Circuit simulation through coordinated EM and solid-state device numerical analyses

Abstract

A high-frequency circuit simulation technique is presented, based on the selfconsistent, coordinated solution of Maxwell’s equation and semiconductor device equations. This makes it possible to evaluate signal propagation along arbitrary network, including non-linear devices. Distributed device simulation is exploited, allowing actual fabrication-technology parameters to be taken into account. Charge-transport properties of GaAs are considered, and the simulation of a Gunn-diode based oscillator, working in the 20 GHz range, is illustrated. Introduction GaAs Gunn devices are customarily used for the implementation of microwave and millimeter-wave oscillators. An accurate analysis of such kind of circuits poses a number of challenging problems: the operating mode of Gunn-diode based harmonic oscillators, in fact, inherently involves quite complex charge transfer mechanisms, occurring within the solidstate device, and, at the same time, strongly depends on the electromagnetic propagation effects in the surrounding circuit. In this summary, a comprehensive circuit-simulation technique is presented, which selfconsistently takes into account the charge-transport properties of GaAs (by means of numerical device-simulation algorithms) and the details of fi eldpropagation along the passive network. The approach described in [1] has been extended here to GaAs devices, and applied to the analysis of an active antenna exploiting a Gunn diode. Analysis method The simulation scheme can be regarded as an extension of the Lumped-Element FiniteDifference Time-Domain algorithm [2]. In most devices of practical interest, the activedevice size is small, compared with signal wavelength, so that EM-fi eldpropagation can be neglected within the device itself; under such an assumption, two sets of equations are then to be almost independently solved: namely, a full-wave solution of Maxwell’s equations is obtained on the passive network domain, whereas quasi-stationary device equations describe the lumped-element behavior. Interaction between the device(s) and the passive network is accounted for by means of proper formulation of boundary conditions for both systems. Compact device models can be incorporated along the lines described in [3], while in [1] distributed modeling of silicon solid-state device has been introduced. To this purpose, transport equations (in the drift-diffusion approximation) are discretized and numerically solved over a distributed domain[4]. Here, the method is extended to GaAs by accounting for the empirical relationship among electric fi eldand electron mobility [5]: The expression above has been discretized and incorporated into the mixed-mode simulation code. Simulation results The structure sketched in Fig. 1 has been simulated; it consists of a single element of an array antenna, fabricated by etching the metalization plane of a single-side, copper-plated substrate. An aperture of 27.5 0.8 mm is obtained, across which a GaAs Gunn diode is placed. The circuit is completed by an external network which provides the diode bias. Such a network is scarcely critical for the antenna performance, and is therefore modeled through a simple equivalent-circuit approach (compact device models were used in this case). To begin with, the Gunn diode alone has been considered: the device is biased in the negative differential-resistance region, and some small doping fluctuations are introduced. According to the theory of Transferred Electron Devices (TEDs) [6], this triggers the growth of a charge dipole, which drifts under the action of the electric fi eld. Under certain conditions, a cyclic oscillation is recovered, which is correctly predicted by the simulation. Fig. 2 shows the carrier distribution within the device at different time intervals, whereas the device terminal current is plotted in Fig. 3, from which a transit frequency of 4.19 GHz can be inferred. Simulation of the whole circuit is illustrated by the remaining fi gures: more specifi cally, influence of some technological parameters has been investigated. Dependency on the diode placement across the aperture is illustrated by Figs. 4; in these cases, higher-order harmonic modes are excited, so that the Gunn diode does not operate in the transit-time mode any longer; a dipole cannot travel along the whole diode within a period and is “quenched” on its way [7]. Frequency is therefore settled by the external resonant circuit; depending on the diode position, different resonant modes dominate: each fi gure also reports the corresponding radiation diagram, as directly computed by the tool. The influence of diode geometry is instead illustrated by Fig. 5. In the transit-time mode, frequency should inversely depend on the diode length; in the “quenched-domain” mode illustrated above, instead, a much weaker dependence is expected. Nevertheless, as illustrated by the simulation results, signifi cant influence on the waveform amplitudes is found, which in turn appreciably reflects on the oscillator effi ciency. Conclusions The extension of the LE-FDTD scheme to the distributed modeling of GaAs devices has been introduced. This allows for the accurate analysis of a wide range of microwave and millimeter wave circuits. The simulation of an active antenna has been carried out by this method: it is worth remarking that the behavior of the Gunn diode exploited here intrinsically depends on the distributed device nature, and could not be easily accounted for by simpler device models. In the same way, the full-wave analysis accomplished by the proposed method provides details of the resonant behavior of the coupled diode-antenna structure, including dependency on some aspects of the fabrication technology, which could hardly be gained otherwise. Finally, apart from the particular application example presented here, it is also worth stressing that the proposed technique may cover a fairly wide set of applications, ranging from cross-talk analysis in high-speed digital circuits to MMIC analysis.