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Transcript
Negative photoconductivity due to coherent trapping of electrons in n-GaAs
T.O.Klaassen1, E.E.Orlova2, J.N.Hovenier1 and F. Ghianni1*
1Kavli
Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands
for Physics of Semiconductors, Russian Academy of Sciences, GSP-105, 603950, N. Novgorod, Russia
*Now at: CBS, P.O. Box 4000, 2270 JM Voorburg, The Netherlands
e-mail: [email protected]
2 Institute
Abstract
Experimental set up
A planar antenna on epitaxial n-GaAs, illuminated by an
external THz source, has been used to create intense THz fields
to study donor and cyclotron resonance transitions in a
magnetic field at low temperature. When the THz field is
resonant with such a transition, the resulting extremely strong
coupling between the two levels leads to coherent population
trapping by single frequency excitation. This effect is visible
through the observed negative photoconductivity.
Using standard lithography, a 220 nm thick gold selfcomplementary log-periodic antenna with a 3  3 m apex. has
been fabricated on an epitaxial n-GaAs layer on SI substrate
(ND= 4.1014cm-3, NA< 1.1014cm-3) The distance between the
triangular AuGeNi electrodes, necessary to apply a bias
current, is 15 µm. (see Fig.2)
Introduction
The shallow donor spectra in semiconductors have been
studied extensively in the past. A complete assignment of the
many experimentally observed transitions has been given for nGaAs, together with the results of accurate theoretical
calculations of the transition energies, including those of the
so-called auto-ionising states [1,2] Because of the relatively
easy accessible THz frequency and magnet field range needed
for the observation of the n-GaAs spectrum, this shallow donor
has been used as a model system for the Hydrogen atom in
large magnetic fields. These spectra are studied at liquid
helium temperature by monitoring the magnetic field
dependence of the photoconductive signal while sweeping the
magnetic field at constant THz frequency radiation.
Commonly, an optically pumped far-infrared laser is used as
monochromatic, wavelength multi-line, source. Apart from this
linear spectroscopy also work on coherent effects has been
reported earlier [3,4]. Here we present experimental results on
the THz photo-conductivity under very strong resonant optical
fields, which that point to the occurrence of coherent trapping
of electrons in dressed donor states and Landau levels.
(3,1,0) (2,1,0)
3p
+1
(1,-1,0)
2p
+1
-1
Transition energy (cm )
150
CR
100
Photo of the log-periodic antenna (light gray part) The
rough area under the antenna indicates the presence of
the electrode layer underneath, used for the
application of a bias current.
The FIR magneto-photoconductivity is measured using a
constant current bias source and a pulsed THz laser at various
wavelengths: here we discuss only the data collected at λ =
118.8 µm . The OPFIR laser delivers 300 μs long pulses with a
peak intensity at of about 0.5 W. The radiation is directed to
the sample in the bore of a superconducting magnet through
oversized dielectric waveguides and focussed with an
adjustable polythene Fresnel lens onto the antenna. The sample
is placed on a translation stage in order to position the antenna
apex in the beam focus. Assuming on overall coupling
efficiency of only 5%, the maximum THz intensity in the apex
region is estimated to be about 250 kW/cm2, which equals a
THz electric field strength of about 5 kV/cm.
Experimental results
2s
2p
50
0
2p
-1
0
0
1
2
3
4
5
6
7
8
Magnetic field (T)
Fig. 1
Fig.2
Magnet field dependence of transition energies from
the 1s ground state to some of the donor states, and
the cyclotron resonance transition (CR). The dashed
line shows some of the observable transitions for a
field sweep at λ = 118.8 µm.
In fig. 3 two photoconductive spectra are shown: the upper
spectrum, taken with low bias current and low THz intensity,
shows the usual photo-conductive response, a decrease in
electrical resistance of the sample at those field values where
the applied THz field is resonant with a transition between the
donor groundstate and an excited state. This conductivity
increase arises from the electrons that, after excitation in an
excited state, end up in the conduction band, for instance under
excitation of an acoustic phonon. Also a much smaller
probability for direct excitation into the band exists. The
second trace is obtained with a large bias current and very
strong THz radiation, and shows an increase in the sample
resistance compared to that without THz radiation at the same
magnetic field positions. This phenomenon is observed not
only for the 1s→2p+1 transition which has a very large
transition probability, but also for weaker transitions like the
1s→3p+1 transition and transitions to auto-ionising states like
the (1,-1,0) and (2,1,0). The cyclotron resonance transition
(CR) also exhibits this strong “negative” photo-conductive
effect (NPC). The large increase in conductivity with
increasing bias current is due to impact ionisation.
_
3p+
10
+
2p max THz
Ibias=30A
no THz
1
30 nA
10
CR
1
0
2
3
4
5
6
7
Magnetic field (T)
Fig. 3
Sample resistance as a function of magnetic field for
two extreme experimental conditions at λ = 118.8 µm.
In fig. 4 the shape of the 1s→2p+1 and the CR transition under
low bias as a function of THz field intensity are shown. Very
strong saturation effects occur, and for the maximum intensity
even an increase of resistance is observed at the centre of both
transitions. Also a considerable direct excitation into the
conduction band occurs. (for 4< B< 6T range no allowed
transitions occur)
THz
power
Resistance (kOhm)
100
10
I bias
= 30 nA
+1
1
2p
3
4
temperatures the effective electron mobility depends on the
intensity of the THz field. The mobility first decreases and for
intensities ≥ 2 mW/cm2 increases again with THz intensities up
to 200 mW/cm2, the maximum intensity reported.
low THz
110
210
From THz photo-Hall experiments on donor and CR
transitions in GaAs [5] it is known that at cryogenic
5
CR
6
Resistance (kOhm)
Resistance (kOhm)
no THz
Ibias = 100 nA
100
Discussion
300 nA
+1
2p
CR
3 A
10 A
30 A
1
3
4
5
6
Magnetic field (T)
Fig. 5 Sample resistance at maximum THz intensity
as a function of bias current. The dashed curves show
the zero THz intensity traces.
This increase is due to heating of the conduction electrons by
absorption of THz radiation, which results in a decrease of the
ionised impurity scattering. As can be deduced from the data in
fig’s.4 and 5, the negative photoconductivity (NPC) is not due
to heating of the conduction electrons by the THz field, nor by
its influence on the impact ionisation mechanism. Under strong
impact ionisation conditions and zero THz intensity, clearly the
conduction electron density is virtually independent of field,
whereas the NPC only occurs at resonance. A preliminary
explanation for this effect would be the formation of donor and
Landau level states, “dressed” by THz photons, that “trap” part
of the electrons. The reduction of the conduction electron
density would then lead to the observed increase in sample
resistance. The estimated 5 kV/cm maximum THz field
represents 5 mV over the 10 nm radius of the donor Bohr orbit,
with a binding energy of 5.7 meV. A THz field of that
magnitude can easily induce coherent effects.
Magnetic Field [T]
Fig. 4. Sample resistance at low bias as a function of THz
intensity: saturation of the 2p+1 and the CR transition.
The influence of the bias current at constant maximum THz
intensity is presented in fig. 5. With increasing bias current the
sample resistance in the absence of THz radiation decreases
strongly. (the increase with increasing B-field is due to the
normal magneto-resistance effect) The resistance at resonance
in the presence of THz radiation is independent of bias current
and, for small bias currents, smaller with THz radiation than
without. However, for Ibias ≥ 10 μA the resistance at resonance
with high intensity THz radiation is larger than without THz
radiation: under those conditions negative photoconductivity
occurs. Experiments have also been performed at
wavelengths of 70.5, 96.5 and 184.3 m on those transitions
which are observable for those frequencies in magnetic fields
up to 7T. Essentially the same effects as reported here for λ =
118.8 µm are observed for transitions between donor states as
well as for the CR transition. Clearly the resistance at
resonance under intense THz fields is determined by the
optical field and not at all by the bias current.
Acknowledgements. E.E. Orlova acknowledges support
by NWO as visiting scientist.
References
[1] A. van Klarenbosch, T.O. Klaassen, W.Th. Wenckebach,
C.T. Foxon, ”Identification and ionization energies of
shallow donor metastable states in GaAs:Si” J. Appl. Phys.
67, 6323-8 (1990).
[2] P.W. Barmby, J.L. Dunn, C.A. Bates, T.O. Klaassen,
“High-field calculations for shallow-donor impurities in
bulk GaAs: A finite difference approach”, Phys. Rev.
B 57, 9682-9 (1998).
[3] P.C.M. Planken., et.al., “Far-infrared time-resolved
measurement of the coherence lifetime of shallow-donor
transitions in GaAs”, Phys. Rev. B51, 9643-7 (1995) .
[4] B.E.Cole, et.al “Coherent manipulation of semiconductor
quantum bits with terahertz radiation”, Nature Lett. 410, .
60-63 (2001)
[5] J. Burghoorn, et.al , “Far-infrared photo-Hall experiments
on shallow donor transitions in n-GaAs, Proceed. 15th
ÏRMMW Conference, Orlando, December 1990, SPIE
1514(1990)369-70.