Inhomogeneous free-electron distribution in InN nanowires: Photoluminescence excitation experiments

Photoluminescence excitation (PLE) spectra have been measured for a set of self-assembled InN nanowires (NWs) and a high-crystalline quality InN layer grown by molecular-beam epitaxy. The PLE experimental lineshapes have been reproduced by a self-consistent calculation of the absorption in a cylindrical InN NW. The differences in the PLE spectra can be accounted for the inhomogeneous electron distribution within the NWs caused by a bulk donor concentration $\left(N_D^{+}\right)$ and a two-dimensional density of ionized surface states $\left(N_{ss}^{+}\right)$. For NW radii larger than 30 nm, $N_D^{+}$ and $N_{ss}^{+}$ modify the absorption edge and the lineshape, respectively, and can be determined from the comparison with the experimental data.

Figure 1

(Color online) PL and PLE spectra of a representative NW sample (G041) and a high-crystalline quality InN layer measured at 10 K. Open circles (triangles) and solid (dashed) line correspond to the PLE and PL spectra of NWs (layer), respectively.

Figure 2

(Color online) (a) Normalized PL spectra of sample G041 for different excitation energies indicated for each spectrum (values are given in electron volt). (b) PLE spectra of sample G041 detected at two different energies: 0.679 eV (low energy tail) and 0.685 eV (PL peak energy). One PLE spectrum was enhanced by a constant factor to make easier the comparison between them.

Figure 3

(Color online) PL (dashed line) and PLE (open symbols) spectra detected at the PL peak energy for the different InN NW samples. Spectra are shifted along the vertical axis. Calculated absorption spectra (solid lines) showing the best agreement with the experimental ones are also included.

Figure 4

(Color online) (a) Conduction band edge, $V\left(r\right)=E_c-e\varphi \left(r\right)$ and (b) electron density profiles for InN NWs with $N_D^{+}=3.0\times {10}^{17}{\text{cm}}^{-3}$ and $N_{ss}^{+}=1.0\times {10}^{13}{\text{cm}}^{-2}$, and different radius ranging from 10 (dashed line) to 50 nm (dashed-dotted line). The Fermi level of each NW is also indicated. The energy scale is referred to $E_c$.

Figure 5

(Color online) Optical absorption spectra for the same InN NWs considered in Fig. 4. $R=10$ (dashed line), 20 (dotted line), 40 (solid line), and 50 nm (dashed-dotted line). The $E^{1/2}$ ideal dependence of the absorption of intrinsic bulk InN with a band-gap energy of 0.67 eV is also displayed (open circles). The inset shows the evolution of the absorption edge with the radius.

Figure 6

(Color online) (a) Conduction band and (b) electron concentration profiles of a 40 nm radius InN NW with $N_D^{+}=1.0\times {10}^{17}{\text{cm}}^{-3}$ and two different values of $N_{ss}^{+}$: $1.0\times {10}^{12}$ and $1.0\times {10}^{13}{\text{cm}}^{-2}$. The electron density profiles are also plotted for $N_D^{+}=5.0\times {10}^{17}{\text{cm}}^{-3}$. The inset shows the conduction band profile for the higher $N_{ss}^{+}$ value and the first two conduction band states $\left(l=0\right)$.

Figure 7

(Color online) Calculated absorption spectra of a 40 nm radius InN NW for two different values of $N_D^{+}$: $1.0\times {10}^{17}$ and $5.0\times {10}^{17}{\text{cm}}^{-3}$; and two different values of $N_{ss}^{+}$: $1.0\times {10}^{12}$ and $1.0\times {10}^{13}{\text{cm}}^{-2}$. The $E^{1/2}$ ideal dependence of the absorption for intrinsic bulk InN (open circles) is also displayed.

Figure 8

(Color online) Mapping of $E_{FS}$ as a function of both $N_{ss}$ and radius of the NW.