Ultrafast transport of electrons in GaAs: Direct observation of quasiballistic motion and side valley transfer

Temporally and spatially resolved femtosecond electron dynamics in GaAs is investigated, tracing ultrafast modifications of the Franz-Keldysh absorption spectrum. A complex heterostructure design allows for a study of unipolar transport as well as a nanometer scale definition of layers for both carrier injection and probe of the propagating electron distribution. Transit times through the structure are directly measured for electric fields between $7\mathrm{kV}∕\mathrm{cm}$ and $180\mathrm{kV}∕\mathrm{cm}$ comparing room temperature operation to results for $T_L=4\mathrm{K}$. For low lattice temperatures, quasiballistic electron motion with an average velocity of $5.4\times {10}^7\mathrm{cm}∕\mathrm{s}$ is observed over distances as large as $300\mathrm{nm}$. Realistic Monte Carlo simulations are in excellent agreement with our observations.

Figure 1

Schematic band structure of the $p\text{−}i\text{−}n$ heterostructure under zero applied bias $U$. Under finite bias the difference between the electron and hole quasi-Fermi levels, ${\Phi }_n-{\Phi }_p=eU$, results in a change of the stationary electric field in the intrinsic region. The interband transitions used for generation and detection of the transient electron ensemble are sketched by the arrows. The delay times $t_0$, $t_1$ and $t_2$ represent different stages in the evolution of the electron distribution. The upper part of the figure depicts the aluminum content within the heterostructure.

Figure 2

Spectrally resolved transmission changes for various delay times $t_D$ after optical injection of electron-hole pairs for an electric field of $F=17\mathrm{kV}∕\mathrm{cm}$ and a lattice temperature of $T_L=4\mathrm{K}$. Unbound electron-hole pairs with a sheet density of $5\times {10}^9$.

Figure 3

(a) Experimental results for the buildup of the transmission changes for various electric fields and $T_L=4\mathrm{K}$; (b) corresponding theoretical results obtained from the Monte Carlo simulation described in the text. The inset displays the results for delay times $t_D<700\mathrm{fs}$ on an extended scale.

Figure 4

(a) Experimental results for the buildup of the transmission changes for various electric fields and $T_L=300\mathrm{K}$; (b) corresponding theoretical results obtained from the Monte Carlo simulation in the text. The inset displays the results for delay times $t_D<700\mathrm{fs}$ on an extended scale.

Figure 5

Transit times $t_T$ as defined in the text for a wide range of electric fields comparing the results for $T_L=4\mathrm{K}$ and $T_L=300\mathrm{K}$. The lowermost line corresponds to the theoretical limit of ballistic carrier motion within the $\Gamma$ valley.

Figure 6

Calculated electron density distributions, $n(z,t_D)$, in the heterostructure diode for various delay times and electric fields for a lattice temperature of $T_L=4\mathrm{K}$. The gray area indicates the distribution of electrons in the $\Gamma$ valley, whereas the black area depicts the electrons in the $L$- and $X$-side valleys. The open circles mark the center of mass of the calculated distributions, whereas the full circles indicate the values expected for ideal ballistic flight of $\Gamma$-valley electrons. The full vertical line marks the position where ballistic electrons have acquired the kinetic energy for scattering into the $L$ valley. The grey lines at 60 and $320\mathrm{nm}$ mark the boundaries of the probe region.

Figure 7

The experimental transient for $T_L=300\mathrm{K}$ and an electric field of $17\mathrm{kV}∕\mathrm{cm}$ is compared to results of a Monte Carlo simulation: Black line, full simulation of the spatial-temporal dynamics; grey line, calculation neglecting spatial broadening effects.

Figure 8

The experimental transient for $T_L=4\mathrm{K}$ and an electric field of $40\mathrm{kV}∕\mathrm{cm}$ is compared to results of a Monte Carlo simulation: Calculated with literature values (found in Refs. 15, 19, 20) (solid black line), with two times larger/smaller intervalley deformation potentials (dashed black and solid grey lines, respectively).