PHYSICAL REVIEW B VOLUME 43, NUMBER 3 15 JANUARY 1991-II Quasibaliistic electronic transport in a tunneling hot-electron-transfer amplifier James Leo and Simon J. Bending* Max Pla-nck Ins-titut fu rF'estkorperforschung, Heisenbergstrasse 1, 7000 Stuttgart 80, Federal Republic of Germany (Received 4 June 1990; revised manuscript received 20 August 1990) The operation of a tunneling hot-electron-transfer amplifier has been simulated by treating it as a double-barrier diode where the field across each barrier can be varied independently. Current How is evaluated by calculating the transmission coefficient of the entire structure starting from a coherent-transport framework and then by phenomenologically introducing both elastic and inelas- tic scattering of the electrons in the base region between the two barriers. By directly comparing the numerical results with those obtained experimentally, we have been able to establish an upper bound of the mean free path of electrons in the base of around 45 nm. I. INTRODUCTION As growth and processing techniques of semiconductor devices have improved, the size of structures has reduced to the scale of the inelastic mean free path (MFP) of the carriers traveling through them. When the MFP is of the order of the device length it is said that the electrons are able to travel ballistically and the device is in the meso- scopic regime. A device that has been designed to exploit this regime is the tunneling hot-electron-transfer amplifier (THETA). ' A sketch of the conduction band of a common example is shown in Fig. l. It consists of lay- ers of two semiconductors, GaAs and Al Ga& As. The Al Ga& As forms potential barriers to the movement of electrons in the device whose heights depend on x, the AlAs mole fraction. In practice the device has three highly doped GaAs electrodes that are independently contacted. The electrons originate at the emitter on the left-hand side in Fig. 1, where they are considered to be freely moving and occupy energy states up to the Fermi energy. They then tunnel through the emitter barrier and are collimated into a quasimonoenergetic beam. The reason for this is that the energy distribution of the elec- trons after they have tunneled through the barrier is a convolution of the transmission coe%cient of the emitter barrier and the Fermi-Dirac distribution. The former in- creases exponentially with increasing energy while the latter decreases exponentially. The convolution, there- fore, is strongly peaked. By applying a bias across the emitter barrier, the elec- trons are tunnel injected into the base region of the de- vice with excess energy, i.e. , they are "hot. " These elec- trons traverse the base before impinging on the second barrier called the collector barrier. The collector barrier is graded at the base-collector interface so that, when a positive bias is applied across it, the position of the highest point of the barrier can be lowered, thus provid- ing a spectrometer action in both bias directions. By pos- itively and negatively biasing the collector barrier in this way, the energy distribution of collected electrons can be probed. If this distribution matches the calculated inject- EMITTER B&SE COLLECTOR VeE II I I I I I I I I I I I I I I I I I I I = 120 A 245 rnev 98 rnev I II I I I I I I ll 300 ~ I= I I 100 A g00 A 245 meV FIG. 1. Sketch of the conduction-band edge of a common THETA. The device parameters used for the calculations have been included. ed distribution, then the electrons have not lost a measur- able amount of energy and therefore have traversed the device ballistically. Indeed, with this definition it has been shown that about 50% of the collected current in a THETA is ballistic. ' It also is believed that the grading reduces the amount of reAection from the base-collector interface. In two previous publication, ' electron transport in these devices has been investigated using Monte Carlo simulation, which included scattering effects due to pho- nons, ionized impurities, and plasmons. Two further sources of scattering that were not considered, though, were those due to single-particle, electron-electron in- teractions and interface roughness. Both of these types of scattering differ from phonon and plasmon scattering in that the amount of energy the scattered electrons can lose is not quantized and therefore the energy of the scattered electrons can be continuously distributed. Furthermore, as the Monte Carlo method describes the electrons within a particlelike picture, it does not fully describe reso- nances due to the interference of coherent electron wave functions. It is this feature of transport in mesoscopic structures that we shall address in this paper, in stark contrast to the goals of Refs. 2 and 3. We shall start 43 2187 1991 The American Physical Society