Journal of Crystal Growth 189/190 (1998) 532—536

Electronic structures of p-type GaN codoped with Be or Mgas the acceptors and Si or O as the donor codopants

Tetsuya Yamamoto!,",*, Hiroshi Katayama-Yoshida!,#

! Department of Condensed Matter Physics, Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki,Osaka 567, Japan

" Department of Computational Science, Asahi Chemical Industry Co., Ltd., 2-1 Samejima, Fuji, Shizuoka 416, Japan# PRESTO, Japan Science and Technology Corporation, Kawaguchi, Saitama 332, Japan

Abstract

We have investigated the interactions between p-type dopants (Be and Mg) and n-type codopants (Si and O) in p-typecodoped GaN using first-principles calculations. Our results reveal that the co-incorporation of Be(Mg)

G!with O

Nor

SiG!

in codoped p-type GaN produces high Be(Mg) concentrations with stable ionic charge distributions markedly due toa decrease in the Madelung energy in contrast to p-type GaN doped with only Be(Mg). Our calculations thus predict thatthe “codoping method (doping n- and p-type dopants at the same time)” is effective for the fabrication of high-conductivity p-type GaN with a wurtzite structure. ( 1998 Elsevier Science B.V. All rights reserved.

PACS: 71.15.Nc; 71.20.Nr; 71.55.Eq; 71.55.!i

Keywords: GaN; Codoping; Madelung energy; First-principles calculations

1. Introduction

While blue—green light-emitting diodes andlasers have been the driving force behind the dra-matic improvement in the growth technology ofGaN materials, p-type doping problems remainone of the crucial issues for large scale applicationsin the devices. Several investigations have focusedon the growth of p-type GaN [1—4]. They have

*Corresponding author. Fax: #81 545 62 3199; e-mail:yamateko@cs.fuji.asahi-kasei.co.jp.

proposed the subsequent removal of hydrogen asa general method for improving the p-type dopingof GaN. Various mechanisms, based on first-prin-ciple calculations, to limit the hole concentration inp-type doped GaN have been proposed [5].

Recently, we have proposed a new dopingmethod, the “codoping method” using p-type andn-type dopants simultaneously for the fabricationof high-conductivity p-type CuInS

2with chal-

copyrite structures [6,7] and p-type wide-band-gapsemiconductors such as GaN [8—10] and ZnSe [9],by the use of first-principles calculations. Brandt etal. produced high-conductivity p-type cubic-GaN

0022-0248/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved.PII S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 3 4 6 - 7

Table 1The differences in the calculated Madelung energy between undoped, p-type GaN crystals doped with Be or Mg alone and p-type O- orSi-codoping GaN : Be(Mg). The energy positions are measured relative to the Fermi level of each crystal. The 2nd row contains *E

Mbetween undoped and p-type doped GaN. The 4th row contains *@E

Mbetween Be(Mg)-doped and p-type O(Si)-codoped GaN : Be(Mg)

(eV)

Undoped Be-doped Mg-doped

*EM

— #34.02 #18.45O-codoped Si-codoped O-codoped Si-codoped

*@EM

!2.09 !7.93 !0.95 !6.47

using acceptor dopants (Be) and donor dopants (O)[11,12]. The codopant pair they have used co-incides with one of the four pairs we have predictedas suitable candidates.

Our aim in this work is to clarify the influence ofO or Si codoping on Be or Mg incorporation inp-type codoped GaN using Be or Mg as acceptorsand Si or O as donors. Si [13] and O [14] atomsare the most likely candidates for donors. Ourcalculations clearly demonstrate that the p-typecodoped GaN will exhibit the increased incorpora-tion of Be or Mg acceptors compared with p-typeGaN doped with the acceptors alone.

2. Methodology

The calculations are based on the local-density-functional theory where we treat exchange andcorrelation effects using the parametrization ofHedin and Lundquist and von Barth and Hedin[15—17] and on the augmented spherical wave(ASW) formalism [18]. We adopt the atomic sphereapproximation (ASA) with a correction term for thecalculations. The Madelung energy which reflectsthe long-range electrostatic interactions in the sys-tem is assumed to be restricted to a sum overmonopoles. For valence electrons, we employ theoutermost s and p orbitals for each atom. Westudied the crystal structures of doped and codopedGaN with periodic boundary conditions by gen-erating supercells that contain the object of interest:(1) For GaN doped with Be or Mg alone, wereplace two of the 16 sites of Ga atoms by acceptorsites in model supercells; (2) for GaN codoped withBe(Mg) and O, we replace two of the 16 sites of the

Ga atoms by the Be(Mg) atom sites and one of the16 sites of the N atoms by the O site; (3) for GaNcodoped with Be(Mg) and Si, we replace two of the16 sites of the Ga atoms by the Be(Mg) sites andone of the 14 sites of the remaining Ga atoms by theSi site.

3. Results and discussion

In our earlier theoretical study [8], the electronicstructures of GaN crystals with wurtzite structureshave been established as follows: (1) The mixingbetween the 2s and 2p states of N and the 4s and 4pstates of surrounding Ga, shifts the center of gravityof the local density of states of the N atom towardslower energy regions; (2) while an interaction be-tween the N 2p and the Ga 4s orbitals causes theshift of the 4s states of Ga atoms towards lowerenergy regions, charge transfers from Ga 4p to N 2sand 2p give rise to the shift of Ga 4p levels towardshigher energy regions above the Fermi level. Fromthe ionic characteristics of the chemical bonds inGaN, the understanding of the change in the stabil-ity of the ionic charge distributions by p- or n-typedoping is to recognize that the ion in the solidexperiences a strong electrostatic potential from thesurrounding ions of opposite charge. The maincontributor to the binding energy of the crystalsexhibiting ionic characteristics is electrostatic en-ergy and is called the Madelung energy, E

M.

In Table 1, we summarize the differences in thecalculated Madelung energy between undoped, p-type GaN crystals doped with Be (Fig. 1a) or Mg(Fig. 1b) alone and p-type O- or Si-codopingGaN : Be(Mg) (Fig. 1c and Fig. 1d). We determined

T. Yamamoto, H. Katayama-Yoshida / Journal of Crystal Growth 189/190 (1998) 532–536 533

Fig. 1. Crystal structures of (a) GaN : Be, (b) GaN : Mg, (c) GaN : Be(Mg), O and (d) GaN : Be(Mg), Si. Distances between the twop-type dopants in the supercells are (a) 6.09, (b) 4.51, (c) 4.51 and (d) 3.18 A_ .

the crystal structures under the condition that thetotal energy is minimized. Table 1 shows that p-type doping using Be or Mg leads to the destabili-zation of ionic charge distributions in p-type dopedGaN due to an increase in the Madelung energy.

The calculations reveal that Mg-doping leads tostable charge distributions compared with Be-dop-ing. However, we find that the impurity states dueto doped Mg are more localized on the neighboringN atoms than those due to doped Be. This suggeststhat Mg is a deeper acceptor than Be. Thus, Bespecies can be considered as suitable candidates foruse as acceptor dopants from the above and theexperimental data for the large (&200 meV) ioniz-ation energy for p-type GaN : Mg.

We will focus on Si- or O-codoping in GaN : Be.Table 1 shows that the formation of the complexwith Be—O—Be or Be—N—Si—N—Be is energeticallyfavorable. In addition, Fig. 1a, Fig. 1c and Fig. 1dclearly demonstrate that the codoping of the highlyelectronegative O atoms or Si atoms, which willdonate electrons to adjacent N sites, consistentlyenhances the incorporation of the Be acceptors.Thus, Si- or O-codoping will improve the crystalquality because of the inhibition of the formationof precipitates such as Be

3N

2at high Be concen-

trations.Next, we investigate the interaction between the

Si(O) and the Be atoms in p-type codoped GaN inmore detail. Fig. 2 shows the density of states(DOS) of (a) undoped GaN as a standard reference,(b—d) GaN : Be, Si and (e—g) GaN : Be, O. For site-decomposed DOS at N sites, the sites of N close to

Be were selected. Energy is measured relative to theFermi level (E

F). For both codoped crystals, a hole

at the top of the valence band is found to begenerated. We find that the electronic structuresof the two p-type codoped GaN crystals with high-er concentrations have the same band shape as thatof undoped GaN. The impurity states for thosep-type codoped crystals are in the energy region atthe top of the valence band and are delocalized onthe sites of N atoms, as determined from the site-decomposed DOS and dispersion relations. Thus,the ab initio calculations predict that both Si orO-co-doped GaN : Be has a shallow-acceptorsstate.

For Si-codoped GaN : Be, the analysis of thestate-decomposed DOS indicates that the hole atthe N sites in the complex, Be—N—Si—N—Be, is gen-erated by the strong interaction between Si 4p andBe 2p orbitals as shown in Fig. 2d. This suggeststhat the formation of the complexes composed ofacceptors and donors will give rise to a variation ofthe impurity levels in the band gap: the acceptorlevel is lowered and the donor level is raised simul-taneously. Thus we conclude that Si-codopingleads to higher hole concentrations.

For O-codoped GaN : Be, we find a strong inter-action between the O 2p orbitals and the Be 2porbitals as shown in Fig. 2f and Fig. 2g, whichcauses the variation of the impurity levels similar tothe case of p-type GaN codoped with Si and Be. Inaddition, the interaction between N 2p orbitals anddeeper 2p orbitals of O gives rise to a shift of N 2plevels towards higher energy regions. As a result, we

534 T. Yamamoto, H. Katayama-Yoshida / Journal of Crystal Growth 189/190 (1998) 532–536

Fig. 2. (a) Total density of states (DOS) for undoped GaN.(b—d) Total and site-decomposed DOS for Si codoped GaN : Be.(e—g) Total and site-decomposed DOS for O-codoped GaN : Be.In the site-decomposed DOS for the two p-type codoped GaN,p states at each site are illustrated.

find a higher contribution to the DOS of the holestates at the top of the valence band at the sites ofN close to the Be—O—Be complex than thoseat the other N sites compared with the abovecrystals.

Based on the previous results, it will be possibleto achieve a higher hole concentration by usingSi- or O-codoping for GaN : Be. In addition,we note that complexes such as Be—O—Be andBe—N—Si—N—Be have a short-range dipole scatter-ing mechanism on the mobility which is consider-ably less than the Coulomb potential of isolatedcharged impurities. This gives rise to an enhancedcarrier mobility.

4. Conclusions

We have investigated the role of n-type dopants,Si and O, codoping in doping properties of p-typeGaN doped with Be or Mg using ab initio elec-tronic band structure calculations. Our conclusionsare as follows: (1) The total energy calculationsshow that the formation of Be(Mg)—O—Be(Mg)structures or Be(Mg)—N—Si—N—Be(Mg) ones is en-ergetically favorable; (2) the variation of the im-purity levels caused by the strong interactionsbetween Si(O) and Be(Mg) will enhance the holeconcentrations in p-type codoped GaN. We predictthat the p-type codoped GaN using Be or Mg asacceptors and Si or O as donors will exhibit anincreased incorporation of Be or Mg acceptorscompared with p-type GaN doped with the accep-tors alone.

Acknowledgements

The authors would like to thank Dr. JurgenSticht of Molecular Simulations Inc. (MSI) for histechnical support. In this work, we use ESOCScode of MSI. Their sincere thanks are also due toProfessors S. Gonda and H. Asahi of ISIR, OsakaUniversity, for fruitful discussions and to GeneralManager Dr. T. Yamada and senior scientist Mr. Y.Ueshima (Asahi Chemical Industry Co., Ltd.), whogave their support and encouragement during thecourse of this study.

T. Yamamoto, H. Katayama-Yoshida / Journal of Crystal Growth 189/190 (1998) 532–536 535

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