Monte Carlo analysis of electron transport in small semiconductor devices including band-structure and space-charge effects

Energy Filtering in Doping Modulated Nanoengineered Thermoelectric Materials: A Monte Carlo Simulation Approach

Using Monte Carlo electronic transport simulations, coupled self-consistently with the Poisson equation for electrostatics, we explore the thermoelectric power factor of nanoengineered materials. These materials consist of alternating highly doped and intrinsic regions on the scale of several nanometers. This structure enables the creation of potential wells and barriers, implementing a mechanism for filtering carrier energy. Our study demonstrates that by carefully designing the nanostructure, we can significantly enhance its thermoelectric power factor compared to the original pristine material. Importantly, these enhancements stem not only from the energy filtering effect that boosts the Seebeck coefficient but also from the utilization of high-energy carriers within the wells and intrinsic barrier regions to maintain relatively high electronic conductivity. These findings can offer guidance for the design and optimization of new-generation thermoelectric materials through improvements in the power factor.

High-throughput screening of the transport behavior of tetragonal perovskites

Halide perovskites have attracted attention due to their low cost and excellent optoelectronic properties. Although their optical properties gained widespread consensus, there was still divergence in understanding carrier transport behavior. In this study, the mobility of tetragonal perovskites was investigated by empirical models, including longitudinal acoustic phonon (LAP) and polar optical phonon (POP) models. The results revealed that the mobility predicted from the LAP model was much higher than that from the POP model. A longitudinal optical phonon (LOP) was considered as the decisive scattering source for charge carriers in perovskites. Furthermore, the mobility was extremely sensitive to z-axis strain, and 8 types of perovskites with high carrier mobility were screened. Using the experimental lattice constants, the predicted mobility of CsSnI3 was μe,z = 1428 and μh,z = 2310 cm2 V-1 s-1, respectively. The tetragonal CsSnI3 has high mobility and moderate bandgaps, suggesting potential applications in high-efficiency solar cells.

Quantum kinetic equation for the Wigner function and reduction to the Boltzmann transport equation under discrete impurities

We derive a quantum kinetic equation under discrete impurities for the Wigner function from the quantum Liouville equation. To attain this goal, the electrostatic Coulomb potential is separated into the long- and short-range parts, and the self-consistent coupling with Poisson's equation is explicitly taken into account within the analytical framework. It is shown that the collision integral associated with impurity scattering as well as the usual drift term is derived on an equal footing. As a result, we find that the conventional treatment of impurity scattering under the Wigner function scheme is inconsistent in the sense that the collision integral is introduced in an ad hoc way and, thus, the short-range part of the impurity potential is double-counted. The Boltzmann transport equation (BTE) is then derived without imposing the assumption of random impurity configurations over the substrate. The derived BTE would be applicable to describe the discrete nature of impurities such as potential fluctuations.

Hot electrons in a nanowire hard X-ray detector

Nanowire chip-based electrical and optical devices such as biochemical sensors, physical detectors, or light emitters combine outstanding functionality with a small footprint, reducing expensive material and energy consumption. The core functionality of many nanowire-based devices is embedded in their p-n junctions. To fully unleash their potential, such nanowire-based devices require - besides a high performance - stability and reliability. Here, we report on an axial p-n junction GaAs nanowire X-ray detector that enables ultra-high spatial resolution (~200 nm) compared to micron scale conventional ones. In-operando X-ray analytical techniques based on a focused synchrotron X-ray nanobeam allow probing the internal electrical field and observing hot electron effects at the nanoscale. Finally, we study device stability and find a selective hot electron induced oxidization in the n-doped segment of the p-n junction. Our findings demonstrate capabilities and limitations of p-n junction nanowires, providing insight for further improvement and eventual integration into on-chip devices.

First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials

One of the fundamental properties of semiconductors is their ability to support highly tunable electric currents in the presence of electric fields or carrier concentration gradients. These properties are described by transport coefficients such as electron and hole mobilities. Over the last decades, our understanding of carrier mobilities has largely been shaped by experimental investigations and empirical models. Recently, advances in electronic structure methods for real materials have made it possible to study these properties with predictive accuracy and without resorting to empirical parameters. These new developments are unlocking exciting new opportunities, from exploring carrier transport in quantum matter to in silico designing new semiconductors with tailored transport properties. In this article, we review the most recent developments in the area of ab initio calculations of carrier mobilities of semiconductors. Our aim is threefold: to make this rapidly-growing research area accessible to a broad community of condensed-matter theorists and materials scientists; to identify key challenges that need to be addressed in order to increase the predictive power of these methods; and to identify new opportunities for increasing the impact of these computational methods on the science and technology of advanced materials. The review is organized in three parts. In the first part, we offer a brief historical overview of approaches to the calculation of carrier mobilities, and we establish the conceptual framework underlying modern ab initio approaches. We summarize the Boltzmann theory of carrier transport and we discuss its scope of applicability, merits, and limitations in the broader context of many-body Green's function approaches. We discuss recent implementations of the Boltzmann formalism within the context of density functional theory and many-body perturbation theory calculations, placing an emphasis on the key computational challenges and suggested solutions. In the second part of the article, we review applications of these methods to materials of current interest, from three-dimensional semiconductors to layered and two-dimensional materials. In particular, we discuss in detail recent investigations of classic materials such as silicon, diamond, gallium arsenide, gallium nitride, gallium oxide, and lead halide perovskites as well as low-dimensional semiconductors such as graphene, silicene, phosphorene, molybdenum disulfide, and indium selenide. We also review recent efforts toward high-throughput calculations of carrier transport. In the last part, we identify important classes of materials for which an ab initio study of carrier mobilities is warranted. We discuss the extension of the methodology to study topological quantum matter and materials for spintronics and we comment on the possibility of incorporating Berry-phase effects and many-body correlations beyond the standard Boltzmann formalism.

Low-temperature-dependent property in an avalanche photodiode based on GaN/AlN periodically-stacked structure

In ultra-high sensitive APDs, a vibrate of temperature might bring a fatal decline of the multiplication performance. Conventional method to realize a temperature-stable APD focuses on the optimization of device structure, which has limited effects. While in this paper, a solution by reducing the carrier scattering rate based on an GaN/AlN periodically-stacked structure (PSS) APD is brought out to improve temperature stability essentially. Transport property is systematically investigated. Compared with conventional GaN homojunction (HJ) APDs, electron suffers much less phonon scatterings before it achieves ionization threshold energy and more electrons occupy high energy states in PSS APD. The temperature dependence of ionization coefficient and energy distribution is greatly reduced. As a result, temperature stability on gain is significantly improved when the ionization happens with high efficiency. The change of gain for GaN (10 nm)/AlN (10 nm) PSS APD from 300 K to 310 K is about 20% lower than that for HJ APD. Additionally, thicker period length is found favorable to ionization coefficient ratio but a bit harmful to temperature stability, while increasing the proportion of AlN at each period in a specific range is found favorable to both ionization coefficient ratio and temperature stability.

Phonon-Enabled Carrier Transport of Localized States at Non-Polar Semiconductor Surfaces: A First-Principles-Based Prediction

Electron-phonon coupling can hamper carrier transport either by scattering or by the formation of mass-enhanced polarons. Here, we use time-dependent density functional theory-molecular dynamics simulations to show that phonons can also promote the transport of excited carriers. Using nonpolar InAs (110) surface as an example, we identify phonon-mediated coupling between electronic states close in energy as the origin for the enhanced transport. In particular, the coupling causes localized excitons in the resonant surface states to propagate into bulk with velocities as high as 10(6) cm/s. The theory also predicts temperature enhanced carrier transport, which may be observable in ultrathin nanostructures.

Ab initio study of hot electrons in GaAs

Hot carrier dynamics critically impacts the performance of electronic, optoelectronic, photovoltaic, and plasmonic devices. Hot carriers lose energy over nanometer lengths and picosecond timescales and thus are challenging to study experimentally, whereas calculations of hot carrier dynamics are cumbersome and dominated by empirical approaches. In this work, we present ab initio calculations of hot electrons in gallium arsenide (GaAs) using density functional theory and many-body perturbation theory. Our computed electron-phonon relaxation times at the onset of the Γ, L, and X valleys are in excellent agreement with ultrafast optical experiments and show that the ultrafast (tens of femtoseconds) hot electron decay times observed experimentally arise from electron-phonon scattering. This result is an important advance to resolve a controversy on hot electron cooling in GaAs. We further find that, contrary to common notions, all optical and acoustic modes contribute substantially to electron-phonon scattering, with a dominant contribution from transverse acoustic modes. This work provides definitive microscopic insight into hot electrons in GaAs and enables accurate ab initio computation of hot carriers in advanced materials.

ab initio study of hot carriers in the first picosecond after sunlight absorption in silicon

Hot carrier thermalization is a major source of efficiency loss in solar cells. Because of the subpicosecond time scale and complex physics involved, a microscopic characterization of hot carriers is challenging even for the simplest materials. We develop and apply an ab initio approach based on density functional theory and many-body perturbation theory to investigate hot carriers in semiconductors. Our calculations include electron-electron and electron-phonon interactions, and require no experimental input other than the structure of the material. We apply our approach to study the relaxation time and mean free path of hot carriers in Si, and map the band and k dependence of these quantities. We demonstrate that a hot carrier distribution characteristic of Si under solar illumination thermalizes within 350 fs, in excellent agreement with pump-probe experiments. Our work sheds light on the subpicosecond time scale after sunlight absorption in Si, and constitutes a first step towards ab initio quantification of hot carrier dynamics in materials.

Photoluminescence characterization in silicon nanowire fabricated by thermal oxidation of nano-scale Si fin structure

Low-temperature photoluminescence (PL) spectra of electron-hole systems in Si nanowires (NWs) prepared by thermal oxidization of Si fin structures were studied. Mapping of PL reveals that NWs with uniform width are formed over a large area. Annealing temperature dependence of PL peak intensities was maximized at 400 °C for each NW type, which are consistent with previous reports. Our results confirmed that the micro-PL demonstrated here is one of the important methods for characterizations of the interface defects in Si NWs.

Extraordinary carrier multiplication gated by a picosecond electric field pulse

The study of carrier multiplication has become an essential part of many-body physics and materials science as this multiplication directly affects nonlinear transport phenomena, and has a key role in designing efficient solar cells and electroluminescent emitters and highly sensitive photon detectors. Here we show that a 1-MVcm⁻¹ electric field of a terahertz pulse, unlike a DC bias, can generate a substantial number of electron–hole pairs, forming excitons that emit near-infrared luminescence. The bright luminescence associated with carrier multiplication suggests that carriers coherently driven by a strong electric field can efficiently gain enough kinetic energy to induce a series of impact ionizations that can increase the number of carriers by about three orders of magnitude on the picosecond time scale.

Studying carrier multiplication in materials is important to understand their transport properties and interaction with light. Hirori et al. show that intense terahertz pulses can generate electron-hole pairs in GaAs quantum wells that then emit infrared light, contrary to the effect with a DC field.

Collision densities and mean residence times for d-dimensional exponential flights

In this paper we analyze some aspects of exponential flights, a stochastic process that governs the evolution of many random transport phenomena, such as neutron propagation, chemical or biological species migration, and electron motion. We introduce a general framework for d-dimensional setups and emphasize that exponential flights represent a deceivingly simple system, where in most cases closed-form formulas can hardly be obtained. We derive a number of exact (where possible) or asymptotic results, among which are the stationary probability density for two-dimensional systems, a long-standing issue in physics, and the mean residence time in a given volume. Bounded or unbounded domains as well as scattering or absorbing domains are examined, and Monte Carlo simulations are performed so as to support our findings.

Monte Carlo Calculation of Hole Transport in Bulk Zincblende Phase of GaN including a Pseudopotential Calculated Band Structure

In this paper, we present ensemble Monte Carlo based calculations of the steady state hole transport properties, i.e. average energy, drift velocity, and band occupancy of zincblende GaN. The Monte Carlo calculation includes the full details of the valence bands and a numerically determined scattering rate derived from an empirical pseudopotential calculation. Calculations are made for electric field strengths up to 1000 kV/cm. It is found that the average hole energies are much lower than the corresponding electron energies at comparable electric field strengths, and that some anisotropy in the drift velocity and average energy appears at the higher fields examined here.

Comparison of Electron and Hole Initiated Impact Ionization in Zincblende and Wurtzite Phase Gallium Nitride

In this paper, we present the first calculations of the electron and hole impact ionizatioi coefficients for both wurtzite and zincblende phase GaN as a function of the applied electrii field. The calculations are made using an ensemble Monte Carlo simulator including the ful details of the conduction and valence bands derived from an empirical pseudopotentia calculation. The interband impact ionization transition rates for both carrier species an determined by direct numerical integration including a wavevector dependent dielectric function It is found that the electron and hole ionization coefficients are comparable in zincblende Ga> at an applied field of ∼ 3 MV/cm, yet vary to a slight degree at both higher and lower applied field strengths. In the wurtzite phase, the electron and hole coefficients are comparable at hig] fields but diverge at lower applied fields. The most striking result is that the ionization rates an predicted to be substantially different for both carrier species between the two phases. It i predicted that the ionization rates for both carrier species in the zincblende phase are significanti; higher than in the wurtzite phase over the full range of applied fields examined.

Rigid ion model of high field transport in GaN

Here we report on high field transport in GaN based on the rigid ion model of the electron-phonon interaction within the cellular Monte Carlo (CMC) approach. Using the rigid pseudo-ion method for the cubic zinc-blende and hexagonal wurtzite structures, the anisotropic deformation potentials are derived from the electronic structure, the atomic pseudopotential and the full phonon dispersion and eigenvectors for both acoustic and optical modes. Several different electronic structure and lattice dynamics models are compared, as well as different models for the interpolation of the atomic pseudopotentials required in the rigid pseudo-ion method. Piezoelectric as well as anisotropic polar optical phonon scattering is accounted for as well. In terms of high field transport, the peak velocity is primarily determined by deformation potential scattering described through the rigid pseudo-ion model. The calculated velocity is compared with experimental data from pulsed I-V measurements. Good agreement is found using the rigid ion model to the measured velocity-field characteristics with the inclusion of dislocation and ionized impurity scattering. The crystal orientation of the electric field is investigated, where very little difference is observed in the velocity-field characteristics. We simulate the effects of nonequilibrium hot phonons on the energy relaxation as well, using a detailed balance between emission and absorption during the simulation, and an anharmonic decay of LO phonons to acoustic phonons, as reported previously. Nonequilibrium phonons are shown to result in a significant degradation of the velocity-field characteristics for high carrier densities, such as those encountered at the AlGaN/GaN interface due to polarization effects.

First-principles mobility calculations and atomic-scale interface roughness in nanoscale structures

Calculations of mobilities have so far been carried out using approximate methods that suppress atomic-scale detail. Such approaches break down in nanoscale structures. Here we report the development of a method to calculate mobilities using atomic-scale models of the structures and density functional theory at various levels of sophistication and accuracy. The method is used to calculate the effect of atomic-scale roughness on electron mobilities in ultrathin double-gate silicon-on-insulator structures. The results elucidate the origin of the significant reduction in mobility observed in ultrathin structures at low electron densities.

First-principles calculation of transport properties of a molecular device

We report first-principles calculations of the current-voltage ( I-V) characteristics of a molecular device and compare with experiment. We find that the shape of the I-V curve is largely determined by the electronic structure of the molecule, while the presence of single atoms at the molecule-electrode interface play a key role in determining the absolute value of the current. The results show that such simulations would be useful for the design of future microelectronic devices for which the Boltzmann-equation approach is no longer applicable.

Interpolation of the spectral responsivity of silicon photodetectors in the near ultraviolet

We improve the methods used to interpolate the responsivity of unbiased silicon photodetectors in the near-ultraviolet region. This improvement is achieved by the derivation of an interpolation function for the quantum yield of silicon and by consideration of this function in the interpolation of the internal quantum efficiency of photodiodes. The calculated quantum-yield and spectral-responsivity values are compared with measurement results obtained by the study of a silicon trap detector and with values reported by other research groups. The comparisons show agreement with a standard deviation of 0.4% between our measured and modeled values for both the quantum yield and the spectral responsivity within the wavelength region from 260 to 400 nm. The proposed methods thus extend the predictability of the spectral responsivity of silicon photodetectors to the wavelength region from 260 to 950 nm. Furthermore, an explanation is proposed for the change in the spectral responsivity of silicon photodiodes that is due to UV radiation. In our improved quantum efficiency model the spectral change can be accounted for completely by the adjustment of just one parameter, i.e., the collection efficiency near the SiO(2)/Si interface.

Hydrodynamic model of temperature change in open ionic channels

Most theories of open ionic channels ignore heat generated by current flow, but that heat is known to be significant when analogous currents flow in semiconductors, so a generalization of the Poisson-Nernst-Planck theory of channels, called the hydrodynamic model, is needed. The hydrodynamic theory is a combination of the Poisson and Euler field equations of electrostatics and fluid dynamics, conservation laws that describe diffusive and convective flow of mass, heat, and charge (i.e., current), and their coupling. That is to say, it is a kinetic theory of solute and solvent flow, allowing heat and current flow as well, taking into account density changes, temperature changes, and electrical potential gradients. We integrate the equations with an essentially nonoscillatory shock-capturing numerical scheme previously shown to be stable and accurate. Our calculations show that 1) a significant amount of electrical energy is exchanged with the permeating ions; 2) the local temperature of the ions rises some tens of degrees, and this temperature rise significantly alters for ionic flux in a channel 25 A long, such as gramicidin-A; and 3) a critical parameter, called the saturation velocity, determines whether ionic motion is overdamped (Poisson-Nernst-Planck theory), is an intermediate regime (called the adiabatic approximation in semiconductor theory), or is altogether unrestricted (requiring the full hydrodynamic model). It seems that significant temperature changes are likely to accompany current flow in the open ionic channel.