A New Empirical Nonlinear Model for HEMT and MESFET Devices

A new large signal model for HEMT’s and MESFET’s, capable of ,modeling the current-voltage characteristic and its derivatives, including the characteristic transconductance peak, gate-source and gate-drain capacitances is described. Model parameter extraction is straightforward and is demonstrated for different submicron gate-length HEMT devices including different d-doped pseudomorphic HEMTs on GaAs and lattice matched to InP, and a commercially available MESFET. Measured and modeled dc and S-parameters are compared and found to coincide well. INTRODUCTION D IFFERENT empirical models suitable for simulation of GaAs MESFETS in nonlinear circuits have been developed [1]-[6]. Some of the models have been incorporated in commercial Harmonic Balance (HB) simulators. These models are used to predict gain, intermodulation distortion, generation of harmonics, etc, versus bias, for circuits like amplifiers, mixers, and multipliers. Recently, Maas et al. [6] pointed out that not only the current-voltage characteristic Zd$[V8s, Vd,] but also their derivatives have to be modeled correctly, especially if the model is supposed to predict intermodulation distortion. In [6], the Id, [V~,] dependence is modeled as a harmonic series, and the coefficients are fitted to both the measured Zd~[V~,,, Vd,] and its derivatives by using singular-value decomposition. Since the above models are intended mainly to describe the performance of MESFETS, there are increasing demands for general FET models, which model both HEMTs and MESFETS. In particular, the characteristic peak in the transconductance versus gate voltage dependence found in most HEMTs must be correctly modeled. In principle, the model utilized in [2], [6] could be used, but many terms are normally needed and parameter extraction requires special techniques. We propose a new simple model, where parameter extraction can be made by simple inspection of the experimental Zd,[V~,, Vd$]and g,,,[V~,] de-characteristics, which models Id, and its derivatives with good accuracy. The model has been applied to FETs based on the following material structures: AIGaAs-GaAs, pseudomorphic (AIGaAs-InGaAs-GaAs) (homogeneously doped and single and double d-doped), lattice matched to InP (AIInAsGaInAs-InP), and GaAs MESFET’S with good results. Manuscript received July 10, 1992; revised July 30, 1992, The authors are with the Department of Applied Electron Physics, ChaImers University of Technology, S-41296, Goteborg, Sweden. IEEE Log Number 9203679. THE MODEL The drain currentfunction is expressed in accordance with previous models as z~,[~gs,V~sl = ZJA [V~,lZdB [V~,l (1) where the first factor is dependent only on the gate voltage and the second only on the drain voltage. The ZdB[Vd,] term is the same as the one used in other models [1], [4]. For Zd,4[V~,l, however, we propose a function whose first derivative has the same ‘bell shaped’ structure as the measured transconductance function g~ [V~~].The hyperbolic tangent (tanh) function describes the gate voltage dependencies and its derivatives well and is normally available in commercial HB-simulators i.e.: Zd, = Zpk(1 + tanh (*)) (1 + ~Vd,) tanh (~~ds) (2) where zpkis the drain current at which we have maximum transconductance, with the contribution from the output conductance subtracted. h is the channel length modulation parameter and a is the saturation voltage parameter. The parameters a and h are the same as those in the Statz and Curtice models. i is in general a power series function centered at VP~with V~,as a variable i.e. i = ~l(~gs – ~pk) + P2W-,S– ~pk)2+ ~3(J7g, – ~pk)3 + > (3) where P’P~is the gate voltage for maximum transconductance g~P~. The selected Id, [V~~, Vd,] function has well defined derivatives. An advantage of the selected model is its simplicity. The different parameters can as a first approximation be easily obtained by inspection of the measured Id, [V~$, Vd,] at a saturated channel condition as follows: all higher terms in 4 are assumed to be zero, h is determined from the slope of the ]d~–Vd~characteristic, Ipk and VPLare determined at the peak transconductance g~@. The intrinsic maximum transconductance gn@ is calculated from the measured maximum transconductance gmp~rn b’ taking into account the feedback effect due to the source resistance,R,, which can be obtained from dcmeasurement [7]: