Binding energies of hydrogen-like impurities in a
semiconductor in intense terahertz laser fields
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*/me = 0.0665 with me being the electron rest mass and the static dielectric constant
K = 12.9. The dependence of binding energies E1s and E2s as well as transition energy
E2s - E1s 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 E2s - E1s 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, E1s, E2s and
E2s - E1s decrease;
c) E2s depends a bit weakly on the radiation field than E1s does;
d) the strong effect of the radiation field on binding energy and transition energy can be
observed at a*0 ~ 1; and
e) E1s, E2s and E2s -E1s 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.
|