A. N. Khondker

Transmission line analogy of resonance tunneling phenomena: The generalized impedance concept

This paper presents a simple yet accurate method for solving the Schrodinger equation to calculate the quantum mechanical transmission probability across arbitrary potential barriers. It is based on the concept of wave impedance analogous to transmission line theory. The quantum mechanical transmission probability in a resonant tunneling device can be easily calculated using this method.

Calculation of the traversal time in resonant tunneling devices

Transmission line techniques are used to calculate the traversal time of electrons in resonant tunneling structures. It is suggested that the real part of the quantum‐mechanical wave impedance Re[(2ℏ/m*)ψ’/ψ], at resonance, can be used to calculate the electron traversal time. Furthermore, it is shown that for symmetric structures the lifetime and evolution time of electrons are the same. The sum of the lifetime and the evolution time equals the electron traversal time. Traversal time variations for the asymmetric well are discussed.

An efficient technique to calculate the normalized wave functions in arbitrary one-dimensional quantum well structures

We present a simple yet unified technique to calculate: (i) the eigenenergies and the normalized eigenstates in quantum wells, (ii) the energy broadened spatially varying density-of-states in leaky quantum wells where the particle lifetime is finite, and (iii) the energy position dependent density-of-states in quantum wells where phase-breaking and/or inelastic scattering processes are present. The method is based on the Green’s function formalism. The method is particularly attractive in numerical calculations of multibarrier devices in which the estimation of the self-consistent potential is desired.

A model for PolySilicon MOSFET's

A model is developed to describe the high value of threshold voltage and the low value of channel mobility observed in n-channel polysilicon (poly-Si) MOSFETs. The model takes into account charge-coupling between the gate and grain boundary traps. The charge-coupling appears as an image charge in Poissons equation and the charge neutrality equation. Finally, a drift-diffusion mode of conduction is used to describe the channel conductance beyond the strong inversion threshold.

Quantum transport in mesoscopic devices: Current conduction in quantum wire structures

A theory based on the Keldysh formalism is developed to study carrier transport in inhomogeneous quantum effects devices that operate at higher temperatures under large applied bias voltages. The scattering rates due to dissipative processes within devices are estimated self-consistently from the nonequilibrium particle density and the density of states. Unlike many existing models, the present model guarantees the conservation of the current and the number of particles in active devices. We have applied our model to study carrier transport in GaAs quantum wire devices and report several interesting results. It is found that a sudden increase in the polar-optical phonon scattering rates may result in a negative current at some critical energies when the bias voltage is positive. At low temperatures, the conductance of quantum wires shows quantized steps as a function of the applied bias voltage. Moreover, a negative differential conductance (NDC) is observed in the current–voltage characteristics of devic...

A model for resonant and sequential tunneling in the presence of scattering

In this paper we present a model to calculate the coherent and the sequential tunneling (or incoherent) transmission probabilities across a double‐barrier heterojunction in the presence of scattering centers. The model, based on the previously reported transmission‐line technique, provides a simple, yet powerful method to integrate these two different tunneling mechanisms. It is shown that if the scattering processes are taken into account, the coherent tunneling mechanism is strongly affected near the resonant peaks. On the other hand, the incoherent tunneling process, which arises due to the presence of scattering centers, dominates as the scattering lifetime is decreased. Effects of the scattering process on the current‐voltage characteristics are investigated.

Self-consistent analysis in the presence of phase-randomizing processes for double-barrier structures

We present a model, based on the nonequilibrium retarded Green’s function method of the quantum kinetic (Keldysh) theory, that describes carrier transport in three‐dimensional quantum structures with translational invariance in the transverse direction. The transport equations include inelastic phase‐breaking processes and describe the transport of both the coherent and incoherent electrons within the same framework with a set of first‐order coupled linear differential equations. These equations can be solved without resorting to evaluating the Green’s function. The model accounts for local space charges in Poisson’s equation and is suitable for modeling the steady‐state current‐voltage characteristics of double‐barrier structures. A realistic model for these devices should include the effects of inelastic processes and space charge simultaneously. However, as an illustration, we present numerical results for double‐barrier devices by assuming that the electrons undergo elastic phase‐breaking collisions o...

An efficient self‐consistent model for resonant tunneling structures

We present an efficient self‐consistent current‐voltage model for the double‐barrier resonant tunneling (RT) structure. In the existing self‐consistent models, normalized wave functions are used to describe the distribution of space charge in the RT structure. The present model, instead, uses the concept of group velocities for electrons. The use of group velocities for electrons simplifies the model by eliminating the need for the calculation of normalized wave functions.

Envelope function description of double‐heterojunction quantum wells

An envelope function model is used to investigate properties of the two‐dimensional electron gas (2DEG) confined in a double‐heterojunction quantum well formed by the AlGaAs/InGaAs/GaAs system. This type of well has been used in the pseudomorphic modulation‐doped field‐effect transistor (MODFET). The position of the Fermi level and the average distance of the carriers in the well have been calculated as a function of the 2DEG concentration ns. Results presented in this paper may be used to model the I‐V and C‐V characteristics of pseudomorphic MODFETs. Furthermore, these results confirm a better containment property of carriers in this type of well compared to that formed at the AlGaAs/GaAs system.

ON THE CONDUCTANCE AND THE CONDUCTIVITY OF DISORDERED QUANTUM WIRES

We present a model, based on the Keldysh formalism, to study the transport properties of disordered quantum wires of finite lengths. Unlike the phenomenological models, we estimate the electron in‐ and out‐scattering rates using the local density of states of various transverse modes that allow electrons to change their directions. The formulation, therefore, guarantees the conservation of both the charge and the current at any cross section of the device. Using the model we calculate the average two‐probe conductances of quantum wires that are terminated at nonideal contacts.