Computational electromagnetics for nanowire solar cells

This review article provides an overview of various novel nanowire array solar cells and highlights the aspects of electromagnetic simulations that are a valuable tool for understanding the optical processes leading to their distinct properties. As the computational methods commonly used for the task are well established, we focus on the question how numerical modeling can be used to assess the performance of a design and reveal the working principle of the devices. We conclude that scientific literature identifies numerical simulations as paramount for design and interpretation of experimental dat

tdkp/AQUA: Unified modeling of electroluminescence in nanostructures

This article summarizes the capabilities of the optoelectronic simulation framework tdkp/AQUA aimed at the description of electroluminescence in semiconductor nanostructures such as light-emitting diodes. tdkp is a stand-alone finite-element software able to accurately calculate strain, built-in fields due to spontaneous and piezoelectric polarization, bound quantum states using k · p theory, gain and luminescence spectra in zero- to three-dimensional structures. AQUA calculates transport through nanostructures using a model which accounts for the distinct behaviour of carriers confined to active regions and unconfined carriers. Furthermore, it computes electroluminescence spectra via a self-consistent coupling of the confined carriers to quantum-mechanical calculations using tdkp. Two examples are presented which highlight the versatility and generality of the developed framewor

Reliable k ⋅ p band structure calculation for nanostructures using finite elements

The k⋅p envelope function method is a popular tool for the study of electronic properties of III-V nanostructures. The equations are usually transferred to real-space and solved using standard numerical techniques. The powerful and flexible finite element method was seldom employed due to problems with spurious solutions. The method would be favorable for the calculation of electronic properties of large strained nanostructures as it allows a flexible representation of complex geometries. In this paper, we show our consistent implementation of the k⋅p envelope equations for nanostructures of any dimensionality. By including Burt-Foreman operator ordering and ensuring the ellipticity of the equations, we are able to calculate reliable and spurious solution free subband structures for the standard k⋅p 4×4, 6×6 and 8×8 models for zinc-blende and wurtzite crystals. We further show how to consistently include strain effects up to second order by means of the Pikus-Bir transformation. Finally, we analyze the performance of our implementation using benchmark example

Unified simulation of transport and luminescence inoptoelectronic nanostructures

Computer simulation of microscopic transport and light emission in semiconductor nanostructures is often restricted to an isolated system of a single quantum well, wire or dot. In this work we report on the development of a simulator for devices with various kinds of nanostructures which exhibit quantization in different dimensionalities. Our approach is based upon the partition of the carrier densities within each quantization region into bound and unbound populations. A bound carrier is treated fully coherent in the directions of confinement, whereas it is assumed to be totally incoherent with a motion driven by classical drift and diffusion in the remaining directions. Coupling of the populations takes place through electrostatics and carrier capture. We illustrate the applicability of our approach with a well-wire structur

Harmonic balance analysis for semiconductor lasers under large-signal modulation

The dynamic characteristics of an edge-emitting laser under large-signal modulation are analyzed in the frequency domain using a harmonic balance method on device level. The simulations reveal the nonlinearities of the carrier dynamics in the quantum well region which strongly influence the optical power in the higher harmonic

Single-mode performance analysis for vertical-cavity surface-emitting lasers

In this work, the simulation of the single-mode stability in vertical-cavity surface-emitting lasers (VCSELs) is presented using a microscopic electro-opto-thermal model. Experimental data for oxide-confined VCSELs emitting at 850 nm with different contact metal designs are also available. It is shown that detailed models for the optical losses in the cavity consisting of outcoupling and absorption are required in order to explain the experiments. The role of cavity losses and spatial hole burning in the nonlinear electro-opto-thermal simulation framework is discussed in a quantitative manne

Operator ordering, ellipticity and spurious solutions in k · p calculations of III-nitride nanostructures

We analyze the ellipticity of the standard k · p wurtzite model for the symmetrized and the Burt-Foreman operator ordering. We find that for certain situations the symmetrized Hamiltonian is unstable, leads to unplausible results and can cause spurious solutions. We show that the operator ordering in wurtzite must be completely asymmetric to be stable. The asymmetric operator ordering is elliptic and consequently no spurious solutions are obtained. Therefore we recommend the use of a complete asymmetric operator ordering for nitride device simulatio

Investigation of the Purcell effect in photonic crystal cavities with a 3D Finite Element Maxwell Solver

Photonic crystal cavities facilitate novel applications demanding the efficient emission of incoherent light. This unique property arises when combining a relatively high quality factor of the cavity modes with a tight spatial constriction of the modes. While spontaneous emission is desired in these applications the stimulated emission must be kept low. A measure for the spontaneous emission enhancement is the local density of optical states (LDOS). Due to the complicated three dimensional geometry of photonic crystal cavities the LDOS quantity has to be computed numerically. In this work, we present the computation of the LDOS by means of a 3D Finite Element (FE) Maxwell Solver. The solver applies a sophisticated symmetry handling to reduce the problem size and provides perfectly matched layers to simulate open boundaries. Different photonic crystal cavity designs have been investigated for their spontaneous emission enhancement by means of this FE solver. The simulation results have been compared to photoluminescence characterizations of fabricated cavities. The excellent agreement of simulations and characterizations results confirms the performance and the accuracy of the 3D FE Maxwell Solve

Investigation of the Purcell effect in photonic crystal cavities with a 3D Finite Element Maxwell Solver

Photonic crystal cavities facilitate novel applications demanding the efficient emission of incoherent light. This unique property arises when combining a relatively high quality factor of the cavity modes with a tight spatial constriction of the modes. While spontaneous emission is desired in these applications the stimulated emission must be kept low. A measure for the spontaneous emission enhancement is the local density of optical states (LDOS). Due to the complicated three dimensional geometry of photonic crystal cavities the LDOS quantity has to be computed numerically. In this work, we present the computation of the LDOS by means of a 3D Finite Element (FE) Maxwell Solver. The solver applies a sophisticated symmetry handling to reduce the problem size and provides perfectly matched layers to simulate open boundaries. Different photonic crystal cavity designs have been investigated for their spontaneous emission enhancement by means of this FE solver. The simulation results have been compared to photoluminescence characterizations of fabricated cavities. The excellent agreement of simulations and characterizations results confirms the performance and the accuracy of the 3D FE Maxwell Solve

Computational study of an InGaN/GaN nanocolumn light-emitting diode

A comprehensive three-dimensional analysis of the operation of an In0.4Ga0.6N/GaN nanocolumn light-emitting diode is presented. Focus is put on the investigation of the nature and location of the emitting states. Calculations of strain and polarization-induced internal fields show that the strong lateral dependence of the potential gives rise to states confined to the periphery and to the center of the nanocolumn. However, lateral confinement of states near the column center is weak such that a quantum-well-like treatment of the remaining bound states seems appropriate where coherence is lost in the lateral directions. Within this picture, a coupled and self-consistent three-dimensional simulation of carrier transport and luminescence is presented, thus accounting for screening and lateral transport effects. Results are compared to a planar quantum-well device