Index

COMPOUND SEMICONDUCTOR FIELD-EFFECT TRANSISTORS(MESFETs)

Device Modeling for CAD

For device modeling suitable for Computer Aided Design (CAD), one has to model the I-V characteristics for the entire range of drain-source voltages, not only in the saturation regime.
An empirical interpolation expression for the full, extrinsic MESFET I-V characteristics was proposed using a hyperbolic tangent function

where is an empirical constant that accounts for the finite output conductance in saturation, and is the extrinsic channel conductance of the linear region, given by

where is the intrinsic channel conductance at very low drain-source voltage, and for a uniformly doped channel, from Eqn.(6.9):

The finite output conductance in saturation, described in terms of the constant in Eqn.(6.24), may be related to the short channel effects and to parasitic currents in the substrate, such as space charge limited current.
Hence, the output conductance may be greatly reduced by using a heterojunctions buffer to prevent carrier injection into the substrate.
The models discussed above are suitable for CAD of GaAs MESFETs and GaAs MESFET circuits, however, some important second-order effects are not included in these models, e.g.,
- subthreshold current and drain voltage induced shift in the threshold voltage,
- deviation from the gradual channel approximation (GCA), which may be especially important at the drain side of the channel,
- possible formation of a high field region (i.e., a dipole layer) at the drain side of the channel,
- inclusion of diffusion and incomplete depletion at the boundary between the depletion region and the conducting channel,
- ballistic or overshoot effects,
- effects of donor diffusion from the contact regions into the channel,
- effects of the passivating silicon nitride layer, and
- effects of traps.
These factors may still be included indirectly by adjusting the model parameters such as mobility, saturation velocity, pinch-off voltage, etc., however, in a rigorous way, they can only be handled using numerical solutions, though for practical circuit simulators used in circuit design, analytical or very simple numerical models are still a necessity.

Backgating and Sidegating Effects

These effects may strongly influence GaAs MESFET I-V characteristics.
Backgating describes the effect of the substrate bias on the MESFET characteristics, and sidegating refers to the effect of a nearby device on the characteristics of a given MESFET.
These effects are related to the finite depletion region, which exists at the boundary between the MESFET active layer and the substrate.
The width of this layer depends on the density of traps and on the position of the Fermi level in the substrate and may be found using an
equivalent p- junction" model, which predicts a certain dependence of the depletion width and of the threshold voltage on the substrate bias.
However, in practical circuits, sidegating usually plays a more important role than backgating, and an accurate modeling of sidegating effects is quite difficult.
An empirical equation (similar to the body bias equation in MOSFETs) is utilized in order to describe sidegating:

where is the threshold voltage unaffected by sidegating, is the source potential, is the potential causing the sidegating or backgating, and is a constant with a typical value of 0.1.

Fig.6.3 Experimental (symbols) and calculated (solid line) threshold voltage dependence on sidegating voltage.

For sidegating, is a function of the distance between the device and the sidegating contact, with the experimental data presented in the literature predicting that is inversely proportional to this distance, and, usually, sidegating becomes negligible only when this distance becomes quite large (at least 30 to 40 m).

Gate Leakage Current

The gate leakage current may play an important role in compound semiconductor field effect transistors where the gate and the channel are separated by the depletion region of the Schottky contact in GaAs MESFETs.
For enhancement mode compound semiconductor FETs, the gate current can play a dominant role and may even affect the value of the "intrinsic" drain-source current .
The gate current is modeled by two equivalent Schottky diodes connected from the gate to the source and from the gate to the drain.
Using the well known diode equation, the total gate current can be found as

where Jss is the reverse saturation current density, calculated using either the thermionic or the thermionic-field emission theory, L and W are the gate length and gate width respectively, and are the intrinsic gate-source and gate-drain voltages respectively, and are the gate-source and gate-drain Schottky diode ideality factors respectively, and is the thermal voltage.

Fig.6.4 MESFET equivalent circuits: (a) conventional equivalent circuit, and (b) equivalent circuit that takes into account the effect of the gate current on the channel current.

To a first order approximation, this simple model may be adequate for a semi-quantitative description of the gate current in GaAs MESFETs.
A more accurate description proposed introduced effective electron temperatures at the source side and the drain side of the channel.
The electron temperature at the source side of the channel is taken to be close to the lattice temperature, i.e., T, whereas the drain side electron temperature is assumed to increase with the drain-source voltage to reflect the heating of the electrons in this part of the channel where the electric field is large.
This effect can easily be taken into account by modifying Eqn.(6.28) to read

where and are the reverse saturation current densities for the gate-source and the gate-drain diodes respectively, and
In most GaAs MESFETs, the reverse gate saturation current is dependent on the reverse bias, and this dependence can be described by:

where are the reverse diode conductances, and g is the reverse bias conduction parameter.
These expressions reproduce MESFET leakage characteristics in excellent agreement with the experimental data.
Under forward bias, assuming thermionic emission mechanism,
The equivalent circuit of Fig.6.4(b) takes into account the effect of gate current on the channel current.
Actually, the gate current is distributed along the channel, with the largest current density taking place near the source side of the channel, which leads to a redistribution of the electric field along the channel, with an increase in the field near the source side of the device, and an overall decrease in the drain current.
This drop can even result in a negative differential resistance.

Practice Problems

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

6.10