Coulomb Damped Relaxation Oscillations in Semiconductor Quantum ...

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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 13, NO. 5, SEPTEMBER/OCTOBER 2007

Coulomb Damped Relaxation Oscillations in Semiconductor Quantum Dot Lasers Ermin Malić, Moritz J. P. Bormann, Philipp Hövel, Matthias Kuntz, Dieter Bimberg, Member, IEEE, Andreas Knorr, and Eckehard Schöll

Abstract—We present a theoretical simulation of the turn-on dynamics of InAs/GaAs quantum dot semiconductor lasers driven by electrical current pulses. Our approach goes beyond standard phenomenological rate equations. It contains microscopically calculated Coulomb scattering rates, which describe Auger transitions between quantum dots and the wetting layer. In agreement with the experimental results, we predict a strong damping of relaxation oscillations on a nanosecond time scale. We find a complex dependence of the Coulomb scattering rates on the wetting layer electron and hole densities, and we show their crucial importance for the understanding of the turn-on dynamics of quantum dot lasers. Index Terms—Coulomb scattering rates, quantum dot (QD) lasers, relaxation oscillations.

I. INTRODUCTION EING EXCELLENT candidates for future data and telecom applications, semiconductor quantum dot (QD) lasers are in the focus of current research [1]. In particular, great effort has been put into the development of infrared QD lasers for high data transmission rates. QD lasers show a high potential for fast dynamical response, which is strongly dependent on the frequency and the damping rate of relaxation oscillations (ROs) [2] evolving during the turn-on processes of a gain switched laser. Damped ROs, e.g., are known to be advantageous for open eyes and low bit-error rates (BER) at large bit rates [3]–[5]. QD lasers have been found to show a strong damping of ROs compared to quantum well lasers [6], [7]. The underlying dynamic mechanisms are still being discussed [8], [9]. In this paper, a detailed microscopic analysis of the turnon dynamics of single-mode InAs/GaAs QD lasers pumped by a nanosecond current pulse is presented [10]. We go beyond the standard phenomenological laser rate equations [11]–[16] similar to those used in quantum well lasers [17]–[19] by incorporating microscopic kinetic equations, which describe the Coulomb scattering processes [20], [21]. This approach takes into account the microscopic interaction and charge transfer between QDs and the wetting layer (WL) evolving in the process of fabricating self-organized QDs [22]. We calculate the Coulomb

B

Manuscript received October 31, 2006; revised July 25, 2007. This work was supported in part by Studienstiftung des deutschen Volkes, and in part by the research center Sfb 296, Deutsche Forschungsgemeinschaft. E. Malić, M. J. P. Bormann, P. Hövel, A. Knorr, and E. Schöll are with the Institut fuer Theoretische Physik, Technische Universitaet Berlin, 10623 Berlin, Germany (e-mail: [email protected]; [email protected]; ph¨[email protected]; [email protected]; [email protected]. tu-berlin.de). M. Kuntz and D. Bimberg are with the Institut fuer Festkoerperphysik and Center of Nanophotonics, Technische Universitaet Berlin, 10623 Berlin, Germany (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/JSTQE.2007.905148

matrix elements and determine the scattering rates for capture processes between continuous WL and localized QD states in the framework of the Boltzmann equation. We show that for typical QD lasers, the interplay of the induced emission and absorption and the scattering processes leads to strongly damped ROs in both the photon and charge carrier densities. Our simulations explicitly take the strongly nonlinear dependence of scattering rates on the WL carrier densities into account. This paper is organized as follows. In Section II, we describe the theoretical background and discuss the set of coupled equations of motion for the photon and charge carrier densities. The Coulomb scattering rates are determined and analyzed as a function of the WL carrier density in Section III. Section IV contains our results on the turn-on dynamics of both the photon density and charge carriers in QDs and WL. We discuss the generation of relaxation oscillations and their properties. Finally, Section V concludes the paper. II. THEORETICAL MODEL The laser dynamics is determined by the rate equations for the photon density nph and the charge carrier densities in QDs nb and in the WL wb , where b = e, h stands for electrons and holes, respectively n˙ b = −

1 nb + Sbin N QD τb

− Rind (ne , nh ) − Rsp (ne , nh ), n˙ ph = −2κnph + ΓRind (ne , nh ) + βRsp (ne , nh ),

(1) (2)

WL

w˙ b =

j(t) nb N ˜ sp (we , wh ). (3) + − Sbin N WL − R eo τb N QD

The explanation of the used abbreviations is given in the following discussion of the different contributions. We consider a two-level system for electrons and holes in the QDs, since the carrier relaxation processes within the WL and within the QD states are much faster (∼1 ps) than capture processes from the WL into the QDs at high WL carrier densities [23]. As a result, only the energetically lowest electron and hole levels in the QDs contribute crucially to the laser dynamics [20]. The latter is determined by the following contributions. 1) An important contribution to the dynamics of QD lasers is made by carrier–carrier scattering processes. The scattering rates Sein , Seout , Shin , Shout of electrons (e) and holes (h) in out −1 + Se/h ) are a measure and scattering times τe/h = (Se/h for the strength of these processes. We derive these rates microscopically and analyze their dependencies upon the WL carrier densities in Section III.

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MALIC´ et al.: COULOMB DAMPED RELAXATION OSCILLATIONS IN SEMICONDUCTOR QUANTUM DOT LASERS

2) The induced processes of emission and absorption are ˆ (ne + nh − N QD ) nph . Here, expressed by the rate Rind ≡ W QD N denotes twice the QD density (taking into regard spin ˆ ≡ W A, with W as the Einstein coefficient degeneracy) and W and with A as the WL normalization area. In our approach, the carrier–light interaction is considered with the assumption of only one effective light mode (single photon number nph ) dominating over all other modes. The optical confinement factor Γ in (2) expresses the difference of the optical and electronic active area. It can be split into an in-plane and a vertical confinement factor Γ ≡ Nl Γxy Γz with Nl as the number of QD layers [1]. The in-plane component Γxy is given by the product of the QD density N QD and the in-plane size of a QD Axy (coverage with QDs). The vertical confinement Γz expresses the vertical overlap of QDs and optical modes, averaged over the plane of area A. 3) The spontaneous emission given by Rsp (ne , nh ) ≡ ˜ ne nh is governed by bimolecular recombination [17], [18]. W The WL spontaneous recombination rate is expressed by ˜ sp (we , wh ) = W ˜ we wh with W ˜=W ˜ N QD /N WL and W ˜ ≡ R QD with the WL effective density of states N WL = W/N 4 × 1013 cm−2 . Both spontaneous emission and induced processes are proportional to the Einstein coefficient W = |µ|2 ω 3 √ 3π ε 0 ¯h ( c/ ε bg ) with the dipole moment µ, the background dielectric constant εbg , the vacuum permittivity ε0 , the velocity of light c, Planck’s constant ¯ h, and the frequency ω. 1 ln(r1 r2 )] c expresses the 4) The coefficient κ = [κint − 2L total cavity loss, where L is the cavity length, and r1 , r2 are the facet reflection coefficients [1]. The internal losses κint = 200 m−1 are adapted to the experimental realization of QD lasers [24]. Finally, the spontaneous emission coefficient β stands for the probability that the photons generated during the spontaneous emission contribute to the considered laser mode in the cavity. 5) Pump processes are expressed by the injection current density pulse j(t). Equation (3) also contains the elementary charge e0 . III. COULOMB SCATTERING RATES The active medium of the investigated InAs/GaAs QD lasers consists of self-assembled QDs formed spontaneously on a WL within the Stranski–Krastanow growth. As a result, the considered QD-WL structure shows a finite number of discrete electronic states localized around the QDs, as well as a quasicontinuum of delocalized electron and hole states at higher energies within the WL. The interaction of these different states is crucial for the carrier dynamics in a QD laser. The applied injection current pulse initially generates charge carriers in the WL. These have to be captured into the bound QD states before the laser transition can take place. Since in the lasing regime, the WL carrier density is very high, the capture processes are dominated by Coulomb scattering (nonlocal Auger recombination) [23], [25], [26], which is also supported by the modeling of QD transport experiments [27], [28]. Our approach also includes the electron–phonon scattering for the cooling process in the WL, but neglects it for scattering into the QD states.

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Fig. 1. Scheme of the QD-WL structure showing the considered Auger capture processes for electrons. (a) Electron–electron scattering. (b) Electron–hole scattering.

The Coulomb scattering rates describing the capture of carriers from the WL into the QD states for electrons and holes are calculated microscopically as a function of the WL electron and hole density we or wh , respectively. The Coulomb interaction is considered up to the second order in the screened Coulomb potential and under the restriction to time scales where the Markov approximation is applicable [29], [30], [32] ρ˙ b = Sbin (1 − ρb ) − Sbout ρb

(4)

where ρb is the occupation probability in the electron/hole QD state (b = e, h). This Boltzmann-like equation contains Coulomb in- and out-scattering rates given by 2π in/out in/out ∗ ∗ Sb = Mbn lm (2Mbn lm − δb,b Mbn m l )flm n b ¯h lm n b b (5) × δ E b + Enb − Elb − Em with the sum over all WL states (occupation probabilities ρbl , ρbm , in ρbl ρbm (1 − ρbn ) and and ρbn ) and with the abbreviations flm n b = out b b b b b b b flm n b = ρn (1 − ρm )(1 − ρl ). E , El , Em , and En are the respective energies. Fig. 1 illustrates the considered QD-WL structure showing the electron–electron (b = b) and electron–hole (b = b) Auger capture processes. While an electron scatters from a WL state into the energetically lower ground state of a QD, another electron [Fig. 1(a)] or a hole [Fig. 1(b)] scatters into an energetically higher level within the WL. The energy conservation is fulfilled at the end of the entire process. The capture of holes proceeds analogously [20]. For the evaluation of the Coulomb matrix elements Mabcd and the scattering integrals in (5), we use the approach of [7] and [12]: For a WL extended in the x-y plane, the wave function for the whole QD-WL system can be separated into the inρ), the z-component ξσb (z), and the Bloch plane component ϕbl (

b function u ( r) ρ) ξσb (z) ub ( r). Φbl,σ ( r) = ϕbl (

(6)

The in-plane component of the confined QD states is approximated by the eigenfunctions of the two-dimensional harmonic 2 b ωb ρ) = m¯hb πω b exp(− m2¯ oscillator ϕbQD (

h ρ ) with the electron (hole) effective mass mb and oscillator frequency ωb , assuming that QDs have a small aspect ratio [31]. The in-plane component of the WL states is described by orthogonalized plane

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Fig. 2. Illustration of the effective well width approximation. At L eff , the wave functions of the finite well have decreased to one-tenth of their maximal value. Within the effective well width approximation, we consider the eigenfunction of the infinite barrier well with the effective well width L eff .

waves (OPWs) [22] |ϕk =

1 |ϕ˜k − ϕiQD |ϕ˜k |ϕiQD N (k) i

(7)

with the plane waves (PWs) ϕ˜k = √1A exp(i k · ρ

) and the nor i malization factor N (k) = 1 − | i ϕQD |ϕ˜k |2 . The index i denotes the different bound states of a QD. The OPWs are more realistic than just PWs, since they take the influence of the QD confinement potential into account by orthogonalizing the PWs ρ). The PW approach leads ϕ˜k to the bound QD state ϕiQD (

to considerably larger Coulomb matrix elements and scattering rates [22]. The strong confinement in the direction perpendicular to the WL is considered by assuming an infinite barrier at z = ±L/2

and, hence, a wave function ξ(z) = L2 cos( Lπ z) for |z| ≤ L/2 and ξ(z) = 0 for all other z. For numerical reasons, we apply the effective well width approximation [33]. Here, the wave function of a finite barrier well with a physical well width L is approximated by the infinite barrier wave function with an effective width Leff (see Fig. 2). The calculation of the scattering rates takes the quasiFermi distribution over the involved electronic states into account. Furthermore, we include screening by applying the twodimensional static limit of the dynamic Lindhard equation W (q) ≡

Vq2D Vq2D →

(q) 1 + κq0

(8)

with the dielectric function (q), the two-dimensional inverse screening length κ0 =

b=e,h

2mb e20 ε0 εbg ¯ h2

¯ 2 π ωb h 1 − exp − kB T mb

and the two-dimensional Fourier transform of the Coulomb matrix element Vq2D . The influence of the background is expressed by the phenomenological dielectric constant εbg . Having determined the wave functions and the screening, we can now give a fully analytical expression for the Coulomb matrix elements describing capture processes from WL states

Fig. 3. Coulomb scattering rates for electrons and holes calculated within the OPW approach.

into the ground state of a QD Mb k 2 k 3 k 1 = c0

¯h

1

F (q) exp −

k1 − q κ0 + q 2mb ωb (9)

with

q = k2 − k3 , q = 0 and c0 ≡ e2 /(ε0 εbg A3/2 ) ¯hπ/(mb ωb ). The Coulomb matrix element is determined by the exponential function resulting from the eigenfunction of the two-dimensional harmonic oscillator and by the form factor  2 2 1 2 4π 2  . + (1 − e−L q )  F (q) = 2 − 6 4π 2 Lq Lq + 4π L 2 q q + 2 Lq L

To calculate the scattering rates from (5), we set the energy of the QD electron and hole states according to [34], taking QDs of a length of 17 nm into account. We correct these energies for the room temperature using the Varshni equation E(T ) = E(0) − (αT 2 /(β + T )) with the coefficients α, β taken from [35]. In Fig. 3, the Coulomb scattering rates for electron and hole capture processes in the investigated InAs/GaAs QD-WL structure are shown as a function of the respective WL electron and hole densities. Generally, the Coulomb scattering rates are larger for increasing WL carrier densities wb due to the increase of available scattering partners. The Pauli exclusion principle, however, stops the increase of the out-scattering for higher wb , resulting in a maximum of Sbout . The out-scattering processes become irrelevant for large WL carrier densities. Due to the larger effective mass, the population of WL states with holes proceeds more slowly. As a result, the effect of the Pauli exclusion principle is stronger on electrons explaining the faster decrease of Seout in Fig. 3. The in-scattering processes become dominant at considerably large WL carrier densities. At small wb , the number of available scattering partners is low. Sbin increases with the increasing population of the WL states. Due to the already mentioned faster population of electronic states, Sein is enhanced much faster than Shin . At very high wb , even the in-scattering processes become


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Fig. 5. Response of the QD charge carrier densities n e (t), n h (t) to a current pulse (described in Fig. 7). The insets show blow-ups of the ROs (the inset axes have the same units as the main graph). Fig. 4. Comparison of the Coulomb out-scattering rates for electrons and holes calculated within the OPW and the PW approach. A similar result is obtained for the in-scattering rates.

weaker because the WL states are entirely filled. As a result, the electron–electron and electron–hole processes shown in Fig. 1 become less probable. Fig. 4 compares the Coulomb scattering rates for electrons and holes obtained within the approach of OPWs and of simple PWs. Taking the influence of the QD confinement potential into account, i.e., applying the OPW method, leads to a general reduction of scattering rates. For the PW approach, the Coulomb matrix elements and the scattering rates are enhanced due to the nonvanishing overlap of the QD and WL wave functions. This overlap is higher for hole states since they are energetically closer to the corresponding WL states. As a result, the enhancement of the scattering rates for holes is stronger. IV. TURN-ON DYNAMICS In this section, we discuss the turn-on dynamics of InAs/GaAs QD lasers. We apply an injection current density pulse j(t) of 5 ns width (symmetric Gaussian-like pulse with a rise and fall time of 100 ps) to obtain an inversion. During the pulse, the WL states become filled with charge carriers. Driven by the Coulomb interaction they are captured into the bound QD states. The set of coupled nonlinear differential equations (1)–(3) describes the dynamics of an InAs/GaAs QD laser. The parameters1 are fixed in agreement with recent experimentally investigated QD laser structures [5], [24]. The microscopically calculated Coulomb scattering rates are included into the equations, taking explicitly into account their strongly nonlinear dependence upon the WL carrier densities we , wh . The peak current density is assumed to be slightly above the laser threshold. The numerical solution of (1)–(3) is shown in Figs. 5–8. Fig. 5 illustrates the dynamics of carrier densities ne , nh . Both quantities show weak relaxation oscillations before 1 κ = 0.4 ps−1 , W = 4.7 × 10−3 ps−1 , N QD = 2.0 × 1010 cm−2 , A = 4.0 × 10−9 m2 , L = L eff = 8 nm, β = 5.0 × 10−5 , Γ = 5 × 10−3 , εbg = 13.18, E e (T = 0) = 280 meV, E h (T = 0) = 190 meV. In the simulation, T = 300 K.

Fig. 6. Response of the WL carrier densities w e (t), w h (t) to a current pulse (shown in Fig. 7).

reaching the corresponding stationary values. The rise time is dominated by the in-scattering term (picosecond range) in (1), whereas the fall time is much longer due to slower radiative processes (nanosecond range). The electron density ne has a higher stationary value than nh due to the larger electron inscattering rate Sein (see Fig. 3). In Fig. 6, the evolution of the WL carrier densities we (t), wh (t) as response to the application of the injection current pulse j(t) is shown. In analogy to the QD carrier densities ne (t), nh (t), their rise and fall times are determined by scattering and radiative processes, respectively, resulting in clearly different time scales. Contrary to ne (t), nh (t), the stationary value of the WL hole density wh is higher than the one of we . The reason lies in the higher in-scattering rate Sein (see Fig. 3) that leads to a loss of charge carriers in the WL. The insets show the generation of weak but strongly damped ROs. The dynamics of the photon density nph is shown in Fig. 7(a). After a turn-on delay of 0.8 ns, the photon density increases exponentially. It performs ROs with a frequency of 12.5 GHz that are damped toward a stationary value. The photon density shows much more pronounced ROs than the QD and WL carrier densities. The dynamics of nb is slowed down by the capacitative inertia of the charge carriers. The ROs result from the interplay of electron filling, induced emission, and absorption processes. The Coulomb scattering rates S b are not given in an analytical form, and they show a strongly nonlinear dependence on the

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tions that could slow down the dynamics. We expect, however, qualitatively similar results when considering additional bulk– QD interactions. V. CONCLUSION

Fig. 7. (a) Response of the photon density n ph (t) to a current pulse (dashed) t −t 0 n j(t) = j0 exp[−( 2. 5ns ) ] with a rise and fall time of 100 ps (n = 56) and with j0 = 1.1jt where jt is the threshold current density. All initial values are set to zero except for the WL carrier densities w e , w h , which are set to 0.1% of their maximum values. (b) Experimental result for an InAs/GaAs QD laser with a wavelength of 1.3 µm.

We have presented the theory and numerical simulations of the turn-on dynamics of InAs/GaAs QD semiconductor lasers. Our theory combines standard laser rate equations with microscopic kinetic equations describing Coulomb scattering rates for capture processes between continuous WL states and localized QD states. We calculate the rates microscopically, and take their strongly nonlinear dependence upon the WL carrier density into account. Our simulations predict the generation of relaxation oscillations on a nanosecond time scale during the turn-on processes of QD lasers. Our results are in a good agreement with the experimental data predicting a strong damping of relaxation oscillations. We show that the characteristic strong damping of the relaxation oscillations in a QD laser can be explained by the Coulomb interaction of the charge carriers within the QD-WL structure. Other processes, such as electron– phonon scattering and WL–bulk interaction, play a minor role for a qualitative description of the turn-on dynamics. Their inclusion would improve our model, and would prospectively lead to a better quantitative agreement with the experiment. ACKNOWLEDGMENT The authors would like to thank H. C. Schneider (Kaiserslautern), M. Lorke, and F. Jahnke (Bremen) for valuable discussions. REFERENCES

Fig. 8. Phase portrait of the photon density n ph versus the QD electron density n e showing the dynamic response of the QD laser to a current pulse (like in Fig. 7).

WL carrier densities. Hence, the frequency and the damping rate of relaxation oscillations cannot be expressed analytically. The delay time is due to the initially empty QD states that first need to be filled with charge carriers. After the current pulse is switched off, nph decays exponentially. The phase portrait in Fig. 8 illustrates this interplay. The evolution of the photon density nph is shown as a function of the QD electron carrier density ne . In Fig. 7(b), the results are compared to the ROs measured in QD lasers that correspond to our modeled WL-QD structure [24]. In the experiment, the photon density shows a dynamics that is in reasonable agreement with the theoretical result. In both cases, similar pronounced ROs with a frequency on an inverse nanosecond time scale are obtained. In particular, the turn-on delay time of the dynamics is reproduced (0.8 ns); the oscillation frequency, however, is predicted to be twice as fast as that in the experiment. Furthermore, the relative amplitude of ROs is smaller than in the experiment. These deviations may probably be traced back to several approximations, such as the use of a single-mode theory and the neglect of WL–bulk interac-

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Ermin Malić was born in Livno, Bosnia, in 1980. He received the Diploma in physics from Technische Universität Berlin, Berlin, Germany, in 2005. He was a Visiting Scholar at Massachusetts Institute of Technology, Cambridge, MA, in 2006. His research interests include microscopic modeling of quantum dot lasers and theory of optical properties of carbon nanotubes. Mr. Malić is a Fellow of Studienstiftung des deutschen Volkes.

Moritz J. P. Bormann was born in Munich, Germany, in 1978. He received the Diploma from the Institute for Theoretical Physics, Technische Universität Berlin, Berlin, Germany, in 2007. His research interests include modeling of the nonlinear dynamics of optoelectronic devices, such as quantum dot lasers, with a focus on application of those devices and models.

Philipp Hövel was born in Berlin, Germany, in 1980. He received the Diploma in physics from the Technische Universität Berlin, Germany, in 2004. From 2002 to 2003, he was a Visiting Scholar with the Duke University, Durham, NC. His current research interests include semiconductor quantum dot lasers, nonlinear dynamics and chaos control, in particular investigating time-delayed feedback methods.

Matthias Kuntz was born in Berlin, Germany, in 1975. He received the Diploma in physics and the Ph.D. degree in physics from the Technische Universität Berlin, Germany, in 2000 and 2005, respectively. His research interests include direct modulation and mode-locking of quantum dot edge emitters and the modeling of the dynamics of these devices.

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Dieter Bimberg (M’92) received the Diploma in physics and the Ph.D. degree in physics from Goethe University, Frankfurt, Germany, in 1968 and 1971, respectively. From 1972 to 1979, he was a Principal Scientist with the Max Planck Institute for Solid State Research in Grenoble, France, and Stuttgart, Germany. He joined the Technical University of Aachen, Aachen, Germany, as a Professor of electrical engineering in 1979. Since 1981, he has been the Chair of Applied Solid State Physics with the Technische Universitaet Berlin, Berlin, Germany, where he has been the Executive Director of the Solid State Physics Institute since 1990, and the Director of the Center of Nanophotonics since 2004. He has authored more than 800 papers, patents, and books resulting in more than 16000 citations worldwide. His research interests include the physics of nanostructures and photonic devices, including quantum dot lasers and amplifiers, wide-gap semiconductor heterostructures, and ultrahigh-speed photonic devices. Dr. Bimberg received the Russian State Prize in Science and Technology in 2001, and the Max-Born-Award and Medal in 2006. He is a member of the German Academy of Natural Sciences Leopoldina and the American Physical Society.

Andreas Knorr was born in Erfurt, Germany, in 1965. He received the Diploma in physics and the Ph.D. degree in physics from Friedrich-Schiller University of Jena, Jena, Germany, in 1990 and 1993, respectively. From 1991 to 1992, he was a Visiting Scholar with the Universities of New Mexico and Arizona. From 1994 to 2000, he was a Research Associate with the University of Marburg, Marburg, Germany. Since 2000, he has been a Professor of theoretical physics with the Technische Universität Berlin, Berlin, Germany. From 2003 to 2004, he was a Guest Professor with the University of Arizona, Tucson, and with NTT, Tokio, Japan. Since 2004, he has been the Vice Chairman of the Collaborative Research Center “Growth Related Properties of Semiconductor Nanostructures,” Berlin, Germany. He is the author of over 100 research publications and has given over 25 invited presentations at international conferences. His research interests include nonlinear optics, quantum electronics, laser theory, and dynamics of low-dimensional nanostructures. From 1991 to 1993, he was a Fellow of the Studienstiftung des deutschen Volkes.

Eckehard Schöll was born in Stuttgart, Germany, in 1951. He received the Diploma in physics from the University of Tübingen, Tübingen, Germany, in 1976, the Ph.D. degree in applied mathematics from the University of Southampton, Southampton, U.K., in 1978, and the Dr. rer.nat. degree and the venia legendi from Aachen University of Technology, Aachen, Germany, in 1981 and 1986, respectively. From 1983 to 1984, he was a Visiting Assistant Professor with the Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI. Since 1989, he has been a Professor of theoretical physics with the Technische Universität Berlin, Berlin, Germany, where he has been the Director of the Institute for Theoretical Physics since 2001. His research interests include nonlinear dynamics, pattern formation, chaos, noise, control, theory of transport in semiconductor nanostructures, laser dynamics, and self-organized growth kinetics. He is the author of about 300 research papers and three books. He has been the Editor of several monographs and topical journal issues. Prof. Schöll has organized several international conferences including Dynamics Days Europe in 2005.