Physics of defects and hydrogen in dilute nitrides

S.B. Zhang, A. Janotti, S.-H. Wei and C.G. Van de Walle

Abstract: First-principles theory is capable of unveiling physical properties of the various defectsin dilute nitrides. The authors discuss some of their recent results for native defects, N–N pairs, aswell as for hydrogen in GaAsN and GaPN. The studies have shown that defect physics of dilutenitrides is qualitatively different from that of conventional semiconductors owing to theinvolvement of nitrogen. This leads to a number of phenomena ranging from the existence of anew class of intrinsic traps, such as the N–N split interstitials, AsGa–N and VGa–N pairs, toa surprising modification of the fundamental bandgap by hydrogen.

1 Introduction

Dilute nitrides are emerging materials for optoelectronics.These materials provide the opportunity to study semi-conductor alloys where atoms of very large size mismatchare mixed purposely by modern epitaxial growth tech-niques. Extensive efforts have been made towards theunderstanding of the electronic properties of such alloys,in which size-mismatch-induced spatial localisation of theelectronic states appears to have played a very importantrole, in contrast to conventional alloys. In comparison,however, relatively little progress has been made towardsthe understanding of the defect and impurity properties inthis class of materials despite the fact that such studies areessential for realising the vast technological potential ofdilute nitrides. The electronic-state localisation of thenitrogen atoms is also a key for the understanding of thedefect=impurity properties as, in many aspects, theselocalised states are no different, in their characteristics,from any impurity states.

Regarding defects and impurities, recent experimentshave demonstrated the following unique properties:

(i) Significantly low minority carrier lifetimes due to someunspecified defect(s) that is probably nitrogen-related. Toosmall minority carrier lifetimes lead to too small diffusionlengths, hindering solar cell performance.(ii) Exceptional modification of the fundamental bandgapby donor-like impurities. For example, it was shown thatSi could increase the bandgap of GaAsN significantly.More strikingly, hydrogen could increase the gap byseveral hundreds of meV, fully recovering the optical gapof GaAs.(iii) While hydrogen is typically an amphoteric impurity inconventional semiconductors, experimental evidence showsthat H behaves exclusively as a donor in dilute GaAsN andGaInAsN.

(iv) Unexpected interaction among defects=impuritiesmediated by N in the host; for example, it was recentlyshown that the presence of hydrogen could increase theconcentration of Ga vacancies in GaAs. This effect issignificantly enhanced in GaAsN. A recent experiment alsoindicates that the concentration of anion antisite in dilutenitrides can be significantly higher than that in thecorresponding binary semiconductors.

In this paper, we will address some of these basic issuesconcerning defects and impurities by reviewing some of therecent first-principles total energy calculations. We discussthe theory of defects in epitaxial materials. It appears thatepitaxy is the key for the growth of the dilute nitrides andthe physics of the defects=impurities in such materials couldbe qualitatively different from those semiconductors grownby more traditional methods. We will discuss the formationof nitrogen and native defect complexes and nitrogen–hydrogen complexes, followed by a brief summary.

2 Theory of defects in epitaxial materials

Defect physics in epitaxial materials can be qualitativelydifferent from that in melt-grown materials. This is becauseepitaxial films are often not in a true equilibrium with otherbulk phases. As a result, despite the fact that the calculatedthermodynamic solubility (or solid solubility) of N in bulkGaAs is exceedingly low (½N�< 1014cm�3 at T ¼ 650 �C)[1–3] owing to the formation of a fully relaxed, secondaryGaN phase and yet, single-phase epitaxial films grown atT ¼ 400–650 �C with [N] as high as �10% have beenreported [4–9]. To explain the approximately eight ordersof magnitude difference in the nitrogen solubility inGaAs:N, surface-reconstruction-induced subsurface strainhas been considered [3]. While the calculated N solubilitywithin this model is significantly larger than in previouscalculations, it is still four orders of magnitude too smallcompared with experiments, and it is not clear how thesurface energetics during the growth would affect defectformation and impurity incorporation deep inside the bulk.

Recently, we suggested that the formation of thesecondary GaN phase could be suppressed during epitaxialgrowth [10]. Indeed, a key factor in fabricating high [N]homogeneous GaAs:N films is to eliminate the formation ofthe GaN precipitates [11]. As such, there could exist anew region of atomic chemical potentials ðmGa; mAs; mNÞavailable for epitaxial growth but not for melt growth.

q IEE, 2004

IEE Proceedings online no. 20041037

doi: 10.1049/ip-opt:20041037

S.B. Zhang, A. Janotti and S.-H. Wei are with the National RenewableEnergy Laboratory, Golden, CO 80401, USA

C.G. Van de Walle is with Palo Alto Research Center, 3333 Coyote HillRoad, Palo Alto, CA 94304, USA

Paper first received 20th May and in revised form 20th July 2004

IEE Proc.-Optoelectron., Vol. 151, No. 5, October 2004 369

The chemical potentials are the energies of individual atomsin the reservoirs (such as in the gas sources) that affectimpurity substitutional energy [12]. First, let us considerequilibrium N solubility. The absolute formation energy of acharge-neutral defect or impurity is defined [12] as

DHf ¼ EtotðdefectÞ � EtotðhostÞ þ nGamGa þ nAsmAs þ nNmN

ð1Þwhere Etot(host) is the total energy of a supercell host usedin the calculation, EtotðdefectÞ is the total energy for thesame supercell but with a defect, and n ¼ ðnGa; nAs; nNÞ isthe number of particles being removed to form the defectfrom the host to a reservoir of chemical potentialsm ¼ ðmGa; mAs; mNÞ: If one sets the energies of bulk Ga,bulk As and N2 gas as the reference zeros, then the chemicalpotentials satisfy

mGa � 0; mAs � 0 and mN � 0 ð2ÞThis happens because if m> 0; an elemental solid (or gasphase) will spontaneously form that hinders any furtherincrease of m: For GaAs to be thermodynamically stable,it also requires that mGa þ mAs ¼ mGaAs ¼ DHðGaAsÞ ¼�0:62 eV; which is the calculated formation enthalpy ofGaAs. Thus, defect formation energies in GaAs:N arefunctions of only two independent variables, ðmAs; mNÞ;satisfying (see Fig. 1)

DHðGaAsÞ � mAs � 0 and mN � 0 ð3ÞPhysically, less negative mAs ðor mNÞ corresponds to moreAs(or N)-rich growth conditions, and vice versa. Spon-taneous formation of the secondary bulk GaN phase puts afurther restriction on the chemical potentials, namely

mGa þ mN � mGaN ð4ÞBecause mGaN ¼ DHðGaNÞ ¼ �1:57 eV; the upper limit formN is not mmax

N ¼ 0 in (3), but mmaxN ¼ �1:57þ 0:62 ¼

�0:95 eV at the As-rich limit ðmAs ¼ 0Þ: This defines the‘original region’ in Fig. 1. Nitrogen substitution is a specialcase of (1)

DEsub ¼ DEtot � mN þ mAs ð5Þwhere DEtot ¼ EtotðNAsÞ � EtotðGaAsÞ: The higher the mmax

N

(and the lower the mminAs ), the lower the minimum DEmin

sub is.The calculated DEmin

sub is 1.64 eV, which accounts for theextremely low [N] in melt-grown GaAs:N.

Second, let us consider surface-enhanced N solubility.In the epitaxial growth, a relaxed GaN bulk phase couldform if both of the following conditions are met:

(i) N accumulates and precipitates at the surface to formGaN layer. This implies the spontaneous formation of aGaN surface layer, which, at low temperature, is equivalentto having a single nitrogen substitution energy DE

surfsub equals

zero.(ii) The layer thickness exceeds the critical thickness fordislocation formation.

Condition (i) precedes condition (ii), thus, setting a upbound for mN and a low bound for mAs for epitaxial GaAs:N[cf. (5)], that is

DEsurfsub mmin

As ; mmaxN

� �¼ DE

surftot � mmax

N þ mminAs ¼ 0 ð6Þ

where

DEsurftot ¼ E

surftot ðNAsÞ � E

surftot ðGaAsÞ ð7Þ

is the total energy difference of an N substituting an As onthe surface. If one neglects the energy due to nitrogen–nitrogen interaction at the surface, DE

surftot would be

independent of the surface N concentration. Therefore,one can solve (6) to find ðmmin

As ; mmaxN Þ; rather than plug

ðmminAs ; m

maxN Þ into (5) to determine DEmin

sub ; and from which [N]can be calculated using standard Boltzmann statistics.

Nitrogen incorporates into GaAs via an N–As exchangemechanism at the topmost surface layer [13–16]. A typicalGaAs (001) surface is an As-terminated ð2� 4Þ surfaceshown in the inset of Fig. 2 [17], where the n ¼ 1 and n ¼ 3layers contain six and eight As atoms per 2� 4 cell,respectively. Figure 2 shows DEsub for the surface sites 1and 3D and for the bulk site, as a function of the atomicchemical potentials along the N- and As-rich boundaries inFig. 1. We see that:

(i) DEsubð3DÞ and DEsubðbulkÞ are only moderately higherthan DEsubð1Þ; by 0.30, and 0.24 eV, respectively. Thus,DEsub is relatively insensitive to where the N atom is at thesurface layer, or even inside the bulk.(ii) Using the lower DE

surfsub value ¼ DEsubð1Þ; in [10]

we determined that ðmminAs ; m

maxN Þ ¼ ð�0:44 eV; 0Þ; at which

Fig. 1 Physically accessible region of the chemical potentialsðmAs; mNÞ is shown (from [10])

‘Original region’ is defined by (2) and (4), while the ‘expanded þ original’region is defined by (2) and (6)

Fig. 2 N substitutional energies DEsub as functions of ðmAs; mNÞ(from [10])

Inset: GaAsð2� 4Þ surface, indicating the various substitution sites; anionis denoted by a dark circle while Ga is denoted by a light circle

IEE Proc.-Optoelectron., Vol. 151, No. 5, October 2004370

DEminsub (bulk) is significantly reduced from the original

1.64 eV to 0.24 eV. This gives rise to [N] �4% at 650 �C:The corresponding accessible ðmAs;mNÞ is the (expandedþoriginal) region in Fig. 1.

In essence, the physics of surface-enhanced N solubilityresides in the difference between the formation energy ofGaN on the GaAs surface and that of relaxed bulk GaN. Thedifficulty of forming GaN at the GaAs surface leads to ahigher achievable mN ; thus, a higher epitaxial N solubility.

The above discussion does not consider kinetic effects onthe nucleation processes of the secondary GaN phase.Consequently, N concentration is expected to increase withtemperature T. In reality, however, at high T and high Nconcentration, N nucleation can occur even before DE

surftot

approaches zero, because the diffusion of the surfacenitrogen atoms enhances the possibility of a surface Nfinding a low-energy nucleation site. This can lower theachievable mN and reduce N solubility. A number ofexperiments [5, 9, 18] indeed showed that [N] in high-concentration samples is nearly unchanged or decreases as Tincreases in the range 400–650 �C:

3 Nitrogen and native defect complexes

The expanded region of the chemical potentials discussedabove forms a new basis for the study of defects and

impurities in epitaxially grown dilute III–V nitrides. At highmN ; (and thus, N concentration), defect physics changesqualitatively from that at low N concentration in at least twofundamental ways: (i) the dominant defects are no longerthe same; and (ii) the electronic properties of the leadingdefects can be qualitatively different from the correspondingdefects in the absence of N. To study minority-carrier traps,we have considered [10] the charge-neutral defects in GaAsshown in Fig. 3:

(i) N–N split interstitial. Here, an N2 molecule replaces onehost As atom. Each N is threefold co-ordinated. The splitinterstitial is important because of the small size of theN atom and the exceptionally strong N–N bond. Thecalculated N–N bond length is 1:39 �A; compared to 1:10 �Afor an N2 molecule.(ii) N–As split interstitial. The N–As pair is a variation ofthe N–N split interstitial in (i). Here, the calculated N–Asbond length is 1:85 �A:(iii) ðAsGa –NAsÞnn pair, where nn stands for the nearestneighbour. The N is very electronegative. Therefore, italways attracts donor defects such as AsGa: Moreover, NAs

is associated with compressive strain due to the small size ofN, while AsGa is associated with tensile strain due to twoextra electrons in the non-bonding orbital. The ðAsGa –NAsÞnn-pair has a 0.5-eV binding energy. Thus, isolated AsGa israre at high N concentration. The neutral N–As separation

Fig. 3 Calculated atomic positions

a Substitutional Nb N–Nc N–As split interstitialsd ðAsGa –NAsÞnn complexes (from [10])As is the dark circle, Ga is the light circle and N is labelled

IEE Proc.-Optoelectron., Vol. 151, No. 5, October 2004 371

in the nn-pair is 2:86 �A; 47% larger than the sum of theiratomic radii. Hence, the nn-pair, where both N and As arethreefold co-ordinated, is qualitatively different from anyother distant AsGa –NAs pairs. Note, however, that recentcalculations showed that the atomic configurations of anðAVÞBIII –NAV pair, where AV ¼ As; P and BIII ¼ Ga; In,depend sensitively on the charge states of the complex. Forexample for doubly positively charge pairs, the N–(group-V)separation is considerably smaller than the neutral ones andis in fact comparable to the sum of atomic radii.(iv) ðVGa –NAsÞnn pair. The neutral pair has a relativelysmall binding energy of <0:05 eV: However, owing to alevel repulsion between the NAs and VGa gap states (seebelow), the binding increases with the charge state to about0.43 eV for q ¼ 3:

Figure 4a shows the defect formation energy DHf as afunction of the atomic chemical potentials. At the expandedN solubility limit, the dominant defect in GaAs:N is theðN–NÞspl split-interstitial, not the AsGa antisite observedin As-rich GaAs. The calculated DHf ðN–NÞspl ¼ 1:52 eVis considerably smaller than either AsGa ð2:24 eVÞ;ðAsGa –NAsÞnn ð1:96 eVÞ or ðN–AsÞspl ð2:49 eVÞ: Thecalculated ðN–NÞspl concentration at T ¼ 650 �C is

½C� ¼ 1� 1014 cm�3; which, however, further increaseswhen the complex is charged. Figure 4b shows thecalculated single-particle gap states, along with thebandgaps of bulk GaAs and GaAs:N at an N concentrationx ¼ 3:125%: In bulk GaAs, AsGa has a mid-gap doubledonor state, whereas VGa has several acceptor states near thevalence band maximum (VBM). In contrast in GaAs:N, themid-gap state is removed by the formation of the ðAsGa –NAsÞnn pairs because the NAs state at the conduction bandminimum (CBM) pushes down the AsGa mid-gap state tonear the VBM. The effects of NAs on the VGa states arenegligible because they are close to the VBM. However,both ðN–NÞspl and ðN–AsÞspl have a deep level (0.38 and0.62 eV above the VBM or 0.66 and 0.42 eV below theCBM, respectively) with single electron occupancy. Wehave suggested [10] that these split interstitials could beimportant recombination centres for minority carriers [19].

4 Nitrogen and hydrogen complexes

4.1 H�2 complexes in GaPN

Either intentional or unintentional, hydrogen is an importantimpurity in semiconductors [20]. For example, abundantunintentional H exists during growth in, for example,MOCVD or MBE, when hydrides are used as the gassources. Hydrogen often interacts with host materials[21–23], as well as with other impurities=defects causingchanges in the electronic properties [24]. Being a fastdiffuser [25], atomic hydrogen can also be used to probe,either electronically or structurally, the various defectproperties in semiconductors.

Until recently, however, the interaction between hydro-gen and nitrogen in III–V semiconductors has been verymuch unexplored [26]. Recently, infrared study of GaPN:Hrevealed [27] three distinct local vibrational frequencies;288.5, 2054.1 and 1049:8 cm�1: To explain the data, an H–N–H dihydride model of trigonal symmetry was proposed[27] where two H atoms are bonded directly to an N atom,as shown in Fig. 5a. There are, however, several difficultieswith this model:

Fig. 4 Defect formation energies and single-particle defectenergies

a Defect formation energies (from [10]); ordinates and legends are thesame as in Fig. 2b Calculated single-particle defect energy levels with electron occupationindicated by arrows; band diagrams are those of GaAs ðeg ¼ 1:57 eVÞ andGaAs:N ðeg ¼ 1:04 eVÞ calculated at the zinc blende [10] special k points

Fig. 5 Atomic structures for the various diatomic H and Ncomplexes in GaP:N, along with the calculated formation energies(in eV=H) (from [33])

Filled atoms are P, the grey atoms are Ga, and the small grey atoms are Na Unstableb a-H�2; Ef ¼ 0:09c b-H�2; Ef ¼ 0:16d HAB

2 ; Ef ¼ 0:43

IEE Proc.-Optoelectron., Vol. 151, No. 5, October 2004372

(i) The N is fivefold co-ordinated which has never beenobserved before in any nitrides.(ii) The two H stretching frequencies differ drastically bya large amount, 830 cm�1: In contrast, the calculateddifference in the stretching frequencies for Si–H2 dihydrideon a silicon (001) surface is more than one order ofmagnitude smaller, only 50 cm�1 [28].(iii) The isotope shifts of the above two modes aredistinctly different: 5.4 and 1:7 cm�1:

From a more fundamental point of view, no diatomic H2

complexes, other than the H2 molecules [29, 30], have beenpredicted stable [31] nor have they been observed in anyIII–V semiconductors, even though in Si an H�2 complexwas not only comparable in energy to the H2 molecule [32]and has been observed [33], but also plays an essential rolein the nucleation and growth of the technologicallyimportant H platelets [23].

Using first-principles total energy calculations, we [34]have investigated the various H structural configurations inGaP either associated with N, or without N. It was foundthat nitrogen plays a pivotal role in the relative stabilitybetween the H�2 complexes and H2 molecules. Without N,H�2 is 0.3 eV per H higher in energy than H2: With one N,however, H�2 is 0.26 eV per H lower than H2: Under typicalexperimental conditions in [27], eF � 0:5 eV; H�2 is alsostable against other forms of hydrogen complexes, includingagainst dissociating into two isolated H–N complexes. Thecalculated local frequencies and isotope shifts using the H�2model were in good agreement with experiment. In contrast,the H–N–H model (involving one dihydride) is unstableagainst spontaneous transformation into the H�2 complex(involving, instead, two monohydrides).

The formation energy per hydrogen is defined as

DHf ¼1

n½Etotðhostþ nH; qÞ � EtotðhostÞ � nmH þ qeF �

ð8Þwhere Etotðhostþ nH; qÞ and EtotðhostÞ are total energiesfor a configuration with n H atoms in the host (GaP:N orGaP) at a charge state q, and for the pure host, respectively,mH is the chemical potential of the H reservoir, and isreferenced to H2 molecule in the free space at T ¼ 0; andeF is the Fermi energy with respect to the valence bandmaximum (VBM).

Case without N:

(i) Interstitial H2: The H2 molecules are located at thetetrahedral interstitial sites, either next to Ga [denoted asH2(Ga)] or P [denoted as H2(P)]. The H2(Ga) is more stablethan H2(P). The H2(Ga) has a formation energy DHf ¼0:46 eV=H with the [111] and [100] orientations almostdegenerate in energy. For H2ðGaÞ; the H–H bond length is0:78 �A; and the GaP host lattice is only weakly perturbed bythe H2 molecule.(ii) H�2 complex. The H�2 consists of one H at thebond centre (BC) site and one H at the antibonding (AB)site [21, 22]. Strictly speaking, there are two distinct H�2configurations in binary semiconductors, a and b; wherea ¼ BCðGaÞ þ ABðVÞ (Fig. 5b) and b ¼ BCðVÞ þ ABðGaÞ(Fig. 5c), where V and Ga in parentheses denote the nearest-neighbour group-V anion and Ga, respectively. a-H�2 ismore stable than b-H�2; but even a-H�2 is 0.3 eV=H higher inenergy than H2(Ga). The calculated H(AB)–P and H(BC)–Ga bond lengths are 1.46 and 1:56 �A; respectively.

Case with N: We have studied the changes in a-H�2 andb-H�2 in GaPN where a-H�2 remains more stable than b-H�2

[34]. For a-H�2; the H(AB)–N bond length is 1:05 �A and theH(BC)–Ga bond length is 1:53 �A: The distance betweenH(BC) and N is, however, 1:97 �A; which is 81% longer thanthe sum of the H–N radii of 1:09 �A: This is a strongindication that no chemical bond forms between the two. Toconfirm this, the charge density distributions were plottedfor individual H states, as well as for the total valencecharge density (in Fig. 6); the data show no trace of anyH(BC)–N bond. The formation energy of the a-H�2 is DHf ¼0:09 eV=H: In contrast, the H–N–H model in Fig. 5a is notonly unstable, it spontaneously transforms into the a-H�2configuration without any energy barrier. We also studiedHAB

2 [34] where both H are in the antibonding positions, oneclose to N and the other close to Ga (see Fig. 5d ). In thiscase, the H–N and H–Ga bond lengths are 1.05 and 1:61 �A;respectively. Both the Ga and N atoms are displaced alongthe [111] and ½1 1 1� directions to form planar structures.It, however, has a much higher formation energy DHf ¼0:43 eV=H and is, therefore, unlikely to form.Effects of N on the H pairs: Figure 7 shows how N affectsthe energy of the various H pairs. First, regarding the H2

molecules, nitrogen has little effect on H2(V) but lowers the

Fig. 6 Total valence charge density plot showing the lack of theH(BC)–N bond (from [33])

Contours are in units of 1:13� 10�4 electrons=cell

Fig. 7 Calculated formation energy (in eV=H) for the variousdiatomic H complexes (from [33])

a Without Nb With N

IEE Proc.-Optoelectron., Vol. 151, No. 5, October 2004 373

energy of H2(Ga) by 0.2 eV=H. The reason is that N is moreelectronegative than P so it takes more electrons away fromthe vicinity of the Ga than P does. Because interstitial H2

prefers low charge density regions, the net result of thecharge transfer is that H2(Ga) becomes more stable thanH2(N). Secondly, nitrogen drastically reduces the energiesof both H�2 complexes by about 0.7 eV=H. It also lowers theenergy of HAB

2 in Fig. 5d by a similar 0.6 eV=H. One canquantitatively understand this universal reduction bycomparing the H–N and H–P bond strengths in ammoniaðNH3Þ and phosphine ðPH3Þ: The difference in the cohesiveenergy between the two is 2.03 eV per molecule or 0.68 eVper H, in remarkable agreement with the above calculation.This somewhat unexpected effect places the H�2 complexessignificantly lower in energy than the H2 molecule, whichhas never been the case in conventional III – Vsemiconductors.H�2 dissociation: The unusually strong H–N bond raisesthe question of whether the H pairs are stable againstdissociation into two individual H–N complexes, especiallywhen the N concentration is larger than H. This wouldmaximise the number of H–N bonds. We have calculatedthe a-H�2 binding energy from distant H–N pairs of variouscharge states [34]. It was found that for eF � 0:55 eV; twodistant ½HðBCÞ-N�þ plus two electrons have lower energythan the charg neutral a-H�2: For eF � 0:55 eV; however, theopposite is true. The reason is because H(AB) has a lowdefect level near the VBM. Even though the H–Ga bond inH�2 is less strong than the H–N bond, the electronic energygain by two-electron transfer from a relatively high eF to thedefect level of H(AB) is enough to overcome the bondenergy loss. The experiments in [27] were done with eF �0:5 eV: Hence, regardless of the relative H=N ratio, H�2 isalways the most stable and, thus, the most abundant H centrein GaP:N.H vibrational frequencies: We also investigated the localvibration modes of H in GaP:N [34]. The vibrationalfrequencies are calculated by evaluating the force-constantmatrix K [25, 35], where the matrix elements Kij werecalculated via the Hellman–Feynman force induced on theith atom by the displacement of the jth atom. The results areshown in Table 1.

The highest frequency mode (mode-1) at 3081:2 cm�1 isassociated with the stretching of the H(AB)–N bond. Thecalculated isotopic shift is 6:3 cm�1: Both are in reasonableagreement with experiment [27], at 2885.5 and 5:8 cm�1;respectively. A 7% error here is typical for the LDAcalculations. As expected from the H�2 model, this H–N

mode is little affected by the 69Ga–71Ga isotopes. Themiddle-range frequency mode (mode-2) at 2051:3 cm�1 isassociated with H(BC)–Ga bond stretching. It changes by0:4 cm�1 if one replaces 14N by 15N and 69Ga by 71Ga:Experimentally, the isotopic shift for this mode is 1:7 cm�1:Because H(BC) is not directly bonded to N, a qualitatively

smaller N isotope shift for mode-2 can be expected. Also,the isotope effect due to the heavier Ga atoms should besmall. Interestingly, the highest H–N mode in experimentð2885:5 cm�1Þ is significantly smaller than the normal modein ammonia of 3444 cm�1: A 16% reduction here is quitedifficult to understand based on the H–N–H model.However, it has been shown [24, 33] in Si that significantreduction between 11 to 21% is possible for the H(AB)–Sistretching mode due presumably to the large local strain thatweakens the H(AB)–host atom bond [24]. Finally, thelowest frequency mode at 968:3 cm�1 was found to bedoubly degenerate, corresponding to the wagging of theH–N bond, again in good agreement with experiment.The 1:2 cm�1 isotope shift in this case is caused by replacing14N by 15N:

4.2 H�2 complexes in GaAsN

Recent experimental results by Xin et al. [36, 37] showedthat hydrogen incorporation increases with nitrogen con-centration [N] in InGaAsN alloys grown by gas-sourceMBE. Based on Hall measurements, Xin et al. suggestedthat H acts as an isolated donor in InGaAsN, and makes theas-grown undoped samples slightly n-type. Annealingabove 700�C reduces the hydrogen concentration [H] andrenders the samples p-type. This behaviour differs from theeffect of hydrogen in other semiconductors, where H acts asa passivation agent, but not as a source of doping in its ownright. A second puzzling result emerged from experimentsby Baldassarri et al. [38] and Polimeni et al. [39], whichrevealed that post-growth hydrogenation of InGaAsN alloyscan lead to a complete reversal of the drastic bandgapreduction caused by N, observed for various N and Inconcentrations in InGaAsN alloys. These results suggeststrong interactions between hydrogen and nitrogen in III–V–N alloys. The authors of [38, 39] attributed the InGaAsbandgap restoration to the binding of H to the N atom in apassivation process. However, there is no microscopictheory on the nature of these interactions, i.e. neither theatomic nor the electronic structures of the hydrogen donorsand of the N–H complex responsible for the bandgapopening in GaAsN and InGaAsN alloys have been studied.

Using first-principles total energy calculations, westudied the atomic structure and stability of the varioushydrogen-related configurations (see Fig. 8) and their effectson the electronic properties of GaAsN alloys [40]. It wasfound that monatomic H in dilute GaAsN acts as a donor forall Fermi level positions in the bandgap. This is quitesurprising because, in conventional semiconductors, mona-tomic H can exist in either donor or acceptor charge statesdepending on the Fermi energy position [41]. For complexesthat involve two H atoms, it was found that a H�2(N) complexis more stable than an interstitial H2 molecule because of thestrong bonding between hydrogen and nitrogen, similar toH�2 in GaP. The formation of the H�2(N) complexes leads to acomplete removal of the bandgap reduction in GaAsN withrespect to GaAs. These findings also apply to InGaAsNalloys, thus providing a qualitative explanation to theexperimental observations.

First, consider the donor ðþÞ; neutral (0) and acceptorð�Þ states of a monatomic H in the various monohydrideconfigurations; in the bond-centre sites next to N ðBCNÞ andfar away from N ðBCAsÞ; in the N and Ga antibonding sites(ABN and ABGa) and in the tetrahedral interstitial sites. Theresults showed that BCN is the lowest energy configurationfor all charge states. Other configurations are at least 1 eVhigher in energy except for ABN: In the positively chargedBCþN configuration (Fig. 8a), the H atom strongly binds to

Table 1: Local vibrational frequencies and isotope shifts(in cm�1) for the H�2 complex in GaP:N

Mode 1 (shift) 2 (shift) 3 (shift)

Calculated 3081.2 (6.3) 2052.3 (0.4) 968.3 (1.2)

Experimental 2885.4 (5.4) 2054.1 (1.7) 1049.8

Difference 195.7 (0.9) 21.8 (-1.3) 281.5

Modes 1 and 2 are the stretching modes whereas mode 3 is a doubly

degenerate wagging mode. The calculated results are compared to

experiment [26]

IEE Proc.-Optoelectron., Vol. 151, No. 5, October 2004374

the N atom with a H–N bond length of 1:05 �A: The Ga atomis displaced along the [111] direction to the basal planeformed by its three nearest-neighbour As atoms. The Ga–Hdistance is 2:41 �A; 53% longer than the 1:58 �A expectedfrom their respective atomic radii. The N atom is displacedalong the opposite ½1 1 1� direction. In the positively chargedABþN configuration (Fig. 8b), the H atom at the antibondingsite strongly binds to the N atom with a N–H bond length of1:05 �A: In this case, similar to the BCþN case, both N and Gaare displaced away from each other to their respective basalplanes.

The ABþN configuration has a formation energy that is0.37 eV higher than BCþN ; mainly because the electroncharge density of the host at the BCþN site is higher than thatat the ABþN site. Thus, the Coulomb binding energy for Hþ

at the BCN site is larger. This is in contrast to pure GaNwhere Hþ prefers the ABN site [42]. The Ga–N bond lengthis 2:05 �A in GaAsN, which is 7% longer than that in GaN of1:92 �A: Owing to the longer host Ga–N bond, the BC-siteHþ is less strained in GaAsN. Reduced strain energies arealso responsible for the stabilisation of the BC0

N and BC�Nconfigurations in GaAsN.

The lowest formation energies for each charge state areplotted in Fig. 9 as a function of eF : Thus, as long as [H] isless than [N] (typically a few atomic percent for dilutealloys), monatomic H in GaAsN exists only in the donorcharge state, with the ðþ=�Þ level above the CBM. Theseresults are in clear contrast to those in GaN and GaAs, theparent compounds, where H is an amphoteric impurity,positively charged in p-type samples but negatively chargedin n-type samples [31, 41, 42]. The difference can beexplained by the exceptionally large bowing effect of N thatlowers the CBM of GaAsN [2, 43, 44] below both the CBMof GaAs and GaN, as well as below the H ðþ=�Þ level.In the case of InGaAsN, the presence of indium lowers theCBM even further below that of GaAsN. Hence, it isexpected that the hydrogen ðþ=�Þ level will be even furtherabove the CBM. In general, when the host CBM level isvery low [45], monatomic H can behave exclusively as adonor, as has been proposed for ZnO [46] and InN [47].

However, similar behaviour due solely to an alloying effecthas not been suggested before.

The experiments in [36, 37] also showed that the totalhydrogen concentration [H] is higher than the free electronconcentration in as-grown unintentionally n-dopedInGaAsN. This implies that hydrogen is also present ininactive states such as interstitial H2 molecules or H�2complexes [21, 22]. Furthermore, our calculations show thatthe formation of HðBCþNÞ has only a minor effect on thebandgap. Hence, a defect other than active Hþ has to beresponsible for the large bandgap opening (of several tenthsof an eV) observed in post-growth hydrogenation experi-ments [38, 39]. To identify this defect, we have studied anumber of H�2(N) complexes that involve two hydrogenatoms adjacent to a nitrogen [40]. Table 2 shows that thea-H�2(N) complex (Fig. 8c) has the lowest formation energy,DHf ¼ �0:07 eV=H: In this complex, H(1) is at theantibonding site, similar to HðABþNÞ in Fig. 8b, with aN–H bond length of 1:05 �A: H(2) is at the bond-centre sitewith a Ga–H bond length of 1:54 �A: No chemical bond isformed between H(2) and N as the N–H separation of2:06 �A is 93% longer than the 1:07 �A expected from theirrespective atomic radii. The b-H�2(N) complex (Fig. 8d;DHf ¼ 0:01 eV=H) is slightly higher in energy than thea-H�2(N) complex by about 0.1 eV=H. The N–H(1) bondlength is 1:05 �A and the Ga–H(2) bond length is 1:60 �A:Here, both the N and Ga atoms assume the planarconfiguration, raising the strain energy of the b structure

Fig. 8 Ball-and-stick models for the hydrogen and nitrogencomplexes in GaAsN (from [39])

a Monohydride complex: bond-centre site next to N ðBCNÞb Monohydride complex: antibonding site ðABNÞc Dihydride complex: a-H�2 (N)d Dihydride complex: b-H�2 (N)

Fig. 9 Formation energies of monatomic H in GaAsN as afunction of the Fermi energy eF (from [39])

Only the lowest energy BCN configuration is shown for each charge stateðþÞ; (0), and ð�Þ; vertical dashed line indicates the calculated bandgap ofGaAsN

Table 2: Formation energies (in eV per H) of the double-Hcomplexes in GaAsN and GaAs

Conf a-H�2 b-H�2 H2(Ga) H2(V) HAB2

GaAsN 20.07 0.01 0.23 0.46 0.26

GaAs 0.72 0.67 0.28 0.38 0.92

H2(Ga) and H2(V) refer to H2 molecules at the tetrahedral interstitial site

next to Ga and anions (one of which is N for GaAsN), respectively.

HAB2 refers to a complex where both H atoms are at the antibonding sites

IEE Proc.-Optoelectron., Vol. 151, No. 5, October 2004 375

with respect to the a structure. The a-H�2(N) complex is alsostrongly favoured by as much as 0.3 eV=H over theinterstitial H2 molecule ðDHf ¼ 0:23 eV=HÞ: In contrast,in GaAs the interstitial H2 molecule is considerably morestable.

The formation energy of HðBCþNÞ increases as the Fermienergy eF increases (Fig. 9). A study of detailed balancebetween Hþ and H�2 suggests that the relative concentration½Hþ�=½H� decreases with [H], whereas ½H�2�=½H� increases.Interestingly, however, the absolute ½Hþ� increases with [H]instead of decreasing. As a result, the Fermi energy alsoincreases with [H]. At ½H� ¼ 1019 cm�3; the calculated ½Hþ�of 1016 cm�3 agrees with the experimental free-electronconcentration of 7� 1015 cm�3 [37]. This suggests that amajority of the single H complexes are ionised so the ðþ=�Þlevel is indeed shallow. At higher [H], comparable to [N],however, the role of H is shifted towards restoring the GaAsbandgap by H�2: An analysis of the density of states near theband edges suggests that while N incorporation lowers theCBM of GaAs to 0.6 eV for 3:125% N, H�2 formation pushesthe CBM back up completely, an observation that holds forevery [N] being studied: 1.5625, 3.125 and 6:25%;respectively. This remarkable effect can be qualitativelyunderstood via a three-step process schematically shown inFig. 10.

First, the bonding of hydrogen to N leads to large atomicdisplacements along the h111i direction, breaking one of theGa–N bonds. This eliminates one of the nitrogen-derivedGaAsN CBM states [2], creating a N dangling bond (DB)-

like state in the valence band and a Ga DB-like state near theGaAsN CBM. Secondly, the binding of H(1) to the N DB-

state creates a N–Hð1ÞB bonding state deep in the valenceband and a N–Hð1ÞA antibonding state in the GaAsconduction band. Owing to their spatial proximity, someinteraction between the N–Hð1ÞA state and the reactiveGa DB-like state can be expected. Thirdly, the binding ofH(2) to the Ga DB-like state creates a bonding Ga–Hð2ÞBstate below the VBM and an antibonding Ga–Hð2ÞA stateinside the conduction band of GaAs. The net result of theprocess depicted in Fig. 10 is that one GaAsN CBM state iscompletely removed by the formation of one H�2(N)complex.

As H is gradually introduced during post-growthhydrogenation [37, 38], the concentration of ½H�2� increases,whereas the concentration of non-hydrogenated Ndecreases. The bandgap also increases because theN-induced gap reduction is proportional to the concen-tration of non-hydrogenated N. This process approachescompletion when [H] is larger than [N], which leads to theexposure of the original GaAs bandgap. The sameconclusion can also be straightforwardly applied toInGaAsN alloys, which have an even lower CBM thanGaAsN. A similar conclusion was also reached in [48].

5 Summary

We have reviewed some of the recent developments in thetheoretical understanding of defects=impurities in diluteIII–V-nitrides. Key in the development that has enableddefect studies is the extension of the atomic chemicalpotentials to the so-called epitaxial regime. Defect physicsqualitatively different from that of conventional III–Vcompounds was obtained. For example, the nitrogensolubility could be many orders of magnitude higher thanthat under bulk equilibrium. It was also demonstrated thatnitrogen split interstitials, negligible in conventional III–Vcompounds, could play a very important role in this familyof materials. We also reviewed the role of hydrogen in thedilute nitrides. It was shown that while being onlymetastable in conventional semiconductors, the H�2 com-plexes have exceptional stability due to the involvement ofnitrogen. This allows for the identification of H-related IRspectra in the dilute nitrides, as well as a whole new range ofH-related electronic properties, including the exclusivedonor behaviour of H and the complete reversal of thebandgap reduction by the nitrogen atoms.

6 Acknowledgments

This work was supported by the U. S. DOE-SC-BES undercontract No. DE-AC36-99GO10337.

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