Tunnelling ionization of deep centres in high-frequency electric fields

Abstract

Experimental and theoretical work on the ionization of deep impuritycentres in the alternating terahertz field of high-intensity far-infrared laserradiation, with photon energies tens of times lower than the impurityionization energy, is reviewed. It is shown that impurity ionization is due tophonon-assisted tunnelling which proceeds at high electric field strengths intodirect tunnelling without involving phonons. In the quasi-static regime oflow frequencies the tunnelling probability is independent of frequency.Carrier emission is accomplished by defect tunnelling in configurationspace and electron tunnelling through the potential well formed by theattractive force of the impurity and the externally applied electric field. Thedependence of the ionization probability on the electric field strength permitsone to determine defect tunnelling times, the structure of the adiabaticpotentials of the defect, and the Huang–Rhys parameters of electron–phononinteraction.Raising the frequency leads to an enhancement of the tunnelling ionization andthe tunnelling probability becomes frequency dependent. The transition from thefrequency-independent quasi-static limit to frequency-dependent tunnelling isdetermined by the tunnelling time which is, in the case of phonon-assistedtunnelling, controlled by the temperature. This transition to the high-frequencylimit represents the boundary between semiclassical physics, where the radiationfield has a classical amplitude, and full quantum mechanics where theradiation field is quantized and impurity ionization is caused by multiphotonprocesses. In both the quasi-static and the high-frequency limits, theapplication of an external magnetic field perpendicular to the electric fieldreduces the ionization probability when the cyclotron frequency becomeslarger than the reciprocal tunnelling time and also shifts the boundarybetween the quasi-static and the frequency-dependent limits to higherfrequencies.At low intensities, ionization of charged impurities may also occur through thePoole–Frenkel effect by thermal excitation over the potential well formed by theCoulomb potential and the applied electric field. Poole–Frenkel ionizationprecedes the range of phonon-assisted tunnelling on the electric field scale andenhances the ionization probability at low electric field strengths. Applyingfar-infrared lasers as sources of a terahertz electric field, the Poole–Frenkel effectcan clearly be observed, allowing one to reach a conclusion regarding the charge ofdeep impurities.