We present a study of carrier relaxation in GaAs in the quantum- kinetics regime. The results cannot be explained by Bolzmann kinetics. They are in satisfactory agreement with quantum-kinetic theory calculation of the occupation number in k-space

Bar-Ad, S.

Chemla, D.S.

El Sayed, K.

Kner, P.

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C s n 3 F 4 0 6 W . -  - / I  LBL-38016 uc-404 Lawrence Berkeley Laboratory e UNIVERSITY OF CALIFORNIA Materials Sciences Division To be presented at Quantum Electronics and Laser Science, Anaheim, CA, June 2-7, 1996, and to be published in the Proceedings Photocarrier Relaxation in the Quantum Kinetics Regime S .  Bar-Ad, P. Kner, K. El Sayed, and D.S. Chemla November 1995 ~ ~~~~~ ~ Prepared for the U.S. Department of Energy under Contract Number DE-AC03-76SF00098 , DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. Neither the United States Government nor any agency thereof, nor The Regents of the University of Califor- nia, nor any of their employees, makes any warranty, express or im- plied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any informatiqn, apparatus, product, or process disclosed, or represents that its use would not infringe pri- vately owned rights. Reference herein to any specific commerdal product, process, or service by its trade name, trademark, manufac- turer, or otherwise, does not necessarily constitute or imply its en- dorsement, recommendation, or favoring by the United States Gov- ernment or any agency thereof, or The Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or The Regents of the University of California and shall not be used for advertisng or product endorsement pur- poses. Lawrence Berkeley Laboratory is an equal opportunity employer. 4 LBL 38016 uc-404 . PHOTOCARRIER RELAXATION IN THE QUANTUM KINETICS REGIME S. Bar-Ad', P. Kner', K. El Sayed2, and D. S. Chemlal 1 Department of Physics University of California Berkeley, CA 94720 and Materials Sciences Division Lawrence Berkeley Laboratory University of California Berkeley, CA 94720 2Department of Physics University of Florida Gainesville, FL November 1995 f This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Division of Materials Sciences of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098. Q'r .- --= 1s GTj I &  Photocarrier Relasation in the Quantum Kinetics Resinie S. Bar-Ad (‘), P. Kner(’), K. El Sayxi@), D.S. Chemla(a) (a) Departnrent oJPhvsics, Unirersi[v oJCalifornio at Berkeley and Materials sciences Division, Lawrence Berkeley National Laboratory Ads 2-300, I Cyclolron Rd, Berkeley, C4 94720 Phone: (510) 486-5264 Fox: (51 0) 486-5530 eniail: shinish@ux5.Ibl.gov (b) Department of Physics, University of Florida atGainesville Abstract We prescnt a study of carrier relaxation in GaAs in the Quantum-Kinctics regime. The results cannot be explained by Bolzinann Kinetics. They are in satishctory agreement with Quantum-Kinetic theory calculation of (lie occupation nunibcr in k-space. S. Bar-Ad et d., Ptiotoc;:i-ricr Rdiir:itioii ... Photocarrier Relaxation in the Quantum Kinetics Regime S. Bar-Ad (a), P. Kner(”), K. El Say#’), D.S. Chemla‘”’ (n) Depnrttiient of Physics, University of Cali/ornia at Berkeley and h4nterinis sciences Division, Lmiirence Berkeley nnt ionnl Laborntory MY 2-300, I Cyclotron Rd, Berkeley, C4 91720 (6) Depnrtnient of Ph_vsics, Uniwrsi fy of Florida atGoinemille - The tliennalimtion of tionequilibrium carrier distributions involve fitridarnentals of tliermodynamics and solid states physics. Femtosecond spectroscopy has been employed to study this process,[l] and was analysed in tlie framework of Bolzmann Kinetics.[Z] However, during and shortly afier an ultrashort laser excitation, carrier kinetics are drastically altered. At this early stage the Coulomb potential is stilt unscreened and there is essentially no energy conservation in two-particle scattering events, instead scattering becomes non-local in  time. I n  this regime the evolution of momentum-dependent occupation numbers can only be described by Quantum Kinetics, including memoly structure in tlie scattering integrals. [3] We present a study of carrier relasation in bulk GaAs at room temperature in the Quantum-Kinetics regime. We use a modified freqtienq-resolvcd pump-probe technique, \\it11 pitirip and probe durations independently adjustable from 30fs to 10Ofs. Figure la  shows differential absorption spectra @AS) for 70fs pump and probe at low excess energy. The evolution from a hole-burning-like signal with a characteristic Dynamic Fermi-Edge Singularity @FEs)[4,5] at At- -5Ofs, to a quasi-thermalized profile at At-30fs is clearly seen, in agreement with previous expenments[l]. DAS obtained with 30fs pulses are S~IO\MI in Fig. lb, the higher excitation energy minimizing excitonic eff‘ects. Surprisingly, tlie DAS show an instantaneous response at low energies. Within -5Ofs the DAS is characteristic of a thermalized distribution. The negative signal on the Iugli-energy side, characteristic of the DFES, is absent. Tliere is practically no response at the peak of tlie pump spgruin, in fact hole-burning is not observed nt ali. Such a behavior cannot be esplained by Bolwnann Kinetics, which predict gradual difiision of the initial spectral hole. With 100-fs excitation 2 S. Bar-Ad ef a/., Pilotocat-ricr Rcl;ts;ition ... high above thc band edge and a 304s probc we also dclcct an inslantaiicous resporisc at low energies and no spectral liolc (Fig. 2). This last rcsult is iii agrccnicnt will1 anot licr rccerit espcrinicnt.[6] These observations cannot be explained in tcrriis of coliererit elfccts. Screening by nonequilibnum carriers is expected to be inefktive, as indicated by the excitons’ response. It should riot reduce the Sominerfeld enliancenient significantly. Emission of optical plionoiis is clcarly important. Howevcr, evaluation of the emission rate by Ferini goldcn-nile is inapproprialc, siiicc the inverse optical phonon energy is comparable to tlie time scale of tlie nieasiirenicnts.[7] A consistent esplanation ~ I I  only bc given in llic framework of Qunntum Kinctics. A complete model of the DAS in this fonnalisin is presently iinnvailnblc. Howcucr, \vc giic, in  Fig. 3, an example Quantum Kinetic calculation that includcs clcctron-clcctron scattcring only, showing tlie time-evolution of tlie occupation number in k-space for cscitalion by a 2.043 primp pulse well above tlie band edge. Tlie photocarriers rapidly scatter out of the cnergy window i n  \vliich rhcy were created. Due to the memory, kinetic overshoots develop. We find indications of such ovcrslioots also in tlie esperiinental data. A complete description of tlie DAS requircs inclusion of tlie sliort colicrent probe. We stress that a very short probe is essenfinl for the obsendon of Qunnlum Kinctic cflccts, which are due to the non-locality of scattering. for a probe longer tliaii tlie range of non-locality (memor)l depth), >70 fs, the kinetics become indistinguisliable from local Boltzrnann Kinct ics. References: [I] W.H. Knoy C. Hirlimann, D.A.B. Miller, J. Shali, D.S. Clienila and C.V. Shank, Pliys. Rev. Lett. 56, 1 19 1 (1986). [2] S.M. Goodnick and P. Lugli, Pliys. Rev. B37,2578 (19SS). [3] K. El-Sayed, L. Banyai and H. Haug, Pliys. Rev. BSO, 154 1 (1 994). [4] J.-P. Foing, D. H u h ,  M. JolFre, M.K. Jackson, J.-L. Oudar, C. Tanguy and M. Combescot, Pliys. Rev. Lett. 68, 110 (1992). [5 ]  M.-A. Mycek, J.-Y. Bigot, I. Pemkis and D.S. Clicmla, J. of Nonlin. Opt. Pliys. and Mat. 4, 497 (1995). [GI A. Alesandrou, V. Berger and D. Hulin, Phys. Rcv. B52,4651(1995). [7] A.V. Kuznetsov, Pliys. Rev. B44,8721 (1991) and Pliys. Rev. B U ,  13381 (1991). S .  Bar-Ad et a/., Photoc;in-icr Rc1:is;ltioii ... . .  Figure captions: Figure 1: Spectrally-resolved differential absorption signals nieasured with 704s pulses (a) and 30-fs pulses @). Tlie signals, tneasured for a carrier density of - I*IO” are representative of lower excitation densities as well, down to - I * 10l6 cmJ. Tlie zero dclay is identical for both experiments. Tlie arrows indicate the center laser energy in  cncli a s e .  Figure 2: Spectrally-resolved difl-erential absorption signals iiieasured with a 30-fs probe and two different pump durations - 100 fs (solid) and 30 fs (dashed). I n  both cases an iininediate response is observed at the band edge. The bottom pawl shona the spcctnirii of the 1004s pump (solid) and that of the 30-fs proWunflterd pump (dashed). Figure 3: The time-evolution of the occupation nuniber in k-space after an escitation with a single 20 fs pump pulse, calculated in the framework of Quantum Kinetic theory. 4 e 0.s om. . -133 fs t=.:+ ....... ........................ 1 9.01 9.- I I 1 3  1.40 1.42 1.U 1.46 1.43 1% l a  t 5 t 2 -27 fs o m  0.W 9.M o=b.. m ,,,_I .... ... .._ 0.02 o m * - - . .  :. ....... . .  9.02 9.04 1 e . .  I 138 1.40 1.42 1.44 1.40 130 1U 0.06 0.02 c m ......... probe and unfiltered pump - filtered pump 3 v .. . 0.03 0.02 0.01 0.00 

Photocarrier relaxation in the quantum kinetics regime

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Photocarrier relaxation in the quantum kinetics regime

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