Teraherz Field Effects Overview

The ionisation of dopants (i.e., donor and acceptor impurities) provides the major source of carriers (i.e., electrons and holes) in semiconductors. The ionised dopants are also the major sources of electron-impurity scattering in semiconductor devices, which determine the transport and optical properties of the device systems at low-temperatures. Hence, the investigation of ionisation of dopants (such as binding energies of donors and acceptors, transition energies and probabilities among di.erent impurity states, etc.) is fundamental in understanding almost all physically measurable properties in semiconductors. In the absence of an intense electro-magnetic (EM) radiation field, the binding energies of dopants and the transition energies among di.erent impurity states in popularly used semiconductor materials are known [1] and the theoretical approaches to calculate these impurity states are welldocumented [2].
It should be noted that in semiconductor materials such as GaAs, Ge and Si, the binding energies of donor and acceptor impurities are of the order of terahertz (10¹² Hz or THz) photon energies [3] so that an intense THz radiation can a.ect strongly the impurity states. With development and application of coherent, high-power, long-wavelength, frequency-tunable and linearly polarised radiation sources such as THz or far-infrared (FIR) free-electron lasers (FELs) [4], it has now become possible to measure the e.ect of an intense laser radiation on ionisation and perturbation of dopants (especially shallow impurities) in different semiconductor systems. In recent years, using THz FELs [such as Free Electron Laser for Infrared eXperiments (FELIX) in The Netherlands and CW FELs at UCSB] as intense radiation sources, THz-photon-induced impact ionisation in InAs heterostructures [5], time-resolved shallow donor spectrum in Si-doped GaAs [6] and Lyman transitions in Be-doped GaAs [7] have been investigated through, e.g., transport and/or photoconduction measurements. The results obtained experimentally indicate that in the presence of intense laser radiation such as FEL fields, i) impurity states in di.erent semiconductor systems are perturbated by the intensity and frequency of the THz laser fields [5-7]; ii) photoconduction experiments are more sensitive than optical measurements for detecting transition energies of impurity states in semiconductors [6,7]; and iii) some interesting intense radiation phenomena, such as impact ionisation of dopants [5] and splitting and broadening of the impurity spectrum [7], can be observed. In order to understand these fundamentally new experimental findings and to predicate new radiation phenomena, it is essential to know theoretically how an intense laser field affects the binding energies of impurities in semiconductors.
Below numerical results are presented for semiconductor materials such as GaAs. The material parameters for GaAs taken within the calculations are the effective-electron-mass ratio m^*/m_e = 0.0665 with m_e being the electron rest mass and the static dielectric constant _K = 12.9. The dependence of binding energies E_1s and E_2s as well as transition energy E_2s - E_1s on THz laser radiation fields is shown in Figures 1 - 4.

Fig.1: Binding energies, E1s and E2s, as a function of THz radiation frequency for different radiation intensities. R* y is the effective Rydberg constant and for GaAs R*y =5.44 meV.	Fig.2: Transition energy between 2s and 1s impurity states, E2s - E1s, as a function of radiation frequency for different radiation intensities.
Fig.3: E1s and E2s as a function of radiation intensity for different radiation frequencies.	Fig.4: E2s - E1s as a function of radiation intensity for different radiation frequencies.

From these results, we see that:
a) in the presence of the radiation fields, E1s and E2s are altered from respectively -R^*_y and -R^*_y/4 at low-field limit to zero at high-field limit and E_2s - E_1s is altered from 3R^*_y/4 at low-field limit to zero at high-field limit.
b) with increasing radiation intensity and/or decreasing radiation frequency, E_1s, E_2s and E_2s - E_1s decrease; c) E_2s depends a bit weakly on the radiation field than E_1s does;
d) the strong effect of the radiation field on binding energy and transition energy can be observed at a^*₀ ~ 1; and
e) E_1s, E_2s and E_2s -E_1s depend more strongly on radiation frequency than on radiation intensity because a^*₀ ~ F₀/w².
The results discussed above indicate that in the presence of the intense THz laser fields, the binding energies of the impurity states can be reduced and the impurity spectrum in semiconductors can be shifted significantly by the radiation. It should be noted that the current generation of the FELs can provide intense THz radiation sources in the frequency and intensity range f ~ 0.1 - 10 THz and F₀~0.1 - 100kV/cm [14] so that the condition a^*₀ = e³F₀/h² Kw² ~ 1 can be satisfied by most of the popularly used semiconductor materials. It has now become possible to investigate the effects of the intense laser radiation on ionisation and perturbation of dopants in semiconductor systems by using current generation of THz or FIR FELs.