Stability criterion for Gunn diodes with injection-limiting cathodes

According to McCumber [1] a Gunn diode with an ohmic cathode (i.e., "differential cathode conductivity"
\sigma_{c} = \delta
) is stable in a constant-voltage circuit if
n_{0}L \le (n_{0}L)_{crit} \equiv 2.7 \times 10^{11}
cm
^-2
where
n_{0}L
is the doping-length product. We show that the same stability criterion applies to Gunn diodes with an injection-limiting cathode
(\sigma_{c} \rightarrow 0)
, if
(n_{0}L)_{crit}
is allowed to be a function of
\sigma_{c}L
. The value of
(n_{0}L)_{crit}
increases by 30 percent if
(\sigma_{c}L)
varies from infinity (ohmic cathode) to zero (injection-limiting cathode). If a cathode with negative differential conductivity is realizable, it may be possible to extend the
(n_{0}L)
region of stable operation of Gunn diodes drastically.