Stephen W. Teitsworth

Nonlinear transient response of extrinsic Ge far‐infrared photoconductors

Physical mechanisms responsible for nonlinear phenomena and anomalous transient response of cooled extrinsic far‐infrared photoconductors are discussed. A simple model describing carrier generation, trapping, and impact ionization is presented, which describes the transient response on fast time scales 10−3 to 10−4 sec, neglecting changes in space charge. Carrier heating by a dc electric field produces relatively fast, damped oscillatory response to external excitation. A small‐signal analysis of these equations is a test of stability. An analysis of the role of ideal electrical contacts and space charge is also presented. The very slow (∼1 sec) overshoot and transient response commonly observed in cooled extrinsic photoconductors is explained by the dynamics of trapped space charge near the injecting electrical contact. A small‐signal analysis determines the characteristic time constants for these processes, which are typically ∼1 sec. Calculated examples of the recombination and ionization coefficients,...

Theory of localized phonon modes and their effects on electron tunneling in double‐barrier structures

The role of localized phonon modes in phonon‐assisted tunneling in GaAs/AlAs double‐barrier resonant tunneling structures is considered for a range of temperatures and magnetic fields. Phonon modes are calculated using a dielectric continuum model and electron‐phonon Hamiltonians are presented for the most important modes. Formulas for phonon‐assisted tunneling currents are derived that express the inherently three‐dimensional process in a simple one‐dimensional form. It is found that the excess current due to phonon‐assisted tunneling in typical structures is caused primarily by two types of localized modes: confined modes in the well and symmetric interface modes, with interface modes dominating in structures with narrow wells. Current peaks broaden with increasing temperature, and for temperatures ≳20 K the resolution of features due to distinct phonon types is very difficult. The application of a magnetic field parallel to the current flow leads to a complex spectrum of sharp current peaks correspondi...

Theory of periodic and solitary space charge waves in extrinsic semiconductors

Abstract We present a theory of the existence and stability of traveling periodic and solitary space charge wave solutions to a standard rate equation model of electrical conduction in extrinsic semiconductors which includes effects of field-dependent impurity impact ionization. A nondimensional set of equations is presented in which the small parameter β = (dielectric relaxation time) / (characteristic impurity time) ⪢ 1 plays a crucial role for our singular perturbation analysis. For a narrow range of wave velocities a phase plane analysis gives a set of limit cycle orbits corresponding to periodic traveling waves. while for a unique value of wave velocity we find a homoclinic orbit corresponding to a moving solitary space charge wave of the type experimentally observed in p-type germanium. A linear stability analysis reveals all waves to be unstable under current bias on the infinite one-dimensional line. Finally, we conjecture that solitary waves may be stable in samples of finite length under voltage bias.

Symmetry-breaking transitions in networks of nonlinear circuit elements

We investigate a nonlinear circuit consisting of N tunnel diodes in series, which shows close similarities to a semiconductor superlattice or to a neural network. Each tunnel diode is modeled by a three-variable FitzHugh–Nagumo-like system. The tunnel diodes are coupled globally through a load resistor. We find complex bifurcation scenarios with symmetry-breaking transitions that generate multiple fixed points off the synchronization manifold. We show that multiply degenerate zero-eigenvalue bifurcations occur, which lead to multistable current branches, and that these bifurcations are also degenerate with a Hopf bifurcation. These predicted scenarios of multiple branches and degenerate bifurcations are also found experimentally.

Chaotic motion of space charge wave fronts in semiconductors under time-independent voltage bias

A standard drift-diffusion model of space charge wave propagation in semiconductors has been studied numerically and analytically under dc voltage bias. For sufficiently long samples, appropriate contact resistivity, and applied voltage-such that the sample is biased in a regime of negative differential resistance-we find chaos in the propagation of nonlinear fronts (charge monopoles of alternating sign) of electric field. The chaos is always low dimensional, but has a complex spatial structure; this behavior can be interpreted using a finite-dimensional asymptotic model in which the front (charge monopole) positions and the electrical current are the only dynamical variables.

Effects of interface phonon scattering in multiheterointerface structures

In this paper, the commonly used but idealistic formulation of quantized optical‐phonon modes for a heterostructure system with only two heterojunctions (i.e., single quantum‐well structures) is extended to the more realistic case of multiheterointerface structures. By applying the macroscopic dielectric continuum approach, dispersion relations and interaction Hamiltonians for interface‐phonon modes are derived for a double‐barrier structure and scattering rates based on these results are used to determine the range of practical validity of the idealistic model using interaction Hamiltonians appropriate for single quantum wells with infinite barrier widths. It is found that when the dimensions of the structures are larger than approximately 30 A, this simplified description can be applied to multiheterointerface structures in general with reasonable accuracy.

Controllable bistabilities and bifurcations in a photoexcited GaAs/AlAs superlattice

Self-sustained photocurrent oscillations and bifurcation processes have been experimentally investigated in an undoped, photoexcited GaAs/AlAs superlattice by varying the laser intensity. Within a certain range of laser intensities, a bistability of the photocurrent can be observed in the photocurrent versus voltage characteristics. The width of the bistability region can be controlled by varying the laser intensity. In the bistable regime, the photocurrent oscillations disappear via a subcritical Hopf bifurcation with increasing applied voltage. Outside this regime, the transition from oscillations to a static state is a supercritical Hopf bifurcation for lower laser intensities, while at higher laser intensities a homoclinic connection is observed.

Onset of current oscillations in extrinsic semiconductors under DC voltage bias

We present a model which describes the onset of current instabilities and space-charge domains in extrinsic semiconductors (especially p-Ge) under DC voltage bias. Just above the onset voltage for current instability we have found numerically small-amplitude fast oscillations due to the periodic motion of solitary waves which decay before reaching the receiving contact. For slightly larger applied voltages there is an abrupt and slightly hysteretic transition to slower large-amplitude solitary waves similar to those in the Gunn effect. An amplitude equation is derived for long samples which reveals a quasicontinuum of oscillatory modes that become linearly unstable at onset.

Emergence of current branches in a series array of negative differential resistance circuit elements

We study a series array of nonlinear electrical circuit elements that possess negative differential resistance and find that heterogeneity in the element properties leads to the presence of multiple branches in current–voltage curves and a nonuniform distribution of voltages across the elements. An inhomogeneity parameter rmax is introduced to characterize the extent to which the individual element voltages deviate from one another, and it is found to be strongly dependent on the rate of change of applied voltage. Analytical expressions are derived for the dependence of rmax on voltage ramping rate in the limit of fast ramping and are confirmed by direct numerical simulation.

Space Charge Instabilities and Nonlinear Waves in Extrinsic Semiconductors

We review the role of nonlinear space charge waves in the electrical conduction properties of extrinsic semiconductors, particularly ultrapure p-type Ge at low temperature. Recent experimental results can be interpreted using a drift-diffusion rate equation model which includes nonlinear electric field dependencies of the drift velocity and impurity capture and impact ionization rates. Under time-independent (dc) current bias, phase plane analysis of a reduced dynamical system indicates the presence of moving solitary waves which are dynamically unstable. Under dc voltage bias, numerical simulations for finite-length samples and Ohmic boundary conditions reveal dynamically stable solitary waves that travel periodically across the sample. Near the onset of time-dependent behavior we find a Hopf bifurcation to fast small-amplitude current oscillations which are associated with periodic motion of traveling waves that decay before reaching the end of the sample. Numerical estimates of wave speed, wave size and onset behavior are in excellent agreement with available experimental data. Finally, we discuss the sensitivity of dynamical behavior to material parameters such as impurity concentration.