Institut f¨ur Angewandte Photophysik Fachrichtung Physik Fakult¨at Mathematik und Naturwissenschaften Technische Universit¨at Dresden Intraband Dynamics in the Optically Excited Wannier-Stark Ladder Spectrum of Semiconductor Superlattices Dissertation zur Erlangung des akademischen Grades Doctor rerum naturalium (Dr. rer. nat.) vorgelegt von Ben Rosam geboren am 23. Oktober 1973 in Schlema Dresden 2004 verteidigt am 22.04.2005 Contents Publications 3 1 Introduction 7 1.1 The Semiconductor Superlattice: A Model System . ..... 11 2 The Eigenspectrum of Biased Semiconductor Superlattices 15 2.1 Flat-Field Energy Spectrum of a Superlattice . ...... 15 2.2 Wannier-Stark Ladder States . 17 2.2.1 Wannier-Stark Ladder States Detected in the Optical Spectrum . 19 2.2.2 Exciton Wannier-Stark Ladder Transitions . .... 21 2.3 Wave Packets of Wannier-Stark Ladder States: Bloch Oscillations . 27 2.3.1 Manipulation of the Dynamics of Bloch Oscillations . ..... 29 2.4 Wannier-Stark Ladder States in the Regime of Zener Tunneling . 35 3 ZenerTunnelingEffectinSemiconductorSuperlattices 39 3.1 Techniques of Optical Interband Spectroscopy . ...... 40 3.2 ExperimentalTechniques. 43 3.2.1 Linear Absorption Spectroscopy . 43 3.2.2 Time-Resolved Spectroscopy, Transient Four-Wave-Mixing . 44 3.3 Zener Tunneling in Designed Bandstructures . ..... 48 3.4 ExperimentalSet-Up. 52 3.5 Experimental Results and Discussion . 53 3.5.1 Zener Breakdown in a High-Barrier Superlattice . .... 53 3.5.2 Field-Induced Delocalization of Wannier-Stark Ladder States . 56 3.5.3 Tunneling-Reduced Lifetime of Wannier-Stark Ladder States . 60 4 Terahertz Emission of Exciton Wannier-Stark Ladder Wave Packets in Semiconductor Superlattices 71 4.1 Intraband Dynamics Monitored in Terahertz Spectroscopy ........ 75 4.1.1 Mechanisms of Terahertz Emission in Biased Superlattices . 75 4.2 Mechanisms of Difference-Frequency Mixing in Biased Superlattices . 78 4.3 ExperimentalTechniques. 80 4.3.1 Terahertz Time-Domain Spectroscopy . 80 4.3.2 Free-Space Electro-Optic Sampling . 82 1 Contents 4.4 ExperimentalSet-Up. 89 4.4.1 SpectralPulseShaping . 94 4.5 Experimental Results and Discussion . 98 4.5.1 Superlattice Geometry and Characterization . .... 98 4.5.2 Terahertz Emission of Bloch Oscillations: Investigation of Field- and Density-Dependence . 100 4.5.3 Measurement of the Transient Depolarization Field . ...... 108 4.5.4 Manipulation of the Intraband Dynamics of Exciton Bloch Oscil- lations ............................... 111 4.5.5 Intraband Dipole of Wannier-Stark Ladder Excitons . ..... 117 4.5.6 Difference-Frequency Mixing of Exciton Wannier-Stark Ladder Tran- sitions ............................... 123 Conclusions 133 Outlook 139 List of Symbols 143 Bibliography 145 2 Publications Parts of this work have been published or presented: Articles [1] B. Rosam, D. Meinhold, F. L¨oser, V. G. Lyssenko, S. Glutsch, F. Bechstedt, F. Rossi K. K¨ohler, and K. Leo: Field-Induced Delocalization and Zener Breakdown in Semi- conductor Superlattices, Phys. Rev. Lett. 86, 1307 (2001) [2] F. L¨oser, B. Rosam, D. Meinhold, V. G. Lyssenko, M. Sudzius, M. M. Dignam, S. Glutsch, F. Bechstedt, F. Rossi, K. K¨ohler, and K. Leo: Nonlinear transport in superlattices: Bloch oscillations and Zener breakdown, Physica E 11, 268 (2001). [3] S. Glutsch, F. Bechstedt, B. Rosam, and K. Leo: Zener tunneling effect of excitons in shallow superlattices, Phys. Rev. B 63, 085307 (2001). [4] D. Meinhold, B. Rosam, F. L¨oser, V. G. Lyssenko, F. Rossi, Jian-Zhong Zhang, K. K¨ohler, and K. Leo: Polarization revival of a Bloch-oscillating wave packet in conjunction with resonant Zener tunneling, Phys. Rev. B 65, 113302 (2002). [5] B. Rosam, K. Leo, M. Gl¨uck, F. Keck, H. J. Korsch, F. Zimmer, and K. K¨ohler: Lifetime of Wannier-Stark states in semiconductor superlattices under strong Zener tunneling to above-barrier bands, Phys. Rev. B 68, 125301 (2003). [6] Lijun Yang, Ben Rosam, Jean-Marc Lachaine, Karl Leo, and M. M. Dignam: In- traband Polarization and Terahertz Emission in Biased Semiconductor Superlattices with Full Excitonic Basis, Phys. Rev. B 69, 165310 (2004). [7] B. Rosam, L. Yang, K. Leo, and M. M. Dignam: Terahertz Generation by Difference- Frequency Mixing of Exciton Wannier-Stark Ladder States in Biased Semiconductor Superlattices, Appl. Phys. Lett. 85, 4612 (2004). [8] Lijun Yang, Ben Rosam, Karl Leo, and M. M. Dignam: Density-dependent THz emission in biased semiconductor superlattices: From Bloch oscillations to plasma oscillations, Phys. Rev. B, submitted. 3 Publications Conference Contributions [1] B. Rosam, D. Meinhold, F. L¨oser, V. G. Lyssenko, K. Leo, S. Glutsch, F. Bechstedt, and K. K¨ohler: Field-Induced Delocalization and Zener Breakdown in Semiconduc- tor Superlattices, Sixth International Workshop on Nonlinear Optics and Excitation Kinetics in Semiconductors, Marburg, Germany, 2000. [2] B. Rosam, D. Meinhold, F. L¨oser, V. G. Lyssenko, K. Leo, M. Gl¨uck, A. R. Kolovsky, H. J. Korsch, and K. K¨ohler: Lifetime Broadening of Wannier-Stark States under Strong Zener Tunneling, Quantum Electronics and Laser Science Conference, Balti- more, United States, 2001. [3] D. Meinhold, B. Rosam, F. L¨oser, V. G. Lyssenko, and K. Leo: Observation of wave packet revivals in semiconductor superlattices, Quantum Electronics and Laser Science Conference, Baltimore, United States, 2001. [4] B. Rosam, D. Meinhold, F. L¨oser, V. G. Lyssenko, S. Glutsch, F. Bechstedt, F. Rossi, M. Gl¨uck, A. R. Kolovsky, H. J. Korsch, K. K¨ohler, and K. Leo: Dynamics of Zener Tunneling in Semiconductor Superlattices, The 12th International Con- ference on Nonequilibrium Carrier Dynamics in Semiconductors, Santa Fe, United States, 2001. [5] F. L¨oser, B. Rosam, D. Meinhold, V. G. Lyssenko, M. Sudzius, M. M. Dignam, S. Glutsch, F. Bechstedt, F. Rossi, K. K¨ohler, and K. Leo: Nonlinear transport in superlattices: Bloch oscillations and Zener breakdown, Rutherford Memorial Work- shop on Semiconductor Nanostructures, Queenstown, New Zealand, 2001 [6] D. Meinhold, V. G. Lyssenko, K. Leo, and B. Rosam: Polarization revival of a Bloch-oscillating wave packet at resonant Zener tunneling in GaAs shallow super- lattices, 10th International Symposium on Nanostructures, St. Petersburg, 2002. Proceedings of SPIE 5023, June 2002, 498–500. [7] C. P. Holfeld, B. Rosam, D. Meinhold, S. Glutsch, W. Sch¨afer, J. Zhang, M. Gl¨uck, H. J. Korsch, F. Rossi, K. K¨ohler, and K. Leo: New results on high-field transport in semiconductor superlattices, invited talk, 26th International Conference on the Physics of Semiconductors , Edinburgh, 2002. Institute of Physics Conference Series Number 171, 177–184, 2002. [8] B. Rosam, D. Meinhold, K. Leo, F. Keck, M. Gl¨uck, H. J. Korsch, and K. K¨ohler: Strong reduction of the lifetime of Wannier-Stark states in semiconductor superlat- tices by tunneling to higher bands, 13th International Conference on Nonequilibrium Carrier Dynamics in Semiconductors, Modena, 2003. 4 1 Introduction It is an issue of fundamental importance in solid-state physics to explore the carrier spectrum and carrier dynamics in a periodic potential in the presence of a uniform static electric field. Closely related is the understanding of the field-dependent op- tical and transport properties of semiconductors. The knowledge is important for applications, for example to the construction of semiconductor heterostructures with engineered properties which have far-reaching applications, with opto-electronic de- vices being a key example. In their early works, F. Bloch [1] (1928) and C. Zener [2] (1934) predicted two fundamental quantum mechanical phenomena of competing nature which have been a topic of great interest and controversy over the last decades. For high electric fields, Bloch predicted the oscillatory spatial motion of carriers in the periodic dis- persion relation of an energy band. Zener showed that interband tunneling of carriers can occur for high fields leading to an electrical breakdown. These pioneering find- ings triggered a long-standing theoretical debate, whether the coherent carrier Bloch oscillations can exist or instead the intraband coherence is destroyed by Zener tun- neling to higher bands. A related question is whether or not the Wannier-Stark ladder discretization of the carrier spectrum is observable. A milestone of research on this issue was the proposal to realize semiconductor crystals with an artificial periodicity, semiconductor superlattices, by L. Esaki and R. Tsu [3] in 1970. Advances in semiconductor epitaxial growth technology allowed them to be grown. In superlattices, the carrier band structure can be tailored by the proper choice of their geometry. Therefore, they became a playground for the study of coherent high-field transport phenomena in a periodic potential with applied static electric field. Key experimental results1 could be obtained: for example, the demonstration of negative-differential-conductivity in transport measurements [7], the observation of Wannier-Stark ladder resonances in the optical spectrum [8, 9] and its dynamic analog, Bloch oscillations in four-wave-mixing experiments [10,11]. In this work, semiconductor superlattices were employed to investigate the intra- band dynamics in the optically excited Wannier-Stark ladder spectrum. The work is dedicated to the investigation of both high-field transport phenomena which were introduced above. It is organized as follows: In the first Chapter, the employed semi- conductor heterostructure system is introduced. It is followed by an introductory 1Reviews