Anomalous ambipolar transport in depleted GaAs nanowires

We have used a polarized microluminescence technique to investigate photocarrier charge and spin transport in depleted $n$-type GaAs nanowires ($\approx {10}^{17}{\mathrm{cm}}^{-3}$ doping level). At 6 K, a long-distance tail appears in the luminescence spatial profile, indicative of charge and spin transport, and only limited by the length of the nanowire (NW). This tail weakly depends on excitation power and temperature. Using a self-consistent calculation based on the drift-diffusion and Poisson equations as well as on photocarrier statistics (Van Roosbroeck model), it is found that this tail is due to photocarrier drift in an internal electric field nearly two orders of magnitude larger than electric fields predicted by the usual ambipolar model. This large electric field appears because of two effects. First, for transport in the spatial fluctuations of the conduction band minimum and valence band maximum, the electron mobility is activated by the internal electric field. This implies, in a counterintuitive way, that the spatial fluctuations favor long-distance transport. Second, the range of carrier transport is further increased because of the finite NW length, an effect which plays a key role in one-dimensional systems.

Figure 1

Spatial fluctuations of the conduction and valence band, caused by statistical fluctuations of the donor concentration. Also shown are the electron and hole transport processes by hopping, and the mechanisms for recombination of the main line and of the tail.

Figure 2

Curve a shows the NW intensity spectrum at the excitation spot for a small excitation power of 45 $\mu \mathrm{W}$. Also shown is a Gaussian fit of the main line (curve ${\mathrm{a}}^{\prime }$) which reveals a low-energy tail which extends down to $1.48\text{eV}$. Curve d shows the corresponding polarization spectrum and reveals a large photoelectron spin polarization of nearly $50\%$. For comparison, the intensity and polarization spectra of an undepleted NW are shown in curves b and c, respectively. Shown in the inset are the dependencies of the luminescence intensity at the excitation spot as a function of excitation power. As expected from Eq. (1), for the undepleted NW, the intensity is proportional to the excitation power while, for the depleted NW, it is proportional to the square of this power.

Figure 3

Curve b shows the intensity spatial profile at 6 K, for an energy of 1.512 eV, for an excitation power of 45 $\mu \mathrm{W}$. This curve exhibits a slow tail, which is not found for a $p$-type NW (curve a). These curves extend well beyond the laser profile (shown in curve g), which is an evidence for photocarrier transport along the NW. Shown in curves c and d are the intensity profiles in the conditions of curve b, but for an excitation power of 180 $\mu \mathrm{W}$ and 1 mW, respectively. Curve ${\mathrm{d}}^{\prime \prime }$ shows the spatial profile of the difference signal, related to the spin orientation, and is almost undistinguishable from curve d. Curve e shows the intensity spatial profile for an increased lattice temperature of 30 K. Curve g shows the profile calculated for an excitation power of 45 $\mu \mathrm{W}$ (same as curve a), but assuming a usual ambipolar transport, i.e., without a dependence of the electron mobility on electric field ($E_e=0$). Curves ${\mathrm{b}}^{\prime }, {\mathrm{c}}^{\prime }$, and ${\mathrm{d}}^{\prime }$ and ${\mathrm{e}}^{\prime }$ show the corresponding profiles calculated using the model of Sec. 3, that is, including a dependence of the mobility on the electric field. While curves ${\mathrm{b}}^{\prime }$ and ${\mathrm{c}}^{\prime }$ coincide with the experimental profiles, curves ${\mathrm{d}}^{\prime }$ and ${\mathrm{e}}^{\prime }$ underestimate the amplitude of the slow tail. This suggests the relevance of a quasiballistic transport in this large electric field. The corresponding predicted profiles, shown in curves ${\mathrm{d}}^{\prime \prime \prime }$ and ${\mathrm{e}}^{\prime \prime \prime }$, are obtained using Eq. (13) and coincide very well with the experimental profiles.

Figure 4

The bottom panel shows the calculated spatial profiles of the hole concentration for increasing values of $E_e$. The top panel shows the corresponding spatial profiles of the internal electric field. For a very small value of $E_e$ the decay is rapid, corresponding to the usual ambipolar case as described by Eq. (12). Upon increase of $E_e$, a tail appears in the charge profile, while a large internal electric field builds up at large distance.

Figure 5

Spatial profiles of electron diffusive (curve b) and drift (curve a) currents, as well as of the hole diffusive (curve d) and drift (curve c) currents, calculated with $E_e={10}^{-3} \mathrm{V}/\mu \mathrm{m}$. The inset shows the electric field value at 10 $\mu \mathrm{m}$ from the excitation spot, as a function of the NW length. The strong reduction of electric field for a length larger than 150 $\mu \mathrm{m}$ demonstrates the length-dependent transport.