P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, J. Shah, R. L. Fork, J. E. Cunningham, J. E. Henry, and C. V. Shank

A T& TBell Laboratories, Holmdel, New Jersey 07733

  The process of intervalley scattering of optically excited carriers in GaAs is investigated using optical pulses of 6 fs duration. The fast time resolution in these experiments obvi- ates the need for elaborate deconvolution analyses which have been a limitation in previous work. (1,2) Average scattering rates are determined for both the G - X and G - L intervalley scattering events.

  Pump-probe experiments were done with two 6 fs pulses, with the GaAs sample at room temperature, to resolve the fast scattering of the carriers out of the G valley. The scattering time, which is primarily determined by scattering into both the X and L valleys, was measured to be 33 fs. Measurements were also made at low temperatures, where the increase in energy band gaps prevents the photoexcited electrons from scattering into the X valley, for excitation with a sufficiently narrow spectral bandwidth. This allows us to separately determine the G -L scattering rate at T= 35 K.

The experiment was performed using compressed optical pulses phase corrected to third order in a manner described previously. (1) The duration of the excitation pulses was measured to be in the range 6-10 fs using the second harmonic up-conversion technique. The spectral distribution of the pulses was in the range 1.85-2.15 eV. The pulse repetition rate was 8 kHz and the pulse energy was about 1 nJ. The pulses were split using a modified Michelson interferometer configuration to form the two excitation pulses. The two pulses were focused with a 5 cm focal length lens into a 0.1 m m-thick sample of GaAs grown by molecular beam epitaxy. Both faces of the sample were antireflection coated. The excitation pulse energy at the sample was approximately 0.1 nJ per pulse, which corresponds to carrier densities on the order of a few times 10^18 cm^-3. The carrier density was estimated by measuring the number of photons absorbed in the material. The spot size of the focused beam was measured to be 30 m m in diameter.

  In Fig. I we have plotted the induced transmittance measured with 6 fs optical pulses. A rapid decay is observed followed by a slow decay with a time constant of 1. 5 ps consistent with previous measurements. (1,2,4) This longer time constant has been previously interpreted as being due to thermalization of the carrier distribution to the lattice temperature via carrier-phonon interactions within the G band. (4) The fast time component is revealed by subtracting the 1.5 ps time response from the data leaving a clearly resolved single fast decay with a time constant of 33 fs. No variation in the decay time constant was observed for densities in the range 3x10^18 - 6x10^18 cm^-3.

We interpret the 33 fs decay in terms of the band structure of GaAs. Excitation at 2.0 eV produces three distributions of electrons and holes. Transitions originate from the heavy- and light-hole bands and the split-off band, with relative strengths of approximately 40%, 40%, and 20%, respectively. Several scattering processes can contribute to removing carriers from the optically excited regions. Due to the large bandwidths of our pump and probe pulses, optical phonon emission or absorption by either electrons or holes does not make a significant contribution to our signal. However, the more energetic portions of the hot-electron distribution can scatter to both the X and L valleys and leave the optically excited region. There are no valleys to which the holes can scatter so we attribute the rapid 33 fs decay of the signal to scattering of the hot-electron distribution to the X and L valleys, integrated over energy.

We can obtain further information on the scattering processes by varying the temperature of the lattice. When the lattice temperature is lowered to 35 K, the band gaps increase by 100-140 meV. (5) This eliminates scattering into the X valley for a sufficiently narrow spectral bandwidth excitation (for example, that of a 50 fs duration pulse, as discussed below).

The pump-probe experiment was repeated using a somewhat longer pump pulse (50 fs) at 2.0 eV and a probe pulse of 6 fs, with the sample mounted in a Dewar. The results are plotted in Fig. 2. At 295 K an initial rapid decay in the induced transmittance, integrated over the bandwidth of the 6 fs probe pulse is observed that is instrument limited, which is consistent with the data of Fig. 1. The peak change in the induced integrated transmittance is a few percent. For delays greater than I ps, a rise in the transmittance is seen which we attribute to electrons that were scattered to the X valley and return to the rvalley.,The time constant for this process is several picoseconds. At 35 K a slower initial decay is observed, as expected, since scattering events to the X valley are no longer energetically allowed.

  At 35 K, there is no apparent rise at longer times since electrons that return from the L valley will arrive below the optically probed region in the G valley, in contrast to those returning at higher energies from the X valley. The initial rapid decay is measured to be 80 fs and is the time for carriers to scatter to the L valley. This is consistent with the value of 100 fs determined from photoluminescence studies. (6) The scattering rate is dependent on the density of final states accessible to the carriers, so it should be emphasized that this scattering time value is for carriers excited with photons of average energy 2 eV. For these experimental conditions the average electron excess energy at T = 35 K is about 420 meV (with a full width at half maximum of 30 meV) above the G valley conduction minimum, for electrons excited from the heavy-hole band. The electrons originating from the light hole band have an average excess energy of about 270 meV (with a FWHM of 30 meV), so that they are below the L valley conduction minimum and cannot scatter there by optical phonon emission. Note also that the temperature de- pendence of the signal further confirms our earlier hypothesis that the fast initial decay of the signal arises primarily from electron scattering and not hole scattering.

  We can make an estimate of the X valley scattering time. At 295 K the measured time constant is 33 fs and represents the sum of both X and L valley scattering events, averaged over electron energy distributions. The electron distribution originating from the heavy-hole and light-hole band transi- tions is centered at 420 meV above the r' valley conduction minimum, with a broad bandwidth of several hundred meV. The center of the distribution is thus at about the same posi- tion relative to the L valley as was the case for the narrow bandwidth excitation at T = 35 K. Subtracting off the L valley scattering rate characterized by the 80 fs time constant we,determine that scattering into the X valley occurs in about 55 fs. This time is an average over the electron energy distribution photoexcited with a 6 fs pulse centered at 2.0 eV.

A word of caution should be made about the values of scattering times obtained here. Since these times are strongly dependent on the density of final states in the satellite valleys, they will depend on the carrier energy distribution that is optically injected. Care should be taken in comparing the various numbers quoted in the literature since they are de- pendent on the energy spectrum of the carriers for each par- ticular case. The fact that several carrier distributions are present due to the different valence bands adds to the com- plications. An accurate modeling of the dynamics of the carriers should be possible with the help of Monte Carlo simulations.

In conclusion, we have been able to utilize the time resolution made possible by compressed 6 fs optical pulses to directly resolve the dynamics of intervalley scattering in GaAs.

We are grateful to D. S. Chemia for valuable discussions, and to D. W. Taylor and F. A. Beisser for expert technical contributions.

1. A. J. Taylor, D. J. Erskine, and C. L. Tang, J. Opt. Soc. Amer. B 2, 663 (1985); M. J. Rosker, F. W. Wise, and C. L. Tang, Appi. Phys. Lett. 49, 1726 (1986); F. W. Wise, 1. A. Walmsley, and C. L. Tang, Appi. Phys. Lett. 51, 605 (1987)@ C. L. Tang, 1. A. Walmsley, and F. W. Wise, Appl. Phys. Lett. $2, 850 (1988).

2. W. Z. Lin, J. G. Fujimoto, and E. P. Ippen, Appi. Phys. Lett. 50, 124 (1987); W. Z. Lin, J. G. Fujimoto, E. P. Ippen, and R. A. Logan, Appi. Phys. Lett. 51, 161 (1987); W. Z. Lin, R. W. Schoenlein, J. G. Fujimoto, and E. P. lppen, IEEE J. Quanti.,m Electron. 24, 267 (1988).

3. R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, Opt. Lett. 12, 483 (1986).

4. R. F. Leheny, J. Shah, R. L. Fork, C. V. Shank, and A. Migus, Solid State Commun. 31, 809 (1979).

5. S. Adachi, J. Appl. Phys.,58, RI (1985).

6.  T. Shah, B. Deveaud, T. C. Damen, W. T. Tsang, A. C. Gossard, and P. Lugli, Phys. Rev. Lett. 59,2222 (1987).