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THz carrier oscillations in GaAs heterostructures detected via two color femtosecond pump probe spectroscopy
Physica B 314 (2002) 154–157
THz carrier oscillations in GaAs heterostructures detected via two color femtosecond pump probe spectroscopy a . M. Eckardta,c,*, A. Schwanh.auera, L. Robledoa, S. Malzera, G.H. Dohler , b b M. Betz , A. Leitenstorfer a
Institute of Semiconductor Physics, FA-University Erlangen, D-91058 Erlangen, Germany b Physics-Department E11, Technical University Munich, D-85748 Garching, Germany c Institute of Semiconductor Physics, FA-University Erlangen, Erwin Rommel Str. 1, 91058 Erlangen, Germany
Abstract Realistic Monte Carlo simulations as well as first experimental data show that classical, quasi ballistic, phasecoherent electron oscillations are possible in relative wide suitably designed confining potentials. Three different confining potentials have been investigated and the oscillation frequencies expected from the calculations were observed in the pump & probe experiments. r 2002 Elsevier Science B.V. All rights reserved. PACS: 73.63.Hs; 73.23.Ad Keywords: THz oscillations; High field transport
The goal of the present study is to demonstrate theoretically and experimentally that quasi ballistic phase coherent, moderately attenuated (classical) THz-oscillations of electrons in suitably designed confining potential wells are possible, in spite of rather high scattering rates. We use the space charge potential of pþ –i–n–i–pþ -structures in combination with band gap grading in Alx Ga1x As heterostructures. In Fig. 1 an example is shown. Using pump pulses with a duration of about 80 fs [1] and a mean photon energy close to the GaAs band gap an electron–hole plasma is generated at the left corner of the potential well. The electrons are periodically accelerated and *Tel.: +49-9131-852-8319; fax: +49-9131-852-7293. E-mail address: [email protected] (M. Eckardt).
decelerated by the combined space charge- and the grading-induced quasi-field, while the holes are generated at their ‘final destination’ at the p-layer. Due to a suitably chosen n-doping density the potential is flat enough to prevent the (extremely efficient) scattering of ballistically accelerated electrons into the L- or X-valleys (see Fig. 1). The coherent oscillation of the electron ensemble is relatively little affected by the LO phonon scattering processes. These processes favor small momentum transfer [2]. Hence, they do not yield drastic changes of the group velocity. Thus, a few THz oscillations of the ensemble are possible before coherence is lost (and before the electrons are relaxed in energy down to the potential minimum). Short circuited selective contacts to the doping layers allow for external electron–hole recombination between subsequent pulses. In
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 1 4 5 0 - 8
M. Eckardt et al. / Physica B 314 (2002) 154–157
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(a)
(b)
Fig. 2. Calculated spatial electron distribution as a function of delay time for sample A.
Fig. 1. Bandstructure of sample A (b). Between two p-contact layers there is an intrinsic region with a d-n-doping. The Alprofile (a) allows for both selective carrier injection and selective detection with pump & probe experiments.
order to obtain information about the temporal and spatial evolution of the electron ensemble transient transmission changes at variable delay times are monitored in the ‘probe stretch’ (see Fig. 1) at photon energies close to the local band gap by the probe pulse. The transmission changes are due to changes of the Franz–Keldysh absorption, associated with the periodic field of the dipole formed by the (stationary) holes and the oscillating electrons. At any delay time the observed local field changes correspond to the fraction of carriers presently to the right of the ‘probe stretch’. We perform realistic Monte Carlo simulations which take into account all relevant scattering processes (acoustic-, optic-, polar-optic-, intervalley-phonons, ionized impurities), including their dependence on temperature and Al-concentration andFcrucial for a realistic simulationFthe dynamics of the carrier generation. Depending on the shape of the potential we find for both simulation
(see Fig. 2) and experiment that the electrons perform more or less attenuated oscillations within the nm-scaled confining potential. Simulations and experiments confirm that the oscillations are efficiently suppressed if scattering to X- and Lvalleys is present. Intervalley scattering destroys the coherence practically immediately. In Fig. 3, the observed transient Franz–Keldysh signal in a sample corresponding to Fig. 1 is shown together with results of the Monte Carlo simulations. At probe energies close to the bandgap of the probe stretch (x ¼ 0:10), only carriers on the right side of the stretch do contribute to the field screening and therefore to the transmission changes. Therefore, the observed transmission change should be proportional to the electrons on the right side. The agreement between experiment and theory (Fig. 3) is surprisingly good. The Monte Carlo simulations show that the oscillations are partly suppressed by the anharmonicity of the potential. Fig. 4 shows a pþ –n–pþ -structure. The homogeneously n-doped region between the p-contactlayers forms a parabolic well. Again, a carrier injection stretch is incorporated on the left side. The Monte Carlo simulations show an even better coherence of the oscillating electrons (Fig. 5). Two such designed samples were grown, which should
156
M. Eckardt et al. / Physica B 314 (2002) 154–157
(a)
(b)
Fig. 3. Comparison between theory and experiment. Crosses are the measured transmission changes, solid line is the calculated number of electrons on the right side of the probe stretch (both at T ¼ 10 K).
exhibit different oscillation frequencies (due to different n-doping and well widths) and pump & probe experiments were made. However, the interpretation of the experimental data is not straight forward. A parabolic well does not contain one unique electric field and probing close to the bandgap of the whole well results in a mixture of Franz–Keldysh absorption signals. Nevertheless, oscillations in the transmission changes are clearly visible, which are comparable to the real space oscillation frequency of the electrons (expected from the simulations). Moreover the sample with higher doping and smaller well width (sample B) shows a higher oscillation frequency compared to the sample with the lower doping and wider well width (sample C) (see Fig. 6). This supports our interpretation of coherent real-space oscillations. In conclusion, we have shown the theoretical possibility for quasi-ballistic electron oscillations in space charge potentials as well as first experimental indications for that. The
Fig. 4. Bandstructure of sample B (b); the space charge potential of the depleted n-layer of a pþ –n–pþ -structure (n¼ 1 1017 cm3 ; p¼ 2 1018 cm3 ) forms a parabolic well. (a) Al-profile.
Fig. 5. Calculated spatial electron distribution as a function of delay time for the sample B with (narrow) parabolic potential well.
M. Eckardt et al. / Physica B 314 (2002) 154–157
157
most prominent LO-phonon scattering process favors small momentum transfer so that the group velocity of the electrons is not drastically affected. Key techniques are bandgap engineering as well as fs-pump & probe spectroscopy both used for spatial selective carrier generation and detection. The transmission changes do show oscillations in the expected frequency range (1.5 or 2.8 THz), what supports our interpretation of quasi-ballistic electron oscillations.
References Fig. 6. Measured transmission change from two parabolic wells with different curvature, sample B (a) and C (b), and calculated electron center of mass (at T ¼ 10 K). Oscillation in the signal can be seen and the two samples exhibit different oscillation frequencies, which are in quite good agreement with the theory.
[1] A. Leitenstorfer, S. Hunsche, J. Shah, M.C. Nuss, W.H. Knox, Phys. Rev. B 61 (2000) 16642. [2] C. Moglestue, Monte Carlo Simulation of Semiconductor Devices, Chapman & Hall, New York, 1993.
THz carrier oscillations in GaAs heterostructures detected via two color femtosecond pump probe spectroscopy a . M. Eckardta,c,*, A. Schwanh.auera, L. Robledoa, S. Malzera, G.H. Dohler , b b M. Betz , A. Leitenstorfer a
Institute of Semiconductor Physics, FA-University Erlangen, D-91058 Erlangen, Germany b Physics-Department E11, Technical University Munich, D-85748 Garching, Germany c Institute of Semiconductor Physics, FA-University Erlangen, Erwin Rommel Str. 1, 91058 Erlangen, Germany
Abstract Realistic Monte Carlo simulations as well as first experimental data show that classical, quasi ballistic, phasecoherent electron oscillations are possible in relative wide suitably designed confining potentials. Three different confining potentials have been investigated and the oscillation frequencies expected from the calculations were observed in the pump & probe experiments. r 2002 Elsevier Science B.V. All rights reserved. PACS: 73.63.Hs; 73.23.Ad Keywords: THz oscillations; High field transport
The goal of the present study is to demonstrate theoretically and experimentally that quasi ballistic phase coherent, moderately attenuated (classical) THz-oscillations of electrons in suitably designed confining potential wells are possible, in spite of rather high scattering rates. We use the space charge potential of pþ –i–n–i–pþ -structures in combination with band gap grading in Alx Ga1x As heterostructures. In Fig. 1 an example is shown. Using pump pulses with a duration of about 80 fs [1] and a mean photon energy close to the GaAs band gap an electron–hole plasma is generated at the left corner of the potential well. The electrons are periodically accelerated and *Tel.: +49-9131-852-8319; fax: +49-9131-852-7293. E-mail address: [email protected] (M. Eckardt).
decelerated by the combined space charge- and the grading-induced quasi-field, while the holes are generated at their ‘final destination’ at the p-layer. Due to a suitably chosen n-doping density the potential is flat enough to prevent the (extremely efficient) scattering of ballistically accelerated electrons into the L- or X-valleys (see Fig. 1). The coherent oscillation of the electron ensemble is relatively little affected by the LO phonon scattering processes. These processes favor small momentum transfer [2]. Hence, they do not yield drastic changes of the group velocity. Thus, a few THz oscillations of the ensemble are possible before coherence is lost (and before the electrons are relaxed in energy down to the potential minimum). Short circuited selective contacts to the doping layers allow for external electron–hole recombination between subsequent pulses. In
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 1 4 5 0 - 8
M. Eckardt et al. / Physica B 314 (2002) 154–157
155
(a)
(b)
Fig. 2. Calculated spatial electron distribution as a function of delay time for sample A.
Fig. 1. Bandstructure of sample A (b). Between two p-contact layers there is an intrinsic region with a d-n-doping. The Alprofile (a) allows for both selective carrier injection and selective detection with pump & probe experiments.
order to obtain information about the temporal and spatial evolution of the electron ensemble transient transmission changes at variable delay times are monitored in the ‘probe stretch’ (see Fig. 1) at photon energies close to the local band gap by the probe pulse. The transmission changes are due to changes of the Franz–Keldysh absorption, associated with the periodic field of the dipole formed by the (stationary) holes and the oscillating electrons. At any delay time the observed local field changes correspond to the fraction of carriers presently to the right of the ‘probe stretch’. We perform realistic Monte Carlo simulations which take into account all relevant scattering processes (acoustic-, optic-, polar-optic-, intervalley-phonons, ionized impurities), including their dependence on temperature and Al-concentration andFcrucial for a realistic simulationFthe dynamics of the carrier generation. Depending on the shape of the potential we find for both simulation
(see Fig. 2) and experiment that the electrons perform more or less attenuated oscillations within the nm-scaled confining potential. Simulations and experiments confirm that the oscillations are efficiently suppressed if scattering to X- and Lvalleys is present. Intervalley scattering destroys the coherence practically immediately. In Fig. 3, the observed transient Franz–Keldysh signal in a sample corresponding to Fig. 1 is shown together with results of the Monte Carlo simulations. At probe energies close to the bandgap of the probe stretch (x ¼ 0:10), only carriers on the right side of the stretch do contribute to the field screening and therefore to the transmission changes. Therefore, the observed transmission change should be proportional to the electrons on the right side. The agreement between experiment and theory (Fig. 3) is surprisingly good. The Monte Carlo simulations show that the oscillations are partly suppressed by the anharmonicity of the potential. Fig. 4 shows a pþ –n–pþ -structure. The homogeneously n-doped region between the p-contactlayers forms a parabolic well. Again, a carrier injection stretch is incorporated on the left side. The Monte Carlo simulations show an even better coherence of the oscillating electrons (Fig. 5). Two such designed samples were grown, which should
156
M. Eckardt et al. / Physica B 314 (2002) 154–157
(a)
(b)
Fig. 3. Comparison between theory and experiment. Crosses are the measured transmission changes, solid line is the calculated number of electrons on the right side of the probe stretch (both at T ¼ 10 K).
exhibit different oscillation frequencies (due to different n-doping and well widths) and pump & probe experiments were made. However, the interpretation of the experimental data is not straight forward. A parabolic well does not contain one unique electric field and probing close to the bandgap of the whole well results in a mixture of Franz–Keldysh absorption signals. Nevertheless, oscillations in the transmission changes are clearly visible, which are comparable to the real space oscillation frequency of the electrons (expected from the simulations). Moreover the sample with higher doping and smaller well width (sample B) shows a higher oscillation frequency compared to the sample with the lower doping and wider well width (sample C) (see Fig. 6). This supports our interpretation of coherent real-space oscillations. In conclusion, we have shown the theoretical possibility for quasi-ballistic electron oscillations in space charge potentials as well as first experimental indications for that. The
Fig. 4. Bandstructure of sample B (b); the space charge potential of the depleted n-layer of a pþ –n–pþ -structure (n¼ 1 1017 cm3 ; p¼ 2 1018 cm3 ) forms a parabolic well. (a) Al-profile.
Fig. 5. Calculated spatial electron distribution as a function of delay time for the sample B with (narrow) parabolic potential well.
M. Eckardt et al. / Physica B 314 (2002) 154–157
157
most prominent LO-phonon scattering process favors small momentum transfer so that the group velocity of the electrons is not drastically affected. Key techniques are bandgap engineering as well as fs-pump & probe spectroscopy both used for spatial selective carrier generation and detection. The transmission changes do show oscillations in the expected frequency range (1.5 or 2.8 THz), what supports our interpretation of quasi-ballistic electron oscillations.
References Fig. 6. Measured transmission change from two parabolic wells with different curvature, sample B (a) and C (b), and calculated electron center of mass (at T ¼ 10 K). Oscillation in the signal can be seen and the two samples exhibit different oscillation frequencies, which are in quite good agreement with the theory.
[1] A. Leitenstorfer, S. Hunsche, J. Shah, M.C. Nuss, W.H. Knox, Phys. Rev. B 61 (2000) 16642. [2] C. Moglestue, Monte Carlo Simulation of Semiconductor Devices, Chapman & Hall, New York, 1993.