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DOE OSTI2024

An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model

A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density $f$ = $f$ ($x, v, t$) converges to an isotropic function $M (v)$$ρ$$(x, t)$, called the drift-diffusion limit, where $M$ is a Maxwellian and the physical density $ρ$ satisfies a second-order parabolic PDE known as the drift-diffusion equation. Numerical approximations that mirror this property are said to be asymptotic preserving. In this paper we build a discontinuous Galerkin method to the semiconductor model, and we show this scheme is both uniformly stable in $ε$, where 1/$ε$ is the scale of the collision frequency, and asymptotic preserving. Here in particular, we discuss what properties the discrete Maxwellian must satisfy in order for the schemes to converge in $ε$ to an accurate $h$-approximation of the drift-diffusion limit. Discrete versions of the drift-diffusion equation and error estimates in several norms with respect to $ε$ and the spacial resolution are also included.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Analysis of a New Implicit Solver for a Semiconductor Model

Here, we present and analyze a new iterative solver for implicit discretizations of a simplified Boltzmann--Poisson system. The algorithm builds on recent work that incorporated a sweeping algorithm for the Vlasov--Poisson equations as part of nested inner-outer iterative solvers for the Boltzmann--Poisson equations. The new method eliminates the need for nesting and requires only one transport sweep per iteration. It arises as a new fixed-point formulation of the discretized system which we prove to be contractive for a given electric potential. We also derive an accelerator to improve the convergence rate for systems in the drift-diffusion regime. We numerically compare the efficiency of the new solver, with and without acceleration, against a recently developed nested iterative solver.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2007

Hypersonic Magneto-Fluid-Dynamic Compression in Cylindrical Inlet

Hypersonic magneto-fluid-dynamic interaction has been successfully performed as a virtual leading-edge strake and a virtual cowl of a cylindrical inlet. In a side-by-side experimental and computational study, the magnitude of the induced compression was found to be depended on configuration and electrode placement. To better understand the interacting phenomenon the present investigation is focused on a direct current discharge at the leading edge of a cylindrical inlet for which validating experimental data is available. The present computational result is obtained by solving the magneto-fluid-dynamics equations at the low magnetic Reynolds number limit and using a nonequilibrium weakly ionized gas model based on the drift-diffusion theory. The numerical simulation provides a detailed description of the intriguing physics. After validation with experimental measurements, the computed results further quantify the effectiveness of a magnet-fluid-dynamic compression for a hypersonic cylindrical inlet. At a minuscule power input to a direct current surface discharge of 8.14 watts per square centimeter of electrode area produces an additional compression of 6.7 percent for a constant cross-section cylindrical inlet.

Shang, Joseph S.↗

DOE OSTI2021

Spatial profiles of photon chemical potential in near-field thermophotovoltaic cells

Emitted photons stemming from the radiative recombination of electron–hole pairs carry chemical potential in radiative energy converters. This luminescent effect can substantially alter the local net photogeneration in near-field thermophotovoltaic cells. Several assumptions involving the luminescent effect are commonly made in modeling photovoltaic devices; in particular, the photon chemical potential is assumed to be zero or a constant prescribed by the bias voltage. The significance of photon chemical potential depends upon the emitter temperature, the semiconductor properties, and the injection level. Hence, these assumptions are questionable in near-field thermophotovoltaic devices with nanoscale separation distances between the emitter and the cell. In the present work, an iterative solver that combines fluctuational electrodynamics with the drift-diffusion model is developed to tackle the coupled photon and charge transport problem, enabling the determination of the spatial profile of photon chemical potential beyond the detailed balance approach. Here, the difference between the results obtained by allowing the photon chemical potential to vary spatially and by assuming a constant value demonstrates the limitations of the conventional approaches. This study is critically important for performance evaluation of near-field thermophotovoltaic systems with nanoscale vacuum gaps.

30 DIRECT ENERGY CONVERSION↗

NASA NTRS2001

Electro-Thermal Simulation Studies of SiC Junction Diodes Containing Screw Dislocations Under High Reverse-Bias Operation

The objective of this work was to conduct a modeling study of SiC P-N junction diodes operating under high reverse biased conditions. Analytical models and numerical simulation capabilities were to be developed for self-consistent electro-thermal analysis of the diode current-voltage (I-V) characteristics. Data from GRC indicate that screw dislocations are unavoidable in large area SiC devices, and lead to changes in the SiC diode electrical response characteristics under high field conditions. For example, device instability and failures linked to internal current filamentation have been observed. The physical origin of these processes is not well understood, and quantitative projections of the electrical behavior under high field and temperature conditions are lacking. Thermal calculations for SiC devices have not been reported in the literature either. So estimates or projections of peak device temperatures and power limitations do not exist. This numerical study and simulation analysis was aimed at resolving some of the above issues. The following tasks were successfully accomplished: (1) Development of physically based models using one- and two-dimensional drift-diffusion theory for the transport behavior and I-V characteristics; (2) One- and two-dimensional heat flow to account for internal device heating. This led to calculations of the internal temperature profiles, which in turn, were used to update the electrical transport parameters for a self-consistent analysis. The temperature profiles and the peak values were thus obtainable for a given device operating condition; (3) Inclusion of traps assumed to model the presence of internal screw dislocations running along the longitudinal direction; (4) Predictions of the operating characteristics with and without heating as a function of applied bias with and without traps. Both one and two-dimensional cases were implemented; (5) Assessment of device stability based on the operating characteristics. The presence of internal non-uniformities, particularly filamentary structures, was probed and demonstrated; (6) Cause and physical origins of filamentary behavior and unstable I-V characteristics were made transparent; (7) It was demonstrated that diodes containing defects would be more prone to thermal breakdown associated with the temperature dependent decrease in the thermal conductivity; and (8) Finally, negative differential resistance (S-shaped NDR) which can potential lead to device instability and filamentary behavior was shown to occur for diodes containing a line of defects such as could be associated with a screw dislocation line.

Joshi, R. P.↗

DOE OSTI2025

Charge carrier extraction and recombination effects in GaInAs/GaAsP multi-quantum well solar cells

The carrier extraction and transport mechanisms as well as the relative contributions of radiative and non-radiative recombination processes are investigated in high-quality strain-balanced GaInAs/GaAsP multi-quantum well solar cells recently implemented in record efficiency multijunction solar cells. A comprehensive suite of complementary characterization techniques including temperature- and suns-dependent photoluminescence and photovoltaic measurements are employed to analyze thermal escape and tunneling rates, which demonstrate the need to move beyond simple drift-diffusion models of p–n junctions. This study examines the processes that best characterize the operation of these devices across varying temperatures using a simple two-diode model, incorporating multiple transport protocols, and provides insights into the performance-limiting processes and pathways for their optimization.

14 SOLAR ENERGY↗

NASA NTRS1995

Theoretical Study of Response of InGaAs Metal-Semiconductor-Metal Photodetectors

We present a theoretical investigation of the response of metal-semiconductor-metal (MSM) photodetectors made of InGaAs lattice-matched to InP using a two-dimensional drift-diffusion model with a thermionic-field emission boundary condition for the heterojunctions. The effect of including a top InAlAs layer to increase the effective barrier height of the metal fingers on the InGaAs active layer is thoroughly examined and found to limit the collection of the photocurrent signal due to the electron and hole barriers that it forms with InGaAs. Due to the thickness and height of the InAlAs barrier layer in existing designs, the tunneling current obtained from the model is found to be negligibly small to significantly affect the output signal current. In an attempt to obtain a better response, different design structures including one where a quasi-Schottky contact is utilized are studied and their speed of response, breakdown voltage, and dark current are compared to that of the usual InGaAs device.

Salem, Ali F.↗

DOE OSTI2021

Temperature Coefficients of Perovskite Photovoltaics for Energy Yield Calculations

Temperature coefficients for maximum power (TPCE), open circuit voltage (VOC), and short circuit current (JSC) are standard specifications included in data sheets for any commercially available photovoltaic module. To date, there has been little work on determining the TPCE for perovskite photovoltaics (PV). We fabricate perovskite solar cells with a TPCE of -0.08 rel %/°C and then disentangle the temperature-dependent effects of the perovskite absorber, contact layers, and interfaces by comparing different device architectures and using drift-diffusion modeling. A main factor contributing to the small TPCE of perovskites is their low intrinsic carrier concentrations with respect to Si and GaAs, which can be explained by its wider band gap. In this work, we demonstrate that the unique increase in Eg with increasing temperatures seen for perovskites results in a reduction in JSC but positively influences VOC. The current limiting factors for the TPCE in perovskite PV are identified to originate from interfacial effects.

14 SOLAR ENERGY↗

NASA NTRS1996

Comparison of Non-Parabolic Hydrodynamic Simulations for Semiconductor Devices

Parabolic drift-diffusion simulators are common engineering level design tools for semiconductor devices. Hydrodynamic simulators, based on the parabolic band approximation, are becoming more prevalent as device dimensions shrink and energy transport effects begin to dominate device characteristic. However, band structure effects present in state-of-the-art devices necessitate relaxing the parabolic band approximation. This paper presents simulations of ballistic diodes, a benchmark device, of Si and GaAs using two different non-parabolic hydrodynamic formulations. The first formulation uses the Kane dispersion relationship in the derivation of the conservation equations. The second model uses a power law dispersion relation {(hk)(exp 2)/2m = xW(exp Y)}. Current-voltage relations show that for the ballistic diodes considered. the non-parabolic formulations predict less current than the parabolic case. Explanations of this will be provided by examination of velocity and energy profiles. At low bias, the simulations based on the Kane formulation predict greater current flow than the power law formulation. As the bias is increased this trend changes and the power law predicts greater current than the Kane formulation. It will be shown that the non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation are limited due to the binomial approximation which was utilized in the derivation.

Smith, A. W.↗

DOE OSTI2025

Co‐Doping Approach for Enhanced Electron Extraction to TiO 2 for Stable Inorganic Perovskite Solar Cells

Inorganic perovskite CsPbI 3 solar cells hold great potential for improving the operational stability of perovskite photovoltaics. However, electron extraction is limited by the low conductivity of TiO 2 , representing a bottleneck for achieving stable performance. In this study, a co‐doping strategy for TiO 2 using Nb(V) and Sn(IV), which reduces the material's work function by 80 meV compared to Nb(V) mono‐doped TiO 2 , is introduced. To gain fundamental understanding of the processes at the interfaces between the perovskite and charge‐selective layer, transient surface photovoltage measurements are applied, revealing the beneficial effect of the energetic and structural modification on electron extraction across the CsPbI 3 /TiO 2 interface. Using 2D drift‐diffusion simulations, it is found that co‐doping reduces the interface hole recombination velocity by two orders of magnitude, increasing the concentration of extracted electrons by 20%. When integrated into n–i–p solar cells, co‐doped TiO 2 enhances the projected T S80 lifetimes under continuous AM1.5G illumination by a factor of 25 compared to mono‐doped TiO 2 . This study provides fundamental insights into interfacial charge extraction and its correlation with operational stability of perovskite solar cells, offering potential applications for other charge‐selective contacts.

14 SOLAR ENERGY↗

DOE OSTI2022

Influence of carrier trapping on radiation detection properties in $\mathrm{CVD}$ grown 4H-SiC epitaxial layers with varying thickness up to 250 µm

We report low doped n-type 4H-SiC epitaxial layers of thickness 50, 150, and 250 µm grown by hot wall chemical vapor deposition were used to fabricate Ni/4H-SiC Schottky radiation detectors. The epitaxial layers were grown on the (0001) face of highly conductive bulk 4H-SiC substrates 8° offcut towards the $\langle 11\bar{2}1\rangle$ direction. The 50, 150, and 250 µm thick epilayer detectors, under optimized settings, showed energy resolutions of 2.0%, 0.78%, and 0.63%, respectively for 5.48 MeV alpha particles. Deep level transient spectroscopy studies showed that the observed variation in the detector resolution is linked to the defect parameters in the devices. Least-squares fitting of the bias dependence of the charge collection efficiency according to a drift-diffusion model, revealed minority carrier diffusion lengths of 16, 10, and 9.2 µm, respectively, implying that the detectors are not limited by minority carrier trapping. The detector performance was observed to be primarily dependent on the concentration and capture cross-sections of the lifetime killing electron traps Z 1/2 and EH 6/7 .

36 MATERIALS SCIENCE↗

DOE OSTI2021

Defect characterization and charge transport measurements in high-resolution Ni/n-4H-SiC Schottky barrier radiation detectors fabricated on 250 μ m epitaxial layers

Advances in the growth processes of 4H-SiC epitaxial layers have led to the continued expansion of epilayer thickness, allowing for the detection of more penetrative radioactive particles. In this work, we report the fabrication and characterization of high-resolution Schottky barrier radiation detectors on 250 μm thick n-type 4H-SiC epitaxial layers, the highest reported thickness to date. Several 8 × 8 mm 2 detectors were fabricated from a diced 100 mm diameter 4H-SiC epitaxial wafer grown on a conductive 4H-SiC substrate with a mean micropipe density of 0.11 cm -2 From the Mott–Schottky plots, the effective doping concentration was found to be in the range (0.95–1.85) × 10 14 cm -3 , implying that full depletion could be achieved at ~5.7 kV (0.5 MV/cm at the interface). The current-voltage characteristics demonstrated consistently low leakage current densities of 1–3 nA/cm 2 at a reverse bias of -800 V. This resulted in the pulse-height spectra generated using a 241Am alpha source (5486 keV) manifesting an energy resolution of less than 0.5% full width at half maximum (FWHM) for all the detectors at -200 V. The charge collection efficiencies (CCEs) were measured to be 98–99% with no discernable correlation to the energy resolution. A drift-diffusion model fit to the variation of CCE as a function of bias voltage, revealed a minority carrier diffusion length of ~10 μm. Deep level transient spectroscopy measurements on the best resolution detector revealed that the excellent performance was the result of having ultralow concentrations of the order of 1011 cm-3 lifetime limiting defects—Z 1/2 and EH 6/7 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

High-resolution radiation detection using Ni/SiO 2 /n-4H-SiC vertical metal-oxide-semiconductor capacitor

In this article, we demonstrate the radiation detection performance of vertical metal-oxide-semiconductor (MOS) capacitors fabricated on 20 μm thick n-4H-SiC epitaxial layers with the highest energy resolution ever reported. The 100 nm SiO2 layer was achieved on the Si face of n-4H-SiC epilayers using dry oxidation in air. The Ni/SiO2/n-4H-SiC MOS detectors not only demonstrated an excellent energy resolution of 0.42% (ΔE/E 100) for 5.48 MeV alpha particles but also caused a lower enhancement in the electronic noise components of the spectrometer compared with that observed for the best high-resolution Schottky barrier detectors. The MOS detectors also exhibited a high charge collection efficiency (CCE) of 96% at the optimized operating bias despite the presence of the oxide layer. A drift-diffusion model applied to the CCE vs gate bias voltage data revealed a minority (hole) carrier diffusion length of 24 μm. Capacitance mode deep level transient spectroscopy (C-DLTS) scans in the temperature range 84–800 K were carried out to identify the resolution limiting electrically active defects. Interestingly, the C-DLTS spectra revealed both positive and negative peaks, indicating the simultaneous presence of electron (majority) and hole (minority) trap centers. It has been inferred that at the steady-state bias for the C-DLTS measurement, the MOS detector operates in the inversion mode at certain device temperatures, causing holes to populate the minority trap centers and, hence, manifests minority carrier peaks as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗