Dispersion Current (Idb)

Dispersion in a GaAs MESFET or HEMT drain-source current is evidenced by the observation that the output conductance and transconductance beyond some transition frequency is higher than that inferred by the DC measurements. A physical explanation often attributed to this phenomenon is that the channel carriers are subject to being trapped in the channel-substrate and channel-surface interfaces. Under slowly varying signal conditions, the rate at which electrons are trapped in these sites is equal to the rate at which they are emitted back into the channel. Under rapidly varying signals, the traps cannot follow the applied signal and the high-frequency output conductance results.

The circuit used to model conductance dispersion consists of the elements RDB, CBS (these linear elements are also parameters) and the nonlinear source I_db(V_gs, V_ds). The model is a large-signal generalization of the dispersion model proposed by Golio et al. [3]. At DC, the drain-source current is just the current I_ds. At high frequency (well above the transition frequency), the drain source current will be equal to I_ds(high frequency) = I_ds(DC) + I_db. Linearization of the drain-source model yields the following expressions for y₂₁ and y₂₂ of the intrinsic Agilent EEHEMT1 model:

where

Evaluating these expressions at the frequencies = 0 and = infinity, produces the following results for transconductance and output conductance:

for = 0,

for = infinity,

Between these 2 extremes, the conductances make a smooth transition, the abruptness of which is governed by the time constant disp = RDB • \91 \9 CBS. The frequency f₀ at which the conductances are midway between these 2 extremes is defined as

The parameter RDB should be set large enough so that its contribution to the output conductance is negligible. Unless the user is specifically interested in simulating the device near f₀, the default values of RDB and CBS will be adequate for most microwave applications.

The Agilent EEHEMT1 I_ds model can be extracted to fit either DC or AC characteristics. In order to simultaneously fit both DC I-V characteristics and AC conductances, Agilent EEHEMT1 utilizes a simple scheme for modeling the I_db current source whereby different values of the same parameters can be used in the I_ds equations. The DC and AC drain-source currents can be expressed as follows:

Parameters such as VGO that do not have an AC counterpart (i.e., there is no VGOAC parameter) have been found not to vary significantly between extractions utilizing DC measurements versus those utilizing AC measurements. The difference between the AC and DC values of Ids, plus an additional term that is a function of Vds only, gives the value of Idb for the dispersion model

where I_dbp and its associated conductance are given by:

for V_ds > VDSM and KDB ≠ 0,

for V_ds < -VDSM and KDB ≠ 0,

for -VDSM V_ds VDSM or KDB = 0,

By setting the 8 high-frequency parameters equal to their DC counterparts, the dispersion model reduces to I_db=I_dbp.  Examination of the I_dbp expression reveals that the additional setting of GDBM to zero disables the dispersion model entirely. Since the I_dbp current is a function of V_ds only, it will impact output conductance only. However, the current function

will impact both g_m and g_ds. For this reason, the model is primarily intended to utilized g_m data as a means for tuning

Once this fitting is accomplished, the parameters GDBM, KDB and VDSM can be tuned to optimize the g_ds fit.