Electronic structures of substitutional C and Oimpurities in wurtzite GaN

Chang Liu, Junyong Kang *

Department of Physics, Xiamen University, Xiamen 361005, People�s Republic of China

Abstract

The electronic structures of the substitutional O on N site and C on Ga site in wurtzite GaN have been studied

by employing ab initio �mixed-basis + norm conserving non-local pseudo-potential� method and a 32-atom wurtzite

supercell with and without lattice relaxations. Present calculations indicate that the host Ga atoms bonding to O

impurity relax outward slightly while one of them draws along the c-axis toward another. The charge density distri-bution appears distinctly lower with lattice relaxations near the host Ga atoms bonding to the O impurity. These results

suggest that the substitutional O with cation–cation-bond configuration is likely to act as the DX center in wurtzite

GaN with heavy O dopants. On the other hand, the host N atoms bonding to the substitutional C relax inward largely

which is accompanied by one of them turning toward another. The charge density distributions around the substitu-

tional C are distinctly higher with lattice relaxations. The results of the energy band structure suggest that the sub-

stitutional C acts as a deep electron trap that is expected to offer electrons under light excitation.

� 2003 Elsevier Science B.V. All rights reserved.

Keywords: Wurtzite GaN; Impurities; Lattice relaxation; DX center; Electronic structure

1. Introduction

III-nitrides exhibit some unique properties,

such as wide direct band gaps, strong interatomic

bonds, high external luminescence quantum effi-ciencies, and high thermal conductivity, which

make them ideal materials for high-brightness blue

light emitting diodes [1], blue lasers [2], and high-

temperature/high-power transistors [3,4]. Al-

though the growth techniques are increasingly

improved, some impurities, such as representative

carbon, oxygen and hydrogen elements, are unin-

tentionally incorporated as contaminants during

growth, which greatly influence the electronic

quality of III-nitrides, so it is important to un-

derstand their properties.Despite their importance for device application,

too little is still known about impurities in the III-

nitrides. The experimental investigations in this

field [5] are accompanied by first-principles calcu-

lations of impurities, such as C, Si, O and H [6–12].

Some authors suggested that substitutional C onto

cation site is likely to form DX-like configuration

in GaN according to their calculated results [6,8].Others believed that the DX centers originate from

the residual O impurities in GaN on basis of ex-

perimental results [12].

* Corresponding author. Tel.: +86-592-2185962; fax: +86-

592-2189426.

E-mail address: jykang@xmu.edu.cn (J. Kang).

0925-3467/03/$ - see front matter � 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0925-3467(03)00049-1

Optical Materials 23 (2003) 169–174

www.elsevier.com/locate/optmat

In this work, we made theoretical study to un-

derstand the configurations of substitutional C

and O impurities in wurtize GaN. Both of oxygen

impurity on substitutional N site and carbon atom

on substitutional Ga site, which may form DX

states, were concentrated on below. Furthermore,total and atomic partial densities of states were

calculated and analyzed with and without lattice

relaxation. Charge density distributions and band

structures were also studied for above two cases.

2. Calculation method

The calculations were performed by employing

an ab initio �mixed-basis + norm conserving non-

local pseudo-potential� method, which has been arather mature scheme in solid-state physics calcu-

lations. Norm-conserving non-local pseudo-po-

tentials are used in N, O and C elements. Local

orbits were generated from s and p state pseudo-

wave functions of nitrogen and p state pseudo-wave function of oxygen (or carbon). The

plane-wave cutoff energy was set to 14 Ry. We used

the Ceperly–Alder formula to form the exchange

and correlation energy, and the other constructions

were just as the same as those in Ref. [13]. Oxygen

(or carbon) impurities were placed in a 32-atom

wurtzite supercell. Moreover, the equilibrium lat-

tice constant of GaN unit was obtained to bea0 ¼ 0:303 nm by using the first-principles total-

energy calculation and determining the equilibrium

volume in total-energy versus cell-volume curves.

3. Results and discussion

3.1. Oxygen on nitrogen site

Substitutional oxygen on N site in GaN has

been shown to be the principle unintentional heavy

n-type dopant of as-grown GaN [14,15]. In thiscalculation, lattice relaxations around the substi-

tutional O atom and its four nearest-neighbor Ga

atoms were investigated. We considered the chan-

ges of total-energy with lattice relaxations and de-

termined the final atomic positions corresponding

to the minimum total energy. Both the substitu-

tional O and the nearest-neighbor Ga in [0 0 0 1]

direction are relaxed outward and thus the bond

length between them increases about 0.3%, as

schematic diagram shown in Fig. 1(a). This bond

does not break along the c-axis to form a broken-

bond (BB) type DX center. However, among threeother equivalent nearest-neighbor Ga atoms, two

of them move outward along the bonds by 2.5%

while one of them turns along c-axis besides the2.5% bond increase, as shown in Fig. 1(b). The

turning Ga atom draws near another Ga and de-

creases a bond angle, which is likely to form

cation–cation-bond (CCB). Despite the increased

bonds are possible to break, the degree of CCB ismore apparent than that of BB, while, in Ref. [7], it

Fig. 1. Schematic space (a) and top-view diagram (b) of mi-

crostructure around substitutional O without (solid) and with

(open) lattice relaxations.

170 C. Liu, J. Kang / Optical Materials 23 (2003) 169–174

is mentioned that the CCB DX center for oxygen

transforms itself into the BB type DX state in

wurtzite structure. Therefore, we believed that the

substitutional O atom in wurtzite GaN tends to be

the CCB type rather than the BB type if it forms

DX center.To understand energy states induced by the

substitutional O impurity, the energy band struc-

ture and the density of states (DOS) of O-doped

wurtzite GaN were calculated with and without

lattice relaxations. The energy states induced by the

substitutional O appear in the band gap below the

conduction band, as shown in Fig. 2(a). The states

shift about 0.13 eV closer to the conduction band inalmost k pionts after the lattice relaxations. At thesame time, the DOS (Fig. 2(b)) in the band gap

increases largely. Generally, the O atom substitut-

ing on N site has one more valence electron than

that of N and is likely to act as donors, providing

electron. Contrarily, the DX center in semicon-

ductors tends to trap two electrons due to a nega-

tive electron correlation energy U though its statesare closer to the bottom of the conduction band.

To understand whether the higher DOS in the band

gap is favourable for more electrons to be trapped,

we calculated the charge density around the sub-

stitutional O with and without lattice relaxations.

Fig. 3 shows charge density distribution of the

Ga layer nearest to the O atom. The charge density

in the central region of the three Ga atoms

bonding to the O impurity is distinctly higher

without lattice relaxations. This indicates that

the substitutional O with lattice relaxations is fa-vourable to trap more electrons, which agrees to

the negative-U model for the DX center. For these

reasons, we believed that the substitutional O with

CCB configuration is likely to act as the DX center

in wurtzite GaN. It has been well known that the

DX centers are usually formed in n-type AlxGa1�xAs with x > 0:20 or GaAs under high pressure orwith heavy dopants [16,17]. Similarly, O impuritywas measured to form the DX centers in

AlxGa1�xN with x larger than about 0.3 [18] or

under hydrostatic pressure higher than 20 GPa

[19]. In our calculation, O impurity concentration

is at least n > 1018 cm�3. The heavy O dopants

seem to be responsible for the formation of the DX

center with CCB configuration.

3.2. Carbon on gallium site

Carbon, as a group-IV atom, is an amphoteric

impurity in III-nitrides. It is likely to act as a do-

nor on gallium site and as an acceptor on nitrogen

Fig. 2. Energy band structure (a) and total DOS (b) of substitutional O on N site without (solid) and with (dash) relaxations.

C. Liu, J. Kang / Optical Materials 23 (2003) 169–174 171

site. Since the substitutional C on N site is inves-

tigated and discussed more widely, we only con-

centrate on the substitutional C on Ga site below.

The lattice relaxations around the substitutional

C atom on Ga site and its four nearest-neighbor N

atoms were also examined by calculation. The

substitutional C and the nearest-neighbor N atom

bonding in the c-axis relax in opposite directionand lead to the bond between them decreasing by

about 19%, as schematic diagram shown in Fig. 4.

The value is close to 18% calculated by Bogu-

slawski et al. [6]. Similarly, the three other equiv-

alent nearest-neighbor N atoms relax inward and

bring about 14% decreases of the bond lengths.

Besides this, one of them turns along c-axis anddraws near another N. Because of the intenseshrinking of nearest-neighbor N atoms to C im-

purity, the bonds between the C and nearest-

neighbor N atoms are impossible to break to form

a BB type of DX center in wurtzite GaN. How-

ever, whether the two drawn near N atoms canform anion–anion-bond and result a DX center

required further examination from the view point

of the charge density around the substitutional C.

Fig. 5 shows the charge density distributions of

the Ga atom layer containing C and its nearest N

atom layer. The charge density distribution

around the N atoms bonding to the C impurity is

distinctly higher with lattice relaxations. Further-more, the charge density increase can also be ob-

served on the Ga atom layer containing C atom

with lattice relaxations. This indicates that the

substitutional C with lattice relaxations is favour-

Fig. 3. Charge density distributions of the Ga layer nearest to

O atom: (a) without relaxations and (b) with relaxations. (The

atoms marked by � superscript are the influences from atoms in

vicinal layers.)

Fig. 4. Schematic space (a) and top-view diagram (b) of mi-

crostructure around substitutional C without (solid) and with

(open) lattice relaxations.

172 C. Liu, J. Kang / Optical Materials 23 (2003) 169–174

able to offer more electrons. In light of this, the

substitutional C with lattice relaxations is likely to

act as a donor rather than the DX center inwurtzite GaN.

However, the substitutional C is seldom mea-

sured to act as the donor in practise. To explain

this phenomenon, the energy band structures are

plotted in Fig. 6. The energy states induced by the

substitutional C on Ga site appear in the middle of

the band gap without lattice relaxations. Although

the state shifts about 0.57 eV closer to the con-duction band after the lattice relaxations, they are

still the deep electron trap, about 1 eV below the

conduction band. The electrons of the substitu-

tional C are hardly to ionized to the conduction

band even at high temperature lower than melting

point. Thus we believe that the influence of the

C-related donor is only visible in optical devices.

4. Conclusions

We have employed ab initio calculation with

and without lattice relaxations. The electronic

Fig. 5. Charge density distributions of the Ga atom layer

containing C (a,b) and its nearest N atom layer (c,d). ((a,c)

without relaxations; (b,d) with relaxations. The atoms marked

by � superscript are the influences from atoms in vicinal layers.)

Fig. 6. Energy band structure of substitutional C on Ga site

without (solid) and with (dash) lattice relaxations.

C. Liu, J. Kang / Optical Materials 23 (2003) 169–174 173

structures of the substitutional O on N site and C

on Ga site in wurtzite GaN have been investigated.

The results show that the nearest-neighbor Ga

atoms around the O dopant relax outward along

the bonds slightly. Besides this, one of them turns

toward another. At the same time, the chargedensity in the center region of the host Ga atoms

bonding to the O impurity appears distinctly lower

with lattice relaxations. These results indicate that

the substitutional O on N site acts as the CCB

type of DX center in wurtzite GaN with heavy

O dopants. On the other hand, the four nearest-

neighbor host N atoms around the substitutional

C relax inward largely, while one of them drawnear another slightly. The charge density distri-

butions around the substitutional C show much

higher with lattice relaxations. The results of the

energy band structure show that the substitutional

C acts as the deep electron trap that is expected to

offer electrons under light excitation. In practice,

complexes, such as ON–VGa, CGa–CN, ON–CN and

so on, are likely to form in GaN. Since the limits ofcomputer and time these complexes will be calcu-

lated in our further works.

Acknowledgements

This work was partly supported by the Special

Funds for Major State Basic Research Projects,National Natural Science Foundation, grants

from the Ministry of Education, and the Natural

Science Foundation of Fujian Province of China.

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