UP2(1): Ultrafast high-field transport in GaAs

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 shorter.

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) GaAs sample.

Fig. 1 (a) Incident electric field Ein(t). (b) Transmitted electric field Etr(t). (c) Difference between Ein(t) and Etr(t), Eem(t), 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..

UP2(2): Phase-resolved 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.

UP2(3): Phase-resolved 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 Ga_0.47In_0.53As/Al_0.48In_0.52As 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. Appl. Phys. Lett. 93 (2008) 151106.