Adsorption of ammonia at GaN(0001) surface in the mixed ammonia/hydrogen ambient - a summary of ab initio data

Adsorption of ammonia at NH3/NH2/H covered GaN(0001) surface was analyzed using results of ab initio calculations. The whole configuration space of partially NH3/NH2/H covered GaN(0001) surface was divided into zones differently pinned Fermi level: at Ga broken bond state for dominantly bare surface (region I), at VBM for NH2 and H covered (region II), and at CBM for NH3 covered surface (region III). The extensive ab intio calculations show validity of electron counting rule (ECR) for all mixed coverage, for bordering these three regions. The adsorption was analyzed using newly identified dependence of the adsorption energy on the charge transfer at the surface. For region I and II ammonia adsorb dissociatively, disintegrating into H adatom and HN2 radical for large fraction of vacant sites while for high coverage the ammonia adsorption is molecular. The dissociative adsorption energy strongly depends on the Fermi level at the surface (pinned) and in the bulk (unpinned) while the molecular adsorption energy is determined by bonding to surface only, in accordance to the recently published theory. The molecular adsorption is determined by the energy of covalent bonding to the surface. Ammonia adsorption in region III (Fermi level pinned at CBM) leads to unstable configuration both molecular and dissociative which is explained by the fact that Ga-broken bond sites are doubly occupied by electrons. The adsorbing ammonia brings 8 electrons to the surface, necessitating transfer of the electrons from Ga-broken bond state to Fermi level, energetically costly process. Adsorption of ammonia at H-covered site leads to creation of NH2 radical at the surface and escape of H2 molecule. The process energy is close to 0.12 eV, thus not large, but the inverse process is not possible due to escape of the hydrogen molecule.


I. Introduction
Since the inception of MOVPE based nitride device technology, the physical properties of GaN(0001) surface and the growth of nitride layers have been investigated intensively, using both experimental and theoretical methods. These investigations led not only to the considerable understanding of the system but also to development of the new methods, which are now sufficiently mature to simulate the semiconductor (insulator's) surfaces fully accounting influence of the charged surface states and the fields close to the surface. [1][2][3][4][5][6] Recently, the dependence on the position of Fermi energy and doping was also accounted for. 6,7 These new methods led to discovery of new features fundamentally changing basic notions related to processes at semiconductor surfaces, introducing the dependence of adsorption energies on pinned and doping in the bulk for unpinned Fermi level surfaces. [6][7][8] Basic properties of clean, hydrogen-and ammonia-covered GaN(0001) surface were obtained by DFT calculations without reference to doping or charged surface states. [9][10][11][12][13][14] According to these results the clean GaN(0001) surface does not undergo any reconstruction, the quantum surface states located in the bandgap are characterized by large dispersion of about 1.6 eV and are partially filled, i.e. the surface is metallic and the Fermi level is pinned. 10,11 More recent DFT simulations, using field-charge model indicate however that the clean GaN(0001) surface undergoes reconstruction to 2 x 1 row structure 4 . The energy difference between these two structures is very small and the numerous energy minima were found, that could lead to the relaxation termination in the local minimum, different from global minimum energy state. The states related to surface Ga atoms broken bonds are located at 0.6 eV below conduction band minimum (CBM), pinning Fermi level. Van de Walle and Neugebauer constructed phase diagram of GaN(0001) surface in ammonia ambient, using coordinates of chemical potential of hydrogen and nitrogen, finding regions of stability of several surface structures. 12,13 These results were confirmed by the DFT determination of the stable structures of polar and nonpolar GaN(0001) surfaces by Ito et al. 14 The reaction of ammonia with the bare and H-covered surface was investigated by several groups by ab initio modelling, [15][16][17][18][19][20] Fritsch et al. simulated several configurations of GaN(0001) surface showing that ammonia adsorption is dissociative to H and NH 2 radical and transformation of GaN(0001) flat surface into p(2 x 2) vacancy reconstruction. The NH 2 radical was bound to gallium and H atom to gallium and nitrogen broken bonds respectively 15 . This reconstruction was not confirmed by any other calculations. The adsorption energy barrier was found to be of order of 0.5 eV. The DFT calculations by Pignedoli et al. also confirmed ammonia decomposition into H and NH 2 during adsorption at clean GaN(0001) surface. 15,17 In these calculations however, the surface remained flat with both products adsorbed on-top of Ga surface atoms. Similar, dissociative adsorption of ammonia at clean GaN(0001) surface, with the NH 2 radical adsorbed in the asymmetric bridge position, was obtained by Bermudez. 18,19 Kempisty et al. modeled adsorption of ammonia on highly Hcovered GaN(0001) surface showing that ammonia is adsorbed molecularly in barrierless process 20 . The adsorption energy was high in excess of 2.5 eV. Recently intensive investigations of ammonia adsorption were conducted by the same authors 6 . They found that the ammonia adsorbed on relatively low H-occupied surface decomposes into NH 2 radical and H adatom in accordance with the results of Pignedoli et al. and Bermudez. [16][17][18][19] The adsorption energy is about 2.8 eV for the hydrogen coverage up to 0.75 ML, for higher coverage it is drastically reduced. Therefore in this region adsorption is molecular, locating the molecule in the 'on-top' position. The molecular adsorption energy, independent of the coverage, is close to 2.0 eV. For the adsorption on top of adsorbed H adatom, the Ga-H-N weak bond created, with the energy gain on adsorption of 0.8 eV, therefore reevaporation of the NH 3 molecule is possible. Finally the configuration dissociates into NH 2 radical and desorbing H 2 molecule.
The experimental investigations of the ammonia adsorption at GaN(0001) are not numerous. Supersonic molecular beams investigation of the ammonia adsorption indicated that ammonia adsorption is barrier-free process that proceeds via precursor-mediated mechanism, leading to ultimate dissociative stage in which the molecule disintegrates to NH x radicals 21 . It is not clear whether the surface was clean or hydrogen covered.
In the present work, the coverage diagram presenting Fermi level pinning at GaN(0001) surface will be constructed employing electron counting rule (ECR) 22 and DEF simulations. The ammonia adsorption using newly determined charge transfer dependence will be determined for entire configuration space of GaN(0001) in contact with NH 3 -N 2 -H 2 ambient.

II. The simulation procedure
In the calculations reported below reported below, a freely accessible DFT code SIESTA, combining norm conserving pseudopotentials with the local basis functions, was employed. 23,24 The basis functions in SIESTA are numeric atomic orbitals, having finite size support which is determined by the user. The pseudopotentials for Ga, H and N atoms were generated, using ATOM program for all-electron calculations. SIESTA employs the normconserving Troullier-Martins pseudopotential, in the Kleinmann-Bylander factorized form 25  GaN layers slabs, should be rescaled by an approximate factor α = E g-exp /E g-DFT =3.4eV/2.13eV ≈ 5/3 ≈ 1.6. Integrals in k-space were performed using a 3x3x1 Monkhorst-Pack grid for the slab with a lateral size 2x2 unit cell and only Γ-point for 4x4 slabs 29 . As a convergence criterion, terminating a SCF loop, the maximum difference between the output and the input of each element of the density matrix was employed being equal or smaller than 10 -4 .
Relaxation of the atomic position is terminated when the forces acting on the atoms become smaller than 0.02 eV/Å. Born-Oppenheimer approximation was used for determination of the energy barriers in which an effective procedure, based on nudged elastic band (NEB) method was applied. [30][31][32] The NEB method finds minimum energy pathways (MEP) between two stable points, which has to be predetermined first. The MEP is characterized by at least one first order saddle point, finding the energy barrier corresponding to activated energy complex approximation in chemical reaction kinetics. In the present formulation NEB module was linked to SIESTA package paving the way to fast determination of the energy and conformation of the species along the optimized pathways.

III. The results
In the description below the coverage of GaN(0001) surface is calculated as the fraction of saturated Ga bonds by attached atoms. Thus zero coverage corresponds to the absence of species attached at the surface. Accordingly, the partial coverage is that in which a part of the surface sites has attached species while the rest have their broken bond nonsaturated. The full coverage is such that all Ga atoms have attached species, saturating all their bonds.
The following classification of the coverage is used: the presence of single species such as H, NH 2 , etc is denoted as unary coverage. Consequently the two chemical species, such as H-NH 2 , H-NH 3 , NH 2 -NH 3 will be denoted as binary coverage. And finally the ternary H-NH 2 -NH 3 coverage is possible. In the all above cases either full or partial coverage could exist potentially, i.e. some part of Ga broken bonds could remain unsaturated.
As it was discovered recently [6,7], adsorption energy depends on the electric charge transfer between the solid bulk and the emerging states of the adsorbate. In the absence of the charge transfer, the adsorption energy attains the value, determined by the energy of the bonding. In addition, in some cases the adsorption energy could be possibly affected by the interactions with the neighbors. The notion that the adsorption energy may be affected by interaction with the neighbors on surfaces of metals and semiconductor was recognized and accepted for many years. The novel, recently introduced idea is the energy dependence on the electronic charge transfer [5,6]. The new phenomenon originates from the fact that the exchange of the electron between the Fermi level and the emerging surface state of different energies generates additional energy effect. These two states energy difference, may reach several electronvolts affecting adsorption energy considerably. This contribution changes the adsorption energy in case when the charge transfer is possible, i.e. when the empty states are available. The adsorption on semiconductor surfaces, involving charge transfer from/to the emerging state of the adsorbate depends on the Fermi level at the surface: pinned by surface state or free (unpinned) [6,7]. In the pinned case, the adsorption energy depends on the energy of the pinning surface state, which in most cases is a function of the chemical state of the surface, i.e. its coverage. In the case of the unpinned Fermi level surface, the adsorption energy depends on the position of the Fermi level in the bulk, i.e. the doping. Below we present the systematic discussion of the electronic properties of GaN surface and then the adsorption data are discussed.

A. Uniform state of GaN(0001) surface
The uniform state of the GaN(0001) is such that all sites of the surface are identical chemically i.e. the surface is either clean or fully covered by H, NH 2 and NH 3 species. The clean GaN(0001) surface was subject of intensive research. Therefore concise summary, including the features essential for the nonuniform coverage, is given here. In Figure 1 we Accordingly, the type of the surface state (donor or acceptor) 5 depends on the doping in the bulk as shown in Figure 1. In the case of n-type doping, most frequently by silicon, the Fermi level in the bulk is at the donor defect level which is about 10 meV below CBM.
Therefore the surface state is excessively charged becoming acceptor, with the band bend upwards by about 0.5 eV which leads to relatively small charge separation at the surface. In the case of p-type doping, the electronic charge is shifted to the bulk, resulting in strong excess positive charge on the surface state that behaves as a donor (Fig 1 b). The charge related downward band bending attains 3 eV, causing the immense surface charge effect.
Naturally, such charge separation costs considerable energy. Therefore clean GaN surface is not likely to be encountered in the experiment. The simulation use relatively high temperature for electron distribution enabling screening by the band charge. Note also that the 1 x 1 slab was used, which does not allow emergence of 2 x 1 reconstruction [2,4].
The second uniform state considered is the GaN(0001) surface covered by hydrogen.
As shown in Ref. 33, such coverage is extremely difficult to attain as it requires immense hydrogen pressures 33  The third uniform case, of relevance to the present studies, is the GaN(0001) surface uniformly covered by NH 2 radicals. The electronic properties of such surface are presented in Figure 3. As it is shown, it is similar to the previous one as the Fermi level is pinned at VBM.
As it is shown, this is related to the creation of the Ga-N bonding states located in the valence band (VB). The other molecular states of the radical, located deep in VB are completely occupied. In the result, the fully NH 2 covered surface is electronically identical to that covered by hydrogen: at p-type surface the band are essentially flat, at n-type they are bend upward over the entire gap, due to charged surface acceptor state.  will be treated as the same electronic state of the surface.
In order to determine the configurations of pinning absence, the electron counting rule (ECR) 22 is applied to determine the surface states and the conclusions are verified by DFT calculations in the next Section. Then, the diagram summarizing these changes is presented.
Finally the configurations are used to determine the stable configurations of ammonia at the surface and the adsorption energies.

B. Fermi depinning configurations at GaN(0001) surface -electron counting rule (ECR) state of the surface
The ECR analysis will not account the detailed analysis of bonding in GaN which is different from standard sp 3 bonding typical for III-V semiconductors [35,36]. In accordance to the ARPES results 35  Therefore we will follow standard Pashley arguments 22 .
The clean GaN(0001) surface is terminated by the top Ga surface atom, which has missing N neighbor so that the single Ga bond has no overlap, i.e. gallium bond is broken.
Due to that the energy of this state is located in the bandgap, 0.45 eV below CBM. According to ECR analysis 5/4 electron is missing, thus the Fermi level should be pinned by this state and that was confirmed by DFT data [4,7,10,11].
The unary coverage includes partial occupation by H adatoms, NH 2 radicals or NH 3 admolecules. The state associated with hydrogen on-top of Ga surface atom is located at VBM so it has to be occupied. Gallium contributes 3/4 electron and hydrogen 1 electron.
Therefore the Ga broken bond site contributes 3/4 electron while the one with attached hydrogen 1 + 3/4. These electrons occupy two quantum states associated with hydrogen while Ga broken bonds are empty. Thus the charge redistribution balance gives where α and β are fractions of donors (Ga broken bonds) and acceptors (Ga saturated by hydrogen) respectively. Naturally the fraction of both sites is normalized to unity, i.e.: Effectively the H occupied site behaves as acceptor of 1/4 electron which has to be provided from Ga broken bond state in the bandgap, i.e.: as before α and β are fractions of donors (Ga with NH 3 admolecules) and acceptors (Ga broken bonds) respectively. Total fraction of both sites is normalized to unity, following Eq.
2. Effectively 5/4 electron has to be taken from neighboring NH 3  The flat band termination surface is used.
As shown in Figure 7, the DFT results confirm the Fermi level position between CBM and Ga broken bond state, that is located 0.6 eV below CBM, i.e. in the narrow energy strip. Thus the obtained DFT results are in accordance with ECR analysis.
The full binary NH 2 -NH 3 coverage attains depinning Fermi level at approximately 0.25ML NH 3 content. This may be explained by ECR rule 22 . NH 3 admolecule contributes 5 electrons from nitrogen atom, 3 from three hydrogen atoms and 3/4 from Ga broken bond while NH 2 radical contributes 5 electrons from nitrogen atom, 2 from three hydrogen atoms and 3/4 from Ga broken bond, which has to occupy 8 states associated with NH 3 admolecule and similarly with NH 2 radical: β α β α α and β are fractions of donors (Ga with NH 3 admolecules) and acceptors (Ga with NH 2 radicals) respectively. Total fraction of both sites is normalized to unity, in accordance to The second ECR state exists for Fermi level located between Ga broken bond state and CBM. In this case Ga broken bond state becomes acceptor and the only donor is NH 3 admolecule. Thus the difference is that Ga broken bond states are occupied by two electrons: where α is the fractions the donor NH 3 admolecules. The β, β' and β'' are fractions of the three different acceptors: Ga broken bonds, NH 2 radicals, and hydrogen adatoms, respectively.
Naturally the fractions of all types are normalized to unity: In fact these data once again confirm the transition between these two pinning regimes. The other regime is presented in Figure 11. density of states (P-DOS) (middle) and DOS projected on surface gallium and nitrogenhydrogen (in NH 3 admolecules) atoms (right) for: (a) 0.375 ML NH 3 -0.4375 ML NH 2 ; (b) 0.4375 ML NH 3 -0.375 ML NH 2 (c) 0.5 ML NH 3 -0.3125 ML NH 2 -covered GaN (0001) surface.
These data again confirm possibility of transition between these three pinning regimes and validity of ECR rule.
Another possible configuration is that directly related to NH 3 dissociation, i.e. coverage by mixture of NH 2 radicals and H admolecules. As it was already determined both configurations are characterized by the surface states degenerate with valence band, i.e. both they are acceptors. Denoting the coverage by the radicals by β, and by H adatoms by β', the number of Ga broken bond atoms by α, the following normalization relation is obtained: Accounting that NH 2 radical and H adatom quantum states are occupied by 8 and 2 electrons respectively, the following electron balance equation is obtained: From these relations, the total number of acceptor states may be obtained: The results shown in Figure 12 confirm predictions made using ECR rule extending the Fermi level pinning scenario for bridge configurations at GaN(0001) surface. In addition the number of control calculation was made verifying the Fermi level position at the surface for number of ternary coverage, as reported in Table I.   Table I

c. NH 3 adsorption at empty site
Relatively large (4 x 4) slabs reduces graininess of the simulation of the adsorption processes that attempts to recover the infinite surface. In this study it is assumed that the change of 1/16 of the occupation closely resembles infinitely small variation in the real process. The concentration will be denoted without specific account of the adsorption site which was assumed vacant.
The adsorption of ammonia involving part of the possible configurations, depicted in Figure 13 was already studied recently. The ammonia on the surface partially covered by hydrogen was presented in Refs. 7 and 8. Generally the ammonia adsorption at GaN(0001) surface is barrierless process 8 . The investigations confirmed earlier results indicating that ammonia may be adsorbed dissociatively leading to creation of NH 2 radicals located in bridge position and H adatom in the "on-top" position [16][17][18][19]. Alternatively as reported also it may be adsorbed molecularly in the '"on-top" position 20 . The results, concerning the adsorption energy may be understood using recently formulated theory of charge transfer at the surface contribution to adsorption energy [6,7]. According to the theory charge transfer may affect the energy even by several electronvolts [6,7]. The electronic charge may be transferred between the bulk states close to the Fermi level which is pinned by surface state 6 or it may be nonpinned 7 . In the first case the adsorption energy depends on the type of the surface pinning state 6 or on the doping in the bulk 7 . In accordance to the diagram presented in Figure 11, the three regions correspond to three types of Fermi level pinning and the transition between them -to Fermi level nonpinned.
According to the results presented in Ref. Generally, dissociative adsorption has much larger energy, thus the adsorption of ammonia at relatively clean surface leads to dissociation of ammonia into NH 2 radical and H adatom. For low coverage, up to 0.3 ML the stable configuration is bridge, for higher -"on-top". The hydrogen adatom is always located in the "on-top" position.
For the coverage above 0.6 ML, the adsorption energy is much reduced for both molecular and dissociative process. Generally molecular configuration is always less stable, thus NH 2 coverage is preferred decreasing ammonia content. In fact the increase, similar to the data regarding NH 2 /NH 3 coverage, presented in Ref. 38 could be also explained using the charge transfer theory. In agreement with Eq.8 and data presented in Figure 7, the decrease occurs when Fermi level is shifted from Ga broken bond (region I) to CBM (region III), i.e. at 0.625 ML ammonia coverage. The same applies to data in Ref. 38, and also to Eq. 8 and The adsorption at mixed configuration is also determined by the Fermi level pinning at the surface. Thus the same energy values are applicable to the regions: I, II and III. From the above determined dependences, given by Eqs. 10-12, the following relation may be obtained for the border between region I and II: where α is the coverage by NH 3 admolecules, α' = 0.25α is the fraction of empty sites. The second relation describes relative occupation by acceptors β and β' are coverages by NH 2 radicals and H adatoms. The second border, between region I and III is described by the following relations: the notation is as above. The relative fraction of NH 2 radicals and H admolecules is given by x. The above relations complete description of ammonia at empty sites of GaN(0001) surface.

C. NH 3 adsorption at H-covered site
The adsorption of ammonia at H-covered site of GaN(0001) surface leads to creation of NH 2 admolecule and desorption of H 2 molecule. The total sequence of reaction could be described as follows.
The total energy of such process was determined for the three possible pinning cases: at Ga broken bond, at VBM and CBM. The first case, belonging to region I, was modeled using 4 x 4 slab with the following coverage 0.25ML NH 3 -0.1875ML NH 2 -0.1875ML H.
The adsorption energy was -0.158 eV, i.e. it is negative. Thus the conversion is not preferred energetically suggesting that such process is not likely to occur. It has to be noted that leaves 0.375 sites free thus the adsorption is likely to occur at neighboring empty site.
The other to possible cases belong to regions II and III, i.e. Fermi level pinned at VBm and CBM respectively. These regions were modeled using the following configurations:

IV. Summary
Adsorption of ammonia at NH 3 /NH 2 /H covered GaN(0001) surface was analyzed using results of ab initio calculations. The whole configuration space of partially NH 3 /NH 2 /H covered GaN(0001) surface was divided into the zones of differently pinned Fermi level: at Ga broken bond state for dominantly bare surface (region I), at VBM for NH 2 and H covered (region II), and at CBM for NH 3 covered surface (region III). It is shown that ECR allows to determine the borders of these regions precisely. The extensive ab intio calculations show validity of ECR for all mixed coverage, necessary to define these three regions.
The adsorption was analyzed using newly identified dependence of the adsorption energy on the charge transfer at the surface. It was shown that ammonia adsorb dissociatively, disintegrating into H adatom and HN 2 radical for large fraction of vacant sites while for high coverage the ammonia adsorption is molecular. The dissociative adsorption energy strongly depends on the Fermi level at the surface (pinned) and in the bulk (unpinned) while the molecular adsorption energy is determined by bonding to surface only, in accordance to the recently published theory. The molecular adsorption is determined by the energy of covalent bonding to the surface. Such difference is observed for regions I and II.
It is also shown that ammonia adsorption in region III (Fermi level pinned at CBM) leads to unstable configuration both molecular and dissociative. The drastic change of the adsorption energy is explained by the fact that Ga-broken bond sites are doubly occupied by electrons. The adsorbing ammonia brings 8 electrons to the surface, necessitating transfer of the electrons from Ga-broken bond state to Fermi level. The process is energetically costly so that the total energy is increased, leading to energy increase of both molecular and dissociated processes.
Adsorption of ammonia at H-covered site leads to creation of NH 2 radical at the surface and escape of H 2 molecule. The process leads to the energy increase in the region I. In this case however the neighboring empty sites are available and ammonia could be adsorbed there. In case of region II and III, the process energy is close to 0.12 eV, thus not large.
Nevertheless the inverse process is not possible due to escape of the hydrogen molecule. Thus these processes lead to creation of NH 2 coverage.
All these processes are barrierless. Thus in the case of N-rich MOVPE and HVPE processes, the surface is covered predominantly by mixture of NH 2 radicals and NH 3 admolecules.