arXiv subjects

Stanislaw Krukowski

Publications and source records attributed to Stanislaw Krukowski.

At least 19 recordsLinked to original sources

arXiv2026

Role of quasi-Fermi levels in Si- and Mg-related optical absorption in nitride laser diodes (LDs): material context

Optical absorption and reabsorption of light emitted from active regions in nitride laser diodes (LDs) have been shown to reduce the light extraction efficiency of these devices. It was proven that the presence of Si and Mg may considerably increase the optical absorption. This effect is much stronger in the high-energy (short-wavelength) range of the spectrum. The absorption increase is directly related to the ionization of the Si donor and Mg acceptor levels, which are controlled by the electron and hole quasi-Fermi levels. It is shown that the absorption may be increased because of the higher ionization of Mg caused by the compensation in the p-type region and the high ionization of Si in the n-type region. It was explained theoretically why optical efficiency is increased by removal of doping in waveguides. It was also shown that good material quality leads to a low absorption level, especially in the Mg-doped p-type part of the device.

cond-mat.mtrl-sci↗

arXiv2026

Hydrogen at GaN(0001) surface control of Fermi level pinning: Mg activation of p-type conductivity -- Nakamura process deciphered

Ab initio calculations were used to disentangle the mystery of Nakamura activation of p-type in Mg doped MOVPE grown gallium nitride, the key process leading to the 2014 Nobel Prize in Physics. Calculations were used to obtain the equilibrium state of the hydrogen atom deep in the GaN bulk and at the GaN(0001) surface. It was shown that the H position within bulk GaN depends on the Fermi level: in n-type GaN, it is located in the channel, whereas in p-type GaN, it is attached to the N atom, breaking one of the GaN bonds. In contrast, at the GaN(0001) surface, H is attached in the on-top position for any hydrogen coverage; for low and high H-coverage, the Fermi level is pinned at the Ga - broken bond state and at the valence band maximum (VBM), respectively. The diffusion path from the bulk to the surface was obtained when the Fermi level was high and low, the barrier was zero, and $\Delta E_{bar} \approx 1.717 eV$, which effectively blocked hydrogen escape into the vapor. Thus, high H coverage, that is, high hydrogen pressure in the vapor, prevents H from escaping from the bulk to the surface, whereas at low coverage (low hydrogen pressure), the process is barrierless. It is therefore proven that the hydrogen escape control step in the Nakamura process is the transition of hydrogen from the bulk to the surface, which is controlled by the position of the Fermi level at the surface. Molecular hydrogen desorption from the surface is easy for high H coverage and difficult for low, thus opposite to observed experimentally thus this process is not the determining step in activation. A full thermodynamic estimate of the maximal partial pressure of hydrogen in the vapor, corresponding to the transition of the Fermi level from the Ga-broken bond state to the VBM, was used to establish the maximal hydrogen pressure limit for the p-type Mg activation process.

cond-mat.mtrl-sci↗

arXiv2025

Fundamentals of the metal contact to p-type GaN: new multilayer design

Electrical properties of contact to p-type nitride semiconductor devices, based on gallium nitride were simulated by ab initio and by drift-diffusion calculations. The contact electric properties are shown to be dominated by electron transfer form metal to GaN related to Fermi level difference both by ab initio and model calculation. The results indicate on high potential barrier for holes leading to nonohmic character of the contact. The electrical nature of the Ni-Au contact formed by annealing in oxygen atmosphere is elucidated. The doping influence on the potential profile in p-type GaN was calculated by in drift-diffusion model. The energy barrier height and width for hole transport is determined. Based on these results, new type of the contact, is proposed. The contact is created employing multiple layer implantation of the deep acceptors. The implementation of such design promise to attain superior characteristics (resistance) as compared to other contacts used in bipolar nitride semiconductor devices. The development of such contact will remove one of the main obstacles in the development of highly efficient nitride optoelectronic devices both LEDs and LDs: energy loss and the excessive heat production close to the multiple quantum wells system

cond-mat.mtrl-sci↗

arXiv2025

Quantum effects in surface diffusion: application to diffusion of nitrogen adatoms over GaN(0001) surface

It is shown that quantum effects play determining role in nitrogen adatom diffusion due to several different factors. This could be related to the change of the energy of the quantum states and also due to the redistribution of electrons between the quantum states, both full and resonant, via quantum statistics partially governed by the Fermi energy level. These effects were studied in the case of nitrogen diffusion over clean and gallium covered Ga-terminated GaN(0001) surface. For the fractional coverage the density functional theory (DFT) calculations show that at the saddle point configuration the redistribution of electrons between different quantum states may affect the surface diffusion barrier significantly. The other quantum influence occurs via the change of the minimal energy configuration. Under fractional Ga coverage of GaN(0001) surface the nitrogen diffusion energy barrier proceeds from the resonant states governed energy minimal H3 site across the saddle point in the bridge configuration. At this path the barrier is affected the electron redistribution between surface quantum states both in the initial and the saddle point. In the case of the full GaN coverage the diffusion path is from on-top N adatom configuration via H3 site that corresponds to maximal energy. Therefore the diffusion barrier is Ebar= 1.18 eV for clean and Ebar= 0.92 eV for (1/6) ML to finally Ebar= 1.23 eV for full Ga coverage. Thus the overall barrier is reduced to Ebar= 0.92 eV due to quantum statistics effects. The identified stable N on-top configuration for the full coverage is essential for atomic mechanism of GaN growth in Ga-rich regime.

cond-mat.mtrl-sci↗

arXiv2024

Polarization spontaneous and piezo: fundamentals and their implementation in ab initio calculations

Fundamental properties of spontaneous and piezo polarization are reformulated and critically reviewed. It was demonstrated that Landau definition of polarization as a dipole density could be used to the infinite systems. The difference between the bulk polarization and surface polarity are distinguished thus creating clear identification of both components. The local model of spontaneous polarization was created and used to calculate spontaneous polarization as the electric dipole density. It was shown that the proposed local model correctly predicts c-axis spontaneous polarization values of the nitride wurtzite semiconductors. It was also shown that the proposed model predicts zero polarization in the plane perpendicular to the c-axis, in accordance with symmetry requirements. In addition, the model results are in accordance with polarization equal to zero for zinc blende lattice. These data confirm the basic correctness of the proposed model. The spontaneous polarization values obtained for all wurtzite III nitrides (BN, AlN, GaN and InN) are in basic agreement with the earlier calculations using Berry phase and slab models of Bernardini et al. {Bernardini et al. Phys Rev B 56 (2001) R10024 & 63 (2001) 193201} but not with Dreyer et al. {Dreyer et al. Phys. Rev X 6 (2016) 021038}. Wurtzite nitride superlattices ab initio calculations were performed to derive polarization-induced fields in the coherently strained lattices showing good agreement with the polarization values. The strained superlattice data were used to determine the piezoelectric parameters of wurtzite nitrides obtaining the values that were in basic agreement with the earlier data. Zinc blende superlattices were also modeled using ab initio calculations showing results that are in agreement with the absence of polarization of all nitrides in zinc blende symmetry.

cond-mat.mtrl-sci↗

arXiv2024

Augmentation of the Electron Counting Rule with Ising Model

On semiconductor growth surfaces, surface reconstructions appear. Estimation of the reconstructed structures is essential for understanding and controlling growth phenomena. In this study, the stability of a mixture of two different surface reconstructions is investigated. Since the number of candidate structures is enormous, the structures sampled by Bayesian optimization are analyzed. As a result, the local electron counting (EC) rule alone was found to be insufficient to explain such stability. Then, augmenting the EC rule, a data-driven Ising model is proposed. The model allows the evaluation of the whole enormous number of candidate structures. The approach is expected to be useful for theoretical studies of such mixtures on various semiconductor surfaces.

cond-mat.mtrl-sci↗

arXiv2023

Coulomb contribution to Shockley-Read-Hall (SRH) recombination

Defect-mediated nonradiative recombination, known as Shockley-Read-Hall (SRH) recombination is reformulated. The introduced model considers Coulomb attraction between charged deep defect and the approaching free carrier, showing that this effect may cause considerable increase of the carrier velocity approaching the recombination center. The effect considerably increases the carrier capture rates. It is demonstrated that in the typical semiconductor device or semiconductor medium, the SRH recombination cannot be neglected at low temperatures. The SRH is more effective in the case of low doped semiconductors. Effective screening by mobile carrier density could reduce the effect, leading to SRH rate increase.

cond-mat.mtrl-sci↗

arXiv2022

Macrosteps dynamics and the growth of crystals and epitaxial layers

Step pattern stability of the vicinal surfaces during growth was analyzed using various surface kinetic models. It was shown that standard analysis of the vicinal surfaces provides no indication on the possible step coalescence and therefore could not be used to elucidate macrostep creation during growth. A scenario of the instability, leading go macrostep creation was based on the dynamics of the step train. The critical is step motion at the rear of the train which leads to double and multiple step creation. The condition is that the step density ratio in and out of the train lower than 2 prevents double step formation irrespective of the kinetics. For higher step density ratio low density of the step promotes single step stability. Fast step kinetics from lower terrace stabilizes the single steps slow (high barrier) is promoting step coalescence. The incorporation kinetics from upper terrace role is close to neutral. The creation of double step creates slow the step in front to accelerate and catch the previous double step while those behind catch up the double step creating multistep structure. The multistep are not mobile as the alimentation leads to emission of single step which moves forward. The final structure consist of macrosteps and superterraces with the number of single steps moving forward. Thus the single step motion is essential crystal growth mode despite the presence of the macrosteps. The macrostep are prone to creation of the overhangs which results from surface dynamics coupling to impingement from the mother phase. The angular preferential access of the bulk material to the macrostep edge, leads to diffusive instability. Therefore it is expected that harmful influence of the macrosteps by creation of inclusions and dislocation is stronger during growth from the liquid phase.

cond-mat.mtrl-sci↗

arXiv2021

Polarization doping ab initio verification of the concept charge conservation and nonlocality

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.

cond-mat.mtrl-sci↗

arXiv2019

Phase-amplitude functional theory -- new ab initio calculation method for large size systems

New method for ab initio calculations of the properties of large size system based on phase-amplitude functional is presented. It is shown that Schrodinger equation for many electrons complex system including large size molecules, or clusters and also periodic systems could be translated into functional of two variables, attributed to many electron wavefunctions: phase and the amplitude (i.e. square root of total electron density). The equations for the phase and the amplitude are derived. The kinetic and Coulomb interaction energy are expressed in function of these variables. The equations for one-electron wavefunctions, necessary for the energy spectrum are derived using these two variables.

physics.comp-ph↗

arXiv2017

Exact method of determination of the recombination mode from time resolved photoluminescence data

A method of data analysis is proposed for the determination of the carrier recombination processes in optically excited matter measured by time-resolved photoluminescence, differentiating monomolecular, bi-molecular, tri-molecular, and higher order molecular processes. Our method allows to determine whether the so-called ABC model describes time evolution of optical relaxation of the excited system. The procedure is applicable to the time evolution of any optically excited medium. As an illustration, the method is successfully applied to III-nitride polar and non-polar multi-quantum wells. We show that in this case the mono- and bi-molecular processes determine the carrier relaxation, and the tri-molecular Auger recombination contribution is negligible.

physics.optics↗

arXiv2016

On Composite Discontinuous Galerkin Method for simulations of electric properties of semiconductor devices

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.

math.NA↗

arXiv2014

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

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

cond-mat.mtrl-sci↗

arXiv2013

General aspects of the vapor growth of semiconductor crystals - a study based on DFT simulations of the NH3/NH2 covered GaN(0001) surface in hydrogen ambient

Vapor growth of semiconductors is analyzed using recently obtained dependence of the adsorption energy on the electron charge transfer between the surface adsorbed species and the bulk [Krukowski et al. J. Appl. Phys. 114 (2013) 063507, Kempisty et al. ArXiv 1307.5778 (2013)]. Ab initio calculations were performed to study the physical properties of GaN(0001) surface in ammonia-rich conditions, i.e. covered by mixture of NH3 molecules and NH2 radicals. The Fermi level is pinned at valence band maximum (VBM) and conduction band minimum (CBM) for full coverage by NH3 molecules and NH2 radicals, respectively. For the crossover content of ammonia of about 25% monolayer (ML), the Fermi level is unpinned. It was shown that hydrogen adsorption energy depends on the doping in the bulk for the unpinned Fermi level, i.e. for this coverage. Surface structure thermodynamic and mechanical stability criteria are defined and compared. Mechanical stability of the coverage of such surfaces was checked by determination of the desorption energy of hydrogen molecules. Thermodynamic stability analysis indicates that initally equilibrium hydrogen vapor partial pressure steeply increases with NH3 content to attain the crossover NH3/NH2 coverage, i.e. the unpinned Fermi level condition. For such condition the entire range of experimentally accessible pressures belongs showing that vapor growth of semiconductor crystals occurs predominantly for unpinned Fermi level at the surface, i.e. for flat bands. Accordingly, adsorption energy of most species depends on the doping in the bulk that is basis of the possible molecular scenario explaining dependence of the growth and the doping of semiconductor crystals on the doping in the bulk

cond-mat.mtrl-sci↗

arXiv2013

Fermi level influence on the adsorption at semiconductor surfaces - ab initio simulations

Chemical adsorption of the species at semiconductor surfaces is analyzed showing the existence of the two contributions to adsorption energy: bond creation and charge transfer. It is shown that the energy of quantum surface states is affected by the electric field at the surface, nevertheless the potential contribution of electron and nuclei cancels out. The charge transfer contribution is Fermi level independent for pinned surfaces. Thus for Fermi level pinned at the surface, the adsorption energy is independent on the Fermi energy i.e. the doping in the bulk. The DFT simulations of adsorption of hydrogen at clean GaN(0001) and silicon at SiC(0001) surfaces confirmed independence of adsorption energy on the doping in the bulk. For the Fermi level nonpinned surfaces the charge contribution depends on the position of Fermi level in the bulk. Thus adsorption energy is sensitive to change of the Fermi energy in the bulk, i.e. the doping. The DFT simulations of adsorption of atomic hydrogen at 0.75 ML hydrogen covered GaN(0001) surface confirmed that the adsorption energy may be changed by about 2 eV by the doping change from n- to p-type.

cond-mat.mtrl-sci↗

arXiv2012

High efficiency UV emitters - theoretical investigation of GaN/AlN heterostructures

Density functional theory simulations were used to obtain physical properties of GaN/AlN system. Combination of these two compounds into multiquantum well (MQW) structure will induce strong electrostatic effect leading to emergence of high magnitude dipole layers at the AlN/GaN interfaces, which were first postulated by {Tersoff Phys. Rev. B 30(8) pp.4874 (1984)} and already identified in GaN/InN by {Romanowski et al. J. Phys. Chem C 114. 14410 (2010)}. When combining GaN and AlN in to a heterostructure a spatial projection of wavefunctions indicate that valence band offset between states becomes of order of 0.85 V. Systematic analysis of influence of number of Ga atomic layers on the properties of wells have shown that for thickness up to 4 Ga layers, GaN behave as carriers locating potential minimum rather, while for larger thickness it is a standard quantum well. In all cases wells has strongly localized quantum states close to valance band maxima (VBM) and conduction band minimum (CBM). The calculated oscillator strength values rapidly decreases for the well thickness in excess of 8 Ga layers (~21 Å) which indicates that wells for UV emitters should be much thinner than these based on InGaN/GaN systems. The Quantum Confined Stark Effect (QCSE) related changes of the transition energy in function of the geometric arrangement were also obtained.

cond-mat.mtrl-sci↗

arXiv2011

Polarization and polarization induced electric field in nitrides - critical evaluation based on DFT studies

Density Functional Theory (DFT) calculations were used to evaluate polarity of group III nitrides, such as aluminum nitride (AlN), gallium nitride (GaN) and indium nitride (InN) providing physically sound quantitative measure of polarity of these materials. Two different approaches to polarization of nitride semiconductors were assessed and the conclusions have been used to develop models. It was shown that Berry phase formulation of the electron related polarization component provides a number of various solutions, different for various selection of the simulated volume. The electronic part gives saw-like pattern for polarization. A total number of these solutions, related to well known scaling of the geometric phase, is equal to the number of valence electrons in the system. Summation with similar pattern for ionic part provides several polarization values. Standard dipole density formulation depends on the selection of the simulation volume in periodic continuous way. Using a condition of continuous embedding into the infinite medium, and simultaneously, the zero surface charge representation at crystal boundary provides to physically sound solution. This solution is corresponding to maximal and minimal polarization values and also corresponds to different physical termination of the crystal surfaces, either bare or covered by complementary atoms. This change leads to polarization and electric field reversal. The polarization and related fields in finite size systems were obtained.

cond-mat.mes-hall↗

arXiv2011

Role of structure of C-terminated 4H-SiC(000) surface in growth of graphene layers - transmission electron microscopy and density functional theory studies

Principal structural defects in graphene layers, synthesized on a carbon-terminated face, i.e. the SiC(000) face of a 4H-SiC substrate, are investigated using microscopic methods. Results of high-resolution transmission electron microscopy (HRTEM) reveal their atomic arrangement. Mechanism of such defects creation, directly related to the underlying crystallographic structure of the SiC substrate, is elucidated. The connection between the 4H-SiC(000) surface morphology, including the presence of the single atomic steps, the sequences of atomic steps, and also the macrosteps, and the corresponding emergence of planar defective structure (discontinuities of carbon layers and wrinkles) is revealed. It is shown that disappearance of the multistep island leads to the creation of wrinkles in the graphene layers. The density functional theory (DFT) calculation results show that the diffusion of both silicon and carbon atoms is possible on a Si-terminated SiC surface at a high temperature close to 1600°C. The creation of buffer layer at the Si-terminated surface effectively blocks horizontal diffusion, preventing growth of thick graphene layer at this face. At the carbon terminated SiC surface, the buffer layer is absent leaving space for effective horizontal diffusion of both silicon and carbon atoms. DFT results show that excess carbon atoms converts a topmost carbon layer to sp2 bonded configuration, liberating Si atoms in barrierless process. The silicon atoms escape through the channels created at the bending layers defects, while the carbon atoms are incorporated into the growing graphene layers. These results explain growth of thick graphene underneath existing graphene cover and also the creation of the principal defects at the C-terminated SiC(0001) surface

cond-mat.mtrl-sci↗