Measurements of hot electron cooling dynamics in QWs and superlattices

Hot electron cooling times can be determined from several types of time-resolved photoluminescence (PL) experiments. One technique involves hot luminescence nonlinear correlation [32-34], which is a symmetrized pump-probe type of experiment. Figure 2 of [32] compares the hot electron relaxation times as a function of the electron energy level in the well for bulk GaAs and a 20- period MQW of GaAs/Al0.38Ga0.62As containing 250 A GaAs wells and 250 A Al0.38Ga0.62As barriers. For bulk GaAs the hot electron relaxation time varies from about 5 ps near the top of the well to 35 ps near the bottom of the well. For the MQW the corresponding hot electron relaxation times are 40 ps and 350 ps.

Another method uses time-correlated single-photon counting to measure PL lifetimes of hot electrons. Figure 9.5 shows 3D plots of PL intensity as a function

of energy and time for bulk GaAs and a 250 A/250 A GaAs/Al0.38Ga0.62As MQW [17]. It is clear from these plots that the MQW sample exhibits much longer – lived hot luminescence (i. e. luminescence above the lowest n = 1 electron to heavy-hole transition at 1.565 eV) than bulk GaAs. Depending upon the emitted photon energy, the hot PL for the MQW is seen to exist beyond times ranging from hundreds to several thousand ps. However, the hot PL intensity above the bandgap (1.514 eV) for bulk GaAs is negligible over most of the plot: it is only seen at the very earliest times and at relatively low photon energies.

Calculations were performed [17] on the PL intensity versus time and energy data to determine the time dependence of the quasi-Fermi level, electron temperature, electronic specific heat and, ultimately, the dependence of the characteristic hot-electron cooling time on electron temperature.

The cooling, or energy-loss, rate for hot electrons is determined by LO phonon emission through electron-LO-phonon interactions. The time constant

characterizing this process can be described by the following expression [35-37]:

where Pe is the power loss of electrons (i. e. the energy-loss rate), Ti®LO is the LO

phonon energy (36 meV in GaAs), Te is the electron temperature, and ravg is the time constant characterizing the energy-loss rate.

The electron energy-loss rate is related to the electron temperature decay rate through the electronic specific heat. Since at high light intensity the electron distribution becomes degenerate, the classical specific heat is no longer valid. Hence, the temperature – and density-dependent specific heat for both the QW and bulk samples need to be calculated as a function of time in each experiment so that Tavg can be determined.

The results of such calculations (presented in figure 9.2 of [17]) show a plot of Tavg versus electron temperature for bulk and MQW GaAs at high and low carrier densities. These results show that at a high carrier density [n ~ (2 – 4) x 1018 cm-3], the Tavg values for the MQW are much higher (Tavg = 350-550 ps for Te between 440 and 400 K) compared to bulk GaAs (Tavg = 10-15 ps over the same Te interval). However, at a low carrier density [n ~ (3 – 5) x 1017 cm-3] the differences between the Tavg values for bulk and MQW GaAs are much smaller.

A third technique to measure cooling dynamics is PL up-conversion [17]. Time-resolved luminescence spectra were recorded at room temperature for a 4000 A bulk GaAs sample at the incident pump powers of 25, 12.5 and 5 mW. The electron temperatures were determined by fitting the high-energy tails of the spectra; only the region which is linear on a semilogarithmic plot was chosen for the fit. The carrier densities for the sample were 1 x 1019, 5 x 1018 and 2 x 1018 cm-3, corresponding to the incident excitation powers of 25, 12.5 and 5 mV, respectively. Similarly, spectra for the MQW sample were recorded at the same pump powers as the bulk. Figure 9.6 shows Tavg for bulk and MQW GaAs at the three light intensities, again showing the much slower cooling in MQWs (by up to two orders of magnitude).

The difference in hot electron relaxation rates between bulk and quantized GaAs structures is also reflected in time-integrated PL spectra. Typical results are shown in figure 9.7 for single-photon counting data taken with 13 ps pulses of 600 nm light at 800 kHz focused to about 100 ^m with an average power of 25 mW [38]. The time-averaged electron temperatures obtained from fitting the tails of these PL spectra to the Boltzmann function show that the electron temperature varies from 860 K for the 250 A/250 As MQW to 650 K for the 250 A/17 A superlattice, while bulk GaAs has an electron temperature of 94 K, which is close to the lattice temperature (77 K). The variation in the electron temperatures between the quantized structures can be attributed to differences in electron delocalization between MQWs and SLs and the associated non-radiative quenching of hot electron emission.

As shown earlier, the hot carrier cooling rates depend upon photogenerated carrier density: the higher the electron density, the slower the cooling rate. This effect is also found for bulk GaAs but it is much weaker compared to quantized GaAs. The most generally accepted mechanism for the decreased cooling rates in GaAs QWs is an enhanced ‘hot phonon bottleneck’ [39-41].

In this mechanism a large population of hot carriers produces a non-equilibrium distribution of phonons (in particular, optical phonons which are the type involved in the electron-phonon interactions at high carrier energies) because the optical phonons cannot equilibrate fast enough with the crystal bath; these hot phonons can be re-absorbed by the electron plasma to keep it hot. In QWs the phonons are confined in the well and they exhibit slab modes [40], which enhance the ‘hot phonon bottleneck’ effect.