Ultrafast carrier dynamics in InGaN MQW laser diode

Invited Paper Ultrafast carrier dynamics in InGaN MQW laser diode Kian-Giap Gan* a, Chi-Kuang Sun b, John E. Bowers a, and Steven P. DenBaars a a Department of Electrical and Computer Engineering, University of California, Santa Barbara, California, USA 93106; b Department of Electrical Engineering and Graduate Institute of Electro-Optical Engineering, National Taiwan University, Taipei 10617, Taiwan, R.O.C. ABSTRACT The ultrafast carrier dynamics in InGaN multiple quantum well (MQW) laser diodes were investigated using a timeresolved bias-lead monitoring techniques. Both pump and probe beams were from the second harmonic generation (SHG) of a tunable 100-fs Ti:Sapphire modelocked laser. From the optical selection rules of TE and TM polarized lights, one can selectively excite and probe different valance subbands to conduction band transitions in the MQW structure with different polarized pump and probe light. Using this technique, ultrafast inter-subband hole relaxation processes were found to dominate the observed carrier dynamics. Keywords: Ultrafast carrier dynamics; InGaN MQW laser diode; Inter-subband hole relaxation 1. INTRODUCTION The group-iii nitride semiconductor alloys AlN-GaN-InN are recognized as an important material system for the optoelectronic devices in the spectral range from visible to ultraviolet. In particular, GaN-InN based III-V nitride semiconductors are attracting strong interest for their many commercial applications, such as light emitting diodes (LEDs) and laser diodes (LDs). 1,2 The carrier dynamics, which are important for high speed device design, have recently been studied by femtosecond time-resolved pump-probe 3 or coherent spectroscopy 4,5 with above band gap photons, which generate both extra electron and hole distributions. However, various contributions such as electronelectron scattering, hole-hole scattering, electron-hole scattering, electron-phonon interactions, and hole-phonon interactions, mix together and make it very difficult to extract the fundamental material parameter for one particular scattering process or single type of carrier. C. K. Sun et al. and H. Ye et al. have developed an infrared pumpultraviolet probe technique to isolate electron and hole dynamics and used it to study the electron relaxation dynamics in n-type GaN 6, 7 and hole dynamics in p-type GaN 8. In this paper, we present a time-resolved bias-lead monitoring pump-probe technique 9 that uses two UV pulses of equal amplitude with various polarization configurations (TE-TE, TM-TE, and TM-TM) to study the carrier dynamics in the InGaN MQW laser diode. From the optical selection rules of TE and TM polarized lights, one can selectively excite and probe different valance subbands to conduction band transitions in the MQW structure with different polarized pump and probe light. Using this technique, ultrafast intersubband hole relaxation processes were found to dominate the observed carrier dynamics. 2. EXPERIMENTS AND SAMPLE The schematic diagram of the time-resolved bias-lead monitoring setup is shown in Figure 1. The pump and probe beam are derived from the second harmonic generation (SHG) of a tunable 100-fs Ti:Sapphire modelocked laser. Pump and probe beam are combined collinearly and directed to the laser diode under test. Both the pump and probe beam are mechanically chopped at frequencies of 1.7 khz and 2.0 khz respectively. The photocurrent collected from the laser diode was measured by a lock-in amplifier at 3.7 khz as a function of the delay between the pump and probe beam. In order to avoid the interference signal between the pump and probe in the co-polarization configuration, the frequency of the probe beam was shifted by 40 MHz with an acousto-optic frequency shifter. * giap@ece.ucsb.edu; phone 1 805 893-4235; fax 1 805 893-7990 Ultrafast Phenomena in Semiconductors VII, Kong-Thon F. Tsen, Jin-Joo Song, Hongxing Jiang, Editors, Proceedings of SPIE Vol. 4992 (2003) 2003 SPIE 0277-786X/03/$15.00 83

The laser diode under investigated was ridge waveguide MQW InGaN laser diode. The electro luminescence and the lasing spectrum of the laser diode are shown in Figure 2. Notice that the peak of the electro luminescence at TE and TM are separated by 6.6 nm (50 mev). Figure 1: Schematic diagram of the time-resolved pump-probe experiment Figure 2: Electro-luminescence and the lasing spectrum of the MQW InGaN laser diode 3. BAND STRUCTURE AND OPTICAL SELECTION RULES In the wurtize structure, the selection rules for the optical momentum matrix elements for the transitions between the conduction band and the three valence bands can be derived from the symmetry properties of the zone center wave function 10, 11. In the following section, these acronym will be used, C: conduction, HH: heavy hole, LH: light hole and CH: crystal-field splitoff hole. Figure 3 shows the band structure and the optical selection rule of In 0.15 Ga 0.85 N. At the 84 Proc. of SPIE Vol. 4992

zone center (k = 0), C-HH transition will only occur when the light is polarized perpendicular to the c-axis, i.e., TE polarized. The C-CH transition will favor the TM polarized light, i.e., the light polarized along the c-axis. For the LH band, C-LH transition will mostly occur when the light is TE polarized. Away from the zone center, the C-HH transition remains to be TE polarized while the C-CH transition and the C-LH transition switch polarization, i.e., C-CH transition became TE polarized and C-LH became TM polarized. From the Figure 3, it is clear that TM light will excite holes with higher energy compare to the energy of the holes excited by the TE light. So the holes excited by TM light will relax back to the top of the valance band and thus affected the absorption properties of TE light, but not the other way around, i.e., TM will affected TE but TE will not affected TM. Figure 3: Band structure of In 0.15 Ga 0.85 N at (k z = 0) and the optical selection rules In the quantum well (QW) structure, the valance band turns into different valance subbands. And because of the valance band mixing effect, the optical selection rules will need to be modified. We use finite-difference method to solve the effective-mass equations 12 for the quantum well structure. The band structure parameter was taken from the reference 13 and valance band offset of 33% was used. Figure 4 shows the different valance subbands in the QW structure of 30 Å In 0.15 Ga 0.85 N well and In 0.02 Ga 0.98 N barrier. The solution of the effective mass equation was used to calculate the transition matrix element in order to find the optical transition strength for different valance subbands to conduction band transition. The optical transition strengths for the four lowest valance subband to the conduction band transitions are shown in Figure 5. Note that the first significant TM polarized transition occurs at a higher energy compare with the TE polarized transition and the energy separation (~50 mev) is consistence with the electro luminescence measurement. Since the TM polarized light will excite the higher energy hole compare to the TE polarized light, the same prediction for the bulk InGaN will also applied to InGaN QW, i.e., TM will affected TE but TE will not affected TM. Proc. of SPIE Vol. 4992 85

Figure 4: Valance subbands of In 0.02 Ga 0.98 N-In 0.15 Ga 0.85 N-In 0.02 Ga 0.98 N QW structure and the optical selection rules. Figure 5: Normalized transition strength for the first four subband transitions in the QW. 86 Proc. of SPIE Vol. 4992

4. RESULTS AND DISCUSSIONS Figure 6 shows an example of the time-resolved photo current response signal measured at a below-bandgap wavelength. The positive instantaneous signal is attributed to the two-photon absorption (TPA) and the width of this signal is 0.37 ps and is limited by the autocorrelation width of the laser pulse. Figure 6: Time-resolved photocurrent signal at 425nm When we tune the laser wavelength to be above the bandgap of InGaN MQW, different behaviors were observed for different pump-probe polarization configurations. Figure 7 shows examples trace taken at a wavelength of 400nm. As shown in Figure 4, when both pump and probe are TE polarized, there is a negative instantaneous signal and a negative double-sided exponential decay signal. The negative instantaneous signal is attributed to a phase space filling effect with a fast initial relaxation faster than our system time resolution. This initial fast relaxation can be attributed to the carrier thermalization mainly due to carrier-carrier scatterings. The slower negative exponential decay signal with a time constant of 2 ps is attributed to the carrier energy relaxation where carrier-phonon interaction will lead to a new equilibrium between the carriers and the lattice system. However, when both pump and probe are TM polarized, only negative instantaneous signal can be observed. This resolution-limited response suggests an extremely fast intersubband hole relaxation for the TM-generated hole in the LH2 and HH2 subbands into lower HH1 and LH1 subbands, which are only sensitive to the TE polarized light. In order to study this intersubband hole relaxation process, cross polarization configuration measurement was performed and the result is show in Figure 8. Proc. of SPIE Vol. 4992 87

Figure 7: Time-resolved photocurrent signal at 400nm in TETE, TMTM, and TMTE polarization configurations Figure 8: Time-resolved photocurrent signal at 400nm in TMTE polarization configuration In the cross polarization configuration, positive delay means TM polarized light (pump) enters the laser diode before the TE polarized (probe) and negative delay means TE polarized light (pump) enters the laser diode before TM polarized (probe). At positive delay, there is fast initial decay followed by another positive single-sided exponential decay signal 88 Proc. of SPIE Vol. 4992

with the same time constant (2 ps) as the one observed in the TE-TE polarization configuration. The fast initial raise of the observed TE signal supports the previous suggestion that an extremely fast inter-subband hole relaxation for the TM generated holes in LH2 and HH2 subbands relaxed into the HH1 and LH1 subbands. These LH2 and HH2 subbands transferred holes in the lower HH1 and LH1 subbands will then follow a similar thermalization process as the directly generated holes. It is interesting to notice that at negative delay, the signal remains constant, suggesting weak HH1 and LH1 subbands to LH2 and HH2 subband transitions as expected. 5. CONCLUSION The femtosecond carrier dynamics in InGaN MQW laser diode were studied using a time-resolved bias-lead monitoring technique. Using the optical selection rules in the wurtize QW structure and various pump-probe polarizations configurations, ultrafast inter-subband hole relaxation process can be observed. We believe these ultrafast intersubband hole transitions will have a profound influence on the laser gain dynamics of InGaN laser diodes. REFERENCES 1. S. Nakamura, M. Senoh, and T.Mukai,"High-power InGaN/GaN double-heterostructure violet light emitting diodes", Appl. Phys. Lett., 62, 2390-2392,1993. 2. S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, Y. Sugimoto, T. Kozaki, H. Umemoto, M. Sano, and K. Chocho, "InGaN/GaN/AlGaN-based laser diodes with modulationdoped strained-layer superlattices grown on an epitaxially laterally overgrown GaN substrate", Appl. Phys. Lett., 72, 211-213, 1998. 3. C.-K. Sun, F. Vallee, S. Keller, J.E. Bowers, and S. P. DenBaars, "Femtosecond studies of carrier dynamics in InGaN", Appl. Phys. Lett., 70, 2004-2006, 1997. 4. S. Pau, J. Kuhl, F. Scholz, V. Haerle, M.A. Khan, and C. J. Sun, "Femtosecond degenerate four-wave mixing of GaN on sapphire: Measurement of intrinsic exciton dephasing time", Phys. Rev. B, 56, 12718-12721, 1997. 5. R. Zimmermann, A. Euteneuer, J. Mobius, D. Weber, M, R. Hofmann, W. W. Ruhle, E. O. Gobel, B. K. Meyer, H. Amano, and I. Akasaki, "Trasient four-wave-mixing spectroscopy on gallium nitride: Energy splittings of intrinsic exciton resonances", Phys. Rev. B, 56, 12722-12724, 1997. 6. C.-K. Sun, Y.-L. Huang, S. Keller, U. K. Mishra, and S. P. DenBaars, "Ultrafast electron dynamics study of GaN", Phys. Rev. B, 59, 13535-13538, 1999. 7. H. Ye, G. W. Wicks, and P. M. Fauchet, "Hot electron relaxation time in GaN", Appl. Phys. Lett., 74, 711-713, 1999. 8. H. Ye, G. W. Wicks, and P. M. Fauchet, "Hot hole relaxation dynamics in p-gan", Appl. Phys. Lett., 77, 1185-1187, 1999. 9. K. L. Hall, E. P. Ippen, and G. Eisenstein, "Bias-lead monitoring of ultrafast nonlinearities in InGaAsP diode laser amplifiers", Appl. Phys. Lett., 57, 129-131, 1990. 10. G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductor, Wiley, New York, 1974. 11. S. L. Chuang and C. S. Chang, "Effective-mass Hamiltonian for strained wurtize GaN and analytical solutions", Appl. Phys. Lett., 68, 1657-1659, 1996. 12. S. L. Chuang and C. S. Chang, "A band-structure model of strained quantum-well wurtzite semiconductors", Semicond. Sci. Technol., 12, 252-263, 1997. 13. Y. C. Yeo, T. C. Chong, and M. F. Li, "Electronic band structures and effective-mass parameters of wurtize GaN and InN", J. Appl. Phys., 83, 1429-1436, 1998. Proc. of SPIE Vol. 4992 89