Majority Carrier Transistor Based on Voltage-Controlled Thermionic Emission

A new type of transistor is proposed based on gate-controlled charge injection in unipolar semiconductor structures. Its design has some similarity with the recently fabricated triangular barrier diodes but contains an additional input circuit which allows an independent control of the barrier height for thermionic emission. This circuit is provided by a MOS gate on the semiconductor surface. In the proposed device the current flows perpendicular to the semiconductor surface over a planar potential barrier controlled by the gate. The static transconductance characteristics and dynamical response are analyzed. The characteristic response time is limited by the time of flight of electrons across the structure and can be in the picosecond range. The gate voltage required to switch the output current at room temperature is of order 0.2 V. PACS: 85.30. Hi, 73.40. Lq, 85.30.Tv In the present paper a new type of a majority-carrier transistor is proposed which is based on the phenomenon of charge injection in unipolar semiconductor structures. By charge injection we mean the thermionic emission of carriers over a potential barrier when the barrier height is efficiently controlled by an applied voltage. The physical principle involved can be illustrated by analogy with a vacuum-tube diode. In these diodes, for sufficiently large anode voltage, the current saturates at a value determined by the thermionic emission from the cathode. The value of the saturation current exponentially depends on the barrier height for thermal emission, i.e. the work function of the cathode material. Suppose for a moment that we could control the work function with the help of some ingenious input circuit (gate). Moreover, suppose that the barrier height depends linearly on the gate voltage and rapidly adjusts to its variation. The output current would then depend on the gate voltage exponentially and hence the transconductance would be proportional to the current. For a sufficiently large current we would have high values of the transconductance and therefore fast response time with low power-delay product and noise. Needless to say, we do not possess the means of controlling the work function of a metal in the indicated way. However, in semiconductors the above physical idea can be realized. An example of the charge injection device is provided by the IGFET in its subthreshold regime [1]. Indeed the subthreshold drain current is due to the thermionic emission from the source which in this regime plays the role of a cathode. The potential barrier between the source and the channel linearly decreases with the band bending which is controlled by the gate voltage. In the subthreshold regime IGFET may be called a potential-effect rather than a fieldeffect device. By a reasonable definition the field effect consists in the screening of the electric field under the gate by an accumulation or depletion of the mobile charge in the channel. In IGFET this occurs only in the strong inversion regime where the surface carrier density is proportional to the field. Below threshold the electrons in the channel give no significant contribution to the screening and their concentration is determined by the surface potential rather than the field. In the potential-effect (charge injection) mode of FET the surface charge density cr of electrons in the channel depends exponentially on the gate voltage I~, i.e., 152 R.F. Kazarinov and Serge Luryi a o c e x p ( f l V U n ) where f l = q / k T and n is some ideality factor of order unity. For large a the exponential dependence is lost because of the screening effect and a becomes a linear function of Va which can be represented by making n an increasing function of V G. This transition between the charge-injection and the fieldeffect modes is not sharply defined. We shall consider the charge injection mode to terminate when n deteriorates by a factor of two. As can be shown (Appendix A) this occurs at a value of a = a c given by a ~ = k T s o J q t o . , (1) where to~ and ~ox are, respectively, the oxide thickness and permittivity. For o-> a c because of velocity saturation, the output current also becomes a linear function of V a, i.e., the transconductance saturates ~. This means that by going beyond the subthreshold regime one gains no advantage in the intrinsic speed of operation. On the contrary, working in the strong inversion regime one loses considerably in terms of the power-delay product. It is clear that the charge injection mode of operation of FET would be more attractive than the field-effect mode provided that high values of the output current could be achieved in the subthreshold regime. Unfortunately, this is not the case. For tox ~ 500 A and the saturated velocity, v s ~ 107 cm/s the maximum current one can obtain in the charge injection mode of IGFET is of the order of 10 -z A/cm of gate width. Because of the parasitic capacitances the subthreshold current is usually insufficient for fast operation of the device. Another obstacle against using FETs in the subthreshold regime is the uncertainty in the threshold voltage due to processing variations. The difficulty in reducing the voltage swing to several k T / q lies not with the thermal noise as is sometimes incorrectly thought (for a typical transconductance of IGFET the meansquare fluctuation of the gate voltage due to the thermal noise at room temperature is of order 1-2 mV) but with reproducibility of the device parameters. Indeed, the charge injection current depends critically on the height and the shape of the potential barrier which is not controlled accurately because of the uncertainty in the state of the surface. The device we would like to discuss in this work is designed to overcome the above limitations. The crucial feature of the proposed device is the possibility of extending the charge injection regime to currents typical for FETs in strong inversion. This becomes 1 We consider only the case of a short-channel FET. In the long channel device the subthreshold current is limited by the slow diffusion transport through the flat portion of the channel. This further reduces the maximum transconductance achievable in the charge injection regime possible because the troublesome accumulations of carriers under the gate which limits the subthreshold current in FET is circumvented here. In this device the output current flows perpendicular to the semiconductor surface and is controlled by potential barriers which are parallel to the surface. Structures containing such barriers can be fabricated by Molecular Beam Epitaxy (MBE) and by using ion implantation. As is well-known, these methods give much higher resolution than any lithography. For example, the state-of-art MBE technology allows one to obtain modulation-doped semiconductor layers with the resolution of few tens of ]k [2]. Rectifying diodes based on such barriers were recently fabricated by ion implantation [3] and by MBE using either variable-gap [4] or modulation-doped [5] materials. In these diodes the current is due to charge injection [6]. The structures studied in [4, 5] contained built-in potential barriers of triangular shape, either symmetric (isosceles) or asymmetric. The current-voltage characteristics were nearly exponential up to the current densities of several kA/cm 2 in both directions. For asymmetric diodes the ideality factors were different in forward and reverse directions of current which corresponds to rectification. In general, the ideality factor of a potential barrier is determined by its geometry and the doping profile. Depending on the ideality factor a barrier can be either injecting or blocking. Although the first experimental realizations of the triangular barrier (TB) structures appeared very recently [4, 5], conceptually they represent the simplest charge injectors. In a certain sense the TB concept is a generalization of the Schottky barrier. Indeed, in a forward-biased Schottky diode electrons are injected into the metal from the semiconductor. However, because of the large concentration of electrons in the metal, the injected charge produces no tangible effect on the metal conductivity near the boundary. No charge injection into the semiconductor occurs in a reverse-biased Schottky diode (neglecting a small effect of image-force barrier lowering), and current in this case is limited by the thermionic emission over a barrier of fixed height. A similar situation takes place in all-semiconductor analogs of Schottky barriers such as camel diodes [3] and N n heterojunctions [7]. As before, injection takes place only into a quasi-neutral material. TB offers a fundamentally new feature: efficient injection of charge into a high-field region of a semiconductor. It may be worthwhile to note that this feature also opens an attractive possibility of using TB's for making low-noise transit-time devices similar to but more efficient than the baritts [8], as will be discussed elsewhere. In the present paper we propose a way of introducing an input gate circuit in a TB structure which allows an Majority Carrier Transistor 153 independent control of the barrier height. This is an example of a unipolar transistor operating entirely in the charge injection regime. We suggest that in general such devices may.be called TET which stands for gatecontrolled Thermionic Emission Transistor. We expect that the fundamental advantage of the TET devices lies in the exponential transconductance extended to higher values of the output current. The maximum charge injection current in TET is space charge limited. The exponential dependence allows switching this current by a gate voltage of the order of several kT/q. The characteristic time of switching corresponds to the drift of electrons across the structure and can be in the picosecond range. A certain analogy exists between TET and the recently proposed [9] Permeable Base Transistor (PBT) in which a grid of metal electrodes is embedded in the semiconductor between the source and the drain of the device. Indeed, in the case of a low-doped base the current in PBT is of thermonic nature over the barrier formed by the controlling electrodes. The main difference is that in TET there exists a built-in triangular barrier which allows us to transfer the controlling electrodes to the surface of the semiconductor. The proposed design of TET is introduced in Sect. 1. In the same section we describe the physical principles of the device operation, formulate the requirements on its geometry, and discuss the expected characteristics of the device and their limitations. Some of the conclusions in Sect. 1 are presented without proof, on an intuitive level. The rigorous mathematical treatment is given in Sect. 2 where we calculate the transconductance and the characteristic response time of the device. In Sect. 3 we discuss the possible fabrication of TET and summarize our conclusions. 1. Qualitative Description of the Device The proposed version of the charge injection or Thermionic Emission Transistor (TET) is shown in Fig. 1. The device contains an i layer grown epitaxially on an n § substrate. In the process of growth by MBE a p§ layer is built in the i layer by modulation doping. The thickness 6 of the p§ layer is assumed to be infinitesimal compared to that of the i layer. In practice, 6 can be as small as a few tens of A. The acceptors in the p § layer are completely ionized and form a sheet of negative charge which gives rise to a triangular potential barrier (TB) similar to those studied in [5, 6]. The n + substrate forms one of the terminals of TET, which will be called the cathode. The other two terminals, the anode and the gate are arranged in a periodic pattern of stripes on the surface. Every other stripe represents a metallized n + contact or a silicide ),NO r .:,:+:.:.~:.: ilii!i ili ::::x-:.;:::;:;:x.:.;:::.,.;,:.:-:-::;:;:;,:iii!i!! iliiiill :~:~:!: