In this chapter, the effect of an external static electric field is described within the BenDa niel-Duke model for the conduction band, introduced in the previous chapter. In Section 4

1. Introduction

The Double Barrier Resonant-Tunneling Diode (DBRTD for short) is a new device with interesting electronical and physical features. Its nonlinear behavior with negative differential resistance as well as possible bistable behaviour and. hysteresis gives it very interesting potential applications [1], [2], [3]. The physics is interesting as its functional properties are directly based on, and in fact demonstrate fundamental quantum mechanical phenomena, a characteristic it has in common with other mesoscopic systems [4].

In this paper we set ourselves two aims. Firstly, we will give a description of the DBRTD's operation in the context of a fully quantum mechanical treatment, implying coherent wave propagation and the selfconsistent electronic potential. Secondly, we will compare our model to other approaches, especially to those not assuming wave coherence, but using the alternative mechanism of sequential tunneling. In this respect we mention the work by Luryi [5], Goldman et al. [6], and Sheard and Toombs [7]. Important point of comparison will be the intrinsic bistability in the I-V-characteristic of the DBRTD.
Let us start by giving a short description of the DBRTD: the diode consists of several layers of different semiconducting materials (often GaAs and AlGaAs), doped and undoped ones. We will concentrate on the five central undoped layers: the well sandwiched between two barriers, in turn surrounded by two so-called spacer-layers, in all about 200 A long. All other layers in front of (behind) this central part are conceived of as an ideal reservoir (sink) of thermally distributed


Fig.1 (a) Layer structure of the DBRTD. (b) Schematic diagram of the corresponding electron potential energy under the application of an external bias voltage (dashed line); modelling of the conduction hand edge: in each layer the potential energy is replaced by its average value (solid line)

particles (see Fig. la). This conceptual description or electrical conduction associated with coherent tunneling or particles between reservoirs was developed by Landauer [8] and Buttiker et al [9].

Because of the difference in bandgap energy between the two semiconducting materials, electrons experience a transition from one layer to another as a sudden change in their potential energy (see Fig. lb). We assume an applied bias voltage to this structure to have three effects: first, the reservoir is filled up to a certain Fermi level (or, at non-zero temperature, in accordance with the Fermi-Dirac distribution). This defines the electronic input into the structure. Secondly, the build-up of electronic charge in the undoped layers implies electrostatic potentials across the barriers (see Fig. lb). Finally, a current I will result, flowing perpendicular to the barrier layers.
The I- curve of the DBRTD exhibits its characteristic features: non-linearity, negative differential resistance, and a certain interval of where every corresponds to more than one current value. It is this I- curve that we want our model to explain.
Assuming wave coherence means considering the DBRTD a Hamiltonian system, described by an ordinary ScbrOdinger equation. With a perfect layer structure, the motion perpendicular to the layers can be separated from the motion parallel to the layers. Thus, we can use a 1D tunneling approach (section 2), restoring the three-dimensionality when calculating charge and current densities (section 3). The interdependence of the electron potential and the electron density necessitates a selfconsistent solution (section 4), which is worked out numerically for a symmetric and an asymmetric structure (section 5).