Query: A coupled drift-diffusion model for quantum semiconductor device simulations

Candidate papers:

abstract: In this paper, we derive a coupled Schrodinger drift diffusion self consistent stationary model for quantum semiconductor device simulations. The device is decomposed into a quantum zone (where quantum effects are expected to be large) and a classical zone (where they are supposed negligible) The Schrodinger equation is solved for scattering states in the quantum zone while a drift diffusion model is used in the classical zone. The two models are coupled through interface conditions which are derived from those of N. Ben Abdallah (1998, J. Star. Phys. 90, 627) through a diffusion approximation. Numerical tests in the case of a resonant tunneling diode illustrate the validity of the method.
author_names: Pierre Degond

Asma El Ayyadi
title: A coupled Schrodinger drift diffusion model for quantum semiconductor device simulations
year: 2002

abstract: We consider a one dimensional coupled stationary Schrodinger drift diffusion model for quantum semiconductor device simulations. The device domain is decomposed into a part with large quantum effects (quantum zone) and a part where quantum effects are negligible (classical zone) We give boundary conditions at the classic quantum interface which are current preserving. Collisions within the quantum zone are introduced via a Pauli master equation. To illustrate the validity we apply the model to three resonant tunneling diodes.
author_names: Michael Baro

Naoufel Ben Abdallah

Pierre Degond

Asma El Ayyadi
title: A 1D coupled Schrodinger drift diffusion model including collisions
year: 2005

abstract: We propose a design for a semiconductor structure emitting broadband light in the infrared, based on InAsquantum dots(QDs) embedded into a metamorphic step graded InxGa1 xAs buffer. We developed a model to calculate the metamorphic QD energy levels based on the realistic QD parameters and on the strain dependent material properties; we validated the results of simulations by comparison with the experimental values. On this basis, we designed a p i n heterostructure with a graded index profile toward the realization of an electrically pumped guided wave device. This has been done by adding layers where QDs are embedded in InxAlyGa1 x yAs layers, to obtain a symmetric structure from a band profile point of view. To assess the room temperature electro luminescenceemission spectrum under realistic electrical injection conditions, we performed device level simulations based on a coupled drift diffusion and QD rate equation model. On the basis of the device simulation results, we conclude that the present proposal is a viable option to realize broadband light emitting devices.
author_names: Luca Seravalli

Mariangela Gioannini

Federica Cappelluti

Fabio Sacconi

Giovanna Trevisi

P Frigeri
title: Broadband light sources based on InAs/InGaAs metamorphic quantum dots
year: 2016

abstract: We propose a design for a semiconductor structure emitting broadband light in the infrared, based on InAs quantum dots (QDs) embedded into a metamorphic 4 step graded InxGa1 xAs buffer with x 0.10, 0.20, 0.30, 0.40. We developed a model to calculate metamorphic QD energy levels based on realistic QD parameters and on strain dependent material properties: results of simulations were validated against experimental values. By simulating the broadband metamorphic structure, we demonstrated that its light emission can cover the whole 1.0 1.7 mm range with a bandwidth of 550 nm at 10K. The emission spectrum was then assessed under realistic electrical injection conditions, at room temperature, through device level simulations based on a coupled drift diffusion and QD dynamics model. As metamorphic QD devices have been already fabricated with satisfying performances we believe that this proposal is a viable option to realize broader band light emitting devices such as superluminescent diodes.
author_names: Luca Seravalli

Mariangela Gioannini

Federica Cappelluti

Fabio Sacconi

Giovanna Trevisi

P Frigeri
title: Modelling of broadband light sources based on InAs INxGA1 xAS metamorphic quantum dots
year: 2015

abstract: Our simulations on InP based edge emitting RW lasers have been essentially based on the drift diffusion approach. The model comprises a self consistent description of the electronic properties and the optical field under modifications caused by heating processes. Calculations on the device performance have been done by means of the semiconductor device simulation package TESCA with energy transport equation. The quantum confined carriers are described by a (8X8) kp Hamiltonian, self consistently coupled to the Poisson equation and exchange correlation potentials to give a guess for Coulomb effects. Using the package KPLIB for band structure calculations, modifications of the optical gain, caused by the presence of the strained multi quantum wells, have been simulated and will be discussed.
author_names: Uwe Bandelow

Herbert Gajewski

Hans-Christoph Kaiser
title: Modeling combined effects of carrier injection, photon dynamics, and heating in strained multiple quantum well lasers
venue: Photonics West Optoelectronic Materials and Devices
year: 2000

abstract: Abstract In this study, we consider the three dimensional quantum bipolar drift diffusion model arising from the semiconductor device simulation, which consists of the coupled nonlinear fourth order parabolic equation and Poisson equation. Based on the results of the self similar stability for the one dimensional quantum bipolar drift diffusion equation, we show the stability of planar self similar wave for the three dimensional quantum bipolar drift diffusion model. Using the energy methods, we present the global existence of smooth solutions for the initial value problem of the three dimensional quantum bipolar drift diffusion equation when the initial data are close to the planar self similar wave. We also show that in large time, the solution of the three dimensional quantum bipolar drift diffusion equations tends to the planar self similar wave, at an algebraic time decay rate.
author_names: Fang Liu

Yeping Li
title: Large time behavior of solution to the three dimensional quantum bipolar drift diffusion model from semiconductors
year: 2020

abstract: The device scale simulation of electrically driven quantum light sources based on semiconductor quantum dots requires a combination of the (classical) semiconductor device equations with cavity quantum electrodynamics. In this paper, we extend our previously developed hybrid quantum classical model system where we have coupled the drift diffusion system with a Lindblad type quantum master equation by including a self consistent Schrodinger Poisson problem. The latter describes the (quasi )bound states of the quantum dot carriers. The extended model allows to describe the bias dependency of the emission spectrum due to the quantum confined Stark effect.
author_names: Markus Kantner
title: Simulation of quantum light sources using the self consistently coupled Schrodinger Poisson Drift Diffusion Lindblad syste
venue: 2019 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD)
year: 2019

abstract: 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 O, whereas, the same is much lower (0.27 O) 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.
author_names: Abhijit Kundu

Maitreyi Ray Kanjilal

Moumita Mukherjee
title: Cubic versus hexagonal SiC vertical pin SPST/SPDT/SPMT switches for MMW communication systems: a modified quantum drift diffusion model for switching characteristics analysis
venue: Microsystem Technologies
year: 2019

abstract: The device scale simulation of electrically driven solid state quantum light emitters, such as single photon sources and nanolasers based on semiconductor quantum dots, requires a comprehensive modeling approach, that combines classical device physics with cavity quantum electrodynamics. In a previous work, we have self consistently coupled the semi classical drift diffusion system with a Markovian quantum master equation in Lindblad form to describe (i) the spatially resolved current injection into a quantum dot embedded within a semiconductor device and (ii) the fully quantum mechanical light matter interaction in the coupled quantum dot photon system out of one box. In this paper, we extend our hybrid quantum classical modeling approach by including a Schroedinger Poisson problem to account for energy shifts of the quantum dot carriers in response to modifications of its macroscopic environment (e.g. quantum confined Stark effect due to the diode's internal electric field and plasma screening) The approach is demonstrated by simulations of a single photon emitting diode.
author_names: Markus Kantner
title: Hybrid modeling of quantum light emitting diodes: self consistent coupling of drift diffusion, Schrodinger Poisson, and quantum master equations
venue: OPTO
year: 2019

abstract: Electrons and holes injected into a semiconductor heterostructure containing quantum wells are captured with a finite time. We show theoretically that this very fact can cause a considerable excess contribution to the series resistivity and this is one of the main limiting factors to higher efficiency for GaAs based high power lasers. The theory combines a standard microscopic based model for the capture escape processes in the quantum well with a drift diffusion description of current flow outside the quantum well. Simulations of five GaAs based devices differing in their Al content reveal the root cause of the unexpected and until now unexplained increase of the series resistance with decreasing heat sink temperature measured recently. The finite capture time results in resistances in excess of the bulk layer resistances (decreasing with increasing temperature) from 1 mO up to 30 mO in good agreement with experiment.
author_names: Anisuzzaman Boni

Hans-Juergen Wuensche

Hans Wenzel

P A Crump
title: Impact of the capture time on the series resistance of quantum well diode lasers
year: 2020