COMPOUND SEMICONDUCTOR FIELD-EFFECT TRANSISTORS(MESFETs)
  • In the Shockley model, it is assumed that the electron drift velocity is proportional to the absolute value of the longitudinal electric field E = |dV(x)/dx|, i.e., = E, where is the low-field electron mobility.
  • Under GCA, the potential drop dV across a small length dx along the channel can be written as



    where Id is the drain current, dR is the channel resistance of the small section of length dx, and W is the gate width.

  • Equation (6.4) is valid below pinch-off, i.e., < d.
  • Substituting the expression for dd(x) from Eqn.(6.1) into Eqn.(6.4), and integrating x from 0 to L, and V(x) from 0 to , the following drain current characteristic is obtained


    is the conductance of the undepleted channel.
  • Equation (6.5) is referred to as the fundamental equation for FETs, and is valid only for .
  • From Eqn.(6.5), it can be easily shown that the channel conductance becomes zero when = , hence, it can be argued that the drain current saturates at this value of , called the saturation voltage and, according to the Shockley model, = , and the corresponding drain saturation current becomes



EXAMPLE 6.2: Consider the n-channel GaAs MESFET of Example 6.1 with L = 1 and W = 5 . Determine the saturation drain voltage, drain current, and the transconductance for = 0.3 V, and VDS = 0.1 V and 0.5 V. Assume n = 8500 .

SOLUTION: The saturation drain voltage

= = - = 0.3 + 0.54 = 0.24 V.

The conductance of the undepleted channel


For the first case, (= 0.1 V) is less (= 0.24 V), hence, the device is under linear mode of operation, and the drain current is given by


Since is quite small, hence, from the approximate relation given by Eqn.(6.10), = 60 A/V, which is quite close to the answer obtained.

Now, for the second case, (= 0.5 V) is greater than (= 0.24 V), therefore, the device is under saturation mode of operation, and the drain current is given by



Velocity Saturation Model
  • In the Shockley model, it was assumed that the carrier drift velocity increases linearly with the electric field, and from current continuity, it follows that the carrier drift velocity at the drain side of the gate approaches infinity as the pinch-off condition = d is reached, which is, of course, absurd.
  • Rather, carrier velocity saturation would occur at sufficiently high electric fields, which gives an alternate mechanism for current saturation in the device.
  • A simple way of dealing with carrier velocity saturation is to assume a two-piece linear velocity-field relationship of the form


    where is the carrier saturation velocity, and is the electric field required for carrier velocity saturation.
  • For E(L) , the results from the Shockley model are still valid.
  • Hence, the new saturation voltage, defined as the drain-source voltage at the onset of carrier velocity saturation, can be determined from Eqn.(6.4) in combination with Eqns.(6.1) and (6.5), resulting in the expression



  • From Eqn.(6.13), it can be seen that the saturation voltage corresponding to the Shockley model, i.e., = is recovered when >> 1.
  • On the other hand, in the opposite limit, i.e., when << 1, which corresponds to near velocity saturation in the entire channel, it is found that , where it is assumed that << z(1 - z), where
    or intermediate cases, can be found either by solving Eqn.(6.13) as a third order equation in or by solving the equation numerically.
  • However, a simple interpolation formula for the saturation voltage can be established by combining the results for the two limiting cases, i.e.,


  • Likewise, an interpolation formula, valid for devices with relatively low pinch-off voltages, can be found for the saturation current



  • Note: the square law given by Eqn.(6.16) is of the same form as that used in the SPICE modeling of he saturation current in JFETs, and it has also been used to describe the saturation characteristics in SPICE simulation of GaAs MESFETs.
  • Later, a more general version of Eqn.(6.16) was proposed, which covered devices with higher pinch-off voltages



  • Equation (6.17) can be used to determine the dependence of and the device transconductance on channel doping, gate length, electron mobility, and saturation velocity.
  • The velocity saturation model now allows making a rough estimate of the intrinsic high speed performance of the MESFET.
  • From Eqn.(6.16), one can calculate the transconductance at the saturation point


  • Furthermore, it may be argued that the gate-source capacitance at saturation will be of the order of sLW/d, hence, the cutoff frequency can be written approximately as


  • From Eqn.(6.20), it is obvious that a high can be obtained using a small L and a small , however, it is also desirable to have a device with a high current level, which requires a large doping sheet density (d), thus, the best tradeoff is therefore to use a thin and highly doped channel.

EXAMPLE 6.3: Assuming = 2 105 m/sec, determine the saturation drain voltage, saturation drain current, and the transconductance in the saturation region for = 0.5 V for the n-channel GaAs MESFET considered in Examples 6.1 and 6.2, assuming velocity saturation of the carriers in the channel. Compare the results with those obtained in Example 6.2. Also, estimate the cutoff frequency of the device. Use the data given in Examples 6.1 and 6.2.

SOLUTION: The electric field required for velocity saturation in the channel Es = vs/ = 2 107/8500 = 2.35 kV/cm. Thus, = L = 0.24 V. Since and (= 0.7 V) are of the order, therefore, the saturation drain voltage can approximately be given by


Effect of Source/Drain Series Resistance
  • Source and drain series resistance and may play important roles in determining the I-V characteristics of GaAs MESFETs.
  • These resistances can be taken into account by using the following relationships between the extrinsic (lower case subscripts) and intrinsic (upper case subscripts) drain-source and gate-source bias voltages.


    The saturation current in terms of the extrinsic gate voltage swing is readily obtained by combining Eqns.(6.16) and (6.22):