Quantum Drift-diffusion Model Research Articles

Edge-Terminated AlGaN/GaN/AlGaN Multi-Quantum Well Impact Avalanche Transit Time Sources for Terahertz Wave Generation

Edge-Terminated AlGaN/GaN/AlGaN Multi-Quantum Well Impact Avalanche Transit Time Sources for Terahertz Wave Generation

A splitting scheme for the quantum Liouville-BGK equation

We introduce in this work an efficient numerical method for the simulation of the quantum Liouville-BGK equation, which models the diffusive transport of quantum particles. The corner stone to the model is the BGK collision operator, obtained by minimizing the quantum free energy under the constraint that the local density of particles is conserved during collisions. This leads to a large system of coupled nonlinear nonlocal PDEs whose resolution is challenging. We then define a splitting scheme that separates the transport and the collision parts, which, exploiting the local conservation of particles, leads to a fully linear collision step. The latter involves the resolution of a constrained optimization problem that is handled with the nonlinear conjugate gradient algorithm. We prove that the time semi-discrete scheme is convergent, and as an application of our numerical scheme, we validate the quantum drift-diffusion model that is obtained as the diffusive limit of the quantum Liouville-BGK equation.

Optimization of Doping Concentration to Obtain High Internal Quantum Efficiency and Wavelength Stability in An InGaN/GaN Blue Light-Emitting Diode

We conduct a comprehensive study to investigate the feasibility of achieving high internal quantum efficiency (IQE) and wavelength stability in an InGaN/GaN blue light-emitting diode (LED) through numerical simulations with different doping concentrations. To ensure accurate calculations, we emulated the structure of an LED, fabricated on freestanding GaN with low defect density, abrupt interfaces, and high-performing characteristics, which resemble ideal conditions. Our objective is to determine the optimal doping concentration of the claddings using the Quantum Drift-Diffusion (QDD) model. We tested three concentrations ( ), and found that produced the highest IQE of 82.5%, the most stable wavelength in the range of (0.08–63.25) mA, an optical power of mWs−1, and a forward voltage of V at 20 mA. We suggest that using this concentration leads to the parameters closest to those of the reference device.

Analysis of quantum confinement in nanosheet FETs by using a quantum drift diffusion model

AbstractIn this paper, we have analyzed quantum confinement effects in nanosheet MOSFETs by using a quantum drift‐diffusion (QDD) model. The QDD model is a device simulator which allows to simulate quantum confinement effects in the inversion layer for advanced MOSFETs. The quantum confinement effects in nanosheets have been analyzed by comparing the simulation results by QDD and drift‐diffusion (DD) model. The drain current ratio of DD to QDD is 250.1% at VG = 0.5 V and 180.1% at VG = 0 V. While the maximum electron density of DD exists at the interface between the insulator and the silicon sheet, that of QDD goes to near the center of the silicon sheet. The electron areal density ratio of DD to QDD is 118.3% in the direction of the 10 nm width of the silicon sheet and 176.9% in the direction of the 4 nm width.

An Analysis of Mobility Influence in Optoelectronics Parameters in an InGaN/GaN Blue LED

Simulations on mobility influence in optoelectronics parameters from an InGaN/GaN blue LED using the Nextnano++ software arepresented in this paper. These simulations were performed by changing the hole and electron mobility value for the material compounds according to experimental, theoretical, and doping-concentration data already reported in the literature. The power law mobility is used for the current calculation in the quantum drift-diffusion model. The results indicate the lower hole and electron leakage currents correspond to the lowest mobility values for the InGaN alloy, the greatest amount of recombination occurs in the extreme wells within the active layer of the LED and the stable emission is at 3.6 V with peak wavelength λ^LED=456.7 nm and full width at half maximum FWHM~11.1 nm for the three mobilities. Although experimental and theoretical mobility values reach higher carrier density and recombination, the photon emission is broader and unstable. Additionally, the doping-concentration mobility results in lower wavelength shifts and narrows FWHM, making it more stable. The highest quantum efficiency achieved by doping-concentration mobility is only in the breakdown voltage (ηdop−max=60.43%), which is the IQE value comparable to similar LEDs and is more useful for these kinds of semiconductor devices.

Quantum energy-transport and drift-diffusion models for electron transport in graphene: an approach by the wigner function

The present work aims at formulating quantum energy-transport and drift-diffusion equations for charge transport in graphene from a quantum hydrodynamic model proposed in Luca and Romano (Ann. Phys. 406:30–53, 2019), obtained from the Wigner-Boltzmann equation via the moment method. Here, we only sketch the main ideas and show the most relevant formulas. Further developments are under current investigation by the authors. The interested reader can find the omitted details in the references. In analogy with the semiclassical case, we are confident that the energy-transport and drift-diffusion models have mathematical properties which allow an easier numerical treatment.

Mobility Model Parameters of Strained Si by Using a Quantum Drift Diffusion Model

Mobility Model Parameters of Strained Si by Using a Quantum Drift Diffusion Model

Direct band gap silicon nanowire avalanche transit time thz opto-electronic sensor with strain-engineering

The role of process-induced strain-engineering in inducing indirect to direct band gap transition in Si nanowires (Si-NWs) has been investigated. A very interesting observation reveals that both spatial confinement and process-induced strain induce similar kind of quantum confinement resulting in band gap transition (indirect to direct) in Si-NWs. Further, suitable strain-engineering has resulted in near ballistic transport and subsequently very high electron mobility along nanowire axis has been achieved. Thereafter, the impact of such strain-engineering in tuning peak oscillation frequency, RF power density and opto-electronic properties of Si-NW based laterally-doped pulsed mode Avalanche Transit Time (ATT) oscillators are explored for the first time. The tuning factor is the fraction of insertion of the NWs into the underlying sapphire substrate. For this, a planar ATT device with Si-NWs on Sapphire-On-Silicon (SOS) substrate is proposed. Static, non-linear and thermal analysis are carried out under light and dark conditions, using indigenously developed in-house simulation codes through a self-consistent, quantum drift–diffusion model. The obtained analytical results have been verified with experimental data and considerable agreement has been achieved. The study reveals that the use of Si-NWs has significant technological advantages that include carrier mobility-enhancement and complete band gap transition from indirect to direct. Strain-engineered NW ATTs are revealed to be very much conducive for their useful application as high power (84.25 × 109 W/m2) THz optical switches with excellent thermal stability. For the first time the study reports the suitability of direct band gap pure Si-NW ATTs as potential candidates for application in high power THz opto-electronics.

Terahertz Radiators Based on Si~3C-SiC MQW IMPATT Diodes

Aims:: The potentiality of Multiple Quantum Well (MQW) Impacts Avalanche Transit Time (IMPATT) diodes based on Si~3C-SiC heterostructures as possible terahertz radiators have been explored in this paper. Objective:: The static, high frequency and noise performance of MQW devices operating at 94, 140, and 220 GHz atmospheric window frequencies, as well as 0.30 and 0.50 THz frequency bands, have been studied in this paper. Methods: The simulation methods based on a Self-Consistent Quantum Drift-Diffusion (SCQDD) model developed by the authors have been used for the above-mentioned studies. Results: Thus the noise performance of MQW DDRs will be obviously better as compared to the flat Si DDRs operating at different mm-wave and THz frequencies. Conclusion:: Simulation results show that Si~3C-SiC MQW IMPATT sources are capable of providing considerably higher RF power output with the significantly lower noise level at both millimeter-wave (mm-wave) and terahertz (THz) frequency bands as compared to conventional flat Si IMPATT sources.

Analysis of nonequilibrium phenomena on electric characteristics of advanced MOSFETs by using a quantum energy transport model

AbstractIn this paper, we have investigated nonequilibrium effects for advanced MOSFETs by using a device simulator with quantum energy transport (QET) model. The QET model allows to simulate nonequilibrium carrier transport as well as quantum confinement. The QET model includes the mobility model as a function of carrier temperature in order to consider the nonlocal effects. We have simulated advanced MOSFETs down to 20 nm gate length using the QET model. The QET model is compared with the quantum drift diffusion (QDD) model which includes a mobility model with local assumptions. It is found that the nonlocal mobility model is needed to simulate the advanced MOSFETs with less than 40 nm.

Optoelectronic properties of multiple quantum barriers nano-scale avalanche photo diodes

The important optoelectronic properties like spectral response, excess noise characteristics, time and frequency response of multiple quantum barrier (MQB) nano-scale avalanche photodiodes (APDs) based on Si~3C-SiC material system have been studied. A self-consistent simulation method based on quantum drift-diffusion model has been presented. Simulation results show that the Si~3C-SiC MQB nano-APDs are capable of detecting significantly longer wavelengths as compared to infrared flat Si APDs. The multiplication gain and excess noise factor (ENF) of the MQB APDs have been calculated by varying the number of quantum barriers (QBs). The numerically calculated ENF values of MQB APDs have been compared with the ENF of Si flat conventional APDs of similar dimensions and it is observed that the use of QBs leads to significant reduction in ENF of the APDs. Simulation results also show that MQB nano-APDs possess significantly faster time response and wider frequency response as compared to the Si counterparts.

Asymptotic Behavior of Solutions of the Bipolar Quantum Drift-Diffusion Model in the Quarter Plane

In this study, we consider the one-dimensional bipolar quantum drift-diffusion model, which consists of the coupled nonlinear fourth-order parabolic equation and the electric field equation. We first show the global existence of the strong solution of the initial boundary value problem in the quarter plane. Moreover, we show the self-similarity property of the strong solution of the bipolar quantum drift-diffusion model in the large time. Namely, we show the unique global strong solution with strictly positive density to the initial boundary value problem of the quantum drift-diffusion model, which in large time, tends to have a self-similar wave at an algebraic time-decay rate. We prove them in an energy method.

Si/SiC heterostructure MITATT oscillator for higher-harmonic THz-power generation: theoretical reliability and experimental feasibility studies of quantum modified non-linear classical model

Modelling/simulation and high-frequency characterization of hetero-junction Avalanche Transit Time (ATT) oscillators, operating in tuned harmonic mode, are reported in the paper. An equivalent circuit, that incorporates self-consistent, non-linear, single-frequency impedance and admittance properties of the device at fundamental, 1st harmonic and 2nd harmonic mode of oscillation frequencies within the THz (0.5–1.5 THz) domain, is simulated. The prospects of Si/4H-SiC versus Si/6H-SiC exotic hetero structures are studied and compared for the generation of considerable amount of RF-power at higher harmonic THz region. For this, a generalised non-linear Mixed Quantum Drift Diffusion (MQDD) model is developed indigenously. The authors have made the simulator realistic by incorporating the temperature dependent carrier ionization rate, saturation drift velocity, mobility and effective mass of the base material-pairs in the analysis. In addition to these, the effects of punch-through phenomena as well as parasitic series resistance related detrimental issues are duly addressed in the present analysis. The authors have made the model realistic by studying the performance of the proposed novel structures under room temperature as well as under elevated temperature conditions. Due to the incorporation of hetero-structure in the active region of the device, considerable amount of power could be generated at 2nd harmonic oscillation frequency (~ 1.7 THz). The study shows that both the Si/4H-SiC and Si/6H-SiC hetero-junction devices are oscillating at 0.5 THz (fundamental frequency). Si/4H-SiC hetero-junction device, due to its less lattice mismatch factor, is more efficient (45%) than its Si/6H-SiC (15%) counterpart under similar structural/electrical/thermal operating conditions. The validity of the MQDD model is established in this paper by comparing the data with corresponding experimental observations at microwave/millimeter-wave region. To the best of authors’ knowledge, this is the first report on harmonic power generation from Si/4H-SiC and Si/6H-SiC hetero-junction ATT devices at higher terahertz region.

Three‐Terminal Graphene Nanoribbon Tunable Avalanche Transit Time Sources for Terahertz Power Generation

Herein, the possibilities of tuning oscillation frequency and power in terahertz (THz) graphene nanoribbon (GNR)‐based avalanche transit time (ATT) sources by introducing a third terminal on their planar structure are discussed. In this regard, a three‐terminal planner impact ATT (IMPATT) structure based on GNR on oxide (SiO2) is proposed. Inherent power combining capabilities of parallel‐connected IMPATT structures are utilized to increase the power output at THz frequencies. Static, high frequency, and noise simulations are carried out using in‐house simulation codes based on self‐consistent quantum drift–diffusion model. Results show that around 0.7–5.3% and 9.0–13.3% modulation of frequency and power output are achievable, respectively, in the GNR IMPATT oscillators operating in the frequency range of 1.0–10.0 THz, respectively, by applying a suitable amount of voltage at the third or controlling terminal; however, the enhancement of noise level at the output is observed to be insignificant as a result of using the active third‐terminal control.

Operating behavior of micro-LEDs on a GaN substrate at ultrahigh injection current densities.

Near-ultraviolet micro-LEDs with different diameters were fabricated on GaN substrates. The electroluminescence and the light output power-current density and current density-voltage relationships were measured. A saturated current density of 358 kA/cm2 was achieved with a 20 µm LED. The ideality factor curves showed steps and peaks when the injection current density was increased from 20 to 150 kA/cm2 and an abnormal efficiency increase. The transport and recombination processes of micro-LEDs at high injection current densities were simulated, and the many-body effect and phase space filling in the integrated quantum drift-diffusion model were considered. Serious current crowding was observed above 100 kA/cm2, even for the 20 µm LED.

Cubic versus hexagonal SiC vertical pin SPST/SPDT/SPMT switches for MMW communication systems: a modified quantum drift-diffusion model for switching characteristics analysis

A modified quantum drift-diffusion (QDD) model is developed for non-linear analysis of SiC (4H, 6H and 3C polytypes) pin semiconductor diodes at W-band frequency regime. Effects of incorporation of a buffer layer (n-type), in between substrate and low doped active region of the hexagonal (4H and 6H) pin (p++-p+-n−-n-n++) vertical mesa structure is thoroughly studied in this paper for the improvement of MM-wave performance of the single device. Also, a thin layer of Ge has been introduced in between Si substrate and n+ cubic-SiC layer in 3C-SiC pin-device for minimising the lattice mismatch issue in between Si/3C-SiC interface. The comprehensive analysis establish that the forward characteristics, reverse recovery time (1 ns) and breakdown voltage (171 Volt) in case of 4H-SiC device are quite good in comparison to its cubic (3C) and other hexagonal (6H) counterparts, however, the switching characteristics of 3C-SiC pin diode array is comparatively better than its hexagonal counterparts. This observation could be explained in terms of lowest series resistance in 3C-SiC based single pin device that has been achieved by incorporating Ge layer in mesa structure. The authors have made a comparative analysis among SPST, SPDT and SPMT pin switches made up with 4H, 6H and 3C-SiC poly-types. At 94 GHz, W-band central frequency, series resistance in 4H-SiC single device is 0.59 Ω, whereas, the same is much lower (0.27 Ω) in case of 3C-SiC. Insertion loss and isolation in 3C-SiC pin array of switches are found to be 0.18 dB and 38 dB (SPST switch), 0.19 dB and 67 dB (SPDT switch), 0.20 dB and 90 dB (SPMT shunt type switching array) and 0.23 dB and 74 dB (SPMT series-shunt type switching array). This newly proposed QDD model validation is done through comparative studies between experiment and analytical results for 4H-SiC SPST switches in low-frequency Microwave region. The validated QDD model, coupled with PSpice and Comsol Multi-physics simulator, then used for designing of the W-band devices and corresponding switches. However, as far as author’s knowledge is concerned, no experiment is yet done with SiC pin diodes at W-band frequencies, in literature for comparison. From simulation point of view also such an extensive study on hexagonal and cubic SiC pin diode switches at W-band region has not yet been done by any other researcher group. This paper, for the first time, establishes the feasibility and potentiality of IV-IV group semiconductor based pin (p++-p+-n−-n-n++) switches for W-band applications. Comparative analysis also reveals that 3C-SiC based shunt type pin (p++-p+-n−-n-n++) SPMT switches are the best for MMW-communication systems. Thermal modelling of the designed devices are also compared and reported in this paper. The quasi-3D thermal analysis is done to optimize the mesa and heat-sink diameter/dimensions so as to minimize the thermal runaway issues. The results may further be used for developing low-cost and fast semiconductor switches for potential application in THz communication systems.

The quantum drift-diffusion model: Existence and exponential convergence to the equilibrium

This work is devoted to the analysis of the quantum drift-diffusion model derived by Degond et al. in [7]. The model is obtained as the diffusive limit of the quantum Liouville–BGK equation, where the collision term is defined after a local quantum statistical equilibrium. The corner stone of the model is the closure relation between the density and the current, which is nonlinear and nonlocal, and is the main source of the mathematical difficulties. The question of the existence of solutions has been open since the derivation of the model, and we provide here a first result in a one-dimensional periodic setting. The proof is based on an approximation argument, and exploits some properties of the minimizers of an appropriate quantum free energy. We investigate as well the long time behavior, and show that the solutions converge exponentially fast to the equilibrium. This is done by deriving a non-commutative logarithmic Sobolev inequality for the local quantum statistical equilibrium.

A quantum Drift-Diffusion model and its use into a hybrid strategy for strongly confined nanostructures

In this paper we derive by an entropy minimization technique a local Quantum Drift-Diffusion (QDD) model that allows to describe with accuracy the transport of electrons in confined nanostructures. The starting point is an effective mass model, obtained by considering the crystal lattice as periodic only in the one dimensional longitudinal direction and keeping an atomistic description of the entire two dimensional cross-section. It consists of a sequence of one dimensional device dependent Schrodinger equations, one for each energy band, in which quantities retaining the effects of the confinement and of the transversal crystal structure are inserted. These quantities are incorporated into the definition of the entropy and consequently the QDD model that we obtain has a peculiar quantum correction that includes the contributions of the different energy bands. Next, in order to simulate the electron transport in a gate-all-around Carbon Nanotube Field Effect Transistor, we propose a spatial hybrid strategy coupling the QDD model in the Source/Drain regions and the Schrodinger equations in the channel. Self-consistent computations are performed coupling the hybrid transport equations with the resolution of a Poisson equation in the whole three dimensional domain.

Existence of global attractor for the one-dimensional bipolar quantum drift-diffusion model

In this paper, we investigate a one-dimensional bipolar quantum drift-diffusion model from semiconductor devices. We mainly show the long-time behavior of solutions to the one-dimensional bipolar quantum drift-diffusion model in a bounded domain. That is, we prove the existence of the global attractor for the solution.

Self-consistent quantum drift-diffusion model for multiple quantum well IMPATT diodes

In this paper, the authors have presented a self-consistent quantum drift-diffusion model for multiple quantum well (MQW) impact avalanche transit time (IMPATT) diodes. The bound states in MQWs have been taken into account by self-consistent solutions of the coupled classical drift-diffusion (CLDD) equations and time-independent Schrodinger equations associated with both the conduction and valence bands. The static and high-frequency properties of MQW DDR IMPATTs based on Si$$\sim $$~3C-SiC material system designed to operate near 94-GHz atmospheric window have been studied by means of the above-mentioned self-consistent solutions of coupled CLDD equations and Schrodinger equations followed by a well-established double-iterative field maximum computational technique. A symmetric and two complementary asymmetric doping profiles for the proposed structures have been taken into account for the present study. The RF power outputs of Si$$\sim $$~3C-SiC MQW DDR IMPATTs near 94 GHz obtained from the simulation are compared with the experimentally obtained power outputs of flat DDR IMPATT diodes based on Si, GaAs, and InP at the same frequency band. It is observed that Si$$\sim $$~3C-SiC MQW DDR IMPATTs are capable of delivering significantly higher RF power compared with IMPATTs based on the above-mentioned materials especially when the doping concentrations of 3C-SiC layers are kept higher than those of the Si layers.