Complete RF Analysis of Compound FETs Based on Transient Monte Carlo Simulation

In this paper we described a complete methodology to extract the RF performance of ‘real’ compound FETs from time domain Ensemble Monte-Carlo (EMC) simulations which can be used for practical device design. The methodology is based on transient finite element EMC simulation of realistic device geometry. The extraction of the terminal current is based on the Ramo-Shockley theorem. Parasitic elements like the gate and contact resistances are included in the RF analysis at the post-processing stage. Example of the RF analysis of pseudomorphic HEMTs illustrates our approach.


INTRODUCTION
The remarkable RF performance of compound FETs such as GaAs MESFETs and InGaAs HEMTs with channel lengths down to 0.1 lam is due to well pronounced velocity overshoot, The use of simulation for predictive analysis and design of such devices require in many cases the employment of full scale EMC technique [1][2][3].However, most of the published EMC studies of compound FETs consider simplified device geo- metry and focus mainly on the transport physics and the effect of the enhanced channel velocity on the DC device characteristics.Far more impor- tant for the proper design of modern short channel compound FETs is the RF performance which is determined not only by the high field transport but also by the device geometry and the surface effects.The Tor I-shaped gate, the gate recess and the passivation in such devices critically affect the device parasitics and the overall RF device performance.
In this paper we describe a methodology based on the EMC simulation to investigate the RF performance of FETs.The terminal currents are estimated using the Ramo-Shockley theorem.The device parasitics are included through the proper finite-element description of the gate and recess shapes.The external parasitics are included in the post-processing stage.

TRANSIENT CURRENT
The Heterojunction 2D Finite Element simulator (H2F) and its Monte-Carlo module are described in detail elsewhere [4,5].In the MC simulation the total transient terminal current in response to a step change in the applied voltages required for the y-parameter extraction is the sum of the particle current and the displacement current.According to the Ramo-Shockley theorem [6] the instanta- neous transient current in electrode due to N discrete moving charges within the device is given by the sum of the current I'i(t solely contributed by the movement of the N charged particles with fixed potentials at electrodes and the current I'i'(t) induced due to the time-varying potentials of the electrodes through the capacitive coupling through the electrodes.The current Ii(t) is given by where qj. is the charge of the super-particle, v.i(t is the velocity of the particle andf. is the solution of the Laplace equation V.(cg7jl.)=0 with a unit voltage applied to electrode i, while all other electrodes are grounded.
The current Ii'(t) associated with the time varying potential is calculated from the capacitance matrix components Cij associated with the electrodes of the simulated device.The capacitance matrix components are obtained from the solution of the Laplace equation as Cij--AQi/AVj where AQi is the change in the electrode charge in response to a change in the potential of a particular electrode.When a step perturbation A Vj. of the terminal voltage is applied Ii'(t) flows only during the first time step At and is given by: Ii'(t) Cii A (2)

At
The displacement current during the remaining part of the transient is related to the charges induced on the electrode by the moving particles in the device associated with the redistribution of the mobile charge and is accounted for by Eq. (1).

RF ANALYSIS
The flow diagram of the complete time domain RF EMC analysis is given in Figure 1.The y-para- meters are calculated by Fourier decomposition of the current transients obtained in response to step perturbations in the terminal voltages [7].The cut- off frequency of the simulated device j'm is extracted by solving log[Gsim(logf)]-0 where G. did/dig is the current gain expressed as a function of y-parameters.
In order to extract the maximum frequency of oscillation of the simulated device fsim the max y-parameters are transformed into s-parameters S sim The maximum frequency of oscillation/'sim max

FIGURE
Flow diagram of the RF EMC analysis.
is then extracted by solving log[MAGsim(logf)] =0 where MAG sim is the maximum available gain.
For typical MESFET and HEMT simulation domains, we have adopted the equivalent circuit model presented in Figure 2. The gate resistance, the contact resistances and any external inductive components are excluded from the EMC simula- tion.The source Rsl and the drain Rdl resistances in Figure 2 represent the resistance of the regions between the gate and the source and drain ohmic contacts respectively.To extract accurately the small signal equivalent circuit the y-parameters of the simulated device ysimare transformed into z- parameters Zsim.The estimated source and drain resistances Rsl and Rdl are subtracted from Z sim to obtain the z-parameters Z int of the 'intrinsic' device.Finally Z int are transformed back into y- parameters yint from which the components of the 'intrinsic' small signal circuit can be analytically extracted [7]: In order to evaluate the cut-off frequency f,}eal and the maximum frequency of oscillations feaxl of the 'real' device the gate resistance Rg, the contact resistances R and eventually the inductive com- ponents Lg, L and Ld first have to be incorporated in the z-parameters of the real device Z real which are then transformed into yral.From yreal and S ral the figures of merit of the 'real' device we can estimate feal and frealmax.The intrinsic minimum noise figure is also evaluated from the two-port yparameters and the current traces.We apply the described RF analysis in the simulation of a 120nm T-gate InGaAs channel pHEMT with 22 nm gate to channel separation [8] The y-parameters extracted from the Fourier decomposition of the transients are shown in  , ' " "0"" ""0-..0,...... Ii 20 40 60 80 100 120 Frequency (GHz)     Frequency (GHz) equivalent circuit parameters extracted from the EMC simulations, Vg=-0.2 and Vd 1.5V, to- gether with the experimental values.The higher simulation gmo and fr values is due to the fact that the MC simulations overestimate the velocity overshoot in the channel.The significant effect the gate and contact resistances have on the maximum frequency of oscillation is depicted in Figure 4.The intrinsic noise figure extracted from the transients is shown in Figure 5.

CONCLUSION
In this paper we have presented a comprehensive methodology for the RF analysis of FETs.The methodology is based on the transient EMC simulations of the intrinsic device followed by a post-processing stage during which the parasitic elements are included.It allows realistic estimation of the RF performance from MC simulations.The capabilities of the scheme are illustrated in example simulations for the 120nm gate length pHEMT.

Figures 3 a
Figures 3 a,b.Table I summarises the small signal

FIGURE 2
FIGURE 2 Small signal equivalent circuit of a real FET.Figure also shows the 'intrinsic' and 'simulated' device equivalent circuit.
FIGURE 2 Small signal equivalent circuit of a real FET.Figure also shows the 'intrinsic' and 'simulated' device equivalent circuit.

FIGURE 3 Y
FIGURE 3 Y-parameters as a function of frequency extracted from the Fourier decomposition of the current transients at Vg 0.2 and Va 1.5 V.

FIGURE 4
FIGURE 4 Effect of gate and contact resistances on fmax.

FIGURE 5
FIGURE 5 Intrinsic noise figure for the 120nm pHEMT extracted from the current traces at Vg--0.2 and Va 1.5 V.

TABLE
Small signal equivalent circuit components calculated from the EMC simulations, Vg =-0.2 and Va 1.5 V. Given also are the experimental values, fT and fmax are given at Rg Rc5 f