Ali Abou-Elnour

A comparison between different numerical methods used to solve Poisson’s and Schroedinger’s equations in semiconductor heterostructures

A comparison between different numerical methods which are used to solve Poisson’s and Schroedinger’s equations in semiconductor heterostructures is presented. Considering Schroedinger’s equation, both the Rayleigh–Ritz method and the finite difference method are examined. The accuracy and the computational speed are investigated as a function of both the mesh size and the number of Rayleigh–Ritz functions and the numerical results are compared with analytical solutions for special cases. To solve Poisson’s equation, direct and iterative methods are implemented and the advantages and limitations of each method are discussed. The previous methods are used to solve Poisson’s and Schroedinger’s equations self‐consistently in typical heterostructures to obtain the wave functions, the carrier distribution, and the subband energies.

An efficient and accurate self-consistent calculation of electronic states in modulation doped heterostructures

Abstract The energy levels, the carrier concentration, and the conduction band profile in a modulation doped heterostructure are obtained by using an efficient self-consistent calculation of Poissons and Schroedingers equations. Schroedingers equation is solved by using a variational technique to overcome the limitations of previous models which are arising from mesh size and discretization. The method is applied to characterize a modulation doped AlGaAs/GaAs single well and a pseudomorphic AlGaAs/InGaAs/GaAs structure. Advantages and limitations of the new method are finally discussed.

Closed-form calculations of two-dimensional scattering rates in semiconductor heterostructures

Abstract An efficient and accurate method is investigated to characterize the electron transport in a two-dimensional modulation doped heterostructure. Schroedingers equation is solved by using a variational method to obtain the wave functions in closed form. The subband energies, the corresponding wave functions and the carrier concentration are obtained by solving Poissons and Schroedingers equations self-consistently. The closed form of the wave functions is then used to calculate the important two-dimensional scattering rates. In order to illustrate the efficiency and the accuracy of our model, the results are compared with those obtained from the conventional self-consistent finite difference scheme. The present model is proved to be more efficient and less complicated when used in material and device characterization.

Determination of Electronic States in Low Dimensional Heterostructure and Quantum Wire Devices

An efficient variational technique is applied to solve Schrodinger’s equation in two dimensions. This model is then self-consistently used with a twodimensional Poisson’s equation solver to determine the electronic states inside low dimensional heterostructure and quantum wire devices. Finally, the advantages and limitations of the present model are discussed.

A Rigorous Model of Tunneling and Thermionic Currents in Microwave HFETs

A new model is presented to simultaneously calculate both tunneling and thermionic currents over the heterojunction and over the Schottky barrier (metal-semiconductor contact). The energy band diagram, the subband energies, and the corresponding wave functions are obtained by self-consistent solution of Poissons and Schroedingers equations (SCSPS). The differences between the quasi Fermi levels at the heterojunction and at the metal contact which control the currents are accurately obtained by equating the total current over the heterojunction with the total current over the Schottky barrier. The model is applied to calculate the gate current in typical hetero-FET structures and the obtained results are compared with experimental data.

Influence of alloy composition on the noise behavior of hetero-FETs in millimeter-wave frequency range

The noise behavior of millimeter-wave Hetero-FETs is investigated by using a rigorous physical simulator which takes into account non-stationary transport properties and quantization effects to allow better understanding of the origins of the noise fluctuations. The model is applied to determine the effects of Al composition on the 2DEG transport properties and consequently on the noise behavior of Hetero-FETs. The results are compared to those for GaAs MESFETs with 3DEG channel and possibilities to suppress the dominant noise sources at the different frequencies of operation are finally discussed.

Determination of the influence of doping profile on the performance of mm-wave gunn elements by using an efficient physical simulator

The influence of the doping profile on the performance of mm-wave Gunn elements is studied by applying an enhanced hydrodynamic model (HDM). According to intensive simulation results, any increase in efficiency must by attributed to a changed domain dynamic and not to a more favorable temperature distribution what had been supposed in experimental works. The results further demonstrate how to optimize the doping profile and thus give hints for an optimum design.

An efficient physical device-circuit simulator and its application to accurate design of millimeter wave oscillators

A rigorous one-dimensional physical device-circuit simulator is developed to accurately determine the transport properties and the electrical performance of semiconductor devices embedded into a passive circuit. The simulator is well suited to study the effects of device geometry, doping level, bias voltage, and mounting structure on the performance and to compare the accuracy and the computational efficiency of different physical models. The model is applied to determine the application limits of the drift-diffusion and hydrodynamic models when they are used to characterize the operation and to optimize the structure of cm- and mm-wave oscillators with two-terminal devices, and to produce a set of design curves which indicate the performance limits of different devices under various operating conditions.

D-band operation of a second harmonic GaAs gunn oscillator

A GaAs second harmonic Gunn oscillator for D-band applications is proposed. The doping structure of the active device has been optimized using Monte-Carlo and hydrodynamic models. The load impedance characteristic of a resonant mounting structure in a WR06 waveguide has been consistently taken into account. At sufficiently low load resistances and reactances, output powers of the order of 20–50 mW should be obtainable around 140 GHz under realistic thermal conditions.

A comparison between the noise performance of millimeter wave MESFETs and Hetero-FETs by using a two-dimensional physical simulator

A novel two-dimensional physical simulator is investigated to accurately determine the non stationary transport properties and the quantization effects in subhalf-micrometer gate length FETs. Due to the microscopic nature of our simulator, it is well suited to study the effects of device geometry, doping level, bias voltage, and physical phenomena on the device performance. As an example, the model is applied to compare the noise behavior of millimeter wave MESFETs and Hetero-FETs and to determine the physical phenomena which are dominating their performance.