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Stability of hydrogen on nonpolar and semipolar nitride surfaces: Role of surface orientation
Journal of Crystal Growth 318 (2011) 79–83
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Stability of hydrogen on nonpolar and semipolar nitride surfaces: Role of surface orientation Toru Akiyama , Tomoki Yamashita, Kohji Nakamura, Tomonori Ito Department of Physics Engineering, Mie University, 1577 Kurima-Machiya, Tsu 514-8507, Japan
a r t i c l e in f o
abstract
Available online 26 October 2010
The stability of hydrogen on nonpolar and semipolar orientations during the metal-organic vapor-phase epitaxy growth is systematically investigated on the basis of density-functional total-energy calculations. The calculated surface energies demonstrate that there are several reconstructions depending on the growth conditions. Using surface phase diagrams which are obtained by comparing the calculated adsorption energy with vapor-phase chemical potentials, we find semipolar GaNð1 1 2 2Þ surface forms N–H and Ga–NH2 bonds beyond 1000 K while nonpolar GaN surface without hydrogen is stabilized ranging 1200–1400 K. The stabilization of hydrogen free surfaces in the nonpolar orientation can be interpreted in terms of the electron counting rule, in which surface dangling bonds of Ga and N are empty and filled by electrons, respectively. For InN, on the other hand, the surfaces with hydrogen are stabilized over the wide range of growth conditions regardless of surface orientation. This is because the growth temperatures of InN are much lower than those of GaN. These results thus suggest that the growth kinetics and its orientation dependence could be different between GaN and InN surfaces. & 2010 Elsevier B.V. All rights reserved.
Keywords: A1. Computer simulation A1. Surface structure A2. Metalorganic vapor phase epitaxy B1. Nitrides B2. Semiconducting III-V materials
1. Introduction Group-III nitride semiconductors have been widely used for optoelectronics as well as high-power radio frequency electronics. The epitaxial growth of nitrides such as metal-organic vapor-phase epitaxy (MOVPE) and molecular-beam epitaxy (MBE) has conventionally been performed along the polar [0 0 0 1] direction. However, the growth along the polar direction leads to the formation of large spontaneous and piezoelectric polarization fields along the growth direction, resulting in the separation of electrons and holes which reduce the radiative efficiency of light emitters [1]. To overcome this drawback, growth in nonpolar and semipolar orientations is currently being pursued intensively [2–10]. It has been reported that unlike the conventional GaN growth along the [0 0 0 1] direction relatively lower temperatures have been found to be required to obtain atomically flat ð1 1 2 2Þ surfaces in the MOVPE growth [5]. Moreover, it has well been known that ð1 1 2 2Þ and ð1 1 2 0Þ facets tend to appear at low and high temperatures, respectively, in conventional regrowth techniques on patterned c-plane GaN(0 0 0 1) surface [11,12]. Most recently, the selective area growth on GaNð1 1 2 0Þ surface has also shown that ð1 1 2 2Þ surface is formed under low temperatures while both (0 0 0 1) and ð1 1 2 0Þ surfaces continue to increase for higher temperatures [13]. These experimental facts thus suggest
Corresponding author. Tel.: +81 59 232 1211; fax: + 81 59 231 9726.
E-mail address: [email protected] (T. Akiyama). 0022-0248/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2010.10.072
that surface reconstruction and growth kinetics in GaN are strongly affected by surface orientation. For InN, in contrast, it has been known that the growth is prevented with increasing of H2 pressure and N2 is usually used as a carrier gas. Thermodynamic analysis has also shown that the InN deposition rate decreases with the increase of hydrogen [14], implying that surface reconstructions and growth kinetics on InN surface are different from those of GaN surface. From theoretical viewpoints, the reconstruction on nonpolar and semipolar surfaces for GaN and InN under the MBE growth conditions (i.e., the surfaces without hydrogen) has been investigated, and several stable structures have been found depending on the growth conditions, such as temperature and pressure [15–18]. However, during typical vapor-phase epitaxy such as MOPVE, the surface interacts with an H-rich ambient. Thus, determining the reconstruction taking account of hydrogen and clarifying the stability of hydrogen on the surfaces are important. Although the stable structures of GaN(0 0 0 1) and GaNð0 0 0 1Þ surfaces taking account of hydrogen have been determined based on densityfunctional calculations [19,20], the stability of hydrogen and its temperature and pressure dependence on nonpolar ð1 1 2 0Þ and semipolar ð1 1 2 2Þ orientations still remain unclear. In this study, we systematically investigate the stability of hydrogen, such as H and NH2, on nonpolar and semipolar orientations under growth conditions using total-energy electronicstructure calculations. The stable structures of nonpolar ð1 1 2 0Þ and semipolar ð1 1 2 2Þ surfaces considering hydrogen are determined on the basis of the surface formation energy. Furthermore, the orientation dependence and chemical trends in the stable
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surface structures are discussed using surface phase diagrams, which are obtained by comparing the calculated adsorption energy with vapor-phase chemical potentials.
2. Computational approach Total-energy calculations are performed within the generalized gradient approximation [22] in the density functional theory. We use norm-conserving pseudopotentials [23] for In, Ga, and H atoms, and an ultrasoft pseudopotential [24] for N atoms. Ga 3d and In 4d electrons are treated by partial core corrections [25]. The conjugate-gradient technique is utilized both for the electronic structure calculations and for geometry optimization [26,27]. The optimization of geometry is performed until the remaining ˚ The forces acting on the atoms are less than 5:0 103 Ry=A. valence wave functions are expanded by the plane-wave basis set with a cutoff energy of 28 Ry. The surfaces are simulated using the 1 1 and c(2 2) slab models for ð1 1 2 0Þ and ð1 1 2 2Þ surfaces, respectively, which consist of eight-atomic layers GaN and InN and 9 A˚ vacuum region. In order to compare the results of nonpolar and semipolar surfaces with those on polar surface, we also adopt the 2 2 slab model consisting of four bilayer GaN and InN along the [0 0 0 1] direction and 9 A˚ vacuum region. The bottom surface of the slab is passivated with artificial hydrogen atoms [28], and the lower four layers are fixed at ideal positions. We use eight k points sampling for the 1 1 surface unit, which provides sufficient accuracy in the total energy. Many types of H-terminated surface structures as well as those without hydrogen are considered to determine the stable surface structures under growth conditions. The relative stability among various surface structures including hydrogen (in the case of GaN) is determined using the formation energy Ef given by [19] Ef ¼ Etot Eref nGa mGa nN mN nH mH ,
ð1Þ
where Etot and Eref are the total energy of the surface under consideration and of the reference surface, respectively, mi is the chemical potential of the ith species, and ni is the number of excess or deficit ith atoms with respect to the reference. Here, we assume that the surface is in equilibrium with bulk GaN expressed as
mGa þ mN ¼ mbulk GaN , bulk GaN
ð2Þ
is the chemical potential of bulk GaN. mGa can vary in where m bulk the thermodynamically allowed range mbulk Ga þ DHf r mGa r mGa , where DHf is the heat of formation of bulk GaN (mbulk is the Ga chemical potential of bulk Ga). The lower and upper limits
correspond to N-rich and Ga-rich conditions, respectively. The same formalism is also applied to the study of InN surfaces using bulk the chemical potentials of bulk In ðmbulk In Þ and InN ðmInN Þ as a function of In chemical potential mIn . The calculated values of DHf are 1.24 and 0.37 eV for GaN and InN, respectively, which agree with previous calculations [15,19,21]. The reconstruction under growth conditions, such as temperature and pressure, is determined using the surface phase diagrams, which are obtained by comparing the adsorption energy Ead with the gas-phase chemical potential mgas given by [29] ( ) 3=2 gkB T 2pmkB T mgas ¼ kB Tln z z ð3Þ rot vib , p h2 where kB is the Boltzmann constant, T is the gas temperature, g is the degree of degeneracy of electron energy level, and p is the pressure. zrot and zvib are the partition functions for rotational and vibrational motions, respectively. The structure corresponding to adsorbed surface is favorable when Ead is less than mgas , whereas desorbed surface is stabilized when mgas is less than Ead.
3. GaN surfaces Fig. 1 shows the diagrams of stable nonpolar and semipolar GaN surfaces as functions of mGa and mH using Eq. (1), along with that on GaN(0 0 0 1) surface for comparison. The boundary lines separating different regions correspond to chemical potentials for which two structures have the same formation energy. The diagram for GaN(0 0 0 1) shown in Fig. 1(a) agrees with that in the previous study [19]: For H-rich (high mH ) conditions, the surfaces with H atoms are stabilized. If we assume the pressures of H2 and Ga as pH2 ¼ 76 and pGa ¼ 5:0 104 Torr for 1270–1300 K, respectively (open circles in Fig. 1), the surface with a topmost Ga atom terminated by an NH2 molecule and an H-terminated N adatom attached to the other topmost Ga (Nad–H+ Ga–NH2) is favored for N-rich conditions ðmGa r 1:16 eVÞ. For relatively high mGa conditions larger than 1.16 eV, on the other hand, the H-terminated surface with an H-terminated N adatom (Nad–H +Ga–H) is stabilized. Therefore, these surfaces are expected to emerge during the MOVPE depending on the growth conditions. Since both the Nad–H+ Ga–H and Nad–H+ Ga–NH2 satisfy the electron counting (EC) rule [30], the stabilization of the Nad–H + Ga–NH2 under N-rich conditions can be interpreted in terms of the desorption of Ga atoms. The topmost Ga atoms in the Nad–H+ Ga–H desorb and N atoms appear with decreasing mGa . Owing to H-rich
Fig. 1. Stable structures of (a) polar GaN(0 0 0 1), (b) nonpolar GaNð1 1 2 0Þ, and (c) semipolar GaNð1 1 2 2Þ surfaces as functions of mGa and mH . mH ¼ 0 and mGa ¼ 0 correspond to H2 molecules at T¼ 0 K and bulk Ga (Ga droplet), respectively. Stable region of the surfaces with hydrogen is emphasized by shaded area. Open circles indicate mH and mGa with pH2 ¼ 76 and pGa ¼ 5:0 104 Torr, respectively, ranging from 1270 to 1370 K, which correspond to the experimental conditions [13].
T. Akiyama et al. / Journal of Crystal Growth 318 (2011) 79–83
[0001]
conditions, H atoms terminate the remaining N atoms, resulting in the formation of H-terminated N adatoms and Ga–NH2 bonds. Although similar NH2-terminated surface, such as the H-terminated surface with NH2 (N–H+ Ga–NH2) shown in Fig. 2(a), is also stabilized under H-rich conditions on GaNð1 1 2 0Þ surface, the stable structures shown in Fig. 1(b) are different from those on GaN(0 0 0 1) surface. Even under H-rich conditions ðmH 1 eVÞ, the surface consisting of Ga–N dimers [Ga–N in Fig. 2(b)] is stabilized. This is because dangling bonds of topmost Ga and N atoms are empty and filled by electrons, respectively, satisfying the electron counting (EC) rule [30]. For N-rich conditions during the MOVPE growth the N–H+ Ga–NH2 is favorable (for mGa r1:1 eV) in addition to the Ga–N. The stabilization of the N–H+Ga–NH2 under extreme N-rich condition can be interpreted in terms of the desorption of Ga atoms, as seen in GaN(0 0 0 1) surface. In contrast to these surface orientations, the diagram of GaNð1 1 2 2Þ surface shown in Fig. 1(c) manifests the absence of growth-condition dependence. The H-terminated surface with NH and NH2 (N–H+ Ga–NH+ Ga–NH2) shown in Fig. 3(a) is stabilized over the wide range of mGa and mH , implying that this structure is expected to emerge during the MOVPE regardless of the growth conditions. The stabilization of this surface is related to the polarity of Gað1 1 2 2Þ surface. The ideal cleavage surface is N-terminated surface similar to N-polar GaNð0 0 0 1Þ surface. Thus, two- and three-coordinated topmost N atoms appear in the ideal cleavage
[1100]
[1100]
Fig. 2. Stable geometries of nonpolar GaNð1 1 2 0Þ surfaces under (a) N-rich and (b) Ga-rich conditions (N–H + Ga–NH2 and Ga–N in Fig. 1(b), respectively) during the MOVPE growth. Ga and N atoms are represented by purple (filled) and gray (empty) circles, respectively. Small circles represent hydrogen atoms. The 1 1 unit cell is shown by dashed rectangle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
[1123] Fig. 3. Stable geometries of semipolar (a) GaNð1 1 2 2Þ and (b) InNð1 1 2 2Þ surfaces (N–H+ Ga–NH+ Ga–NH2 in Fig. 1(c) and N–H +In–NH2 in Fig. 5(a), respectively) during the MOVPE growth. Purple (filled) and gray (empty) circles represent Ga/In and N atoms, respectively. Small circles represent hydrogen atoms. The 1 1 unit cell is shown by dashed rectangle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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surface. Since the N–H bond is very stable configuration among possible bonds between Ga, N, and H atoms, H atoms easily terminate topmost N atoms with large energy gain ð 4 eVÞ. To satisfy the EC rule [30], three of eight topmost N atoms have filled dangling bonds (lone-pairs). This structure corresponds to the strong affinity of hydrogen in the stable H-terminated GaNð0 0 0 1Þ surface, where the 2 2 surface with three N–H bonds are stable over the wide range of chemical potential of Ga [20]. In order to discuss the reconstruction under realistic conditions such as temperature and pressure, we obtain the surface phase diagrams as functions of temperature and Ga pressure at pH2 ¼ 76 Torr. Fig. 4 shows the calculated surface phase diagrams of GaN(0 0 0 1), GaNð1 1 2 0Þ, and GaNð1 1 2 2Þ surfaces [31]. The surface phase diagram on GaN(0 0 0 1) shown in Fig. 4(a) demonstrates that both the Nad–H+Ga–NH2 and Nad–H+Ga–H can be formed for temperatures ranging 1270–1370 K for pGa 103 Torr. The diagram also indicates temperature dependence in the structural stability: the Nad–H+Ga–H and Nad–H+Ga–NH2 are stabilized for low and high temperatures, respectively. This temperature dependence can also be seen in GaNð1 1 2 0Þ surface, as shown in Fig. 4(b). The stable region for the Ga–N is located around 1200–1400 K for pGa 103 Torr and the N–H+Ga–NH2 is stabilized for higher temperatures. Thus, in both GaN(0 0 0 1) and GaNð1 1 2 0Þ surfaces, two different types of surface structures can be realized. In contrast, the surface phase diagram on GaNð1 1 2 2Þ shown in Fig. 4(c) indicates that the stable region of the N–H+Ga–NH+Ga–NH2 expands over the wide range of temperature and Ga pressure, implying that this structure always emerges for temperatures ranging 1200–1400 K regardless of Ga pressure. Since the growth kinetics is affected by the reconstruction, the temperature dependence in the stability of H-terminated surfaces could be a possible explanation for the growth on nonpolar and semipolar orientations [5,11–13]. For low temperatures, relatively weak Ga–H bonds still remain on polar GaN(0 0 0 1) surface and both Ga and N dangling bonds exist on nonpolar GaNð1 1 2 0Þ surface. In this case, the adsorption energy of Ga and N on these surfaces could be low compared with that on GaNð1 1 2 2Þ surface, and the adsorption preferentially occurs on GaN(0 0 0 1) and GaNð1 1 2 0Þ surfaces. Thus, it is expected that the growth on polar and nonpolar orientations is enhanced and the growth on semipolar orientation is slower than these orientations, leading to the formation of semipolar surface for low temperatures. For high temperature, on the other hand, the stable N–H bonds are already formed on polar and nonpolar orientations, leading to higher adsorption energy. In such case, the adsorption on semipolar orientation is rather efficient than those on polar and nonpolar orientations because N dangling bonds still remain on the semipolar surface. Although these N dangling bonds are stable compared to Ga–H and Ga dangling bonds, they might be chemically active compared to N–H and Ga–NH2 bonds. Thus, the growth on polar and nonpolar orientations is inhibited, and then polar and nonpolar surfaces are preferentially formed for high temperatures. Although the grown kinetics on these surfaces should be carefully examined, this scenario is qualitatively consistent with the experiments, where the lower temperatures are required to obtain atomically flat ð1 1 2 2Þ surface [5] and the formation of {0 0 0 1} and f1 1 2 0g facets for high temperatures in the selective area growth [11–13].
4. InN surfaces Fig. 5 shows the diagram of stable nonpolar and semipolar InN surfaces as functions of mIn and mH using Eq. (1), along with that on InN(0 0 0 1) surface for comparison. For H-poor (low mH ) conditions, the surface with In adatom and that with In bilayer are
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Fig. 4. Calculated surface phase diagrams of (a) polar GaN(0 0 0 1), (b) nonpolar GaNð1 1 2 0Þ, and (c) semipolar GaNð1 1 2 2Þ surfaces as functions of temperature and Ga pressure under high H2 pressure ðpH2 ¼ 76 TorrÞ conditions. Temperatures for the MOVPE growth in Ref. [13] are also shown.
Fig. 5. Stable structures of (a) polar InN(0 0 0 1), (b) nonpolar InNð1 1 2 0Þ, and (c) semipolar InNð1 1 2 2Þ surfaces as functions of mGa and mH . mH ¼ 0 and mIn ¼ 0 correspond to H2 molecules at T¼ 0 K and bulk In (In droplet), respectively. Stable region of the surfaces with hydrogen is emphasized by shaded area. Open circles indicate mH and mIn with pH2 ¼ 76 and pIn ¼ 5:0 104 Torr, respectively, ranging from 770 to 900 K.
stabilized at moderate In/N rations and In-rich conditions, respectively, consistent with the previous calculations [15]. For H-rich (high mH ) conditions, the surface with a topmost In atoms terminated by an NH2 molecule and an H-terminated N adatom attached to the other topmost In (Nad–H+ In–NH2) is stabilized. If we assume the pressures of H2 and In as pH2 ¼ 76 and pIn ¼ 5:0 104 Torr for 770–900 K, respectively, (open circles in Fig. 5), this surface is favored over the wide range of mH and mIn . Therefore, the Nad–H +In–NH2 is expected to emerge during the MOVPE regardless of the growth conditions. The surfaces with NH2 are also stabilized under H-rich conditions on InNð1 1 2 0Þ and InNð1 1 2 2Þ surfaces as shown in Figs. 5(b) and (c), respectively. If we assume the pressures of H2 and In as pH2 ¼ 76 and pIn ¼ 5:0 104 Torr for 770–900 K, respectively, the H-terminated surfaces with NH2 (N–H+ In–NH2) shown in Figs. 2(a) and 3(b) for InNð1 1 2 0Þ and InNð1 1 2 2Þ, respectively, are stabilized over the wide range of mH and mIn . Since there are many excess electrons on these surfaces, the stability of InN surfaces on nonpolar and semipolar orientations is quite different from that on GaN surfaces. Due to low growth temperatures of InN, the surfaces with large number of N–H bonds become the most favorable configuration even though many excess electrons are generated by N–H bonds. The EC rule [30] is no longer satisfied on semipolar InNð1 1 2 2Þ surfaces. The stabilization of the surfaces with NH2 can also be seen in the calculated surface phase diagrams. Fig. 6 shows the surface phase
diagrams of InN(0 0 0 1), InNð1 1 2 0Þ, and InNð1 1 2 2Þ surfaces as functions of temperature and In pressures at pH2 ¼ 76 Torr. Since mgas of In atom in Eq. (3) is higher than mbulk for low temperatures, the In surfaces containing bulk In (In droplet) are the most stable under low temperature and high In pressure conditions, independent of surface orientation. These surface phase diagrams also demonstrate that the H-terminated surfaces with NH2 (Nad–H+In–NH2 and N–H+In–NH2) are stabilized for high temperatures beyond 675–900 K. Therefore, in contrast to GaN surfaces, the H-terminated surfaces with NH2 such as Nad–H+In–NH2 and N–H+In–NH2 always emerge regardless of surface orientation. The absence of orientation dependence implies that the growth kinetics on nonpolar InNð1 1 2 0Þ and semipolar InNð1 1 2 2Þ surfaces is similar to that on polar InN(0 0 0 1) surface. Since the growth of InN on InN(0 0 0 1) surface is known to be prevented for high H2 pressures, the growth on nonpolar InNð1 1 2 0Þ and semipolar InNð1 1 2 2Þ surfaces is also inhibited due to the entity of hydrogen. Although the adsorption and desorption behavior of In and N on the H-terminated surfaces with NH2 should be verified, it is likely that the desorption of In and N atoms on these surfaces easily occurs.
5. Summary We have investigated the stability of hydrogen on nonpolar and semipolar orientations during the metal-organic vapor-phase
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Fig. 6. Calculated surface phase diagrams for (a) polar InN(0 0 0 1), (b) nonpolar InNð1 1 2 0Þ, and (c) semipolar InNð1 1 2 2Þ surfaces as functions of temperature and In pressure under high H2 pressure ðpH2 ¼ 76 TorrÞ conditions. Temperatures for the MOVPE growth on polar InN(0 0 0 1) surface [32] are also shown.
epitaxy growth on the basis of density-functional total-energy calculations. The calculated surface formation energies have demonstrated several reconstructions depending on the growth conditions. Using surface phase diagrams, we have found that for high H2 pressure conditions semipolar GaN surface with ð1 1 2 2Þ orientation forms N–H and Ga–NH2 bonds below 1500 K while nonpolar GaN surface without hydrogen is stabilized ranging 1200–1400 K. The stabilization of these surfaces can be interpreted in terms of the electron counting rule, in which surface dangling bonds of Ga and N are empty and filled by electrons, respectively. For InN, on the other hand, the surfaces with NH2 are stabilized over the wide range of growth conditions regardless of surface orientation. This is because the growth temperatures of InN are much lower than those of GaN. The surface phase diagrams have revealed that these InN surfaces emerge for high temperature beyond 675–900 K. The results thus suggest that the growth kinetics and its orientation dependence could be different between GaN and InN surfaces.
Acknowledgements We would like to thank Professor K. Hiramatsu and Professor H. Miyake for their discussions and comments. This work was supported in part by a Grant-in-Aid for Scientific Research (No. 21560032) from the Japan Society for the Promotion of Science. Codes used in this work are based on Tokyo Ab-initio Program Package (TAPP). Computations were performed at RCCS (National Institutes of Natural Sciences). References [1] T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, I. Akasaki, Jpn. J. Appl. Phys. 36 (1997) L382. [2] P. Waltereit, O. Brandt, A. Trampert, H.T. Grahn, J. Menniger, M. Ramsteiner, M. Reiche, K.H. Ploog, Nature 406 (2000) 865. [3] R. Sharma, P.M. Pattison, H. Masui, R.M. Farrell, T.J. Baker, B.A. Haskell, F. Wu, S.P. DenBaars, J.S. Speck, S. Nakamura, Appl. Phys. Lett. 87 (2005) 231110.
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Stability of hydrogen on nonpolar and semipolar nitride surfaces: Role of surface orientation Toru Akiyama , Tomoki Yamashita, Kohji Nakamura, Tomonori Ito Department of Physics Engineering, Mie University, 1577 Kurima-Machiya, Tsu 514-8507, Japan
a r t i c l e in f o
abstract
Available online 26 October 2010
The stability of hydrogen on nonpolar and semipolar orientations during the metal-organic vapor-phase epitaxy growth is systematically investigated on the basis of density-functional total-energy calculations. The calculated surface energies demonstrate that there are several reconstructions depending on the growth conditions. Using surface phase diagrams which are obtained by comparing the calculated adsorption energy with vapor-phase chemical potentials, we find semipolar GaNð1 1 2 2Þ surface forms N–H and Ga–NH2 bonds beyond 1000 K while nonpolar GaN surface without hydrogen is stabilized ranging 1200–1400 K. The stabilization of hydrogen free surfaces in the nonpolar orientation can be interpreted in terms of the electron counting rule, in which surface dangling bonds of Ga and N are empty and filled by electrons, respectively. For InN, on the other hand, the surfaces with hydrogen are stabilized over the wide range of growth conditions regardless of surface orientation. This is because the growth temperatures of InN are much lower than those of GaN. These results thus suggest that the growth kinetics and its orientation dependence could be different between GaN and InN surfaces. & 2010 Elsevier B.V. All rights reserved.
Keywords: A1. Computer simulation A1. Surface structure A2. Metalorganic vapor phase epitaxy B1. Nitrides B2. Semiconducting III-V materials
1. Introduction Group-III nitride semiconductors have been widely used for optoelectronics as well as high-power radio frequency electronics. The epitaxial growth of nitrides such as metal-organic vapor-phase epitaxy (MOVPE) and molecular-beam epitaxy (MBE) has conventionally been performed along the polar [0 0 0 1] direction. However, the growth along the polar direction leads to the formation of large spontaneous and piezoelectric polarization fields along the growth direction, resulting in the separation of electrons and holes which reduce the radiative efficiency of light emitters [1]. To overcome this drawback, growth in nonpolar and semipolar orientations is currently being pursued intensively [2–10]. It has been reported that unlike the conventional GaN growth along the [0 0 0 1] direction relatively lower temperatures have been found to be required to obtain atomically flat ð1 1 2 2Þ surfaces in the MOVPE growth [5]. Moreover, it has well been known that ð1 1 2 2Þ and ð1 1 2 0Þ facets tend to appear at low and high temperatures, respectively, in conventional regrowth techniques on patterned c-plane GaN(0 0 0 1) surface [11,12]. Most recently, the selective area growth on GaNð1 1 2 0Þ surface has also shown that ð1 1 2 2Þ surface is formed under low temperatures while both (0 0 0 1) and ð1 1 2 0Þ surfaces continue to increase for higher temperatures [13]. These experimental facts thus suggest
Corresponding author. Tel.: +81 59 232 1211; fax: + 81 59 231 9726.
E-mail address: [email protected] (T. Akiyama). 0022-0248/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2010.10.072
that surface reconstruction and growth kinetics in GaN are strongly affected by surface orientation. For InN, in contrast, it has been known that the growth is prevented with increasing of H2 pressure and N2 is usually used as a carrier gas. Thermodynamic analysis has also shown that the InN deposition rate decreases with the increase of hydrogen [14], implying that surface reconstructions and growth kinetics on InN surface are different from those of GaN surface. From theoretical viewpoints, the reconstruction on nonpolar and semipolar surfaces for GaN and InN under the MBE growth conditions (i.e., the surfaces without hydrogen) has been investigated, and several stable structures have been found depending on the growth conditions, such as temperature and pressure [15–18]. However, during typical vapor-phase epitaxy such as MOPVE, the surface interacts with an H-rich ambient. Thus, determining the reconstruction taking account of hydrogen and clarifying the stability of hydrogen on the surfaces are important. Although the stable structures of GaN(0 0 0 1) and GaNð0 0 0 1Þ surfaces taking account of hydrogen have been determined based on densityfunctional calculations [19,20], the stability of hydrogen and its temperature and pressure dependence on nonpolar ð1 1 2 0Þ and semipolar ð1 1 2 2Þ orientations still remain unclear. In this study, we systematically investigate the stability of hydrogen, such as H and NH2, on nonpolar and semipolar orientations under growth conditions using total-energy electronicstructure calculations. The stable structures of nonpolar ð1 1 2 0Þ and semipolar ð1 1 2 2Þ surfaces considering hydrogen are determined on the basis of the surface formation energy. Furthermore, the orientation dependence and chemical trends in the stable
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surface structures are discussed using surface phase diagrams, which are obtained by comparing the calculated adsorption energy with vapor-phase chemical potentials.
2. Computational approach Total-energy calculations are performed within the generalized gradient approximation [22] in the density functional theory. We use norm-conserving pseudopotentials [23] for In, Ga, and H atoms, and an ultrasoft pseudopotential [24] for N atoms. Ga 3d and In 4d electrons are treated by partial core corrections [25]. The conjugate-gradient technique is utilized both for the electronic structure calculations and for geometry optimization [26,27]. The optimization of geometry is performed until the remaining ˚ The forces acting on the atoms are less than 5:0 103 Ry=A. valence wave functions are expanded by the plane-wave basis set with a cutoff energy of 28 Ry. The surfaces are simulated using the 1 1 and c(2 2) slab models for ð1 1 2 0Þ and ð1 1 2 2Þ surfaces, respectively, which consist of eight-atomic layers GaN and InN and 9 A˚ vacuum region. In order to compare the results of nonpolar and semipolar surfaces with those on polar surface, we also adopt the 2 2 slab model consisting of four bilayer GaN and InN along the [0 0 0 1] direction and 9 A˚ vacuum region. The bottom surface of the slab is passivated with artificial hydrogen atoms [28], and the lower four layers are fixed at ideal positions. We use eight k points sampling for the 1 1 surface unit, which provides sufficient accuracy in the total energy. Many types of H-terminated surface structures as well as those without hydrogen are considered to determine the stable surface structures under growth conditions. The relative stability among various surface structures including hydrogen (in the case of GaN) is determined using the formation energy Ef given by [19] Ef ¼ Etot Eref nGa mGa nN mN nH mH ,
ð1Þ
where Etot and Eref are the total energy of the surface under consideration and of the reference surface, respectively, mi is the chemical potential of the ith species, and ni is the number of excess or deficit ith atoms with respect to the reference. Here, we assume that the surface is in equilibrium with bulk GaN expressed as
mGa þ mN ¼ mbulk GaN , bulk GaN
ð2Þ
is the chemical potential of bulk GaN. mGa can vary in where m bulk the thermodynamically allowed range mbulk Ga þ DHf r mGa r mGa , where DHf is the heat of formation of bulk GaN (mbulk is the Ga chemical potential of bulk Ga). The lower and upper limits
correspond to N-rich and Ga-rich conditions, respectively. The same formalism is also applied to the study of InN surfaces using bulk the chemical potentials of bulk In ðmbulk In Þ and InN ðmInN Þ as a function of In chemical potential mIn . The calculated values of DHf are 1.24 and 0.37 eV for GaN and InN, respectively, which agree with previous calculations [15,19,21]. The reconstruction under growth conditions, such as temperature and pressure, is determined using the surface phase diagrams, which are obtained by comparing the adsorption energy Ead with the gas-phase chemical potential mgas given by [29] ( ) 3=2 gkB T 2pmkB T mgas ¼ kB Tln z z ð3Þ rot vib , p h2 where kB is the Boltzmann constant, T is the gas temperature, g is the degree of degeneracy of electron energy level, and p is the pressure. zrot and zvib are the partition functions for rotational and vibrational motions, respectively. The structure corresponding to adsorbed surface is favorable when Ead is less than mgas , whereas desorbed surface is stabilized when mgas is less than Ead.
3. GaN surfaces Fig. 1 shows the diagrams of stable nonpolar and semipolar GaN surfaces as functions of mGa and mH using Eq. (1), along with that on GaN(0 0 0 1) surface for comparison. The boundary lines separating different regions correspond to chemical potentials for which two structures have the same formation energy. The diagram for GaN(0 0 0 1) shown in Fig. 1(a) agrees with that in the previous study [19]: For H-rich (high mH ) conditions, the surfaces with H atoms are stabilized. If we assume the pressures of H2 and Ga as pH2 ¼ 76 and pGa ¼ 5:0 104 Torr for 1270–1300 K, respectively (open circles in Fig. 1), the surface with a topmost Ga atom terminated by an NH2 molecule and an H-terminated N adatom attached to the other topmost Ga (Nad–H+ Ga–NH2) is favored for N-rich conditions ðmGa r 1:16 eVÞ. For relatively high mGa conditions larger than 1.16 eV, on the other hand, the H-terminated surface with an H-terminated N adatom (Nad–H +Ga–H) is stabilized. Therefore, these surfaces are expected to emerge during the MOVPE depending on the growth conditions. Since both the Nad–H+ Ga–H and Nad–H+ Ga–NH2 satisfy the electron counting (EC) rule [30], the stabilization of the Nad–H + Ga–NH2 under N-rich conditions can be interpreted in terms of the desorption of Ga atoms. The topmost Ga atoms in the Nad–H+ Ga–H desorb and N atoms appear with decreasing mGa . Owing to H-rich
Fig. 1. Stable structures of (a) polar GaN(0 0 0 1), (b) nonpolar GaNð1 1 2 0Þ, and (c) semipolar GaNð1 1 2 2Þ surfaces as functions of mGa and mH . mH ¼ 0 and mGa ¼ 0 correspond to H2 molecules at T¼ 0 K and bulk Ga (Ga droplet), respectively. Stable region of the surfaces with hydrogen is emphasized by shaded area. Open circles indicate mH and mGa with pH2 ¼ 76 and pGa ¼ 5:0 104 Torr, respectively, ranging from 1270 to 1370 K, which correspond to the experimental conditions [13].
T. Akiyama et al. / Journal of Crystal Growth 318 (2011) 79–83
[0001]
conditions, H atoms terminate the remaining N atoms, resulting in the formation of H-terminated N adatoms and Ga–NH2 bonds. Although similar NH2-terminated surface, such as the H-terminated surface with NH2 (N–H+ Ga–NH2) shown in Fig. 2(a), is also stabilized under H-rich conditions on GaNð1 1 2 0Þ surface, the stable structures shown in Fig. 1(b) are different from those on GaN(0 0 0 1) surface. Even under H-rich conditions ðmH 1 eVÞ, the surface consisting of Ga–N dimers [Ga–N in Fig. 2(b)] is stabilized. This is because dangling bonds of topmost Ga and N atoms are empty and filled by electrons, respectively, satisfying the electron counting (EC) rule [30]. For N-rich conditions during the MOVPE growth the N–H+ Ga–NH2 is favorable (for mGa r1:1 eV) in addition to the Ga–N. The stabilization of the N–H+Ga–NH2 under extreme N-rich condition can be interpreted in terms of the desorption of Ga atoms, as seen in GaN(0 0 0 1) surface. In contrast to these surface orientations, the diagram of GaNð1 1 2 2Þ surface shown in Fig. 1(c) manifests the absence of growth-condition dependence. The H-terminated surface with NH and NH2 (N–H+ Ga–NH+ Ga–NH2) shown in Fig. 3(a) is stabilized over the wide range of mGa and mH , implying that this structure is expected to emerge during the MOVPE regardless of the growth conditions. The stabilization of this surface is related to the polarity of Gað1 1 2 2Þ surface. The ideal cleavage surface is N-terminated surface similar to N-polar GaNð0 0 0 1Þ surface. Thus, two- and three-coordinated topmost N atoms appear in the ideal cleavage
[1100]
[1100]
Fig. 2. Stable geometries of nonpolar GaNð1 1 2 0Þ surfaces under (a) N-rich and (b) Ga-rich conditions (N–H + Ga–NH2 and Ga–N in Fig. 1(b), respectively) during the MOVPE growth. Ga and N atoms are represented by purple (filled) and gray (empty) circles, respectively. Small circles represent hydrogen atoms. The 1 1 unit cell is shown by dashed rectangle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
[1123] Fig. 3. Stable geometries of semipolar (a) GaNð1 1 2 2Þ and (b) InNð1 1 2 2Þ surfaces (N–H+ Ga–NH+ Ga–NH2 in Fig. 1(c) and N–H +In–NH2 in Fig. 5(a), respectively) during the MOVPE growth. Purple (filled) and gray (empty) circles represent Ga/In and N atoms, respectively. Small circles represent hydrogen atoms. The 1 1 unit cell is shown by dashed rectangle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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surface. Since the N–H bond is very stable configuration among possible bonds between Ga, N, and H atoms, H atoms easily terminate topmost N atoms with large energy gain ð 4 eVÞ. To satisfy the EC rule [30], three of eight topmost N atoms have filled dangling bonds (lone-pairs). This structure corresponds to the strong affinity of hydrogen in the stable H-terminated GaNð0 0 0 1Þ surface, where the 2 2 surface with three N–H bonds are stable over the wide range of chemical potential of Ga [20]. In order to discuss the reconstruction under realistic conditions such as temperature and pressure, we obtain the surface phase diagrams as functions of temperature and Ga pressure at pH2 ¼ 76 Torr. Fig. 4 shows the calculated surface phase diagrams of GaN(0 0 0 1), GaNð1 1 2 0Þ, and GaNð1 1 2 2Þ surfaces [31]. The surface phase diagram on GaN(0 0 0 1) shown in Fig. 4(a) demonstrates that both the Nad–H+Ga–NH2 and Nad–H+Ga–H can be formed for temperatures ranging 1270–1370 K for pGa 103 Torr. The diagram also indicates temperature dependence in the structural stability: the Nad–H+Ga–H and Nad–H+Ga–NH2 are stabilized for low and high temperatures, respectively. This temperature dependence can also be seen in GaNð1 1 2 0Þ surface, as shown in Fig. 4(b). The stable region for the Ga–N is located around 1200–1400 K for pGa 103 Torr and the N–H+Ga–NH2 is stabilized for higher temperatures. Thus, in both GaN(0 0 0 1) and GaNð1 1 2 0Þ surfaces, two different types of surface structures can be realized. In contrast, the surface phase diagram on GaNð1 1 2 2Þ shown in Fig. 4(c) indicates that the stable region of the N–H+Ga–NH+Ga–NH2 expands over the wide range of temperature and Ga pressure, implying that this structure always emerges for temperatures ranging 1200–1400 K regardless of Ga pressure. Since the growth kinetics is affected by the reconstruction, the temperature dependence in the stability of H-terminated surfaces could be a possible explanation for the growth on nonpolar and semipolar orientations [5,11–13]. For low temperatures, relatively weak Ga–H bonds still remain on polar GaN(0 0 0 1) surface and both Ga and N dangling bonds exist on nonpolar GaNð1 1 2 0Þ surface. In this case, the adsorption energy of Ga and N on these surfaces could be low compared with that on GaNð1 1 2 2Þ surface, and the adsorption preferentially occurs on GaN(0 0 0 1) and GaNð1 1 2 0Þ surfaces. Thus, it is expected that the growth on polar and nonpolar orientations is enhanced and the growth on semipolar orientation is slower than these orientations, leading to the formation of semipolar surface for low temperatures. For high temperature, on the other hand, the stable N–H bonds are already formed on polar and nonpolar orientations, leading to higher adsorption energy. In such case, the adsorption on semipolar orientation is rather efficient than those on polar and nonpolar orientations because N dangling bonds still remain on the semipolar surface. Although these N dangling bonds are stable compared to Ga–H and Ga dangling bonds, they might be chemically active compared to N–H and Ga–NH2 bonds. Thus, the growth on polar and nonpolar orientations is inhibited, and then polar and nonpolar surfaces are preferentially formed for high temperatures. Although the grown kinetics on these surfaces should be carefully examined, this scenario is qualitatively consistent with the experiments, where the lower temperatures are required to obtain atomically flat ð1 1 2 2Þ surface [5] and the formation of {0 0 0 1} and f1 1 2 0g facets for high temperatures in the selective area growth [11–13].
4. InN surfaces Fig. 5 shows the diagram of stable nonpolar and semipolar InN surfaces as functions of mIn and mH using Eq. (1), along with that on InN(0 0 0 1) surface for comparison. For H-poor (low mH ) conditions, the surface with In adatom and that with In bilayer are
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Fig. 4. Calculated surface phase diagrams of (a) polar GaN(0 0 0 1), (b) nonpolar GaNð1 1 2 0Þ, and (c) semipolar GaNð1 1 2 2Þ surfaces as functions of temperature and Ga pressure under high H2 pressure ðpH2 ¼ 76 TorrÞ conditions. Temperatures for the MOVPE growth in Ref. [13] are also shown.
Fig. 5. Stable structures of (a) polar InN(0 0 0 1), (b) nonpolar InNð1 1 2 0Þ, and (c) semipolar InNð1 1 2 2Þ surfaces as functions of mGa and mH . mH ¼ 0 and mIn ¼ 0 correspond to H2 molecules at T¼ 0 K and bulk In (In droplet), respectively. Stable region of the surfaces with hydrogen is emphasized by shaded area. Open circles indicate mH and mIn with pH2 ¼ 76 and pIn ¼ 5:0 104 Torr, respectively, ranging from 770 to 900 K.
stabilized at moderate In/N rations and In-rich conditions, respectively, consistent with the previous calculations [15]. For H-rich (high mH ) conditions, the surface with a topmost In atoms terminated by an NH2 molecule and an H-terminated N adatom attached to the other topmost In (Nad–H+ In–NH2) is stabilized. If we assume the pressures of H2 and In as pH2 ¼ 76 and pIn ¼ 5:0 104 Torr for 770–900 K, respectively, (open circles in Fig. 5), this surface is favored over the wide range of mH and mIn . Therefore, the Nad–H +In–NH2 is expected to emerge during the MOVPE regardless of the growth conditions. The surfaces with NH2 are also stabilized under H-rich conditions on InNð1 1 2 0Þ and InNð1 1 2 2Þ surfaces as shown in Figs. 5(b) and (c), respectively. If we assume the pressures of H2 and In as pH2 ¼ 76 and pIn ¼ 5:0 104 Torr for 770–900 K, respectively, the H-terminated surfaces with NH2 (N–H+ In–NH2) shown in Figs. 2(a) and 3(b) for InNð1 1 2 0Þ and InNð1 1 2 2Þ, respectively, are stabilized over the wide range of mH and mIn . Since there are many excess electrons on these surfaces, the stability of InN surfaces on nonpolar and semipolar orientations is quite different from that on GaN surfaces. Due to low growth temperatures of InN, the surfaces with large number of N–H bonds become the most favorable configuration even though many excess electrons are generated by N–H bonds. The EC rule [30] is no longer satisfied on semipolar InNð1 1 2 2Þ surfaces. The stabilization of the surfaces with NH2 can also be seen in the calculated surface phase diagrams. Fig. 6 shows the surface phase
diagrams of InN(0 0 0 1), InNð1 1 2 0Þ, and InNð1 1 2 2Þ surfaces as functions of temperature and In pressures at pH2 ¼ 76 Torr. Since mgas of In atom in Eq. (3) is higher than mbulk for low temperatures, the In surfaces containing bulk In (In droplet) are the most stable under low temperature and high In pressure conditions, independent of surface orientation. These surface phase diagrams also demonstrate that the H-terminated surfaces with NH2 (Nad–H+In–NH2 and N–H+In–NH2) are stabilized for high temperatures beyond 675–900 K. Therefore, in contrast to GaN surfaces, the H-terminated surfaces with NH2 such as Nad–H+In–NH2 and N–H+In–NH2 always emerge regardless of surface orientation. The absence of orientation dependence implies that the growth kinetics on nonpolar InNð1 1 2 0Þ and semipolar InNð1 1 2 2Þ surfaces is similar to that on polar InN(0 0 0 1) surface. Since the growth of InN on InN(0 0 0 1) surface is known to be prevented for high H2 pressures, the growth on nonpolar InNð1 1 2 0Þ and semipolar InNð1 1 2 2Þ surfaces is also inhibited due to the entity of hydrogen. Although the adsorption and desorption behavior of In and N on the H-terminated surfaces with NH2 should be verified, it is likely that the desorption of In and N atoms on these surfaces easily occurs.
5. Summary We have investigated the stability of hydrogen on nonpolar and semipolar orientations during the metal-organic vapor-phase
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Fig. 6. Calculated surface phase diagrams for (a) polar InN(0 0 0 1), (b) nonpolar InNð1 1 2 0Þ, and (c) semipolar InNð1 1 2 2Þ surfaces as functions of temperature and In pressure under high H2 pressure ðpH2 ¼ 76 TorrÞ conditions. Temperatures for the MOVPE growth on polar InN(0 0 0 1) surface [32] are also shown.
epitaxy growth on the basis of density-functional total-energy calculations. The calculated surface formation energies have demonstrated several reconstructions depending on the growth conditions. Using surface phase diagrams, we have found that for high H2 pressure conditions semipolar GaN surface with ð1 1 2 2Þ orientation forms N–H and Ga–NH2 bonds below 1500 K while nonpolar GaN surface without hydrogen is stabilized ranging 1200–1400 K. The stabilization of these surfaces can be interpreted in terms of the electron counting rule, in which surface dangling bonds of Ga and N are empty and filled by electrons, respectively. For InN, on the other hand, the surfaces with NH2 are stabilized over the wide range of growth conditions regardless of surface orientation. This is because the growth temperatures of InN are much lower than those of GaN. The surface phase diagrams have revealed that these InN surfaces emerge for high temperature beyond 675–900 K. The results thus suggest that the growth kinetics and its orientation dependence could be different between GaN and InN surfaces.
Acknowledgements We would like to thank Professor K. Hiramatsu and Professor H. Miyake for their discussions and comments. This work was supported in part by a Grant-in-Aid for Scientific Research (No. 21560032) from the Japan Society for the Promotion of Science. Codes used in this work are based on Tokyo Ab-initio Program Package (TAPP). Computations were performed at RCCS (National Institutes of Natural Sciences). References [1] T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, I. Akasaki, Jpn. J. Appl. Phys. 36 (1997) L382. [2] P. Waltereit, O. Brandt, A. Trampert, H.T. Grahn, J. Menniger, M. Ramsteiner, M. Reiche, K.H. Ploog, Nature 406 (2000) 865. [3] R. Sharma, P.M. Pattison, H. Masui, R.M. Farrell, T.J. Baker, B.A. Haskell, F. Wu, S.P. DenBaars, J.S. Speck, S. Nakamura, Appl. Phys. Lett. 87 (2005) 231110.
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