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Polarization doping in a GaN-InN system with a graded composition layer was studied using ab initio simulations. The electric charge volume density in the graded concentration part was determined by spatial potential dependence. The emerging graded polarization charge was determined to show that it could be obtained from a polarization difference and the concentration slope. It was shown that the GaN-InN polarization difference is changed by piezoelectric effects. The polarization difference is in agreement with the earlier obtained data despite the relatively narrow bandgap for the simulated system. The hole generation may be applied in the design of blue and green laser and light-emitting diodes.

Atomically thin metal adlayers are used as surfactants in semiconductor crystal growth. The role of the adlayer in the incorporation of dopants in GaN is completely unexplored, probably because n-type doping of GaN with Si is relatively straightforward and can be scaled up with available Si atomic flux in a wide range of dopant concentrations. However, a surprisingly different behavior of the Ge dopant is observed, and the presence of atomically thin gallium or an indium layer dramatically affects Ge incorporation, hindering the fabrication of GaN:Ge structures with abrupt doping profiles. Here, we show an experimental study presenting a striking improvement in sharpness of the Ge doping profile obtained for indium as compared to the gallium surfactant layer during GaN-plasma-assisted molecular beam epitaxy. We show that the atomically thin indium surfactant layer promotes the incorporation of Ge in contrast to the gallium surfactant layer, which promotes segregation of Ge to the surface and Ge crystallite formation. Understanding the role of the surfactant is essential to control GaN doping and to obtain extremely high n-type doped III-nitride layers using Ge, because doping levels >1020 cm−3 are not easily available with Si.

In this work, we study the emergence of polarization doping in AlxGa1-xN layers with graded composition from a theoretical viewpoint. We demonstrate that the charge conservation law applies for fixed and mobile charges separately, leading to nonlocal compensation phenomena involving bulk fixed and mobile charge and polarization sheet charge at the heterointerfaces. The magnitude of the effect allows obtaining technically viable mobile charge density for optoelectronic devices without impurity doping (donors or acceptors). Therefore, it provides an additional tool for the device designer, with the potential to attain high conductivities: high carrier concentrations can be obtained even in materials with high dopant ionization energies, and the mobility is not limited by scattering at ionized impurities., Comment: 16 pages, 4 figures

To improve the properties of semiconductors, it is necessary to construct an integrated crystal growth model that covers all elementary processes of metal–organic vapor phase epitaxy (MOVPE). Altho...

An ab initio-based approach is used to investigate the facet stability of GaN during tri-halide vapor phase epitaxy (THVPE). First, surface reconstructions are analyzed to create surface phase diagrams as a function of the gaseous pressure and temperature. Next, a triangular wedge model is used to compute absolute surface formation energies with the bulk state as a reference. A Wulff construction is used to predict the crystal growth form composed of energetically preferred facets. The calculated results can be used to control the shape of GaN grown by THVPE.

In this paper, ab initio calculations are used to determine polarization difference in zinc blende (ZB), hexagonal (H) and wurtzite (WZ) AlN-GaN and GaN-InN superlattices. It is shown that a polarization difference exists between WZ nitride compounds, while for H and ZB lattices the results are consistent with zero polarization difference. It is therefore proven that the difference in Berry phase spontaneous polarization for bulk nitrides (AlN, GaN and InN) obtained by Bernardini et al. and Dreyer et al. was not caused by the different reference phase. These models provided absolute values of the polarization that differed by more than one order of magnitude for the same material, but they provided similar polarization differences between binary compounds, which agree also with our ab initio calculations. In multi-quantum wells (MQWs), the electric fields are generated by the well-barrier polarization difference, hence, the calculated electric fields are similar for the three models, both for GaN/AlN and InN/GaN structures. Including piezoelectric effect, which can account for 50% of the total polarization difference, these theoretical data are in satisfactory agreement with photoluminescence measurements in GaN/AlN MQWs. Therefore, the three models considered above are equivalent in the treatment of III-nitride MQWs and can be equally used for the description of the electric properties of active layers in nitride-based optoelectronic devices.

Molecular nitrogen and molecular oxygen adsorption at the Al-terminated AlN(0001) surface was investigated using ab initio simulations. It was shown that both species undergo barrierless dissociation during attachment to the surface. The H3 adsorption site was identified as the most favorable for both O and N adatoms. The adsorption energies for O2 and N2 were found to be 14.8 and 6.0 eV, respectively. At the clean surface, separate N and O adatoms have their energies 4.37 eV lower than the NO admolecule. At normal nitrogen pressures, the AlN(0001) surface is fully covered by nitrogen adatoms. It was shown for this coverage that adsorption of oxygen leads to creation of the NO admolecule which is a necessary step for nitric monoxide synthesis. The energetics of NO molecules is related to electronic charge transfer: from the two possible configurations, it is shown that T4 and H3 are donors and acceptors, respectively. The resulting coverage is the mixture of both configurations, controlled by electron cha...

Density Functional Theory (DFT) calculations were used to determine adsorption of oxygen at GaN(0001), i.e. Ga-terminated surface. It was shown that at low coverage the oxygen molecule dissociates during adsorption so that the two separate O adatoms are located in H3 sites. Oxygen adatom saturates three Ga broken bonds, modifying their energy by overlap with Op states, so that the three states are degenerate with valence band (VB). The electron counting rule (ECR) indicate on the electron surplus, the excess electrons are donated to other Ga broken bond states, the adsorption energy is equal to 3.74 eV/atom for clean surface. At the first critical coverage θ O = 5 16 ML , the Fermi level is shifted to conduction band while at the second critical coverage θ O = 3 8 ML it is shifted down to VBM. The adsorption energy is Δ E 1 2 O 2 ( N ) = − 3.67 eV for θ O ≤ 7 24 ML , for θ O = 15 48 ML and θ O = 16 48 ML decreases Δ E 1 2 O 2 ( N ) = − 3.51 eV and Δ E 1 2 O 2 ( N ) = − 3.31 eV , respectively, for θ O = 17 48 the energy jumps to Δ E 1 2 O 2 ( N ) = − 3.60 eV , and for higher coverage θ O ≥ 3 8 the energy rapidly decreases to zero and becomes negative The singular point at θ O = 17 48 ML is essential for stability of oxygen coverage of the surface. The equilibrium pressure at low coverage is 10−5 bar for 1500 K and 10−12 bar 1000 K. It is reduced for higher coverage, due to reduction of the energy and configurational entropy contributions. At the coverage θ O = 17 48 ML the pressure is reduced by several orders of magnitude, indicating extremely high thermodynamic stability of such coverage, which is responsible for chemical inactivity of GaN(0001) surface observed in experiments, the critical factor for mechano-chemical polishing of the substrates for electronic applications.

Ab initio simulations were applied for nonpolar GaN/AlN superlattices of various widths for the first time giving band diagrams and optical transition oscillator strengths. The results confirmed the absence of electric fields in m-plane GaN/AlN multiquantum well (MQW) systems leading to drastically different properties of polar and nonpolar systems, narrow polar and nonpolar GaN/AlN well properties, such as bandgap or oscillator strength. Wider wells show drastic differences related to the presence of electric fields in polar systems. Wide nonpolar wells have bandgaps following parabolic dependence resulting from localization energy. Polar wide well gaps are determined by spontaneous and piezoelectric fields that reduce bandgap for wider wells and barriers. Oscillator strength shows a more dramatic difference between polar and nonpolar wells. Drastic reduction in the oscillator strength is observed for wide polar MQWs. The decrease in the oscillator strength by several orders of magnitude is observed for the increase in the width of wells and barriers. The wide polar wells should have extremely ineffective radiative emission from both direct and across the barrier overlap of electron–hole wavefunctions.

Diffusion of Be was investigated for the main crystallographic directions in HVPE-GaN: c [0001], m [10-10], and a [11-20]. Be was implanted into the samples at room temperature with a dose of 2.9e15 cm-2 with energy of 200 keV. Ultra-high pressure annealing (UHPA) was performed to repair the post-implantation damage and activate the dopant. The annealing was performed at different time (15 and 30 minutes) and temperature (1200 – 1400°C). Depth profiles of Be were measured by secondary ion mass spectrometry (SIMS). Diffusion coefficients were calculated using the complementary error function (erfc) or Boltzmann-Matano analysis. The determined diffusion coefficients were summarized in an Arrhenius plot: D(1/T). From this relation the pre-exponential factor D0 and the activation energy were calculated. In addition, it was possible to calculate the formation energy for interstitial Be as well as gallium vacancy defects.

The diffusion of beryllium in gallium nitride crystals grown in non-polar crystallographic directions by halide vapor phase epitaxy was investigated. The layers were crystallized on (10-10) and (11–20) planes of native ammonothermal substrates of the highest structural quality. The new-grown crystals were prepared to an epi-ready state, implanted with beryllium, and treated with ultra-high-pressure annealing. The crystallographic structure of all the samples before and after ion implantation as well as annealing processes was evaluated by X-ray diffraction measurements. The diffusion of beryllium was investigated by analyzing depth profiles obtained by secondary ion mass spectrometry. The diffusion profiles were box-shaped for both examined non-polar directions. Pre-exponential factors and activation energies for beryllium diffusion in non-polar gallium nitride were determined. A model related to point defect complexes, based on gallium vacancies and oxygen, was proposed for explaining the box-shaped beryllium diffusion profiles and the visible differences in the diffusion range between the two analyzed non-polar directions.

Adsorption of molecular nitrogen and molecular hydrogen at an Al-terminated AlN(0001) surface was investigated using ab initio simulation methods. It was shown that both species undergo dissociatio...

The formation and diffusion of point defects have a detrimental impact on the functionality of devices in which a high quality AlN/GaN heterointerface is required. The present paper demonstrated the heights of the migration energy barriers of native point defects throughout the AlN/GaN heterointerface, as well as the corresponding profiles of energy bands calculated by means of density functional theory. Both neutral and charged nitrogen, gallium, and aluminium vacancies were studied, as well as their complexes with a substitutional III-group element. Three diffusion mechanisms, that is, the vacancy mediated, direct interstitial, and indirect ones, in bulk AlN and GaN crystals, as well at the AlN/GaN heterointerface, were taken into account. We showed that metal vacancies migrated across the AlN/GaN interface, overcoming a lower potential barrier than that of the nitrogen vacancy. Additionally, we demonstrated the effect of the inversion of the electric field in the presence of charged point defects VGa3− and VAl3− at the AlN/GaN heterointerface, not reported so far. Our findings contributed to the issues of structure design, quality control, and improvement of the interfacial abruptness of the AlN/GaN heterostructures.

Comprehensive analysis of GaN(0001) surface in equilibrium with ammonia/hydrogen mixture was undertaken using results of ab initio calculations. Adsorption energies of the species derived from ammonia and molecular hydrogen and their stable sites were obtained. It was shown that the adsorption process type and energy depend on the position of Fermi level at the surface. Hydrogen decomposes into two separate H atoms, always adsorbed in the positions on top of the surface Ga atoms (On-top). Ammonia adsorption at GaN(0001) surface proceeds molecularly to ammonia in the On-top position or dissociatively into NH2 radicals in bridge (NH2-bridge) or On-top positions or into NH radicals in H3 (NH-H3) site. Presence of these species affects Fermi level pinning at the surface due to creation of new surface states. The Fermi level pinning in function of the surface attached species concentration was determined using extended electron counting rule (EECR). Results of ab initio calculations fully proved validity of the EECR predictions. Thermodynamic analysis of the surface in equilibrium with molecular hydrogen and ammonia vapor mixture is made giving the range of ammonia and hydrogen pressures, corresponding to Fermi level pinned at Ga-broken bond state for NH-H3&H and NH3&H and NH2-bridge&H coverage and at VBM for NH3 & H coverage. As the region of Fermi level pinned at Ga broken bond state corresponds to very low pressures, at pressures close to normal, GaN(0001) surface is almost totally covered by H, NH3 and NH2 located in On-top positions. It is also shown however that dominant portion of the hydrogen and ammonia pressures corresponds to Fermi level not pinned. Among them are these corresponding to MOVPE and HVPE growth conditions in which the surface is almost fully covered by NH3, NH2 and H species in On-top positions.

In this paper we show that the surface Fermi level of Ga-polar GaN exhibits a bistable behavior allowing it to be located at two distinct energetic positions at the air/GaN interface which is unusual for other III–V semiconductors such as GaAs or GaSb. To determine the Fermi level position at the air/GaN interface we perform contactless electroreflectance measurements on specially designed UD+ structures [GaN(undoped)/GaN(highly doped)/substrate] doped by Si and Mg. Analyzing the period of Franz-Keldysh oscillation we determine the built-in electric field in the undoped (U) layer. These studies coupled with numerical solutions of the Poisson equation allowed us to determine the position of the Fermi level at the air/GaN interface. We observe a change in the band bending correlated to different Fermi level positions in the doped (D+) layer. We show that depending on the doping type in the D+ layer the Fermi level at the air/GaN interface is located in the upper or lower singularity of surface density of states (SDOS) for Si or Mg doping of D+ layer, respectively. We support our findings with the density functional theory calculations of the SDOS and the dependence of the Fermi level position on the doping concentration in the bulk of a GaN slab.

In this paper, we present systematic improvements to a method that allows us to determine the surface phase diagrams based on ab initio calculations and atomistic thermodynamics. In particular, we include a contribution derived from thermal vibrations of the surface, which is usually omitted in such analysis. On the basis of first-principles phonon calculations, we determine a zero-point vibrational energy and thermal dependencies of vibrational entropy and free energy for atoms and molecules adsorbed on the surface. A series of polar GaN(0001) surfaces are examined. Significant changes are observed in the surface phase diagrams compared to the diagrams obtained by standard density-functional theory calculations without phononic contributions.

Different configurations of the growth zone were examined for crystallization of HVPE-GaN. The motivation for this work was to suppress growth in the lateral directions which appears on the seed edges during crystallization in the [0 0 0 1] direction. This phenomenon is a significant problem for growing thick GaN boules. Changes in the configuration involved placing molybdenum elements close to the growing crystal. Such a solution allowed to decrease the area of material deposited at the edges. The reason for this was examined with Computational Fluid Dynamics simulations. Distributions of reagents over the seed and the resulting supersaturation were examined. The value of the latter was lower near the edges of the crystal where the molybdenum elements were placed.

A new scenario of thermalization process of the adsorbate attached at solid surfaces is proposed. The scenario is based on existence of electric dipole layer in which the electron wavefunctions extend over the positive ions. Thus the strong local electric field exists which drags electron into the solids and repels the positive ions. The electrons are tunneling conveying the energy into the solid interior. The positive ions are retarded in the field, which allows them to loose excess kinetic energy and to be located smoothly into the adsorption sites. In this way the excess energy is not dissipated locally avoiding melting or creation of defects, in accordance with the experiments. The scenario is supported by the ab intio calculation results including density function theory of the slabs representing AlN surface and the Schrodinger equation for time evolution of hydrogen-like atom at the solid surface., Comment: 13 pages, 5figures

Results of growth of high structural quality gallium nitride single crystals doped with silicon are described in this paper. Dichlorosilane was used as precursor of silicon in the hydride vapor phase epitaxy method. Crystallization runs with different flows of dichlorosilane were performed and compared. One-inch free-standing HVPE-GaN crystals of high structural quality and high purity, previously grown on ammonothermal GaN substrates, were used as seeds. Structural, electrical, and optical properties of HVPE-GaN doped with silicon are presented and discussed in detail. A laser diode built on the homoepitaxially grown GaN is demonstrated.

Diffusion of native point defects is examined in the interface region of the InN/GaN heterostructure grown in hexagonal c direction. Heights of migration energy barriers of single vacancies and their complexes with substitutional group-III element are calculated in bulk GaN and InN crystals for two diffusion mechanisms, as well as across the InN/GaN heterointerface. An impact of the in-plane strain, the influence of built-in electric field, as well as the presence of electric dipole on vacancy motion is analysed. The obtained results show that metal vacancies V Ga and V In can migrate across the InN/GaN interface overcoming a potential energy barrier lower than that of V N . Moreover, the smallest energy barrier is related to the in-plane migration of V In what can favor spatial segregation of In atoms near the InN/GaN interface. This phenomenon can significantly contribute to the thermal degradation process of InGaN/GaN QWs, often observed experimentally both during the operation of nitride devices, as well as at the stage of their growth.

The role of bond creation and electron transition contribution were investigated in thermodynamic picture of adsorption obtained from intensive ab initio density functional theory (DFT) calculations. It was shown that electron transitions may reduce the overall energy gain from Al adsorption at AlN(000 1 ) surface by 50%. Accordingly properties of AlN polar N-terminated AlN(000 1 ) surface such as crystallographic structure, the type and energy of the surface states, the band profiles close to the surface were obtained. At the clean surface Al is adsorbed with the energy gain of 9.6 eV at H3 site creating bonds using two Al3p states by the overlap with the neighboring surface N atoms. The excess electrons are transferred to surface N broken bond states. At the critical coverage θ Al - c r = 1 4 M L all these states are occupied, therefore for higher Al coverage the electrons are transferred to Al3pz states. As their energy is higher by 2.5 eV, the adsorption energy gain is dropped to 4.089 eV, i.e. about 50%. For higher coverage Al adatoms are shifted to bridge and on-top configurations reducing the electron transfer and increasing energy gain by 2.5 eV for full coverage of Al adatoms located in the on-top positions. The temperature dependent pressure-coverage diagram was obtained showing the two stable regions. The first, up to 0.25 ML Al ( θ Al ≤ 1 4 M L ) with Al adatoms located in H3 positions, correspond to extremely low Al pressure, below 10−13 bar at 2500 K. The second region, at p Al > 2.18 × 10 - 5 b a r , is stable for high coverage, i.e. for θ Al > 0.999 M L (at 2500 K) with Al adatoms located in the on-top positions. For the pressures between, i.e. 1.80 × 10 - 12 b a r p Al 2.18 × 10 - 5 b a r , nonuniform coverage is stable, composed to these two phases. Finally at the coverage close to 1 ML, Langmuir entropic singularity in chemical potential was detected, corresponding to dramatic increase of the pressure over single Al layer which leads to transition to multiple Al layers and bulk Al.

Electronic and structural properties of $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$ and its extension to copper doped $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}:\mathrm{Cu}$ were studied using combined ab initio simulations and transmission electron microscopy based techniques, including electron energy loss spectroscopy, energy filtered transmission electron microscopy, and energy dispersive x-ray spectroscopy. The stability of the mixed phases was investigated for substitutional and intercalation changes of basic $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$ structure. Four systems were compared: $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$, structures obtaining by Cu intercalation of the van der Waals gap, by substitution of Bi by Cu in quintuple layers, and $\mathrm{C}{\mathrm{u}}_{2}\mathrm{Se}$. The structures were identified and their electronic properties were obtained. Transmission electron microscopy measurements of $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$ and the $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}:\mathrm{Cu}$ system identified the first structure as uniform and the second as composite, consisting of a nonuniform lower-Cu-content matrix and randomly distributed high-Cu-concentration precipitates. Critical comparison of the ab initio and experimental data identified the matrix as having a $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$ dominant part with randomly distributed Cu-intercalated regions having 1Cu-$\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$ structure. The precipitates were determined to have 3Cu-$\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{e}}_{3}$ structure.

Properties of the GaN(0001) surface, fully covered by a mixture of NH 3 molecules and NH 2 radicals, were investigated by DFT simulations. It is shown that for extremely low ammonia content, the Fermi level at the surface is at valence band maximum (VBM), then at the 25% ammonia in coverage it is depinned, moving upward in the bandgap to reach conduction band minimum (CBM) at higher ammonia percentages. It is shown that the 25% ammonia in the coverage is corresponding to a flat band configuration in accordance with ECR arguments. The stability of the mixed NH 2 /NH 3 coverage with respect to detachment of ammonia molecules or molecular hydrogen was also investigated. It was shown that high ammonia fraction leads to instability of the coverage due to detachment of ammonia or of molecular hydrogen. The instability point is reached for 36% and 41% fraction of ammonia in the coverage for desorption of molecular hydrogen and ammonia, respectively. The energy barrier for detachment of molecular hydrogen is consistently higher since the H 2 molecule has to be created first in the course of desorption process. The ammonia is simply detached in the molecular form so that the high energy intermediate configuration is absent.

The InGaN layers were grown using the Metalorganic Vapour Phase Epitaxy on bulk GaN substrates in a stop-and-go-mode (30 s growth, 30 s stop) and then examined using X-ray Diffraction (XRD), Photoluminescence (PL), Atomic Force Microscopy (AFM) and Transmission Electron Microscopy (TEM). The experiment was done in order to study an influence of hydrogen and TMIn flows during the growth-breaks on the InGaN layer. It was found that the presence of hydrogen during the breaks removes indium atoms from the already grown InGaN layer and delays In-incorporation into the subsequent one. As a result, instead of having about 18% of In in the continuously grown InGaN, we have only about 6% (average In-content) and the layer is thinner by more than 20%. In the case of having simultaneously H 2 and TMIn flows on during the breaks, we get three times less of In-atoms torn away and the layer has the thickness unchanged. The simultaneous presence of TMIn and H 2 also gave much smaller surface roughness as compared to the situation when only H 2 was on during the breaks.

Density Functional Theory (DFT) simulations of ammonia adsorption at clean and H-covered surface confirmed that ammonia may dissociate into NH2 radical and H adatom or remain in the molecular form. The remaining hydrogen atoms are attached to Ga atoms where the charge transfer to the surface is possible. The calculations show that for the molecular process, the ammonia adsorption energy is close to 2.0 eV, independent of hydrogen coverage. The dissociative process is strongly H-coverage dependent, for low H-coverage the adsorption energy is close to 2.8 eV, for high coverage changes by more than 4 eV reaching negative values. Thus for low coverage the energetically preferred adsorption is dissociative, for high is molecular. The dissociation energy and preferred mode change are related to the change of the Fermi level pinning from Ga broken bond state to valence band maximum (VBM), confirming the decisive role of charge transfer in the adsorption processes.

Density functional theory studies were conducted to determine an influence of the carrier concentration on the optical and electronic properties of InN/GaN superlattice system. The oscillator strength values, energy gaps and the band profiles were obtained. The band profiles were found to be strongly affected for technically possible heavy n-type doping while for p-type doping the carrier influence, both screening and band shift, is negligible. Blue shift of the transition energy between conduction band minima and valence band maxima was observed for high concentrations of both type carriers.

Density functional theory (DFT) calculations were used to study GaN(0001) surface covered with NH 3 admolecules and NH 2 radicals, corresponding to physical conditions during GaN growth by hydride vapor phase epitaxy (HVPE) and metalorganic vapor phase epitaxy (MOVPE). Using larger representation of the surface i.e. slabs of lateral size 4×4, the effect of the doping was examined. It is shown that for specific surface coverage the electron counting (EC) rule is fulfilled so that the pinning of the Fermi level by surface states and band bending disappears. In this case, according to Krukowski et al. (2013) [14], the doping of the semiconductor ( n - or p -type) and the related Fermi level are extremely important for stability of the surface and the adsorption/desorption processes. The difference in adsorption energies of gallium atoms at n - and p -type GaN(0001) surface exceeds the energy gap. This effect is observed in a narrow range of surface coverage, therefore cannot be detected in the calculations using small systems i.e. 2×2 slabs. This new phenomenon may be crucial for the growth of GaN and the incorporation of dopants and impurities into semiconductor crystals.

Suppression of carbon contamination in GaN films grown using metalorganic vapor phase epitaxy (MOVPE) is a crucial issue in its application to high power and high frequency electronic devices. To know how to reduce the C concentration in the films, a sequential analysis based on first principles calculations is performed. Thus, surface reconstruction and the adsorption of the CH4 produced by the decomposition of the Ga source, Ga(CH3)3, and its incorporation into the GaN sub-surface layers are investigated. In this sequential analysis, the dataset of the adsorption probability of CH4 on reconstructed surfaces is indispensable, as is the energy of the C impurity in the GaN sub-surface layers. The C adsorption probability is obtained based on steepest-entropy-ascent quantum thermodynamics (SEAQT). SEAQT is a thermodynamic ensemble-based, non-phenomenological framework that can predict the behavior of non-equilibrium processes, even those far from equilibrium. This framework is suitable especially when one studies the adsorption behavior of an impurity molecule because the conventional approach, the chemical potential control method, cannot be applied to a quantitative analysis for such a system. The proposed sequential model successfully explains the influence of the growth orientation, GaN(0001) and (000&minus, 1), on the incorporation of C into the film. This model can contribute to the suppression of the C contamination in GaN MOVPE.

Density functional theory simulations have been used to obtain physical properties of AlN/GaN multi-quantum well (MQW) system characterized by equal width of wells and barriers. Such structure could have different thickness that affects their optical and electronic properties. For thickness up to 4 metal atomic layers, GaN region behaves as potential local minimum while for larger thickness it is a standard quantum well. Separation of an electron and hole wavefunction affects negatively radiative transition probabilities. Reduction of optical efficiency for systems with different structure width was determined by calculation of oscillator strength values. Field intensities along c-direction and the change of the energy of the optical transitions, due to quantum confined Stark effect (QCSE), were also obtained. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper, a variant of discretization of the van Roosbroeck equations in the equilibrium state with the Composite Discontinuous Galerkin Method for the rectangular domain is discussed. It is based on Symmetric Interior Penalty Galerkin (SIPG) method. The proposed method accounts for lower regularity of the solution on the interfaces of devices' layers. It is shown that the discrete problem is well-defined and that discrete solution is unique. Error estimates are derived. Finally, numerical simulations are presented., 28 pages, 6 figures

Adsorption of atomic and molecular hydrogen at clean and H-covered GaN(0001) surface was investigated by Density Functional Theory (DFT) simulations using slab models with different terminations of the opposite surface, corresponding to various electric fields in the solid at the surface. According to DFT results adsorption of hydrogen atoms is barrierless, leading to their attachment on top of gallium surface atoms. For H-coverage up to 0.75 ML, H atom adsorption energy exceeds 3 eV, partly due to transfer of electron from high energy Ga surface state, the process that contributes to the energy gain, while for higher coverage the adsorption energy falls down to about 1 eV because the Ga surface state is empty. For H-coverage up to 1 ML adsorption of molecular hydrogen is dissociative while for higher it is molecular with its energy equal to 0.16 eV only. For H-coverage below 0.75 ML, the energy gain at molecular hydrogen adsorption exceeds 2 eV but for H-coverage above 0.75 ML, the energy loss exceeding 2 eV was obtained. For the critical 0.75 ML coverage, the adsorption energy is strongly electric field dependent, being negative and positive for p-GaN and n-GaN respectively, having its overall field related variation exceeding 1.5 eV. The DFT results are in good agreement with the experimental data.

Density functional theory (DFT) is used to simulate the properties of GaN(0001) surface employing a finite slab with additional modifications of the non-real side by termination with variously charged pseudo-hydrogen atoms. Different terminations change the electric field inside the slab and causes a relative shift of the energy of the surface and band states, which is known as Surface States Stark Effect (SSSE). It is shown that single hydrogen atom is barrierlessly adsorbed on GaN(0001) surface in the on-top position. Its adsorption energy strongly depends on the surface coverage by other hydrogen atoms, being above 3 eV and below 1.5 eV for the coverage lower and higher than 0.75 ML, respectively. This large difference is due to the difference of electronic occupation of the surface states. The adsorption energies indicate that hydrogen can be stably attached to the surface up to 0.75 ML coverage. It is shown that the adsorption energy of molecular hydrogen depends to some degree on the electric field at the surface, i.e. doping in the bulk. The dependence of hydrogen coverage on the pressure in the vapor shows that complete removal of hydrogen from GaN(0001) surface is difficult. Also chemical potential of hydrogen at the surface as a function of its coverage is determined. (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Density Functional Theory (DFT) calculations indicate that energetically stable structure of clean GaN(0001) surface posses (2 × 1) reconstruction, having every second row of Ga located near plane of N atoms, that gives rise to Ga-related dispersionless surface electronic state, already identified by angle resolved photoelectron spectroscopy (ARPES) measurements [S.S. Dhesi et al. Phys. Rev. B 56 (1997) 10271, L. Plucinski et al. Surf. Sci 507-10 (2002) 223, S. M. Widstrand et al. Surf. Sci. 584 (2005) 169]. The energy reduction in reconstruction proceeds via change of the hybridization of the occupied Ga surface states from sp3 to sp2, transforming the empty states to pz type. It is also shown that the electric subsurface field, modeled in new slab model which allows to simulate electric fields at the semiconductor surfaces [P. Kempisty et al., J. Appl. Phys. 106 (2009) 054901], strongly affects the energy of electronic states of GaN(0001) surfaces. The change of the field may shift the energy of surface states of bare and hydrogen covered GaN(0001) surface, by several eV with respect to the band states. The phenomenon, denoted as Surface States Stark Effect (SSSE), explains various band bending values, measured at differently doped n-type GaN(0001) surfaces. It is shown also that, for the adsorbate density up to one H atom for each Ga surface atom i.e. 1 monolayer coverage (1 ML), the hydrogen adatoms are located at the on-top positions, i.e. directly above Ga atoms. For these adsorbate densities, the H-related quantum surface state is located slightly below the valence band maximum (VBM) in the case of p-type GaN surface. For n-type GaN, the H-related surface state is located deeply in the valence band, about 2 eV below VBM. For higher, 1.25 ML hydrogen coverage, the two H adatoms create either surface attached H2 ad-molecule (energetically stable) or triple bridge configuration is created (metastable). The H2 ad-molecule is weekly attached to the surface, having the desorption energy barrier equal to 0.16 eV. For 1.25 ML coverage the DFT results were obtained for p-type GaN only. They show that in the ad-molecule case, a new surface electronic state arises which is located about 6.7 eV below VBM. In the case of the bridge configuration, the bridge related surface state is located closely to the conduction band minimum (CBM).

The ab initio DFT simulations of InN/GaN multiquantum wells (MQW) were used to obtain electric potential profile in the system that, after appropriate averaging procedure, reveal electric field in the wells and barriers and electric potential jumps at the interfaces. The field changes and the potential jumps were used to obtain the density of the polarization charges and the dipole layer at InN/GaN interfaces, respectively. It was shown that polarization dipoles are confined within the one double atomic layers, proving that they have different nature from the dipole layers emerging at the semiconductor surfaces or within p−n junctions. In parallel, a new formulation of polarization analysis, based on the energy minimum principle, was used to determine the electric field in polar InN/GaN multiquantum wells, purely within electrostatic framework, without resorting to experimental data. The obtained fields depend on both the well and the barrier thicknesses. DFT data are in good agreement with the continuum ...

Crystallographic structure, total energy, electronic structure, and the most important elastic properties of struvite, NH(4)MgPO(4).6H(2)O, the main component of infectious urinary stones, are presented. The calculations were performed using ab initio full-electron calculations within the density functional theory-generalized gradient approximation (DFT-GGA) framework. The obtained crystallographic symmetry and the calculated lattice parameters and also the elastic constants are in good agreement with the experimental data. The elastic properties are essential for establishing an optimal response of urinary stones during shock-wave lithotripsy. The calculated electronic charge distribution confirms the layered structure of the struvite crystals. The polar character of the crystal, well-known from crystal growth experiments, was also confirmed by the magnitude of spontaneous polarization which was obtained from direct determination of the electrical dipole density. The calculated value of spontaneous polarization is equal to -8.8 microC cm(-2). This feature may play a key role in struvite crystallization, electrically binding the charged active impurities and other active species, and consequently determining urinary stone formation. We also present the results of our own experiment of the mineralization of struvite induced to growth by Proteus bacteria which are mainly isolated from infectious urinary stones.

Recent results in Density Functional Theory (DFT) simulations of ammonia-based growth of gallium nitride on GaN (0001) are reviewed. These simulations are important to the following GaN growth methods that use ammonia as active nitrogen source: ammonothermal, MOVPE, HVPE and also ammonia-source MBE. In the simulations of GaN growth, the two main approaches were discussed: (1) equilibrium, based on chemical potentials of the components, and (2) dynamic, based on consideration of atomistic processes on the surface. These two approaches are unified by the kinetic procedure of determination of the chemical potential levels for nitrogen and hydrogen as a function of partial pressure of ammonia. Here the DFT modeling of GaN(0001) surface employing the technique of the simulation of subsurface electric field is described and employed. The results of DFT modeling include the ammonia and molecular hydrogen adsorption on GaN(0001) surface that allows to determine some basic features of ammonia-based growth of GaN. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Results of liquid phase epitaxy of GaN on MOCVD sapphire/GaN and HVPE free-standing GaN substrates by high pressure solution method are presented. The finite element calculation using experimentally measured temperatures is used for modeling the convective transport in the liquid gallium. The influence of a baffle and thermal conductivity of the various seeds for convection in liquid metal is analyzed in details. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Atomistic processes, involving chlorine, occurring at GaN(0 0 0 1) surface during hydride vapor-phase epitaxy (HVPE) growth, were modeled, using ab-initio quantum mechanical density functional theory (QM DFT) SIESTA code. The process of adsorption of hydrogen chloride (HCl) at the surface was simulated. Both Ga-rich and N-rich surface conditions were considered. For both cases it was assumed that hydrogen is abundant, which leads to H and NH 2 coverage for Ga-rich and N-rich state of the surface, respectively. By modeling a HCl molecule, approaching the surface, it was shown that two states exist: physisorbed at far distance, and chemisorbed at closer location. For both the cases, i.e. N-rich and Ga-rich, the physical adsorption is barrierless. The transition to chemically adsorbed state encounters an energy barrier that severely depends on the state of the GaN(0 0 0 1) surface. In the case of the Ga-rich surface, the barrier is relatively small, of the order of 0.2 eV. In the case of the N-rich surface, a high-energy barrier exists, close to 2 eV. At the final i.e. chemisorbed state, the molecule disintegrates, leaving chlorine atom strongly attached to the topmost Ga atoms; the hydrogen atom is detached and paired with the other hydrogen atom. The adsorption of HCl molecule approaching Ga–H radical, located on top of NH 2 coverage, occurs via physic to chemi-sorbed state. The transition to chemically adsorbed state requires surmounting the energy barrier of about 0.6 eV: free H 2 molecule is left and the Ga–Cl admolecule remains at the surface. As before, H coverage is ineffective in protection of gallium against HCl attack. The desorption of chlorine atom from the GaCl admolecule, attached at the GaN(0 0 0 1) surface, was also analyzed. Single Cl atom desorption encounters a high-energy barrier, of the order of 4.5 eV. The desorption of HCl, involving the additional H atom, needs to overcome a significantly lower-energy barrier, of the order of 0.6 eV, creating a possible path of chlorine removal from the surface.

Surface properties and the principal processes at the growth of gallium nitride on GaN (0001) face in ammonia-based are modeled using DFT (density functional theory – SIESTA code) ab initio calculations and 2-d diffusion analysis. The GaN growth methods are: ammonia-source MBE, MOVPE, and also HVPE. The adiabatic trajectories, calculated for hydrogen-rich and hydrogen-free state of the GaN(0001) surface, include the adsorption of NH3, GaCl and HCl molecules and the desorption of Ga atoms. The adsorption of ammonia and GaCl has no energy barrier. Thus, in contrast to the results concerning Plasma-Assisted Molecular Beam Epitaxy (PA MBE), proving that the GaN(0001) surface remains in metal-rich state, these results indicate that, in the ammonia-rich environment, typical for HVPE and MOVP growth, the GaN(0001) surface remains in the nitrogen-rich state. In the case of HCl adsorption, the energy barrier depends on the surface coverage, and could reach 2.0 eV. The direct desorption of single Ga atom has the energy barrier, close to 7 eV. This indicates that Ga surface diffusion (growth controlling process) length is very large, leading to strong interaction of the step kinetics and the diffusion on the terraces. This interaction leads to double–step intertwined structures both in the case of dislocation-mediated spiral growth and in the step flow growth mode. These morphologies, proposed by the geometric arguments, are observed in the atomic force microscopy (AFM) scans of the GaN(0001) surface. Additionally we have compared the interaction energy of two hydrogen atoms obtained in the DFT SIESTA and the high precision Gaussian in coupled cluster singles, double and perturbation triples CCSD(T) approximation. Both approaches yielded virtually identical interaction energy confirming the validity of DFT analysis of ammonia-rich growth of GaN. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Seeded growth of GaN on 1 in sapphire/GaN templates by high-pressure solution method is presented. Five crystallization runs at the same growth conditions (temperatures, supercooling, nitrogen pressure, time) but different in geometry are described in details. The finite element calculation is used for modeling the convective transport in the liquid gallium. The stream lines, convectional flow velocity vectors and isotherm lines in liquid metal are determined based on experimentally measured temperatures in the crucible wall. The influence of the seed and the baffle for convection in liquid metal is analyzed in details.

Crystal growth of GaN by hydrogen vapor phase epitaxy (HVPE) is still far from being described on the atomic level. The method consists of reaction of HCl with liquid Ga, transport of gallium by volatile compounds GaCl or GaCl 3 , and the deposition on the substrate by the simultaneous reaction of GaCl/GaCl 3 and ammonia (NH 3 ) on the GaN surface. Various aspects of the method have to be modeled using different approaches. Recently, we have modeled reaction of HCl with gallium and the transport of the resulting species by convection and diffusion using CFD modeling of transport. Surface reaction rate was estimated using atomic flux and sticking coefficient. It has been found that the reaction is controlled by transport or surface reaction depending on the flow velocity and the HCl sticking coefficient [P. Kempisty, I. Grzegory, M. Bockowski, S. Krukowski, B. Łucznik, B. Pastuszka, S. Porowski, Phys. Stat. Sol. (a) 203 (2006) 131; P. Kempisty, I. Grzegory, M. Bockowski, S Krukowski, B. Łucznik, B. Pastuszka, S. Porowski, J. Crystal Growth 296 (2006) 31]. The growth of GaN was modeled using atomistic scale simulations. The simulations were carried out using the QM DFT SIESTA code [J.M. Soler, E. Artacho, J.D. Gale, Alberto Garcia, J. Junquera, P. Ordejon, D. Sanchez-Portal, J. Phys.: Condens. Matter 14 (2002) 2745; P. Ordejon, D.A. Drabold, M.P. Grumbach, R.M. Martin, Phys. Rev. B 48 (1993) 14646; P. Ordejon, D.A. Drabold, M.P. Grumbach, R.M. Martin, Phys. Rev. B 51 (1995) 1456]. The model is applied to a 2-d supercell, which corresponds to 2-d periodic boundary conditions suitable for simulation of the surface. Five atomic slabs were used in the direction perpendicular to the surface. The simulations include the analysis of the influence of hydrogen, ammonia and HCl on the atomic structure of the (0 0 0 1) GaN surface (Ga-face). Subsequently, the process of adsorption of various species, such as NH 3 , GaCl and H 2 of the GaN(0 0 0 1) surface, was considered. The energy barriers and the stable configurations were obtained. From this, the energetic properties of elementary kinetic processes were obtained. These results were used for the assessment of the influence of the growth conditions on the growth rate of gallium nitride.

Ab initio studies of a GaN(0001)-Ga system with various thicknesses of a metallic Ga layer were undertaken. The studied systems extend from a GaN(0001) surface with a fractional coverage of gallium atoms to a Ga-GaN metal–semiconductor (m–s) contact. Electronic properties of the system are simulated using density functional theory calculations for different doping of the bulk semiconductor. It is shown that during transition from a bare GaN(0001) surface to a m–s heterostructure, the Fermi level stays pinned at a Ga-broken bond highly dispersive surface state to Ga–Ga states at the m–s interface. Adsorption of gallium leads to an energy gain of about 4 eV for a clean GaN(0001) surface and the energy decreases to 3.2 eV for a thickly Ga-covered surface. The transition to the m–s interface is observed. For a thick Ga overlayer such interface corresponds to a Schottky contact with a barrier equal to 0.9 and 0.6 eV for n- and p-type, respectively. Bond polarization-related dipole layer occurring due to an electron transfer to the metal leads to a potential energy jump of 1.5 eV, independent on the semiconductor doping. Additionally high electron density in the Ga–Ga bond region leads to an energy barrier about 1.2 eV high and 4 A wide. This feature may adversely affect the conductivity of the n-type m–s system.

GaCl synthesis reaction during hydride vapor phase epitaxy (HVPE) growth of GaN in horizontal flow reactor has been analyzed using computerized fluid dynamics (CFD) and molecular estimates of the reaction rates. Finite element code FIDAP (commercially available from Fluent Inc.) [Fidap User Manual, Fluent Inc. [1] ] has been used to obtain the flow pattern in the GaCl synthesis section of the HVPE reactor. As in the typical HVPE design, it was assumed that the flow pattern is weekly dependent on the temperature distribution in the reactor, i.e. the system in this part is virtually isothermal. The HCl+Ga(l) surface reaction rate has been estimated using ideal gas approximation for HCl impingement flux and predefined sticking coefficient for HCl adsorption on liquid Ga surface. In parallel, Ga evaporation process and transport has been accounted in the simulations. Using Ga evaporation rates, the total flux of transporting Ga has been obtained. The flux includes GaCl resulting from the surface reaction rate, and the Ga evaporation flux. The GaCl synthesis rate was obtained in function of the pressure, flow velocity and geometry of the reactor. The HCl to GaCl conversion degree in function of the above parameters was obtained for the several selected values of the sticking coefficient of HCl on liquid Ga surface. It was shown that for the typical design of the reactor, for the sticking coefficient below 0.01, the conversion rates depend on the sticking coefficient. For higher values of the coefficient the GaCl synthesis reaction is diffusion controlled and independent on the surface reaction kinetics. The calculations were made for the temperatures range of 800–1000 °C for which the Ga/GaCl ratio was determined. It was shown that, even in case of relatively low values of sticking coefficient for HCl, such as 0.01, gallium transport is dominated by GaCl for temperatures up to 1300 K. These results suggest that for the temperatures up to 1500 K Ga vapor transport by direct evaporation is inefficient, i.e. the sublimation growth of GaN is inefficient in this temperature range.

HVPE growth in horizontal flow reactor has been analysed using finite element calculations and molecular estimates of the reaction rates. Finite element code FIDAP (commercially available from Fluent Inc.) has been used to calculate the flow pattern in the reactor. In the first approximation it was assumed that the flow pattern is weekly dependent on the temperature distribution in the reactor. It was also assumed that the volume reaction rates can be approximated by temperature independent reaction constants. The HCl + Ga(1) reaction rate has been estimated using ideal gas approximation for HCl vapour. The degree of HCl to GaCl conversion was obtained in function of the pressure, flow velocity and geometry of the reactor. The conversion dependence on the sticking coefficient of HCl on liquid Ga surface was analysed. It is shown that for the typical design of the reactor, high conversion rates were observed, even for the sticking coefficient as low as 0.001.

The carbon incorporation mechanism in GaN(0001) and GaN(000 1¯) during MOVPE was investigated using density functional theory (DFT) calculations. The results confirm that the crucial factors for carbon incorporation are Fermi level pinning and accompanying surface band bending. In addition, the lattice symmetry has a strong dependence on the stability of carbon in a few subsurface layers, which results from interactions between the impurities and surface states. It was shown that these effects are responsible for facilitating or hindering the incorporation of impurities and dopants. The influence of diluent gas species (hydrogen or nitrogen) on carbon incorporation was discussed.