Spectral Measurement of the Breakdown Limit of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>β</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mi>Ga</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:math> and Tunnel Ionization of Self-Trapped Excitons and Holes

Abstract

Owing to its strong ionic character coupled with a light electron effective mass, $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ is an unusual semiconductor where large electric fields (approximately 1--6 MV/cm) can be applied while still maintaining a dominant excitonic absorption peak below its ultrawide band gap (${E}_{g}$ \ensuremath{\sim} 4.6--4.99 eV). 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-band-gap photon excitation, we observe a field-induced redshift of the spectral photocurrent peak associated with exciton absorption and a thresholdlike increase in peak amplitude at high field associated with self-trapped hole ionization. The field-dependent spectral response is quantitatively fitted with an exciton-modified Franz-Keldysh effect model, which includes the electric-field-dependent exciton-binding energy due to the quadratic Stark effect. Saturation of the spectral redshift 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 in $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. Additionally, the field-dependent responsivity provides an insight into the photocurrent-production pathway, revealing the photocurrent contributions of self-trapped excitons (STXs) and self-trapped holes (STHs) in $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. Photocurrent and p-type transport in $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ 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 STXs and STHs in $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ to model the nonlinear 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 $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ can only arise through tunnel ionization of STHs under strong fields.

Topics & Concepts