With strong THz pulses, we measure ultrafast transport of electrons, holes, and an electron-hole plasma in GaAs. The transition from ballistic to drift-like transport is strongly influenced by electron-hole scattering

Bowlan, P.

Elsaesser, T.

Flytzanis, C.

Hey, R.

Kuehn, W.

Reimann, K.

Woerner, M.

English

Repositorium für Naturwissenschaften und Technik

Transition from ballistic to drift motion in high-field transportin GaAsP. Bowlan1, W. Kuehn1, K. Reimann1, M. Woerner1, T. Elsaesser1, R. Hey2, and C. Flytzanis31 Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, 12489 Berlin, Germany2 Paul-Drude-Institut für Festkörperelektronik, 10117 Berlin, Germany3 Laboratoire Pierre Aigrain, École Normale Supérieure, 75231 Paris, FranceAbstract. With strong THz pulses, we measure ultrafast transport of electrons, holes,and an electron-hole plasma in GaAs. The transition from ballistic to drift-like transportis strongly influenced by electron-hole scattering.In an electric field charge carriers in a semiconductor undergo ballistic transport, i.e., the accelera-tion is proportional to the field, in the absence of scattering. Since any scattering process takes a finitetime, every transport will be ballistic on sufficiently short times [1]. If, as is often the case, the mostimportant scattering process is scattering with optical phonons, the relevant time scale is ≈100 fs, de-termined by the optical phonon frequency. For times considerably longer than these scattering times,transport will be drift-like, i.e., the carrier velocity is proportional to the field. On intermediate timescales one expects a gradual transition from ballistic to drift-like transport. Intense femtosecond THzpulses allow for driving carrier transport in semiconductors at very high carrier velocities and provide-202 Ballistic Model MeasuredElectric field (kV/cm)0 1 2 30.00.51.0 Ballisticity(a)(b)(c)0 1 2 Time (ps)(d)1.00.50.0-0.5 (e) Delay (ps)-0.5 0.0 0.51.00.50.0-0.5  Measurement(f)  (g)-0.5 0.0 0.5  Time (ps)Simulation(h)00.20.40.60.81Fig. 1. (a)–(d) Electric fields emitted by the photocarriers for an incident THz field strength of 25 kV/cm. Thefree carriers were generated with a photoexcitation wavelength of 885 nm and an excitation density of n =p ≈ 2 × 1016 cm−3, 1.5 ps before the begin of the THz pulse. The average THz frequency is 3 THz in (a) and2 THz in (c). (b) and (d) show the time dependence of the ballisticity. (e)–(h) Transport for small delays betweenphotoexcitation and THz pulses. The measured emitted field amplitude (e) and the ballisticity (f) are plotted versusdelay and time. For these measurements the photoexcitation wavelength was 800 nm, the density 4 × 1016 cm−3,and the THz field amplitude 50 kV/cm. (g), (h) Corresponding results from our model.    EPJ Web of ConferencesDOI: 10.1051/C© Owned by the authors, published by EDP Sciences, 2013,epjconf 201/04002 (2013)4134104002   This  is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20134104002EPJ Web of Conferencesa time resolution below typical scattering times[2]. In this way it is possible to measure the transitionfrom ballistic to drift-like transport, a particularly interesting regime.To determine the transition between the two types of transport experimentally, both the appliedelectric field and the current must be measured with a time resolution of at least 100 fs. In our mea-surements, we use the electric field of a strong THz pulse and determine its time dependence by electro-optic sampling [3]. The time-dependent current leads to the emission of transient electric fields, whichcan also be measured by electro-optic sampling. If the current is confined to a thin layer, the currentj(t) is proportional to the emitted field Eem(t) [4–6],j(t) = −2Eem(t)/(Z0d). (1)We obtain the emitted field as the difference between the transmitted and incident fields. To extractthe current from the photoexcited carriers we measure the transmitted field transients with and withoutphotoexcitation. The difference between these transients is the field emitted from the photoexcitedcarriers. The corresponding current is then obtained using Eq. (1).Knowing both current and field as a function of time, it is easy to distinguish between ballistic (π/2phase shift between current and field, ballisticity 1) and drift transport (no phase shift, ballisticity 0).We find that if only electrons are present (n-type sample, no photoexcitation), the transport is ballisticover the whole length of the THz pulse. If only holes are present (p-type sample, no photoexcitation),the current for the same carrier density is essentially zero [7,8]. From this we conclude that the holecurrent in all measurements is negligible. For an average frequency of 3 THz and photoexcitation at885 nm (at room temperature this corresponds to the band gap, so that the carriers have nearly noexcess energy) of an undoped sample [equal number of electrons and holes, Fig. 1(a)], the transport isballistic. In contrast, at an average frequency of 2 THz [Fig. 1(c)], there is a transition from ballistictransport at the beginning of the THz pulse to drift transport at later times. The higher the hole den-sity, the faster the transition towards drift transport (comparison of photoexcited n-type, p-type, andundoped samples). Thus, although holes do not contribute appreciably to the current, they influencethe electron transport.For the data in Fig. 1(a) to (d), the photocarriers were generated 1.5 ps before the begin of theTHz pulse. If the photocarriers are generated during the THz pulse, the transport depends on the exacttiming of the generation relative to the THz field [Figs. 1(e) to (h)]. The reason for this is that thecarriers are generated with zero average velocity. Thus, if they are generated at the field extrema, theirinitial velocity (zero) is equal to the velocity they have for ballistic transport. If, however, the carriersare generated at the zeroes of the field, they start with zero velocity, whereas for ballistic transportthey should have a high velocity at this instant of time. This leads to a phase shift between the actualvelocity and the velocity for ballistic transport and thus to lower values for the ballisticity [Figs. 1(f)and (h)].To explain our observations, we have developed a model for high-field carrier transport in semi-conductors that correctly describes both the time dependence of transport on ultrashort time scales andsteady-state transport [9,1,8]. This is achieved by describing electrons and phonons together as newquasiparticles, polarons, in the form of wavepackets. The wavepacket size determines the amount ofscattering. In turn, incoherent energy delivered to the polaron wavepacket will change its size. Thismodel has been used to calculate the data in Fig. 1; they agree very well with the experimental results.References1. W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, Phys. Rev. Lett. 104, 146602(2010)2. R. Ulbricht, E. Hendry, J. Shan, T.F. Heinz, M. Bonn, Rev. Mod. Phys. 83, 543 (2011)3. Q. Wu, X.C. Zhang, Appl. Phys. Lett. 67, 3523 (1995)4. T. Stroucken, A. Knorr, P. Thomas, S.W. Koch, Phys. Rev. B 53, 2026 (1996)5. K. Reimann, Rep. Prog. Phys. 70, 1597 (2007)6. W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, Phys. Rev. B 82, 075204 (2010)04002-p.2XVIIIth International Conference on Ultrafast Phenomena7. P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, C. Flytzanis, Phys. Rev. Lett.107, 256602 (2011)8. P. Bowlan, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, C. Flytzanis, Phys. Rev. B85, 165206 (2012)9. P. Gaal, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, Nature 450, 1210 (2007)04002-p.3

Transition from ballistic to drift motion in high-field transport in GaAs

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Transition from ballistic to drift motion in high-field transport in GaAs

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