Conference-ACSIN-12 & ICSPM 21-Theoretical Investigations for the Formation of InN / GaN ( 0001 ) Heterostructures

The formation processes of InN/GaN heterostructures on GaN(0001) substrate are investigated by means of our ab initio-based approach and Monte Carlo (MC) simulations. Our ab initio calculations reveal that even under Ga-rich conditions the pseudo-(1×1) surface consisting of In in the first layer and Ga in the second layer is more stable than that of Ga in the first layer and In in the second layer. Furthermore, the calculated surface phase diagrams demonstrate that the pseudo-(1×1) surface with In-Ga metal layers can incorporate 2.3 monolayers (MLs) of N atoms under growth conditions. The MC simulations using ab initio calculation data imply that both InGaN alloy and InN/GaN heterostructure can be formed depending on the growth conditions, consistent with the experimental results. On the basis of these findings, the stability of these structures is discussed in terms of the strain accumulation in the resultant structures. [DOI: 10.1380/ejssnt.2014.136]


I. INTRODUCTION
InGaN semiconductor alloys have attracted much attention due to its potential application for light emitting devices, such as light emitting diodes and laser diodes.One of growth methods to fabricate InGaN alloys is molecular beam epitaxy (MBE), in which both In/Ga and N are supplied on the substrate under high vacuum conditions.Recently, Yamaguchi et al. have proposed a new fabrication technique using the MBE, so called droplet elimination by radical beam irradiation (DERI) method [1,2].This technique consists of metalrich growth process and droplet elimination process.In the case of InGaN growth by the DERI method, excess In and Ga form droplets with 2-3 monolayers (MLs) wetting layer on the substrate, and then transfer into epitaxial InGaN occurs by supplying nitrogen radicals.However, X-ray diffraction (XRD) profiles have indicated that two types of structures are synthesized depending on the growth conditions [2].InN/GaN heterostructures have been obtained under metal-rich conditions, whereas In-GaN alloys are grown under N-rich conditions.Despite these experimental findings, the origin for the formation of these structures is not clear at present.
In our previous study, we have investigated the compositional inhomogeneity near surface, interface, and dislocation in InGaN thin films on GaN(0001) substrates by using our empirical interatomic potential and Monte Carlo (MC) simulations [3].We have also investigated reconstruction, adsorption, and incorporation on various nitride semiconductor surfaces on the basis of our ab initiobased approach, in which surface phase diagrams depending on temperature and pressure are obtained by comparing calculated adsorption energy with gas-phase chemical potentials [4][5][6][7].In this study, focusing on the experimental results of InGaN growth by the DERI method, we investigate the growth processes of InN/GaN heterostructures using our ab initio-based approach.In particular, we study the stability of nitrogen-incorporated surfaces on GaN(0001) surface with metal layers.Furthermore, the atomic arrangements during N-incorporation processes are calculated by using MC simulations.

A. Ab-initio calculation
The total-energy calculations are performed within the density-functional theory using the generalized gradient approximation [8].To simulate nuclei and core electrons, we employ norm conserving pseudopotentials [9] for Ga and In atoms and ultrasoft pseudopotential [10] for N atom.The conjugate-gradient technique is utilized both for the electronic structure calculations and for geometry optimization [11].The valence wave functions are expanded by the plane-wave basis set with a cutoff energy of 25 Ry.The surfaces are simulated using slab models consisting of 10 atomic layers with artificial H atoms [12] and a 10 Å vacuum region.We employ the slab geometry with the pseudo-(1×1) periodicity to simulate metal layers on GaN(0001) substrate [4].
As an initial surface structure for nitrogen incorporation on the surface with metal layers, we consider two types of In and Ga metal surface structures on GaN(0001) substrate.One is the Ga-In structure, which consists of four Ga atoms in the first layer and three In atoms in the second layer per pseudo-(1×1) unit cell.The other is the In-Ga structure, which consists of four In atoms in the first layer and three Ga atoms in the second layer.The relative stability between these surface structures is determined by the surface formation energy γ surf given by [13,14] where E tot is the total energy of the surface under consideration, E ref is the energy of reference surface, n In (n Ga ) is the number of In (Ga) atoms and µ In (µ Ga ) is the chemical potential of In (Ga) atoms.The origin of µ In and µ Ga is set to the energy of bulk In (µ In−bulk ) and Ga (µ Ga−bulk ), respectively.The allowable energy ranges of µ In and µ Ga are determined by the heat of formation in bulk InN and GaN, respectively.The calculated heat of formation for InN (GaN) is 0.32 eV (1.20 eV) [13][14][15].Furthermore, in order to study nitrogen incorporation on the surface with metal layers, we calculate surface phase diagrams as functions of temperature and pressure.The surface phase diagram is determined by comparing the free energy of ideal gas per one particle (chemical potential) µ gas with the adsorption energy of N atom E ad obtained by ab initio calculations.The adsorption energy E ad is obtained by the following equation: where E total is the total energy of the surface with adatom, E surface is the total energy of the surface without adatom, and E atom is the total energy of isolated atom.
The chemical potential µ gas of the ideal gas is given by the following equation [16,17]: where k B is Boltzmann's constant, T is the gas temperature, g is the degree of degeneracy of electron energy level, p is the pressure, and ζ trans is the partition function for translational motions.The structure corresponding to adsorbed surface is favorable when E ad is less than µ gas , while the desorbed surface is stabilized when µ gas is less than E ad .

B. Monte Carlo simulations
The MC method is also used to confirm the resultant atomic arrangements of In and Ga atoms during N adsorption processes by employing total energies obtained by ab initio calculations.As a growth substrate, we adopt a surface model which is 24×24 times as large as the pseudo-(1×1) unit-sell.We assume the following assumptions in the MC simulations: (1) The adsorption and desorption of atoms occur at specific sites.(2) During successive adsorption, an exchange process occurs between In and Ga atoms.The atomic arrangements are generated according to the following procedure: (i) select atoms at random; (ii) select an event as described in assumptions ( 1) and (2) at random; (iii) calculate the change in the system energy ∆E between before and after selected event; (iv) if ∆E is negative, accept the new configuration; (v) otherwise, select a random number h uniformly distributed over the interval (0, 1); (vi) if the probability of selected event P is lower than h, accept the old configuration; (vii) otherwise, use the new configuration and the new system energy as the current properties of the system.The probabilities for adsorption P ad , for desorption P des , and for exchange P sub are given by where E surface+atom is the total energy of the surface with adsorption, and E a and E b are total energies of configurations before and after exchange.This procedure is repeated for suitable number of configurations (MC steps) in order to approach equilibrium configurations at T = 850 K [1,18].

III. RESULTS AND DISCUSSION
We determine the initial pseudo-(1×1) surface structure with metal layers on GaN(0001) substrate comparing γ surf of the Ga-In structure with that of the In-Ga structure.Figure 1 shows the calculated surface energies of GaN(0001)-pseudo(1×1) surface with Ga and In atoms as a function of In/Ga chemical potentials.The surface energy under Ga-rich conditions shown in Fig. 1(a) indicates that the In-Ga structure is more stable than the Ga-In structure for 0.18 ≤ µ In − µ In(bulk) ≤ 0 eV, while the Ga-In structure is more stable for 0.3 ≤ µ In − µ In(bulk) ≤ 0.18 eV.The surface energy under In-rich condition shown in Fig. 1(b) also indicates that the In-Ga structure is more stable than the Ga-In structure over the entire range of µ Ga .These results imply that the In-Ga structure is stabilized even under Ga-rich conditions.We thus assume the In-Ga structure as an initial surface structure to investigate N-incorporation processes on the GaN(0001) substrate with metal layers.
Using the In-Ga structure, we next consider N incorporation processes under the growth conditions.Figure 2 shows the calculated surface phase diagram for N adsorption on the In-Ga structure as functions of temperature and N pressure [19].This figure reveal that the phase boundary for adsorption/desorption depends on N coverage.The boundary between the surface with 2.0 monolayers (MLs) of N atoms and that with 2.3 MLs of N atoms is located 980-1600 K.In contrast, the boundary between the surface with 2.3 MLs of N atoms and that with 2.6 MLs of N atoms is located 300-400 K, indicating that the surfaces with more than 2.6 MLs of N atoms are not stable under the experimental conditions.This surface phase diagram thus reveals that N atoms are incorporated into the In-Ga structure until the coverage of N atoms becomes ∼2.3 MLs under growth conditions.The stability of N-incorporated surfaces with 2.3 MLs can be understood by the electron counting rule [20].The number of deficit electrons per unit cell in the surface with 2.3 MLs of N atoms is 0.25 electron, which is the smallest among the surfaces with N atoms considered in this study.
Figure 3 depicts the geometries of stable surfaces during N-incorporation on the In-Ga structure.As shown in Figs.3(a) and 3(b), N atoms are preferentially incorporated between the second layer of metal region and substrate surface when the coverage of N atoms is less than 1 monolayer (ML).These N atoms are located close to the lattice sites of N atoms in GaN on GaN(0001) substrate.Since all the N sites of GaN are occupied by N atoms for the surface with 1 ML of N atoms, further N atoms are incorporated between first and second layers, as shown in Fig. 3(c).Finally, an N atom adsorbs on the first layer, resulting in the formation of N adatom shown in Fig. 3(d).It should be noted that one of In atoms in the first layer is substituted for the Ga atom located in the second layer when the N coverage is larger than 2.0 MLs.This results in mixture of In and Ga atoms between the first and second layers, implying that InGaN alloy can be realized for the surfaces with N coverage larger than 2.0 MLs.
Our analysis of calculated structures indeed clarifies that the formation of the surface with In-Ga mixing can be interpreted in terms of the strain accumulation in the resultant surface structures.Figure 4 shows the deviations of In-N and Ga-N bond lengths from the equilibrium value ∆r as a function of the number of In atoms N In located in the second layer, for the surface with 2.3 MLs of N atoms.This figure reveals that the deviations of both In-N and Ga-N bonds are the smallest at N In = 1, indicating that the lattice strain for the structure with one In atom located in the second layer is less accumulated than that of the other structures.Indeed, the total energy of the most stable structure is ∼1.38 eV lower than those of metastable structures.
On the basis of our ab initio calculations, we furthermore perform the MC simulations to elucidate the formation of InGaN layers during N incorporation.N coverage such as 1.7 MLs, the In composition in the first layer is ∼0.9.This indicates that most of In atoms are arranged in the first layer.In contrast, for the surfaces with large N coverage ranging from 2.3 MLs, the In composition in the first and second layers are ∼0.7 and ∼0.3, respectively.These results can be explained by the strain accumulation shown in Fig. 4.
Finally, we comment on the experimental results on the basis of calculated results.Since the amount of supplied N is controlled by the radio-frequency plasma source in the DERI method, it is expected that small (large) amount of N atoms are supplied on the surface under metal-rich (N-rich) conditions.Thus, the calculated surface with small (large) N coverage can be assigned to the experimental results under metal-rich (N-rich) conditions.Indeed, the calculated surface structures for small N coverage (diamonds and triangles in Fig. 5) tend to form abrupt InN/GaN interface, which can be regarded as a InN/GaN heterostrucure.In contrast, the calculated surface structures for large N coverage (circles and squares in Fig. 5) correspond to the surfaces with In-Ga mixture, which can be regarded as a certain type of InGaN alloys.Although further elaborate calculations including energy barriers for substitutions between In and Ga atoms should be required to discuss the processes more quantitatively, our calculated results are reasonably consistent with the XRD profiles of InGaN alloys on GaN(0001) substrate [2].3(d).Squares and diamonds denote ∆r for Ga-N and In-N bonds, respectively.The notation of circles is the same as in Fig. 1.

IV. CONCLUSION
The formation processes of InN/GaN(0001) heterostructures during N adsorption on the GaN(0001) surface with metal layers have been investigated by performing ab initio total-energy calculations.It has been found that the surface structure consisting of In-first and Gasecond layers is stabilized even under Ga-rich conditions.The surface phase diagram for N incorporation on the In-Ga structure has revealed that this metal layers can incorporate 2.3 MLs of N atoms.Furthermore, the MC simulations have revealed that the mixture of In and Ga atoms in the first and second layers occurs when N coverage is more than 2.0 MLs.This is because Ga atoms located in the second layer are replaced by In atoms located in the first layer to release the strain around the surface.These calculated results are qualitatively consistent with the experimental results, where both InGaN alloy and InN/GaN heterostructure have been synthesized depending on the growth conditions.

FIG. 1 :
FIG. 1: Calculated surface formation energies for Ga and In metal surface structure on GaN(0001) substrate with pseudo-(1×1) periodicity under (a) Ga-rich and (b) In-rich conditions as a function of µGa and µIn, respectively.Black and gray lines denote the formation energies of In-Ga and Ga-In structures, respectively.Geometries are also shown in (a).Light gray, black, and dark gray circles represent In, Ga and N atoms, respectively.

FIG. 2 :
FIG. 2: Surface phase diagram of N incorporation into the metal layers on GaN(0001) substrate as functions of temperature and N pressure.Stable N coverage of each area is also shown.Experimental conditions in Refs.[1] and [17] are shown by vertical bar.Geometries are shown in Fig. 3.
FIG. 3: Geometries of stable surfaces during N-incorporation on the In-Ga structure.Each structure denotes the surface with (a) 0.3, (b) 0.7, (f) 2.0, and (g) 2.3 MLs of N atoms, respectively.The notation of circles is the same as in Fig. 1.

FIG. 4 :
FIG.4: Calculated deviation in bond length from the equilibrium bond length ∆r as a function of the number of In atoms NIn located in the second layer, for the surface with 2.3 MLs of N atoms shown in Fig.3(d).Squares and diamonds denote ∆r for Ga-N and In-N bonds, respectively.The notation of circles is the same as in Fig.1.

FIG. 5 :
FIG. 5: In composition of each layer in the equilibrium configurations at T = 850 K obtained by the MC simulations.Diamonds, and circles represent the composition of the surfaces with 1.7 and 2.3 MLs of N atoms, respectively.