  Self-heating effects of picosecond optoelectronic switches based on vertical
high-voltage structures with p-n-junctions (VPSS) operating in a high-frequency
mode were theoretically studied for the first time. It is shown that strong
temperature dependence of the control radiation absorption coefficient $k(T)$
is the main factor determining the maximum switching frequency $f_{max}$ and
the corresponding maximum crystal temperature $T_{max}$, as well as
distributions of temperature $T$ and current density $j$ over a device area. A
two-dimensional analysis of the simplest electrothermal model of VPSS embedded
into a double coaxial forming line showed that an increase in the switching
frequency $f$ leads to displacement of current to device periphery, where the
temperature is minimal. However, distributions of $T$ and $j$ over the device
area remain stable if $f < f_{max}$ and $T < T_{max}$. Of course, the values
$f_{max}$ and $T_{max}$ depend on the energy of control radiation pulses, pulse
switching power and heat sink conditions. For VPSS based on nondirect-gap
semiconductors (Si, SiC), they varies within 20-120 kHz and 120-160 $^o C$,
quite sufficient for practical application. However, VPSS based on direct-gap
semiconductors (GaAs, InP) are not actually suitable for operation in
high-frequency modes due to too sharp dependence $k(T)$.
