  $\beta-Ga_{2}O_{3}$ is an unusual semiconductor where large electric fields
(~1-6 MV/cm) can be applied while still maintaining a dominant excitonic
absorption peak below its ultra-wide bandgap. This provides a rare opportunity
in the solid-state to examine exciton and carrier self-trapping dynamics in the
strong-field limit at steady-state. Under sub-bandgap photon excitation, we
observe a field-induced red-shift of the spectral photocurrent peak associated
with exciton absorption and threshold-like increase in peak amplitude at
high-field associated with self-trapped hole ionization. The field-dependent
spectral response is quantitatively fit with an eXciton-modified Franz-Keldysh
(XFK) effect model, which includes the electric-field dependent exciton binding
energy due to the quadratic Stark effect. A saturation of the spectral
red-shift with reverse bias is observed exactly at the onset of dielectric
breakdown providing a spectral means to detect and quantify the local electric
field and dielectric breakdown behavior. Additionally, the field-dependent
responsivity provides insight to the photocurrent production pathway revealing
the photocurrent contributions of self-trapped excitons (STXs) and self-trapped
holes (STHs). Photocurrent and p-type transport in $\beta-Ga_{2}O_{3}$ are
quantitatively explained by field-dependent tunnel ionization of excitons and
self-trapped holes. We employ a quantum mechanical model of the field-dependent
tunnel ionization of STX and STH to model the non-linear field-dependence of
the photocurrent amplitude. Fitting to the data, we estimate an effective mass
of valence band holes $(18.8 m_{0})$ and an ultrafast self-trapping time of
holes (0.045 fs). This indicates that minority-hole transport in
$\beta-Ga_{2}O_{3}$ can only arise through tunnel ionization of STH under
strong fields.
