UP2(1): Ultrafast high-field transport
W. Kühn, P. Gaal, K. Reimann, M. Wörner
Since many years there are two trends in the semiconductor industry:
(i) The devices are getting smaller, which leads to higher electric
fields in these devices.
(ii) The frequencies are getting higher, i.e., the times are getting
These two trends are the motivation to study charge transport in
semiconductors at high electric fields on ultrashort time scales.
To do this, we apply the electric fields not via electrical contacts,
but contactless in the form of strong THz pulses. With electro-optic
sampling we measure the time dependence of the electric field of
these pulses. Furthermore, the difference between the electric field
incident on the sample and the electric field transmitted through
the sample directly yields the electric current in the sample. Fig.
1 shows results obtained at room temperature for a thin (500 nm)
n-doped (concentration 2×1016 cm-3)
||Fig. 1 (a) Incident electric field Ein(t).
(b) Transmitted electric field Etr(t).
(c) Difference between Ein(t) and
which is proportional to the current in the sample and thus
to the electron velocity (right ordinate scale). (d) Electron
wavevector k(t) obtained from the time integral of Ein(t).
(e) Band structure of the conduction band in GaAs along the
(100) direction. The hatched areas denote regions with a negative
effective mass. (f) Dots: Experimental results, electron velocity
[taken from (c)] versus wavevector [from (d)]. Line: Theory,
assuming ballistic transport. (g) Same as in (f), but for an
incident electric field amplitude of only 50 kV/cm.
The incident electric field between the times t1
and t2 is positive. Thus the direction of the
force acting on an electron between t1 and t2
stays the same. Between t1 and t2
the electron velocity [Fig. 1(d)], however, first decreases, then
increases, and finally decreases again. This shows that the effective
mass of the electron changes sign, it is first positive, then negative,
and finally positive again. Exactly this behavior is expected for
ballistic motion over a large portion of the Brillouin zone. Our
results show that on a time scale of a few picoseconds and for electric
fields above 20 kV/cm electrons in GaAs perform ballistic transport
even at room temperature [the dots and the lines in Figs. 1(f) and
(g) agree]. For further details see the original publication, Phys.
Rev. Lett. 104 (2010) 146602.
||Fig. 2 Comparison of the emitted electric fields at temperatures
of 300 K [red line, same data as in Fig. 1(c)], 200 K
(green line), and 80 K (blue line).
At lower temperatures (80 and 200 K) we still have ballistic
transport, but the emitted field amplitudes and thus the currents
are up to ten times higher (see Fig. 2). The current density is
given by the charge times the density times the velocity of the
carriers. The only parameter that can change is the carrier density.
(The carrier charge is a constant. The velocity is determined by
the bandstructure, which does not change significantly with temperature.)
Thus we conclude that the THz pulse has generated up to ten additional
electron-hole pairs per initially present electron in the conduction
band, see also Phys.
Rev. B 82 (2010) 075204..
two-dimensional spectroscopy in the mid-infrared spectral range
W. Kühn, K. Reimann, M. Wörner
A novel method for time-resolved two-dimensional spectroscopy has
been developed. Field-resolved detection allows for a collinear
beam geometry and the measurement of optical nonlinearities of arbitrary
order. A first application is shown for an n-type modulation-doped
multiple quantum well structure (see Fig. 3). Our approach allows
the detailed analysis of all types of nonlinear optical signals,
for instance the third-order four-wave-mixing signal, which is in
agreement with former results for this homogenously broadened system.
As a novel feature, we observe a quantum beat with the LO-phonon
frequency of GaAs that is presently being analyzed. J.
Chem. Phys. 130 (2009) 164503.
Fig. 3 (a),
(b) Electric field transients transmitted through the sample
measured with electrooptic sampling for the delay time τ
= 0.35 ps: EAB(t, τ)
(black line), EA(t)
(green line), and EB(t,
τ) (blue line). (c) Subtracting the transients in (b)
from the transient in (a) (dashed line) yields the nonlinear
signal ENL(t, τ)
(green line, enlarged). (d) Two-dimensional transients in
the time domain. (e) Two-dimensional nonlinear signal in the
time domain. (f) Nonlinear signal in the frequency domain.
Red arrows mark pump-probe signals and yellow arrows the third-order
four-wave-mixing signals. (g) Spectral peak at νt
= &nu0 and &nuτ= 0, i.e.,
the pump-probe signal for τ < 0, transformed back into
the time do-main. (h) Four-wave-mixing signal obtained from
the spectral peak at &nut = &nu0
and &nuτ= 0. (i) Quantum beat with an oscillation
period of 110 fs matching the LO-phonon frequency in GaAs
pump-probe experiments on a QCL
W. Kühn, P. Gaal, K. Reimann, M. Wörner
||Fig. 4 (a) Pump-induced change of the transmission
through the QCL as a function of pump-probe delay τ for
different currents. (b) Fourier transform of the transmission
changes shown in (a). (c) Pump-induced shift of the phase of
the transmitted pulse as a function of pump-probe delay τ.
We investigated the ultrafast absorption and gain dynamics in a
quantum cascade laser (QCL) under stationary bias by pump-probe
measurements [KPG08]. The detection with electrooptic sampling allows
for a clear separation of gain/absorption dynamics from changes
of the refractive index. Fig. 4(a) shows the transmission change
induced by the pump pulse, plotted as a function of τ for different
values of the laser current I. Below threshold, the QCL
studied here displays strong absorption on the laser transition.
The positive transmission changes observed below threshold [Fig. 4(c),
I = 0 and 150 mA] are due to a bleaching of this absorption.
The recovery of this absorption requires the depopulation of the
upper subband and the repopulation of the lower subband. Accordingly,
the time constant for the absorption recovery is determined both
by the electron lifetime in the upper subband and by electron heating
and cooling within the manifold of states in the injector. The transmission
change decays nearly to zero reflecting the complete repopulation
of the lower subband. Above threshold, the pump pulse saturates
the gain, in this way depleting the quasistationary population inversion
and inducing a negative transmission change. Such kinetics is superimposed
by oscillations with a frequency of 0.8 THz. The fast initial
component of the gain recovery gives evidence of a very efficient
electron supply from the injector through the injection barrier
into the active part of the QCL structure. The oscillations originate
from coherent electron tunneling through the injection barrier.
Phys. Lett. 93 (2008) 151106.