Electronic properties of zinc-blende Scx Ga1−xN

phys. stat. sol. (b) 243, No. 12, 2780–2787 (2006) / DOI 10.1002/pssb.200541493

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Electronic properties of zinc-blende ScxGa1–xN

A. Ben Fredj*, 1, Y. Oussaifi1, N. Bouarissa2, and M. Said1

1 Unité de Physique des Solides, Faculté des Sciences de Monastir, Boulevard de l’Environnement,

5019 Monastir, Tunisia 2 Department of Physics, Faculty of Science, King Khalid University, Abha, P.O. Box 9004,

Saudi Arabia

Received 16 December 2005, revised 30 May 2006, accepted 1 June 2006

Published online 17 July 2006

PACS 71.20.Nr, 71.55.Eq

Using the empirical pseudopotential approach, we have investigated the electronic properties of GaN, ScN

and their hypothetical alloys ScxGa

1–xN in the zinc-blende structure. The band gaps at Γ-, X- and L-points

as well as the electron effective masses of Γ and X valleys were calculated as a function of scandium mo-

lar fraction x. The agreement between our results and the available experimental and previously calculated

data is fair.

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

Heterostructures based on III–V nitrides gained in recent years considerable interest in the technology of light emitting diodes (LEDs) and lasers aimed to operate in a wide wave length spectrum ranging from visible to ultraviolet. From fundamental view point, III–V nitride semiconductors exhibit very interest-ing microelectronic and optoelectronic properties as well. Most of research works were concentrated on group III nitrides and on GaN in particular [1]. There are other nitrides having interesting properties, such as scandium nitride. ScN is closely lattice matched to GaN, then combining the two binary semi-conductors to form Sc

xGa1–xN alloys or pseudomorphical heterostructures could be useful in technologi-

cal applications [2]. With regards to the structural properties, there are three common crystal structures for the group-III nitrides: wurtzite, zinc blende and rocksalt structures. ScN is known to stabilise in the rocksalt phase. Bai [3] indicates that cubic ScN is a good lattice match for zinc blende III-A nitrides. GaN crystallizes either in zinc blende or in wurtzite structures. The difference in the total energy be-tween these two phases is very small and therefore both of them can be obtained experimentally. Accord-ing to the general trends of the material properties of III–V nitrides, zinc blende GaN should be better suited for controlled n- and p-type doping than wurtzite. Moreover, cubic GaN has a higher drift velocity and a somewhat lower band gap than the wurtzite structure [4]. Because of the high melting temperature of both Sc and ScN, these materials can be used as a high temperature contact for the III–A nitrides and then could replace InN in III–A–N semiconductors alloys for high temperature device design [3]. How-ever, only a limited number of works has been focused on the growth and electronic properties of ScN [3, 5–10]. While zinc-blende ScN is a hypothetical structure only and even in GaN it is only a metasta-ble form that can be stabilized only by epitaxial growth, the mixed alloys might have some stability range in the zinc-blende structure for small semiconductor concentrations. In the present study, a calcula-tion of the electronic band parameters for Sc

xGa1–xN in hypothetical zinc blende structure has been per-

formed. To this end, we have used the empirical pseudopotential method (EPM) under the virtual crystal

* Corresponding author: e-mail: [email protected]

phys. stat. sol. (b) 243, No. 12 (2006) 2781

www.pss-b.com © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Original

Paper

approximation (VCA). Our numerically calculated results regarding the energy band gaps and effective masses over the full computational range of the zinc-blende structure alloy are reported. The rest of the paper is organized as follows. The calculational method is described in Section 2. Theoretical results are presented and compared where possible with the experimental data as well as other theoretical data available in the reference in Section 3. A brief summary is given in Section 4.

2 Calculations

The pseudopotential method is based on both orthogonal plane waves and quasi-free electron approxima-tions (for a review see Ref. [11]). The EPM involves the fitting of the atomic form factors to experiment so as to reproduce the observed gaps at selected points in the Brillouin zone as accurate as possible. The method of optimization of the empirical pseudopotential parameters used in the present work is the non-linear least-squares method [12]. Our non-linear least-squares method requires that the root-mean-square deviation of the calculated level spacing (LS’s) from the experimental ones defined by,

{ }

1

22( , )

( , )

∆

( )

m

i j

i j

E

m Nδ

È ˘Í ˙Í ˙=Í ˙-Î ˚

Â (1)

should be minimum. In Eq. (1), ( , ) ( , ) ( , )

exp cal∆i j i j i j

E E E= - , where ( , )

exp

i jE and ( , )

cal

i jE are the observed and calcu-

lated LS’s between the ith state at the wave vector i

=k k and the jth at j=k k , respectively, in the m chosen pairs (i, j). N is the number of the empirical pseudopotential parameters. The calculated energies given by solving the empirical pseudopotential secular equation depend nonlinearly on the empirical pseudopotential parameters. The starting values of the parameters are improved step by step by iterations until δ is minimized. If we denote the parameters by ( 1, 2, . . . , )p N

νν = and write them as

( 1) ( ) ∆p n p n pν ν ν

+ = + (2)

where ( )p nν

is the value at the n-th iteration. These corrections ∆pν are determined simultaneously by

solving a system of linear equations

( , ) ( , )

exp cal

1 ( , ) ( , )

( ) ( ) ∆ ( ( )) ( ); 1, 2, . . . , ,

N m m

i j i j i j i j i j

i j i j

Q Q Q Q p E E n Q Q Nν ν ν ν ν ν ν

ν

ν¢ ¢ ¢ ¢

=

È ˘- - = - - =¢Í ˙

Î ˚Â Â Â (3)

where ( , )

cal ( )i jE n is the value at the n-th iteration, i

Qν is given by

,

( )*( ) ( ) .i i ii

q i q i

q q qq

H kQ C C

pν

ν

¢

¢¢

∂Ê ˆ= È ˘Î ˚ Á ˜Ë ¯∂Â k k (4)

( )i

H k is the pseudo-Hamiltonian matrix at i

=k k in the plane-wave representation, and the i-th pseudo wave function at

I=k k is expanded as

[ ]( ) ( ) exp ( ) ,i

i i

k q i i q

q

r C i rΨ = +Â k k k (5)

qk being the reciprocal lattice vector. In the present calculations, three pairs of states i

k and jk : (Γ–Γ), (Γ–X) and (Γ–L) which corresponds to three band energy level spacing are used, with

(2π / ) (0, 0, 0)a=k stands for the Γ-point, (2π / ) (1, 0, 0)a=k for the X-point and 1 1 1

2 2 2(2π / ) ( , , )a=k

for the L-point (a is the lattice constant).

2782 A. Ben Fredj et al.: Electronic properties of zinc-blende ScxGa1–xN

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-b.com

Table 1 Band gap energies (eV) of zinc blende GaN and ScN fixed in the fits.

this work other calculations experiment

GaN Γ

ΓE 3.3 3.2a; 3.38b; 3.299c 3.2d, e; 3.3f; 3.25g

X

ΓE 4.57 4.7a; 4.57b; 4.52c

L

ΓE 6.04 6.2a; 5.64b; 5.59c

X

XE 6.82 7.6g

L

LE 6.99 7.0g

ScN Γ

ΓE 5.8 4.8h

X

ΓE 4.7 3.7h

L

ΓE 7.2 6.2h

X

XE 6.08

L

LE 7.71

a Ref. [13]; b Ref. [14]; c Ref. [15]; d Ref. [16]; e Ref. [17]; f Ref. [18]; g Ref. [19]; h Ref. [20]

The energy band-gaps at Γ , X and L high-symmetry points used in the fitting procedure for zinc-blende GaN and ScN are given in Table 1. It is to be noted that for zinc-blende ScN, our energy band gaps are fitted to those of the LDA calculations [20] due to the lack of experimental data on zinc-blende ScN. However, as is well known the LDA typically underestimates the band-gap. Since it is known that in rocksalt ScN the gap correction beyond LDA is about 1 eV, we may expect that a similar correction is needed for zinc-blende ScN. Therefore, a correction beyond LDA of 1 eV is added to all the gaps of interest. In order to check how well can our pseudopotential parameters reproduce other energy band gaps rather than the fitted ones, we have calculated the direct band gap energies X

XE and L

LE for zinc-

blende GaN and compared them with the experimental data reported in Ref. [19] that are directly observ-able critical points (see Table 1). The agreement between our results regarding L

LE and experiment is

excellent, whereas it is better than 11% for X

XE . The calculated X

XE and L

LE energy gaps are also given for

zinc-blende ScN and may serve as a reference due to the lack of experimental data. In the case of the zinc-blende semiconductors such as the case here, only six pseudopotential form factors are sufficient to calculate the band structure. Table 2 lists the final adjusted symmetric ( ( ))

SV G and anti-symmetric

( ( ))A

V G pseudopotential form factors (in Ry) and the used lattice constants (in Å) for zinc-blende GaN and ScN, where G is a reciprocal lattice vector. In fact the symmetric and anti-symmetric form factors are non zero for 2

3, 8,11, . . .G = and 23, 4,11, . . .G = in units of 2(2π / )a , respectively. a is the lattice

constant. For example, (3)S

V and (3)A

V are the Fourier components of the atomic pseudopotential at G = (1, 1, 1). Our treatment for alloys of interest is extended straightforward through the use of the VCA.

Table 2 Pseudopotential form factors and lattice constants for zinc blende GaN and ScN.

material a (Å)

–GaN –4.50a

–ScN –4.88b

symmetric form factors (in Ry )

VS(3) VS(8) VS(11)

–0.347 –0.016 –0.212

–0.434 –0.024 –0.025

anti-symmetric form factors (in Ry )

VA(3) VA(4) VA(11)

–0.160 –0.200 –0.135

–0.058 –0.320 –0.241

a Ref. [16]; b Ref. [20]

phys. stat. sol. (b) 243, No. 12 (2006) 2783


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Paper

Thus, for the mixed ternary crystal 1

Sc Ga Nx x-

being studied here, the potential is expressed as,

ScGaN ScN GaN( ) ( ) (1 ) ( )V r xV r x V r= + - . (6)

The lattice constant of the alloys under consideration is obtained using Vegard’s law.

3 Results

Using the EPM within the VCA, we have calculated the electron energy band structure of ScxGa1–xN as a

function of the Sc molar fraction. In Fig. 1, we display the electronic band structures of zinc-blende GaN and ScN. Note that there is four distinct sets of occupied valence bands where the lowest ones have the usual shape expected for the known zinc-blende materials [21–23]. The conduction bands are more dispersive than the valence ones because they are more ‘free-electron like’. The free electron behaviour results in more dispersive bands and band crossing. The band structures of zinc-blende GaN (Fig. 1a) and zinc-blende ScN (Fig. 1b) look rather qualitatively similar. The main difference between these two band structures is, of course, the fundamental gap as well as the other direct and indirect band gaps that are different in magnitude. The same conclusion can be drawn if we compare between the electronic band structure of zinc-blende GaN and that reported by Miwa and Fukumoto [23] using first-principles calculations. As for electronic band structures of zinc-blende Sc

xGa1–xN (0 < x < 1), which are not pre-

-10

-5

0

5

10

15

20

25

30

35

Ene

rgy

(eV

)

Γ X L Γ K X

-10

-5

0

5

10

15

20

25

En

erg

y(e

V)

ΓΓΓΓ X L ΓΓΓΓ K X

Fig. 1 Electronic band structure for zinc-blende (a) GaN and (b) ScN.

a)

b)

2784 A. Ben Fredj et al.: Electronic properties of zinc-blende ScxGa

1–xN


0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

EX

ΓΓΓΓ

EΓΓΓΓ

ΓΓΓΓ

EL

ΓΓΓΓ

En

erg

y(e

V)

Composition x

Fig. 2 x-dependent band gaps Γ

ΓE , X

ΓE and L

ΓE in zinc blende Sc

xGa

1–xN.

sented here because of their similar picture to that of zinc-blende GaN and ScN, two main features were revealed: (i) the valence band of this ternary remains topologically similar going from GaN to ScN; (ii) magnitudes of band gaps, valence and conduction band positions change with x. From the band structure calculation, we have deduced the band gap energies, namely Γ

ΓE , X

ΓE and L

ΓE of Sc

xGa1–xN at Г-, X- and

L-points, respectively. The results are depicted in Fig. 2. The solid curves indicate the quadratic least-squares fits to our data. As can be seen, the direct band gap energy Γ

ΓE as well as the indirect ones X

ΓE and

L

ΓE show a non-linear behaviour with increasing x. On going from x = 0 (GaN) to x = 1 (ScN), Γ

ΓE in-

creases non-linearly. Using the full-potential linearized augmented plane wave method, Moreno-Armenta et al. [2] have calculated the electronic properties of wurtzite Sc

xGa1–xN for scandium concentrations

from 0% up to 100%. Their results showed that increasing the amount of scandium results in smaller band gaps suggesting hence a different behaviour with Γ

ΓE in zinc-blende Sc

xGa1–xN. The main result in

this study is the crossover from a direct to an indirect band gap which is found at the alloy composition x = 0.39 which corresponds to an energy of 4.89 eV. More commonly, one defines a band gap bowing

parameter b by writing,

[ ]( ) (0) (1) (0) (1 ) .g

E x E E E x bx x= + - - - (7)

The obtained analytical expressions for Γ

ΓE , X

ΓE and

L

ΓE within the expression (7) are as follows:

Γ 2

Γ

X 2

Γ

L 2

Γ

( ) 3.30 5.08 2.57

( ) 4.59 1.22 1.14

( ) 6.08 + 5.72 4.58

E x x x

E x x x

E x x x

= + - ¸Ô

= + - ˝Ô= - ˛

(8)

All energies are in eV. The quadratic terms correspond to the band-gap optical bowing parameters. The relevant values of this parameter as calculated from the x dependent expression (8) are –2.57, –1.14 and –4.58 eV for Γ

ΓE , X

ΓE and L

ΓE , respectively. These values seem to be roughly larger than those ob-

tained for 1

Ga In Asx x-

[24] and 1

InP Sbx x-

[25] ternary alloys suggesting therefore that the disorder effect is more important on energy band gaps of nitrogen containing semiconductors. In fact, the observed bowing parameters exp tb are separate into a contribution

Ib described by the VCA (

I VCAb b= ) and a contri-

bution IIb due to disorder effects [26]. Thus, we do believe that the non-linearity of the energy band-gaps

versus the composition x arises from order effects which exist already in a fictitiously periodic alloy. It is to be noted that the band-gap bowing parameters are negative, meaning that the studied band-gaps bow upwards. However, in most semiconductor alloy systems the gaps bow downwards [13, 27–29]. This is

phys. stat. sol. (b) 243, No. 12 (2006) 2785


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Paper

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350.18

0.19

0.20

0.21

0.22

0.23E

lect

ron

effe

ctiv

em

ass

Composition x

Fig. 3 Electron effective mass (in units of the free electron mass) of Г valley in zinc blende ScxGa

1–xN as

a function of composition x.

quite interesting. However, one should be careful about the results regarding the gaps of the alloy sys-tem. In fact, the calculation for the electronic structure of alloys has been made within the VCA in which the alloy potential is replaced by the concentration weighted average of the constituent potentials while neglecting compositional disorder effects. However, recent experimental and theoretical studies on sev-eral semiconductor alloys indicate that the VCA breaks down whenever the mismatch between the elec-tronic properties of the constituent atoms exceeds a certain critical value [24, 27, 30]. In the present study, the lattice mismatch between GaN and ScN is estimated to be 8% which is a large mismatch. This leaves uncertainty on the accuracy of our VCA results regarding the energy band-gaps. Future experi-mental measurements and first-principles calculations may throw a light on this. Values of the effective mass at principal band extrema provide important information on the semicon-ductor properties. We have calculated the effective masses for the two lowest conduction bands Г and X corresponding respectively to the first region with a direct gap [ ]0, 0.39xŒ and the second region with an indirect gap [ ]0.39,1xŒ . In the first region, we calculate the effective mass at Г-point as a function of scandium composition x (Fig. 3). As can be noted, the electron effective mass at Г increases monotonically with x. The solid curve indicates the quadratic least-squares fit to our data. The calculated electron effective mass (in units of the free electron mass

0m ) in the conduction band minimum at Г valley has been expressed using a

relation similar to that used for band-gap energies (i.e. Eq. (7)). The obtained result in the scandium composition range 0–0.3 yields,

2

,Γ* ( ) 0.185 0.117 0.003 .e

m x x x= + - (9)

Note that the quadratic term in Eq. (9) is too weak and hence the behaviour of the ,Γ*e

m versus x is almost linear. At x = 0 we find again the electron effective mass for zinc-blende GaN (Table 3). Our calculated

Table 3 Electron effective mass in units of the free electron mass in zinc blende GaN and ScN.

material this work

,Γ*( )e

m this work

,X*( )e

m other calculations

,Γ*( )e

m experiment

,Γ*( )e

m

GaN 0.185 0.336 0.127a, b; 0.13c; 0.15d; 0.19e, 0.124f 0.15g ScN 0.381

a Ref. [13]; b Ref. [31]; c Ref. [32]; d Ref. [15]; e Refs. [33, 34]; f Ref. [35]; g Ref. [36]

2786 A. Ben Fredj et al.: Electronic properties of zinc-blende ScxGa

1–xN


0.4 0.5 0.6 0.7 0.8 0.9 1.00.33

0.34

0.35

0.36

0.37

0.38

0.39E

lect

ron

effe

ctiv

em

ass

Composition x

Fig. 4 Electron effective mass (in units of the free electron mass) of X valley in zinc blende ScxGa

1–xN as

a function of composition x.

electron effective mass for zinc-blende GaN agrees reasonably well with the experimental one reported in Ref. [36]. As compared to other theoretical calculations, it is larger than those reported in Refs. [13, 15, 31, 32, 35] and smaller than those obtained by Reynods et al. [33] and Kim et al. [34]. Using cyclo-tron resonance measurements, Drechsler et al. [37] had determined the electron effective mass in hex-agonal GaN film grown by metal organic vapour phase epitaxy on sapphire substrates. Their measured value was found to be

00.22 0.005m± (m0 is the free electron mass). However, when taking polaron

effects into account, the band edge mass was found to be 0

0.20 0.005m± . This value is in reasonable agreement with that found in the present calculations as well as the experimental one reported in Ref. [36] for zinc-blende GaN suggesting therefore that the conduction band minima in GaN in both zinc-blende and wurtzite and their corresponding states are similar in nature in both structures. Likewise in the second region, we calculate the effective mass at X-point as a function of scandium composition x (Fig. 4). We notice that the electron effective mass at X increases as well monotonically with x. The solid curve indicates the quadratic least-squares fit to our data. Our results regarding the electron effective mass (in units of the free electron mass

0m ) in the conduction band minimum at X

valley have been again expressed similarly to those at Γ valley giving in the scandium composition range 0.4–1 the expression:

2

,X* ( ) 0.358 0.112 0.135 .e

m x x x= - + (10)

In view of Table 3, one may note that at x = 1 we find the electron effective mass to be 0.381m0 for zinc blende ScN. In this case, to the best of our knowledge, there is neither experimental data nor other calculated values for the conduction band mass with which we can compare our calculated value. Thus, our results may serve as a reference, whereas at x = 0, the electron effective mass for zinc-blende GaN is estimated to be 0.336m0 (Table 3). This value is in reasonable agreement with that of

0* 0.3t

m m= re-ported recently in Ref. [28] for the X valley in GaN, which in turn is similar to the value obtained by Fan et al. [32].

4 Conclusion

Electronic band structures of zinc blende GaN, ScN and their alloys ScxGa1–xN are calculated using the

empirical pseudopotential method. The composition dependence as a function of the band gap energies has been obtained and the alloy exhibits features of both direct and indirect band gap semiconductors as a function of the composition. Our calculation predicts that the crossover from a direct to an indirect band gap is at x = 0.39. The band gap bowing for Γ

ΓE is found to be constant and negative. Electron effec-

phys. stat. sol. (b) 243, No. 12 (2006) 2787


Original

Paper

tive masses are also calculated at the Г and X valleys for different compositions. Polynomial forms are obtained to approximate both the energy gap and the effective mass as function of scandium composi-tion. For lack of experimental and theoretical data in the literature for ScN, our results are predictions and may serve as a reference. While the present calculations still leaves a doubt on the validity because of the VCA, it might be worthwhile checking with future works. Therefore, more experimental meas-urements and first-principles calculations are needed in order to obtain more accurate and reliable results.

References

[1] W. R. L. Lambrecht and S. N. Rashkeev, phys. stat. sol. (b) 217, 599 (2000).

[2] M. G. Moreno-Armenta, L. Mancera, and N. Takeuchi, phys. stat. sol. (b) 238, 127 (2003).

[3] X. Bai, Growth and Characterization of IIIB-nitride Semiconductors and Devices, Ph.D. Dissertation, Physics

Department, Ohio University, Athens, USA (2000).

[4] E. A. Albanesi, W. R. L. Lambrecht, and B. Segall, Phys. Rev. B 48, 17841 (1993).

[5] F. Perjeru, X. Bai, M. I. Ortiz-Libreros, R. Higgins, and M. E. Kordesch, App. Surf. Sci. 175/176, 490 (2001).

[6] H. Al-Brithen and A. R. Smith, Appl. Phys. Lett. 77, 2485 (2000).

[7] A. R. Smith, H. A. H. Al-Brithen, D. C. Ingram, and D. Gall, J. Appl. Phys. 90, 1809 (2001).

[8] D. Gall, I. Petrov, P. Desjardins, and J. E. Greene, J. Appl. Phys 86, 5524 (1999).

[9] D. Gall, M. Städele, K. Järrendahl, I. Petrov, P. Desjardins, R. T. Haasch, T.-Y. Lee, and J. E. Greene, Phys. Rev.

B 63, 125119 (2001).

[10] X. Bai and M. E. Kordesch, Appl. Surf. Sci. 175/176, 499 (2001).

[11] M. L. Cohen and J. R. Chelikowsky, Electronic Structure and Optical Properties of Semiconductors (Springer-

Verlag, Berlin, 1988).

[12] T. Kobayasi and H. Nara, Bull. Coll. Med. Sci., Tohoku Univ. 2, 7 (1993).

[13] A. Bhouri, F. Ben Zid, H. Mejri, A. Ben Fredj, N. Bouarissa, and M. Said, J. Phys.: Condens. Matter 14, 7017

(2002).

[14] W. J. Fan, M. F. Li, T. C. Chong, and J. B. Xia, Solid State Commun. 97, 381 (1996).

[15] I. Vurgaftman and J. R. Meyer, J. Appl. Phys. 94, 3675 (2003).

[16] T. Lei, T. D. Moustakas, R. J. Graham, Y. He, M. Fanciulli, and S. J. Berkowitz, J. Appl. Phys. 71, 4933 (1992).

[17] T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham, and J. S. Scanlon, Appl. Phys. Lett. 59, 944

(1991).

[18] W. R. L. Lambrecht, B. Segall, S. Strite, G. Martin, A. Agarwal, H. Morkoc, and A. Rocket, Phys. Rev. B 50,

14155 (1994).

[19] S. Logothetidis, J. Petalas, M. Cardona, and T. D. Moustakas, Phys. Rev. B 50, 18017 (1994).

[20] N. Takeuchi, Phys. Rev. B 65, 045204 (2002).

[21] N. Bouarissa and H. Aourag, Solid State Commun. 101, 205 (1997).

[22] N. Bouarissa, Superlattices Microstruct. 26, 279 (1999).

[23] K. Miwa and A. Fukumoto, Phys. Rev. B 48, 7897 (1993).

[24] N. Bouarissa, Phys. Lett. A 245, 285 (1998).

[25] N. Bouarissa, S. Bougouffa, and A. Kamli, Semicond. Sci. Technol. 20, 265 (2005).

[26] J. E. Bernard and A. Zunger, Phys. Rev. B 36, 3199 (1987).

[27] M. Jaros, Rep. Prog. Phys. 48, 1091 (1985).

[28] I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).

[29] S. Bounab, Z. Charifi, and N. Bouarissa, Physica B 324, 72 (2002).

[30] A. Zunger and S. Mahajan, in: Handbook on Semiconductors, Vol. 3, edited by S. Mahajan (Elsevier, New

York, 1994), p. 1399.

[31] S. K. Pugh, D. J. Dugdale, S. Brand, and R. A. Abram, Semicond. Sci. Technol. 14, 23 (1999).

[32] W. J. Fan, M. F. Li, T. C. Chong, and J. B. Xia, J. Appl. Phys. 79, 188 (1996).

[33] D. C. Reynods, D. C. Look, W. Kim, O. Aktas, A. Botchkarev, A. Salvador, H. Morkoc, and D. N. Talwar,

J. Appl. Phys. 80, 594 (1996).

[34] K. Kim, W. R. L. Lambrecht, B. Segall, and M. van Schilfgaarde, Phys. Rev. B 56, 7363 (1997).

[35] K. Kassali and N. Bouarissa, Solid State Electron. 44, 501 (2000).

[36] M. Fanciulli, T. Lei, and T. D. Moustakas, Phys. Rev. B 48, 15144 (1993).

[37] M. Drechsler, D. M. Hofmann, B. K. Meyer, T. Detchprohm, H. Amano, and I. Akasaki, Jpn. J. Appl. Phys.

Lett. 34(2), 1178 (1995).

Documents

Electronic properties of zinc-blende Scx Ga1−xN