IIIV Ternary and Quaternary Compounds
Abstract
III–V ternary and quaternary alloy systems are potentially of great importance for many highspeed electronic and optoelectronic devices, because they provide a natural means of tuning the magnitude of forbidden gaps so as to optimize and widen the applications of such semiconductor devices. Literature on the fundamental properties of these material systems is growing rapidly. Even though the basic semiconductor alloy concepts are understood at this time, some practical and device parameters in these material systems have been hampered by a lack of definite knowledge of many material parameters and properties.
 1.
Structural parameters
 2.
Mechanical, elastic, and lattice vibronic properties
 3.
Thermal properties
 4.
Energy band parameters
 5.
Optical properties
 6.
Carrier transport properties.
The III–V ternary and quaternary alloys considered here are those of Group III (Al, Ga, In) and V (N, P, As, Sb) atoms. The model used in some cases is based on an interpolation scheme and, therefore, requires that data on the material parameters for the related binaries (AlN, AlP, GaN, GaP, etc.) are known. These data have been taken mainly from the LandoltBörnstein collection, Vol. III/41, and from the Handbook on Physical Properties of Semiconductors Volume 2: III–V Compound Semiconductors, published by Springer in 2004. The material parameters and properties derived here are used with wide success to obtain the general properties of these alloy semiconductors.
30.1 Introduction to III–V Ternary and Quaternary Compounds
III–V semiconducting compound alloys are widely used as materials for optoelectronic devices such as lightemitting diodes, laser diodes and photodetectors, as well as for electronic transport devices such as field effect transistors, high electron mobility transistors and heterojunction bipolar transistors. In a ternary alloy, the bandgap energy E_{g} and the lattice parameter a are generally both functions of a single composition parameter, so they cannot be selected independently. In quaternary alloys, on the other hand, the two composition parameters allow E_{g} and a to be selected independently, within the constraints of a given alloysubstrate system. Even though the basic semiconductor alloy concepts are understood at this time, the determination of some practical device parameters has been hampered by a lack of definite knowledge of many material parameters. This chapter provides data on the fundamental material properties of III–V ternary and quaternary alloys. The model used here is based on an interpolation scheme and thus requires that values of the material parameters for the related endpoint binaries are known. We therefore begin with the constituent binaries and gradually move on to alloys. The phenomenon of spontaneous ordering in semiconductor alloys, which can be categorized as a selforganized process, is observed to occur spontaneously during the epitaxial growth of certain alloys, and results in modifications to their structural, electronic and optical properties. This topic is omitted from the coverage [30.1].
30.2 Interpolation Scheme
The electronic energy band parameters of III–V compound alloys and their dependence on alloy composition are very important device parameters, and so they have received considerable attention in the past. Investigations of many device parameters have, however, been hampered by a lack of definite knowledge of various material parameters. This necessitates the use of some kind of interpolation scheme. Although the interpolation scheme is still open to experimental verification, it can provide more useful and reliable material parameters over the entire range of alloy composition [30.2].
30.3 Structural Parameters
30.3.1 Lattice Parameters and LatticeMatching Conditions Between III–V Quaternaries and Binary Substrates
Lattice parameters a and c and crystal density g for some III–V binaries at 300 K
Binary  Zinc blende  Wurtzite  g (\({\mathrm{g/cm^{3}}}\))  

a (Å)  a (Å)  c (Å)  
AlN  –  3.112  4.982  3.258 
4.38  –  –  3.24  
AlP  5.4635  –  –  2.3604 
AlAs  5.66139  –  –  3.7302 
AlSb  6.1355  –  –  4.2775 
αGaN  –  3.1896  5.1855  6.0865 
βGaN  4.52  –  –  6.02 
GaP  5.4508  –  –  4.1299 
GaAs  5.65330  –  –  5.3175 
GaSb  6.09593  –  –  5.6146 
InN  –  3.548  5.760  6.813 
4.986  –  –  6.903  
InP  5.8690  –  –  4.7902 
InAs  6.0583  –  –  5.6678 
InSb  6.47937  –  –  5.7768 
Latticematching conditions for some III–V quaternaries of type \(\text{A}_{x}\text{B}_{1x}\text{C}_{y}\text{D}_{1y}\) at 300 K. \(x=\frac{A_{0}+B_{0}y}{C_{0}+D_{0}y}\)
Quaternary  Substrate  A _{0}  B _{0}  C _{0}  D _{0}  Remark 

\(\mathrm{Ga_{\mathit{x}}In_{1\mathit{x}}P_{\mathit{y}}As_{1\mathit{y}}}\)  GaAs  0.4050  −0.1893  0.4050  0.0132  \(\phantom{0.0}0\leq y\leq{\mathrm{1.0}}\) 
InP  0.1893  −0.1893  0.4050  0.0132  \(\phantom{0.0}0\leq y\leq{\mathrm{1.0}}\)  
\(\mathrm{Al_{\mathit{x}}In_{1\mathit{x}}P_{\mathit{y}}As_{1\mathit{y}}}\)  GaAs  0.4050  −0.1893  0.3969  0.0086  \({\mathrm{0.04}}\leq y\leq{\mathrm{1.0}}\) 
InP  0.1893  −0.1893  0.3969  0.0086  \(\phantom{0.0}0\leq y\leq{\mathrm{1.0}}\) 
Latticematching conditions for some III–V quaternaries of type \(\text{A}_{x}\text{B}_{1x}\text{C}_{y}\text{D}_{1y}\) at 300 K. \(y=\frac{A_{0}+B_{0}x}{C_{0}+D_{0}x}\)
Quaternary  Substrate  A _{0}  B _{0}  C _{0}  D _{0}  Remark 

\(\mathrm{Al_{\mathit{x}}Ga_{1\mathit{x}}P_{\mathit{y}}As_{1\mathit{y}}}\)  GaAs  0  0.0081  0.2025  −0.0046  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\) 
\(\mathrm{Al_{\mathit{x}}Ga_{1\mathit{x}}As_{\mathit{y}}Sb_{1\mathit{y}}}\)  GaSb  0  0.0396  0.4426  0.0315  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\) 
InP  0.2269  0.0396  0.4426  0.0315  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
InAs  0.0376  0.0396  0.4426  0.0315  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
\(\mathrm{Al_{\mathit{x}}Ga_{1\mathit{x}}P_{\mathit{y}}Sb_{1\mathit{y}}}\)  GaAs  0.4426  0.0396  0.6451  0.0269  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\) 
GaSb  0  0.0396  0.6451  0.0269  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
InP  0.2269  0.0396  0.6451  0.0269  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
InAs  0.0376  0.0396  0.6451  0.0269  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
\(\mathrm{Ga_{\mathit{x}}In_{1\mathit{x}}As_{\mathit{y}}Sb_{1\mathit{y}}}\)  GaSb  0.3834  −0.3834  0.4211  0.0216  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\) 
InP  0.6104  −0.3834  0.4211  0.0216  \({\mathrm{0.47}}\leq x\leq{\mathrm{1.0}}\)  
InAs  0.4211  −0.3834  0.4211  0.0216  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
\(\mathrm{Ga_{\mathit{x}}In_{1\mathit{x}}P_{\mathit{y}}Sb_{1\mathit{y}}}\)  GaAs  0.8261  −0.3834  0.6104  0.0348  \({\mathrm{0.52}}\leq x\leq{\mathrm{1.0}}\) 
GaSb  0.3834  −0.3834  0.6104  0.0348  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
InP  0.6104  −0.3834  0.6104  0.0348  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
InAs  0.4211  −0.3834  0.6104  0.0348  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
\(\mathrm{Al_{\mathit{x}}In_{1\mathit{x}}As_{\mathit{y}}Sb_{1\mathit{y}}}\)  GaSb  0.3834  −0.3439  0.4211  0.0530  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\) 
InP  0.6104  −0.3439  0.4211  0.0530  \({\mathrm{0.48}}\leq x\leq{\mathrm{1.0}}\)  
InAs  0.4211  −0.3439  0.4211  0.0530  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
\(\mathrm{Al_{\mathit{x}}In_{1\mathit{x}}P_{\mathit{y}}Sb_{1\mathit{y}}}\)  GaAs  0.8261  −0.3439  0.6104  0.0616  \({\mathrm{0.53}}\leq x\leq{\mathrm{1.0}}\) 
GaSb  0.3834  −0.3439  0.6104  0.0616  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
InP  0.6104  −0.3439  0.6104  0.0616  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\)  
InAs  0.4211  −0.3439  0.6104  0.0616  \(\phantom{0.0}0\leq x\leq{\mathrm{1.0}}\) 
Latticematching conditions for some III–V quaternaries of type \(\text{A}_{x}\text{B}_{y}\text{C}_{1xy}\text{D}\) at 300 K. \(y=A_{0}+B_{0}x\)
Quaternary  Substrate  A _{0}  B _{0}  Remark 

\(\mathrm{Al_{\mathit{x}}Ga_{\mathit{y}}In_{1\mathit{x}\mathit{y}}P}\)  GaAs  0.5158  −0.9696  \(0\leq x\leq{\mathrm{0.53}}\) 
\(\mathrm{Al_{\mathit{x}}Ga_{\mathit{y}}In_{1\mathit{x}\mathit{y}}As}\)  InP  0.4674  −0.9800  \(0\leq x\leq{\mathrm{0.48}}\) 
Latticematching conditions for some III–V quaternaries of type \({\text{AB}}_{x}\text{C}_{y}\text{D}_{1xy}\) at 300 K. \(x=A_{0}+B_{0}y\)
Quaternary  Substrate  A _{0}  B _{0}  Remark 

\(\mathrm{AlP_{\mathit{x}}As_{\mathit{y}}Sb_{1\mathit{x}\mathit{y}}}\)  GaAs  0.7176  −0.7055  \(0\leq y\leq{\mathrm{1.0}}\) 
InP  0.3966  −0.7055  \(0\leq y\leq{\mathrm{0.56}}\)  
InAs  0.1149  −0.7055  \(0\leq y\leq{\mathrm{0.16}}\)  
\(\mathrm{GaP_{\mathit{x}}As_{\mathit{y}}Sb_{1\mathit{x}\mathit{y}}}\)  GaAs  0.6861  −0.6861  \(0\leq y\leq{\mathrm{1.0}}\) 
InP  0.3518  −0.6861  \(0\leq y\leq{\mathrm{0.51}}\)  
InAs  0.0583  −0.6861  \(0\leq y\leq{\mathrm{0.085}}\)  
\(\mathrm{InP_{\mathit{x}}As_{\mathit{y}}Sb_{1\mathit{x}\mathit{y}}}\)  GaSb  0.6282  −0.6899  \(0\leq y\leq{\mathrm{0.911}}\) 
InAs  0.6899  −0.6899  \(0\leq y\leq{\mathrm{1.0}}\) 
30.3.2 Molecular and Crystal Densities
30.4 Mechanical, Elastic and Lattice Vibronic Properties
30.4.1 Microhardness
The hardness test has been used for a long time as a simple means of characterizing the mechanical behavior of solids. The Knoop hardness H_{P} for \(\mathrm{Ga_{\mathit{x}}In_{1\mathit{x}}P_{\mathit{y}}As_{1\mathit{y}}}\) latticematched to InP has been reported [30.5], and is found to increase gradually from 520 kg ∕ mm^{2} for y = 0 (Ga_{0.47}In_{0.53}As) to 380 kg ∕ mm^{2} for y = 1.0 (InP). It has also been reported that the microhardness in Al_{ x }Ga_{1−x}N thin film slightly decreases with increasing AlN composition x [30.6].
30.4.2 Elastic Constants and Related Moduli
Elastic stiffness (C_{ i j }) and compliance constants (S_{ i j }) for some cubic III–V binaries at 300 K
Binary  C_{ i j } (10^{11} dyn ∕ cm^{2})  S_{ i j } (\({\mathrm{10^{12}}}\,{\mathrm{cm^{2}/dyn}}\))  

C _{11}  C _{12}  C _{44}  S _{11}  S _{12}  S _{44}  
AlN  31.5^{a}  15.0^{a}  18.5^{a}  0.458^{a}  −0.148^{a}  0.541^{a} 
AlP  15.0^{a}  6.42^{a}  6.11^{a}  0.897^{a}  −0.269^{a}  1.64^{a} 
AlAs  11.93  5.72  5.72  1.216  −0.394  1.748 
AlSb  8.769  4.341  4.076  1.697  −0.5618  2.453 
βGaN  29.1^{a}  14.8^{a}  15.8^{a}  0.523^{a}  −0.176^{a}  0.633^{a} 
GaP  14.050  6.203  7.033  0.9756  −0.2988  1.422 
GaAs  11.88  5.38  5.94  1.173  −0.366  1.684 
GaSb  8.838  4.027  4.320  1.583  −0.4955  2.315 
InN  19.2^{a}  7.30^{a}  9.35^{a}  0.659^{a}  −0.182^{a}  1.07^{a} 
InP  10.22  5.73  4.42  1.639  −0.589  2.26 
InAs  8.329  4.526  3.959  1.945  −0.6847  2.526 
InSb  6.608  3.531  3.027  2.410  −0.8395  3.304 
Elastic stiffness (C_{ i j }) and compliance constants (S_{ i j }) for some wurtzite III–V binaries at 300 K
Binary  C_{ i j } (10^{11} dyn ∕ cm^{2})  S_{ i j } (10^{−12} cm^{2} ∕ dyn)  

C _{11}  C _{12}  C _{13}  C _{33}  C _{44}  C _{66} ^{a}  S _{11}  S _{12}  S _{13}  S _{33}  S _{44}  S _{66} ^{b}  
AlN  41.0  14.0  10.0  39.0  12.0  13.5  0.285  −0.085  −0.051  0.283  0.833  0.740 
αGaN  37.3  14.1  8.0  38.7  9.4  11.6  0.320  −0.112  −0.043  0.276  1.06  0.864 
InN  19.0  10.4  12.1  18.2  0.99  4.3  0.957  −0.206  −0.499  1.21  10.1  2.33 
Functional expressions for the bulk modulus B_{u}, Young’s modulus Y, and Poisson’s ratio P in semiconductors with zinc blende (ZB) and wurtzite (W) structures
Parameter  Structure  Expression  Remark 

B _{u}  ZB  \((C_{11}+2C_{12})/3\)  
W  \([(C_{11}+C_{12})C_{33}2C_{13}^{2}]/(C_{11}+C_{12}+2C_{33}4C_{13})\)  
Y  ZB  1 ∕ S_{11}  (100), [001] 
\(1/(S_{11}S/2)\)  (100), [011]  
1 ∕ S_{11}  (110), [001]  
\(1/(S_{11}2S/3)\)  (110), [111]  
\(1/(S_{11}S/2)\)  (111)  
W  1 ∕ S_{11}  c ⊥ l  
1 ∕ S_{33}  c ∥ l  
P  ZB  \(S_{12}/S_{11}\)  (100), m = [ 010 ] , n = [ 001 ] 
\((S_{12}+S/2)/(S_{11}S/2)\)  (100), m = [ 011 ] , \(n=[0\bar{1}1]\)  
\(S_{12}/S_{11}\)  (110), m = [ 001 ] , \(n=[1\bar{1}0]\)  
\((S_{12}+S/3)/(S_{11}2S/3)\)  (110), \(m=[1\bar{1}1]\), \(n=[1\bar{1}\bar{2}]\)  
\((S_{12}+S/6)/(S_{11}S/2)\)  (111)  
W  (1/2)[\(1(Y/3B_{{\text{u}}})\)]  c ⊥ l, c ∥ l 
30.4.3 LongWavelength Phonons
Behavior of the longwavelength optical modes in III–V ternary and quaternary alloys
Behavior  Alloy 

One mode  AlGaN (LO; cubic), AlGaN (except for E_{1}(TO); wurtzite), GaInN, AlAsSb 
Two mode  AlGaN (TO; cubic), AlGaN (E_{1}(TO); wurtzite), AlInN, AlGaP, AlGaAs, AlGaSb, AlInP, AlInAs, AlInSb, GaInP, GaInAs, GaNP, GaNAs, GaPAs, GaPSb, GaAsSb, InPAs, InPSb 
One–two mode  GaInSb, InAsSb 
Two–three mode  AlGaInP/GaAs 
Three mode  AlGaAsSb, GaInAsSb, AlGaInAs/InP, InPAsSb 
Three–four mode  AlGaPAs 
Four mode  GaInPSb, GaInPAs/GaAs, GaInPAs/InP 
In a quaternary alloy of the \(\text{A}_{x}\text{B}_{1x}\text{C}_{y}\text{D}_{1y}\) type, there are four kinds of unit cells: AC, AD, BC, and BD. On the other hand, in the \(\text{A}_{x}\text{B}_{y}\text{C}_{1xy}{\text{D}}\) type there are three kinds of unit cells: AD, BD, and CD. We can, thus, expect fourmode or threemode behavior of the longwavelength optical modes in such quaternary alloys ([30.9]; Table 30.9 ). However, the \(\mathrm{Ga_{\mathit{x}}In_{1\mathit{x}}As_{\mathit{y}}Sb_{1\mathit{y}}}\) quaternary showed threemode behavior with GaAs, InSb and mixed InAs/GaAs characteristics [30.10]. The \(\mathrm{Ga_{\mathit{x}}In_{1\mathit{x}}As_{\mathit{y}}Sb_{1\mathit{y}}}\) quaternary was also reported to show twomode or threemode behavior, depending on the alloy composition [30.11].

TO (GaAs): 268–14x cm^{−1}

LO (GaAs): 292–38x cm^{−1}

TO (AlAs): 358 + 4x cm^{−1}

LO (AlAs): \(358+71x26x^{2}\) cm^{−1}.
30.5 Thermal Properties
30.5.1 Specific Heatand Debye Temperature
Specific heat C and Debye temperature θ_{D} for some III–V binaries at 300 K
Binary  C (J ∕ ( g K ) )  θ _{D} (K)  α _{th} (10^{−6}K^{−1}) 

AlN  0.728  988  3.2 (⊥ c), 2.4 (∥ c) 
AlP  0.727  687  
AlAs  0.424  450  4.1 
AlSb  0.326^{a}  370^{a}  4.2 
αGaN  0.42  821  6.2 (⊥ c), 4.9 (∥ c) 
GaP  0.313  493^{b}  4.89 
GaAs  0.327  370  5.73 
GaSb  0.344^{a}  240^{a}  6.35 
InN  2.274  674  3.830 (⊥ c), 2.751 (∥ c) 
InP  0.322  420^{a}  4.56 
InAs  0.352  280^{a}  5.50 
InSb  0.350^{a}  161^{a}  5.04 
30.5.2 Thermal Expansion Coefficient
30.5.3 Thermal Conductivity
The lattice thermal conductivity κ, or the thermal resistivity \(W=1/\kappa\), results mainly from interactions between phonons and from the scattering of phonons by crystalline imperfections. It is important to point out that when large numbers of foreign atoms are added to the host lattice, as in alloying, the thermal conductivity may decrease significantly. Experimental data on various alloy semiconductors, in fact, exhibit strong nonlinearity with respect to the alloy composition. Such a composition dependence can be successfully explained by using the quadratic expression of (30.2) or (30.6) [30.17].
Thermal resistivity values W for some III–V binaries at 300 K. Several cation and anion bowing parameters used for the calculation of alloy values are also listed in the last column
Binary  W (cm K ∕ W)  C _{A−B} (cm K ∕ W) 

AlN  0.31^{a}  
AlP  1.11  \(C_{\mathrm{Al{}Ga}}=32\) 
AlAs  1.10  \(C_{\mathrm{Al{}In}}=15\) 
AlSb  1.75  \(C_{\mathrm{Ga{}In}}=72\) 
αGaN  0.51^{a}  \(C_{\mathrm{N{}P}}=36\) 
GaP  1.30  \(C_{\mathrm{N{}As}}=12\) 
GaAs  2.22  \(C_{\mathrm{N{}Sb}}=10\) 
GaSb  2.78  \(C_{\mathrm{P{}As}}=25\) 
InN  2.22^{b}  \(C_{\mathrm{P{}Sb}}=16\) 
InP  1.47  \(C_{\mathrm{As{}Sb}}=91\) 
InAs  3.33  
InSb  5.41–6.06 
30.6 Energy Band Parameters
30.6.1 Bandgap Energy
Lowest Direct and Lowest Indirect Band Gaps
Bandgap energies, E_{0}, E _{g} ^{X} and E _{g} ^{L} , for some III–V binaries at 300 K. ZB = zinc blende
Binary  E_{0} (eV)  E _{g} ^{X} (eV)  E _{g} ^{L} (eV) 

AlN  6.2  –  – 
AlN (ZB)  5.2  5.34  8.6^{a} 
AlP  3.91  2.48  3.57 ^{a} 
AlAs  3.01  2.15  2.37 
AlSb  2.27  1.615  2.211 
αGaN  3.420  –  – 
βGaN  3.231  4.2^{a}  5.5^{a} 
GaP  2.76  2.261  2.63 
GaAs  1.43  1.91  1.72 
GaSb  0.72  1.05  0.76 
InN  0.7–1.1  –  – 
InN (ZB)  0.56  3.0 ^{a}  5.8 ^{a} 
InP  1.35  2.21  2.05 
InAs  0.359  1.37  1.07 
InSb  0.17  1.63  0.93 
Bowing parameters used in the calculation of E_{0}, E _{g} ^{X} and E _{g} ^{L} for some III–V ternaries. In those cases where no value is listed, linear variation should be assumed. W = wurtzite; ZB = zinc blende
Ternary  Bowing parameter C_{A−B} (eV)  

E _{0}  E _{g} ^{X}  E _{g} ^{L}  
(Al,Ga)N (W)  −1.00  –  – 
(Al,Ga)N (ZB)  0  −0.61  −0.80 
(Al,In)N (W)  −3.70  –  – 
(Al,In)N (ZB)  
(Ga,In)N (W)  −1.640  –  – 
(Ga,In)N (ZB)  0  
(Al,Ga)P  0  0  
(Al,In)P  −0.40  0  
(Ga,In)P  −0.65  −0.200  −0.34 
(Al,Ga)As  −0.37  −0.245  −0.055 
(Al,In)As  −0.720  
(Ga,In)As  −0.580  −0.70  −0.50 
(Al,Ga)Sb  −0.47  0  −0.55 
(Al,In)Sb  −0.43  
(Ga,In)Sb  −0.415  −0.33  −0.40 
Al(P,As)  −0.13  −0.40  −0.38 
Al(P,Sb)  −2.13  −0.277  −0.756 
Al(As,Sb)  −1.19  −0.250  −0.474 
Ga(N,P) (ZB)  −3.9  
Ga(N,As) (ZB)  \({\mathrm{120.4}}+100x\)  
Ga(P,As)  −0.19  −0.240  −0.16 
Ga(P,Sb)  −2.70  −2.700  −2.70 
Ga(As,Sb)  −1.25  −1.20  −1.20 
In(N,P) (ZB)  −15  
In(N,As) (ZB)  −4.22  
In(P,As)  −0.145  −0.145  −0.145 
In(P,Sb)  −1.60  −1.60  −1.60 
In(As,Sb)  −0.600  −0.60  −0.60 
Bandgap energies E_{0} for some III–V quaternaries at 300 K
Quaternary  E_{0} (eV) 

\(\mathrm{Ga_{\mathit{x}}In_{1\mathit{x}}P_{\mathit{y}}As_{1\mathit{y}}}\)/InP  \({\mathrm{0.75}}+{\mathrm{0.46}}y+{\mathrm{0.14}}y^{2}\) 
\(\mathrm{Ga_{\mathit{x}}In_{1\mathit{x}}As_{\mathit{y}}Sb_{1\mathit{y}}}\)/GaSb  \({\mathrm{0.28}}{\mathrm{0.16}}x+{\mathrm{0.60}}x^{2}\) 
\(\mathrm{Ga_{\mathit{x}}In_{1\mathit{x}}As_{\mathit{y}}Sb_{1\mathit{y}}}\)/InAs  \({\mathrm{0.359}}{\mathrm{0.415}}x+{\mathrm{0.718}}x^{2}\) 
\(\mathrm{Al_{\mathit{x}}Ga_{\mathit{y}}In_{1\mathit{x}\mathit{y}}P/GaAs}\) ^{a}  \({\mathrm{1.90}}+{\mathrm{0.57}}x+{\mathrm{0.10}}x^{2}\) 
\(\mathrm{Al_{\mathit{x}}Ga_{\mathit{y}}In_{1\mathit{x}\mathit{y}}As}\)/InP  \({\mathrm{0.75}}+{\mathrm{0.68}}x+{\mathrm{0.06}}x^{2}\) 
\(\mathrm{InP_{\mathit{x}}As_{\mathit{y}}Sb_{1\mathit{x}\mathit{y}}}\)/InAs  \({\mathrm{0.512}}+{\mathrm{0.030}}y{\mathrm{0.183}}y^{2}\) 
HigherLying Band Gaps
Higherlying bandgap energies, E_{1} and E_{2}, for some III–V binaries at 300 K
Binary  E_{1} (eV)  E_{2} (eV) 

AlN  7.76  8.79 
AlP  4.30  4.63 
AlAs  3.62–3.90  4.853, 4.89 
AlSb  2.78–2.890  4.20–4.25 
αGaN  6.9  8.0 
βGaN  7.0  7.6 
GaP  3.71  5.28 
GaAs  2.89–2.97  4.960–5.45 
GaSb  2.05  4.08–4.20 
InN  5.0  7.6 
InP  3.17  4.70 (E _{0} ^{′} ) 
InAs  2.50  4.70 
InSb  1.80  3.90 
Bowing parameters used in the calculation of the higherlying bandgap energies, E_{1} and E_{2}, for some cubic III–V ternaries. In those cases where no value is listed, linear variation should be assumed
Ternary  C_{A−B} (eV)  

E _{1}  E_{2} (E _{0} ^{′} )  
(Ga,In)N  −1.11  −1.26 
(Al,Ga)P  0  0 
(Al,In)P  0  0 
(Ga,In)P  −0.86  0 
(Al,Ga)As  −0.39  0 
(Al,In)As  −0.44  −0.24 
(Ga,In)As  −0.51  −0.27 
(Al,Ga)Sb  −0.31  −0.34 
(Al,In)Sb  −0.30  −0.14 
(Ga,In)Sb  −0.36  −0.15 
Ga(N,P)  0  0 
Ga(N,As)  0  0 
Ga(P,As)  0  0 
Ga(As,Sb)  −0.59  −0.19 
In(P,As)  −0.17  −0.03 
In(As,Sb)  \(\approx{\mathrm{0.8}}\)  \(\approx{\mathrm{1.4}}\) 
30.6.2 Carrier Effective Mass
Electron Effective Mass
Electron effective mass at the Γconduction band (m _{e} ^{Γ} ) and density of states (m _{e} ^{ α } ) and conductivity masses (m _{c} ^{ α } ) at the Xconduction and Lconduction bands of some III–V binaries. ZB = zinc blende
Binary  m _{e} ^{Γ} ∕ m_{0}  Density of states mass  Conductivity mass  

m _{e} ^{X} ∕ m_{0}  m _{e} ^{L} ∕ m_{0}  m _{c} ^{X} ∕ m_{0}  m _{c} ^{L} ∕ m_{0}  
AlN  0.29–0.45  –  –  –  – 
AlN (ZB)  0.26^{a}  0.78^{a}  0.37^{a}  
AlP  0.220^{a}  1.14^{a}  0.31^{a}  
AlAs  0.124  0.71  0.78  0.26^{a}  0.21^{a} 
AlSb  0.14  0.84  1.05^{a}  0.29  0.28^{a} 
αGaN  0.21  –  –  –  – 
βGaN  0.15  0.78^{a}  0.36^{a}  
GaP  0.114  1.58  0.75^{a}  0.37  0.21^{a} 
GaAs  0.067  0.85  0.56  0.32  0.11 
GaSb  0.039  1.08^{a}  0.54  0.44^{a}  0.12 
InN  0.044  –  –  –  – 
InN (ZB)  0.03 ^{a}  
InP  0.07927  1.09^{a}  0.76^{a}  0.45^{a}  0.19^{a} 
InAs  0.024  0.98^{a}  0.94^{a}  0.38^{a}  0.18^{a} 
InSb  0.013 
Bowing parameter used in the calculation of the electron effective mass m _{e} ^{Γ} at the Γconduction bands of some III–V ternaries
Ternary  C_{A−B} (m_{0}) 

(Ga,In)P  −0.01854 
(Al,Ga)As  0 
(Al,In)As  −0.012 
(Ga,In)As  −0.008 
(Ga,In)Sb  −0.010 
Ga(P,As)  0 
Ga(As,Sb)  −0.014 
In(P,As)  0 
In(As,Sb)  −0.027 
Electron effective mass m _{e} ^{Γ} at the Γconduction bands of some III–V quaternaries
Quaternary  m _{e} ^{Γ} ∕ m_{0} 

\(\mathrm{Ga_{\mathit{x}}In_{1\mathit{x}}P_{\mathit{y}}As_{1\mathit{y}}}\)/InP  \({\mathrm{0.04084}}+{\mathrm{0.03384}}y+{\mathrm{0.00459}}y^{2}\) 
\(\mathrm{Al_{\mathit{x}}Ga_{\mathit{y}}In_{1\mathit{x}\mathit{y}}As}\)/InP  0.043 + 0.031x 
Hole Effective Mass
The effective mass can only be clearly defined for an isotropic parabolic band. In the case of III–V materials, the valence bands are warped from spherical symmetry some distance away from the Brillouin zone center (Γ). Depending on the measurement or calculation technique employed, different values of hole masses are then possible experimentally or theoretically. Thus, it is always important to choose the correct definition of the effective hole mass which appropriate to the physical phenomenon considered.
Density of states heavy hole (m _{HH} ^{*} ), averaged light hole (m _{LH} ^{*} ), and spin orbit splitoff effective hole masses (m_{SO}) in some cubic III–V semiconductors. ZB = zinc blende
Material  \(m_{\text{HH}}^{*}/m_{0}\)  \(m_{\text{LH}}^{*}/m_{0}\)  m_{SO} ∕ m_{0} 

AlN (ZB)  1.77^{a}  0.35^{a}  0.58^{a} 
AlP  0.63^{a}  0.20^{a}  0.29^{a} 
AlAs  0.81^{a}  0.16^{a}  0.30^{a} 
AlSb  0.9  0.13  0.317^{a} 
βGaN  1.27^{a}  0.21^{a}  0.35^{a} 
GaP  0.52  0.17  0.34 
GaAs  0.55  0.083  0.165 
GaSb  0.37  0.043  0.12 
InN (ZB)  1.959 ^{a}  0.098 ^{a}  0.186 ^{a} 
InP  0.69  0.11  0.21 
InAs  0.36  0.026  0.14 
InSb  0.38  0.014  0.10 
30.6.3 Deformation Potential
Conductionband (a_{c}) and valenceband deformation potentials (a_{v}, b, d) for some cubic III–V binaries. ZB = zinc blende
Binary  Conduction band  Valence band  

a_{c} (eV)  a_{v} (eV)  b (eV)  d (eV)  
AlN (ZB)  −11.7^{a}  −5.9^{a}  −1.7^{a}  −4.4^{a} 
AlP  −5.54^{a}  3.15^{a}  −1.5^{a}  
AlAs  −5.64^{a}  −2.6^{a}  −2.3^{a}  
AlSb  −6.97^{a}  1.38^{a}  −1.35  −4.3 
βGaN  −21.3^{a}  −13.33^{a}  −2.09^{a}  −1.75^{a} 
GaP  −7.14^{a}  1.70^{a}  −1.7  −4.4 
GaAs  −11.0  −0.85  −1.85  −5.1 
GaSb  −9  0.79^{a}  −2.4  −5.4 
InP  −11.4  −0.6  −1.7  −4.3 
InAs  −10.2  1.00^{a}  −1.8  −3.6 
InSb  −15  0.36^{a}  −2.0  −5.4 
Conductionband (D_{ i }) and valenceband deformation potentials (C_{ i }) for some wurtzite III–V binaries (in eV)
Binary  Conduction band  Valence band  

D _{1}  D _{2}  C _{1}  D_{1}–C_{1}  C _{2}  D_{2}–C_{2}  C _{3}  C _{4}  C _{5}  C _{6}  
AlN  −10.23^{a}  −9.65^{a}  −12.9^{a}  −8.4^{a}  4.5^{a}  −2.2^{a}  −2.6^{a}  −4.1^{a}  
αGaN  −9.47^{a}  −7.17^{a}  −41.4  −3.1  −33.3  −11.2  8.2  −4.1  −4.7  
InN  −4.05^{a}  −6.67^{a}  4.92^{a}  −1.79^{a} 
30.7 Optical Properties
30.7.1 The Reststrahlen Region
It should be noted that in homopolar semiconductors like Si and Ge, the fundamental vibration has no dipole moment and is infrared inactive. In heteropolar semiconductors, such as GaAs and InP, the firstorder dipole moment gives rise to a very strong absorption band associated with optical modes that have a k vector of essentially zero (i. e., longwavelength optical phonons). This band is called the reststrahlen band. Below this band, the real part of the dielectric constant asymptotically approaches the static or lowfrequency dielectric constant ε_{s}. The optical constant connecting the reststrahlen nearinfrared spectral range is called the highfrequency or optical dielectric constant ε_{∞}. The value of ε_{∞} is, therefore, measured for frequencies well above the longwavelength LO phonon frequency but below the fundamental absorption edge.
Static (ε_{s}) and highfrequency dielectric constants (ε_{∞}) for some cubic III–V binaries. ZB = zinc blende
Binary  ε _{s}  ε _{∞} 

AlN (ZB)  8.07 ^{a}  4.25 
AlP  9.6  7.4 
AlAs  10.06  8.16 
AlSb  11.21  9.88 
βGaN  9.40 ^{a}  5.35 ^{a} 
GaP  11.0  8.8 
GaAs  12.90  10.86 
GaSb  15.5  14.2 
InN (ZB)  12.2 ^{a}  7.92 ^{a} 
InP  12.9  9.9 
InAs  14.3  11.6 
InSb  17.2  15.3 
Static (ε_{s}) and highfrequency dielectric constants (ε_{∞}) for some wurtzite III–V binaries
Binary  E ⊥ c  E ∥ c  

ε _{s}  ε _{∞}  ε _{s}  ε _{∞}  
AlN  8.3  4.4  8.9  4.8 
αGaN  9.6  5.4  10.6  5.4 
InN  10.6 ^{a}  7.03 ^{a}  12.3 ^{a}  7.41 ^{a} 
30.7.2 The Interband Transition Region
30.8 Carrier Transport Properties
Hall mobilities for electrons (μ_{e}) and holes (μ_{h}) obtained at 300 K for relatively pure samples of III–V binaries (in cm^{2} ∕ ( V s ) )
Binary  μ _{e}  μ _{h} 

AlN  125  14 
AlP  80  450 
AlAs  294  105 
AlSb  200  420 
αGaN  1245  370 
βGaN  760  350 
GaP  189  140 
GaAs  9340  450 
GaSb  12040  1624 
InN  3100  39 
InP  6460  180 
InAs  33000  450 
InSb  77000  1100 
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