSb]
-3.5
12.5
12
11.5
-4
0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
y
14
13.5
GaInAsSb
[ on GaSb]
[- - - on InAs]
13
1
11
0 0.1
0.2
0.3
0.4
0.5
y
FIGURE 4
Plot of α vs.
y composition of AlInPSb and GaInAsSb.
0.6
0.7
0.8
0.9
1 of the plot of m
∗ vs.
E g shown in Figure 5. The values of the same have been evaluated from the correlation of effective mass and lowest band gap energy plot have been compared with those obtained from interpolation method and the agreement is found to be good. Table 2 shows the values of effective
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188
S. D. Roy
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0 0.5
1 1.5
2
Eg
2.5
3 3.5
4
FIGURE 5
Plot of plot of m
∗ vs.
E g
.
mass calculated from these methods for the quaternaries AlInPSb on InAs,
AlInAsSb on InP, GaInPSb on GaAs and GaInAsSb on InAs. Figure 6 show the variation of the effective mass with composition for the quaternaries AlInAsSb and GaInAsSb.
PHILLIPS IONICITY
Ionicity of the bond is a very important parameter for compound semiconductors. It is defined as the fraction of ionic or heteropolar character in the bond compared with the fraction of covalent or homopolar character. Ionicity gives useful information about the structural properties of material as it is connected with many other parameters of the material. The ionicity of a compound is the key parameter which accounts for the trend from semiconducting to insulating structure and is also responsible for phase transition from four fold to six fold coordinated structure. The concept of ionicity is also very helpful for understanding complex bonding in mixed compound semiconductors where material properties can be changed by varying the composition. Phillips ionicity [12] is defined as f i
C
2
=
E 2 g
=
C
2
E
2 h
+
C 2 where the complex energy gap E g
=
E h
+
iC, E h being the homopolar part and C the heteropolar part. The theoretically predicted variation of Phillips
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Quaternary Compounds Relevant to Optoelectronic Device Design
AlInPSb on InAs
Value of m
∗ e from Value of m
∗ e from
Value of x interpolation method correlation with Eg
0
0.2
0.4
0.6
0.8
1.0
0.1
0.2
0.3
0.4
0.5
0
0.1
0.2
0.3
0.4
0
0.2
0.4
0.6
0.8
1.0
0.17
0.14
0.11
0.09
0.07
0.06
AlInAsSb on InP
0.14
0.13
0.11
0.10
0.08
GaInPSb on GaAs
0.132
0.133
0.132
0.131
0.131
GaInAsSb on InAs
0.046
0.043
0.039
0.035
0.029
0.023
0.14
0.13
0.12
0.10
0.08
0.06
0.14
0.13
0.12
0.12
0.08
0.131
0.132
0.133
0.132
0.131
0.051
0.045
0.038
0.031
0.024
0.017
TABLE 2
Comparison of the values of effective mass of different quaternary crystals
189 ionicity for the different quaternaries with composition has been reported in this paper. We have evaluated Phillips ionicity values ( f i
) for different quaternaries with compositions and results for same are shown in the Figure 7 for the quaternaries AlInAsSb and AlInPSb.
FRÖHLICH COUPLING PARAMETER
This parameter is a measure of interaction between the electrons and longitudinal optical phonons and depends strongly on the ionic polarization of the crystal and is related static and high frequency dielectric constant. The
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190
S. D. Roy
0.18
0.16
0.14
0.12
0.1
0.08
AlInAsSb
[ on GaSb]
[- - - on InP]
0.06
0.04
0.02
0 0.1
0.2
0.3
0.4
0.5
y
0.6
0.7
0.8
0.9
0.05
0.045
GaInAsSb
[ on GaSb]
[- - - on InAs]
1
0.04
0.035
0.03
0.025
0.02
0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
y
Plot of m vs.
y composition of AlInAsSb and GaInAsSb.
1
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Quaternary Compounds Relevant to Optoelectronic Device Design
0.36
0.34
AlInAsSb
[ on GaSb]
[- - - onInP]
0.32
0.3
0.28
0.26
0.3
0.28
0.26
0.24
0 0.1
0.2
0.3
0.4
0.5
y
0.6
0.7
0.8
0.9
0.4
0.38
0.36
AlInPSb
[ on GaAs]
[- - - on InAs]
[.... on GaSb]
1
0.34
0.32
0.24
0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
y
FIGURE 7
Plot of Phillips ionicity vs.
y composition of AlInAsSb and AlInPSb.
1
Fröhlich coupling parameter α
F
[23] is given by
α
F
=
1
2 e
2
/(
2
2 m
∗
ω
Lo
)
1
2
ω
Lo
1
ε ∞
−
1
ε s
,
191
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192
S. D. Roy where ω
Lo is the longitudinal optical phonon frequency and effective mass. We have here evaluated the variation of α
F m
∗ is the electron for mixed quaternary crystals with the concentration by method of interpolation and plots of
α
F vs. concentration for the quaternary AlInAsSb and GaInPSb are shown in
Figure 8, respectively.
THE STATIC AND HIGH FREQUENCY DIELECTRIC CONSTANT
The dielectric constant as well as the refractive index of semiconductor materials is an averaged microscopic value and is very useful and key parameter both from theoretical and applied consideration. And its detailed knowledge is highly relevant for the construction and development of wide variety of sophisticated optoelectronic and semiconductor devices. The dielectric constant is strongly connected with the electronic energy band structures. Mathematical correlations of the static and high frequency dielectric constant with lowest band gap energy of III–V compounds using curve fitting method have been obtained and are given by
ε s
=
17 .
14
−
3 .
50 E g
+
0 .
40 E
2 g
ε ∞
=
14 .
69
−
3 .
08 E g
+ 0 .
31 E
2 g
These plots are shown in Figure 9. The variation of the values of static and high frequency dielectric constant with composition for different quaternary alloys have also been evaluated by interpolation method and from the correlation graph of dielectric constant with lowest band gap energy. The values obtained from these methods have been compared and the agreement is encouraging and these results have been shown in Table 3 for the quaternaries AlGaAsSb on InP and GaInPSb on InP. The compositional variation of m
∗ for the quaternaries
AlGaPSb and GaInPSb have been plotted in Figure 10, respectively.
INTERNAL STRAIN, BOND BENDING AND BOND STRETCHING
FORCE CONSTANT
The concept of valency force fields is very useful for describing the interatomic forces in semiconductors which include bond bending and bond stretching forces and also their combination. Bond bending forces ( β ) being directional are characteristic of covalent bonding whereas bond stretching forces ( α ) being central are found in ionic crystals. Thus the knowledge of these two quantities, particularly the bond bending force parameters are useful for studying electrostatic contributions to deformation potential, electron phonon interaction
[24], third order elastic constants [25], intrinsic strain and stability of crystal structure [12] in zinc blende and wurtzite and other related studies. With the
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Quaternary Compounds Relevant to Optoelectronic Device Design
0.09
0.08
AlInAsSb
[ on GaSb]
[- - - onInP]
0.07
193
0.06
0.05
0.04
0.03
0 0.1
0.2
0.3
0.4
0.5
y
0.2
0.18
0.16
GaInPSb
[ on GaAs]
[- - - on InP]
[.... on InAs]
[ . . on AlSb]
0.14
0.6
0.7
0.8
0.9
0.12
0.1
1
0.08
0.06
0.04
0.02
0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
y
0.8
0.9
FIGURE 8
Plot of Fröhlich coupling parameter α
F vs.
y composition of AlInAsSb and GaInPSb.
1
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194
S. D. Roy
18
17
16
15
14
13
12
11
10
9
0 0.5
1 1.5
2 2.5
lowest band gap energy
3 3.5
16
15
14
13
12
11
10
9
8
7
0 0.5
1 1.5
2 2.5
lowest band gap energy
3
FIGURE 9
Plot of Static and High frequency dielectric cont. vs. lowest band gap energy.
3.5
4
4
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Quaternary Compounds Relevant to Optoelectronic Device Design 195
Value of x
0
0.2
0.4
0.6
0.8
1.0
0
0.2
0.4
0.6
0.8
1.0
AlGaAsSb on InP
Value of ε s
Value of ε s
Value of ε ∞ Value of ε ∞ from interpolation from correlation from interpolation from correlation method with Eg method with Eg
10.80
11.57
12.35
13.13
13.91
14.71
12.97
13.41
13.85
14.30
14.74
15.08
11.09
11.56
12.20
12.90
13.64
14.57
GaInPSb on InP
12.38
12.78
13.32
13.86
14.40
15.08
8.91
9.61
10.32
11.03
11.76
12.48
11.17
11.44
11.71
11.98
12.25
12.53
8.93
9.38
9.97
10.60
11.27
12.09
10.40
10.77
11.27
11.76
12.26
12.87
TABLE 3
Comparison of the values of ε s for the quaternaries AlGaAsSb on InP and GaInPSb on InP increase of ionicity f i the ratio β/α decreases and in the limit f i
→
1 .
00 one would expect the ratio to be nearly equal to zero. The internal strain parameter
ζ have been evaluated for the quaternaries discussed in this paper from the relation
ζ
=
α
−
β
α
+
β using β/α values obtained by interpolation method as this study will be very much helpful for the analysis of strain problems [26] and obtaining good quality crystals under lattice matching condition. The compositional variations for β/α as well as ζ are shown in Figure 11 for GaInPSb and in Figure 12 for
GaInAsSb, respectively.
CONCLUSION
A detailed study of some important design parameters like lowest energy band gap, refractive index, temperature and pressure dependence of lowest energy band gap, coefficient of thermal expansion etc. and lattice matching condition using various combination of crystals on different substrates have been presented in this paper. The knowledge of lowest energy band gap and lattice matching condition using various substrates particularly will be of immense help for the growth and development of compound for specific
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196
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13.5
AlGaPSb
[ on GaAs]
[- - - on InP]
13
12.5
12
11.5
11
10.5
15
10
0
14
0.1
0.2
0.3
0.4
y
0.5
0.6
0.7
0.8
GaInPSb
[ on GaAs]
[- - - on InP]
[.... on InAs]
[ . . on AlSb]
13
12
11
10
9
0 0.1
0.2
0.3
0.4
0.5
y
0.6
0.7
0.8
0.9
1
FIGURE 10
Plot of Static and High frequency dielectric cont. vs.
y composition of AlGaPSb and GaInPSb.
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Quaternary Compounds Relevant to Optoelectronic Device Design
0.23
0.22
0.21
0.2
0.19
0.18
0.17
0.16
0.15
GaInPSb
[ on GaAs]
[- - - onInP]
[ . . . on InAs]
[ . . on AlSb]
0.14
0 0.1
0.2
0.3
0.4
0.5
y
0.76
0.74
0.72
GaInPSb
[ on GaAs]
[- - - onInP]
[ . . . on InAs]
[ . . on AlSb]
0.6
0.7
0.8
0.9
1
197
0.7
0.68
0.66
0.64
0.62
0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
y
FIGURE 11
Plot of β/α as well as ζ vs.
y composition of GaInPSb.
0.9
1 application. With continued theoretical and experimental work, new compounds and devices are coming out and this study will give further impetus to have the idea of origin and control of new devices in various optoelectronic applications.
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S. D. Roy
0.19
0.18
0.17
0.16
0.22
0.21
0.2
GaInAsSb
[ on GaAs]
[- - - onInP]
0.15
0 0.1
0.2
0.3
0.4
0.5
y
0.6
0.7
0.8
0.74
0.73
0.72
0.71
GaInAsSb
[ on GaAs]
[- - - onInP]
0.7
0.69
0.68
0.67
0.66
0.65
0.64
0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
y
FIGURE 12
Plot of β/α as well as ζ vs.
y composition of GaInAsSb.
0.9
0.9
1
1
ACKNOWLEDGEMENTS
The author wishes to thank the University Grants Commission (UGC), India for providing financial assistance through DSA-III in physics in the thrust area
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Quaternary Compounds Relevant to Optoelectronic Device Design 199
“Condensed Matter Physics Including Laser Applications” under its Special
Assistance Programme (SAP) to the Department of Physics for carrying out this work.
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