For high-frequency application of MESFETs, an important figure of merit is the cutoff
frequency
, which is the frequency at which the MESFET can no longer amplify the
input signal. The small-signal input current
is the product of the
gate admittance and the small-signal gate voltage
, assuming that
the device has negligibly small series resistance
![$\displaystyle \widetilde{i}_\mathrm{in}=2\pi \cdot f \cdot C_{\mathrm{G}} \cdot \widetilde{v}_\mathrm{g}$](img865.png) |
(C.12) |
where
is the gate capacitance equals to
and
is the average depletion-layer width under the gate electrode, and
is the small-signal gate voltage. From the definition of the transconductance [37]
![$\displaystyle g_{\mathrm{m}} = \displaystyle\frac{\mathrm{d}I_\mathrm{c}}{\math...
...}}=\displaystyle\frac{\widetilde{i}_{\mathrm{out}}}{\widetilde{v}_{\mathrm{g}}}$](img870.png) |
(C.13) |
the output current becomes
![$\displaystyle \widetilde{i}_\mathrm{out}=g_{\mathrm{m}} \cdot \widetilde{v}_{\mathrm{g}}.$](img871.png) |
(C.14) |
From (C.12) and (C.14) where
, becomes
![$\displaystyle f_\mathrm{t}=\displaystyle\frac{g_\mathrm{m}}{2\pi \cdot C_\mathr...
... N_\mathrm{D}\cdot a^2}{2\pi \cdot \varepsilon_\mathrm{s}\cdot L^2_\mathrm{g}},$](img873.png) |
(C.15) |
From (C.15) one can see that to improve high-frequency performance, a MESFET
with high carrier mobility and short channel length should be used. This is the reason that
n-channel SiC MESFET, which has a higher electron mobility, is preferred.
The
derivation in (C.15) is based on the assumption that the carrier mobility in
the channel is a constant, independent of the electric field. However, for very high-frequency
operations, the longitudinal field, i.e., the electric field direct from the source to the
drain, is sufficiently high that the carriers travel at their saturation velocity.
![$\displaystyle I_\mathrm{Dsat} =(\mathrm{area}\,\mathrm{for}\,\mathrm{carrier}\,...
...= W_\mathrm{g}\cdot(a-W)\cdot {\mathrm{q}}\cdot N_\mathrm{D}\cdot v_\mathrm{s}.$](img874.png) |
(C.16) |
The transconductance is then
![$\displaystyle g_{\mathrm{m}}=\frac{\mathrm{d}I_\mathrm{Dsat}}{\mathrm{d}V_\math...
...isplaystyle\frac{W_\mathrm{g}\cdot v_\mathrm{s}\cdot\varepsilon_\mathrm{s}}{W}.$](img875.png) |
(C.17) |
The value of
is obtained from (C.5).
Finally, from (C.17), we can obtain the cutoff frequency under saturation velocity condition:
![$\displaystyle f_\mathrm{t}=\displaystyle\frac{g_\mathrm{m}}{2\pi \cdot C_\mathr...
...silon_\mathrm{s}/W)}=\displaystyle\frac{v_\mathrm{s}}{2\pi \cdot L_\mathrm{g}}.$](img877.png) |
(C.18) |
Therefore, to increase
, we must reduce the gate length
and
employ a semiconductor with a high velocity. SiC is superior to other semiconductor materials
to operate at higher cutoff frequency due to its higher electron drift velocity.
T. Ayalew: SiC Semiconductor Devices Technology, Modeling, and Simulation