Carrier Tunneling in High-Frequency Electric Fields

Abstract

An enhancement of tunnel ionization of deep impurities in semiconductors in an alternating field as compared to static fields has been observed. The transition between the quasistatic and the highfrequency regime is determined by the tunneling time. For the case of deep impurities this is the time of redistribution of the defect vibrational system which depends strongly on temperature and the impurity structure. A theory of tunnel ionization of deep impurities by high-frequency fields has been developed. [S0031-9007(98) PACS numbers: 72.20.Ht, 72.40. + w The effect of high-frequency coherent radiation on tunneling in semiconductor superlattices and nanostructures has attracted considerable attention recently. The superposition of a static electric field and an alternating field causes a wealth of new phenomena as a result of photon assisted tunneling [1][2][3]. In all these cases tunneling is accomplished by a static electric field, and the radiation influences the barrier penetration probability. An intense radiation field, however, can, in fact, both generate the tunneling barrier and initiate tunneling. Such a tunneling process has been observed with the result that the highfrequency field acts like a static field and the tunneling probability does not depend on frequency [4]. The frequency independent tunneling, however, must be limited to frequencies V with Vt , 1, where t is the tunneling time. This has been shown in a number of theoretical works [5][6][7][8][9][10], but has never been explored experimentally. In contrast to static electric fields where the electron tunnels at a fixed energy, in alternating fields the energy of the electron is not conserved during tunneling. In this case the electron can absorb energy from the field, which should lead to a sharp increase of the tunneling probability with increasing frequency for Vt . 1.Here we report on the first experimental demonstration of this effect observed in tunneling ionization of deep impurities in semiconductors. We show that the transition from the quasistatic regime Vt , 1 to the high-frequency regime Vt . 1 occurs at terahertz frequencies. In the quasistatic regime the electron tunnels at the momentary magnitude of the electric field in a time shorter than the period of oscillation, thus the electric field acts like a static field. The ionization probability is independent of frequency and increases with rising field strength E like exp͑E 2 ͞E 2 c ͒ where E c is a characteristic field [4]. In the high-frequency regime the ionization probability, being characterized by the same field dependence, substantially increases with increasing frequency. In contrast to tunneling ionization of atoms, where only electron tunneling takes place [5], ionization of impurities in solids is accomplished by two simultaneous tunneling processes, electron tunneling and the redistribution of the vibrational system by defect tunneling. A theory of the process is developed showing for the first time that in this case the electron tunneling time is controlled by...

Photon drag effect in(Bi1−xSbx)2Te3three-dimensional topological insulators

“…Using NH 3 , D 2 O, and CH 3 F as active gases for the optically pumped laser, 40-ns pulses with a peak power of P ≈ 10 kW were obtained at different frequencies f (see Table II and Refs. [58][59][60]). The radiation induces indirect (Drude-like) optical transitions because the photon energies are much smaller than the carrier Fermi energy.…”

Excitation of Deep Defects by Intense Terahertz Radiation

“…(7)). The enhancement of tunneling at frequencies higher than the reciprocal tunneling time has been anticipated in a number of theoretical papers [5,10,[23][24][25] but has been demonstrated experimentally only recently [26]. In contrast to static electric fields where the electron tunnels at a fixed energy, in alternating fields the energy of the electron is not conserved during tunneling (see the inset in Fig.…”

“…In order to display in one figure the total set of data covering eight order of magnitude in the square of the electric field, log(E 2 ) was plotted on the abscissa. To make an easy comparison to the exp(E 2 [26]. Straight lines show the dependence according to Eqs.…”

Characterization of deep impurities in semiconductors by terahertz tunneling ionization

“…The phonon-assisted tunneling in static electric fields was first studied numerically in [2]. In semiclassical approximation the ionization probability eðEÞ of deep neutral centers due to phonon-assisted tunneling in an alternating electric fieldẼðtÞ ¼ E cosðotÞ is given by [3] …”

“…Comparing t 2 with the value of h=ð2k B TÞ allows to conclude on the basic structure of the defect adiabatic potentials and yields t 1 according to Eq. (3). From values of the tunneling time t 1 , Eq.…”