Numerical coupling of thermal-electric network models and energy-transport equations including optoelectronic semiconductor devices

In this work the numerical coupling of thermal and electric network models with model equations for optoelectronic semiconductor devices is presented. Modified nodal analysis (MNA) is applied to model electric networks. Thermal effects are modeled by an accompanying thermal network. Semiconductor devices are modeled by the energy-transport model, that allows for thermal effects. The energy-transport model is expandend to a model for optoelectronic semiconductor devices. The temperature of the crystal lattice of the semiconductor devices is modeled by the heat flow eqaution. The corresponding heat source term is derived under thermodynamical and phenomenological considerations of energy fluxes. The energy-transport model is coupled directly into the network equations and the heat flow equation for the lattice temperature is coupled directly into the accompanying thermal network. The coupled thermal-electric network-device model results in a system of partial differential-algebraic equations (PDAE). Numerical examples are presented for the coupling of network- and one-dimensional semiconductor equations. Hybridized mixed finite elements are applied for the space discretization of the semiconductor equations. Backward difference formluas are applied for time discretization. Thus, positivity of charge carrier densities and continuity of the current density is guaranteed even for the coupled model.

Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

Finite-element discretization of 3D energy-transport equations for semiconductors

In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and demonstrated in detail. We compare these new iterations with a standard method that is complemented by a feature to fit in the current context. A further innovation is the computation of solutions in three-dimensional domains, which are still rare. Special attention is paid to applicability of the 3D simulation tools. The programs are designed to have justifiable working complexity. The simulation results of some models of contemporary semiconductor devices are shown and detailed comments on the results are given. Eventually, we make a prospect on future development and enhancements of the models and of the algorithms that we used.

Uber die elektrische Leitfahigkeit und die thermoelektrische Kraft einiger Schwermetallverbindungen.

Thesis (doctoral)--Universitat Jena.

Phasengleichgewichte, Kristallstrukturen und elektrische Eigenschaften der Verbindungen in ternären Systemen M-M’-{Sn, Sb, Bi}

In dieser Arbeit wurden isotherme Schnitte der ternären Systeme Ti-Fe-Sb, Zr-Fe-Sb und Nb-Fe-Sb bei 800 bzw. 600 °C untersucht. Die Bildung von vier von den Binärbereichen getrennten ternären Verbindungen im System Ti-Fe-Sb, drei im System Zr-Fe-Sb und einer Verbindung im System Nb-Fe-Sb wurde festgestellt bzw. bestätigt. In den ersten zwei Systemen ist die Bildung von festen Lösungen auf der Basis von binären sowie ternären Phasen stark ausgeprägt. Es wurde die Abhängigkeit des Strukturtyps der Laves-Phasen M(Fe???Sb?)??? (M = Ti, Zr, Nb) von der Elektronenkonzentration und den Atomradien der Komponenten gezeigt. 18 isotype Verbindungen M?Me’???X??? (M = Zr, Hf; M’ = Fe, Co, Ni; X = Sn, Sb, Bi) des geordneten Fe?P-Strukturtyps wurden synthetisiert. Die Untersuchungen der Transporteigenschaften dieser Verbindungen belegen deren metallischen Charakter. Es wurde die Bildung der neuen equiatomen Verbindungen in den Systemen Zr-Cu-Sn und Hf-Cu-Sn der Strukturtypen TiNiSi bzw. LiGaGe und der Verbindung HfFe???Sb des TiNiSi-Strukturtyps festgestellt. Die Transporteigenschaften der Reihe von festen Lösungen V???Ti?FeSb wurden untersucht. Es wurde gezeigt, dass die größte Erhöhung des Seebeck-Koeffizienten bei der kleinen Konzentration der vierten Komponente erreicht wird. Der höchste Wert des Seebeck-Koeffizienten (370 ?V/K bei 380 K) wurde für die Zusammensetzung V????Ti????FeSb festgestellt. Die Serie der quaternären Phasen Sc???Nb???NiSn, ZrNiIn???Sb???, HfNiIn???Sb???, ZrCo???Cu???Sn und HfCo???Cu???Sn. zeigt die Möglichkeit der Phasenbildung der Strukturtypen AlLiSi, LiGaGe bzw. TiNiSi auch im Fall der Abwesenheit einer oder beider ternärer Randverbindungen. Für die Verbindung Sc???Nb???NiSn wurden Halbleitereigenschaften festgestellt. Insgesamt wurde die Kristallstruktur der 25 neuen, zum ersten Mal synthetisierten ternären und quaternären Verbindungen bestimmt. Schlüsselwörter: Phasendiagramm, Phasengleichgewicht, Kristallstruktur, intermetallische Verbindungen, Halb-Heusler-Verbindungen, thermoelektrische Materialien, elektrischer Widerstand, Seebeck-Koeffizient.

Wer fischt was? – Gemischte Bodenfischereien und ihre Auswirkungen auf die wichtigsten Nutzfischbestände in der Nordsee

Cod, haddock, whiting, saithe, plaice, sole and Norway lobster are 7 main target species of the demersal mixed fisheries in the North Sea, Skagerrak and Eastern Channel. Gadoids and Norway lobsters are mainly taken in the nor-thern North Sea by towed gears except beam trawls while the flatfish fisheries are conducted in the southern North Sea mainly using beam trawls. Recently, the central North Sea appears less fished by demersal gears. Towed nets including seines and beam trawls equipped with meshes of more than 100 mm resp. more than 80 mm were identified as the main gears effecting the depleted cod and reduced plaice stocks. The saithe sector, using towed nets with meshes of more than110 mm, longlines, gill nets and others, appears to affect the 7 species to a lesser extend. These results support the interim effort limitations by gear types, vessel and month as enforced by the European Commission since 2003. TAC regulations alone are considered inefficient to sustainably harvest stocks by mixed fisheries. A fleet-effort management method is developed estimating the fleets’ effects based on the sum of partial exploitation rates of the species in mixed fisheries weighted by the ratio of the precautionary reference Bpa and the actual SSB size as ecological quality objective. Applying such fleet effort management could result in increased catch possibilities of some stocks by fleets selecting mainly few and non-overexploited stocks while respecting precautionary management constraints in minimum SSB or maximum exploitation rates at the same time.

Vertical CNT-Si photodiode array.

A photodiode consisting of nanopillars of thin-film silicon p-i-n on an array of vertically aligned carbon nanotubes (CNTs) with a noncontinuous cathode electrode is demonstrated. The structure exploits the intrinsic enhancement of the CNTs' electric field, which leads to reduction in the photodiode's operating voltage and response time and enhancement of optical coupling due to better light trapping, as compared with the conventional planar photodiode. These improvements translate to higher resolution and higher frame rate flat-panel imaging systems for a broad range of applications, including computed tomography and particle detection.

Theoretical analysis and experimental study of the space-charge-screening effect in uni-traveling-carrier photodiode

A new optimized structure of an UTC (uni-traveling-carrier) photodiode is developed and epitaxied by metal-organic chemical vapor deposition. We fabricated a UTC photodiode of 30 mu m in diameter. Theoretical simulation based on drift-diffusion model was used to analyze the space-charge-screening effect in UTC photodiode primarily in two aspects: the carrier concentrations and the space electric field. The simulation results were generally in agreement with the experimental data.

High-frequency characterization of packaging network in to-can photodiode modules

A simple method for analyzing the effects of TO packaging network on the high-frequency response of photodiode modules is presented. This method is established based on the relations of the scattering parameters of the packaging network, photodiode chip, and module. It is shown that the results obtained by this method agree well with those obtained by the conventional comparison method. The proposed method is much more convenient since only the electrical domain measurements are required. (C) 2008 Wiley Periodicals, Inc.