Nonlinear Dynamics of Electrical Conduction in Extrinsic Photoconductors

An extensive experimental and theoretical treatment of the role of nonlinear dynamics in describing the electrical conduction properties of extrinsic photoconductors is given. Experiments were carried out at 4.2 K on ultrapure p-type far-infrared (FIR) Ge photo- conductors with shallow ((TURN)10 meV) acceptor levels and B-ion-implanted ohmic electrical contacts. Measured d.c. current-voltage (I-V) characteristics are strongly nonlinear for moderate electric fields >0.1(, )V/cm and frequently reveal the onset of spontaneous current oscillations for threshold fields (TURN)1 to (TURN)2 V/cm. Small signal admittance and transient response measurements demonstrate that Ge photoconductors behave as damped nonlinear oscillators with damped ringing frequency determined by the FIR illumination level in the range (TURN)50 Hz to (TURN)5 kHz. When driven with an additional sinus- oidal bias V(,ac) cos (2(pi)f(,dr)t) Ge photoconductors are found to exhibit nonlinear dynamical phenomena including a period-doubling cas- cade to chaotic oscillation which produces excess "deterministic" broadband noise with observed noise temperatures as high as (TURN)10('9) K; chaotic behavior is also found in the spontaneous current oscillation with no added a.c. bias. In addition to period doubling, observed complex behavior includes quasi-periodic oscillation, intermittent switching between different modes of oscillation with concomitant excess low-frequency noise, and chaos suppression through frequency locking for large drive amplitudes V(,ac). A hierarchy of theoretical models extending from a generally valid set of partial differential equations to a simple driven two-dimensional dynamical system is presented. Most of the experimental data is surprisingly well described in terms of the simplest model with dynamical vari- ables the average hole concentration and electric field and in which chaotic behavior arises due to the nonlinear field-dependence of rates for capture and impact ionization. Numerical spatially- dependent steady state solutions for the most general model as well as analysis of two-region models indicate the importance of space charge trapped near the injecting contact in determining long time scales observed for transient response (TURN)1 sec. Theoretical criteria are derived for the onset of oscillatory instabilities; photoconductor properties necessary for chaotic behavior and suggestions for the design of more stable devices are discussed.