Polarized Raman scattering from single $\mathrm{GaN}$ nanowires

Raman spectra of single (hexagonal wurtzite) $\mathrm{GaN}$ nanowires grown by vapor-liquid-solid synthesis were recorded. By investigating the polarization dependence of the Raman intensities of the observed bands as a function of the angle between the long axis of the nanowire and the electric vector of the incident (and scattered) light, one is able to distinguish between nanowires whose crystallographic $c$ axis corresponds to ($c^{*}$ directed), or is substantially perpendicular to ($a^{*}$ directed) the long axis of the nanowire—the two preferred directions of nanowire growth. For $a^{*}$-directed nanowires, polarization-dependent Raman intensity analysis can also determine, within tolerable limits, the orientation of the crystalline $c$ axis with respect to laboratory-fixed coordinates. Simultaneous transmission electron microscopy (TEM) analyses confirm the conclusions derived from the Raman measurements. The polarization-dependent Raman intensities could only be understood if one assumed a complex-valued Raman tensor. The detection of resonance enhancement together with the tendency of the nanowires to grow with a high concentration of defects and the observation of yellow luminescence in the photoluminescence spectrum may account for the complex-valued Raman tensor we observe for $\mathrm{GaN}$ even at sub-band-gap photon energies.

Figure 1

Backscattering experimental geometry. The incoming light $\left(e_i\right)$ directed along the $Z$ axis passes through a $\lambda ∕2$ plate and a $100\times \mathrm{objective}$ $\left(0.8\mathrm{NA}\right)$ and reaches the nanowire at an angle ${\psi }_L$ $\left(e_i^{\prime }\right)$ with respect to its principle axis $\left(X\right)$. The light scattered at angle ${\psi }_S$ is analyzed as either a parallel $\left(e_s^{\prime }\right)$ or a perpendicular $\left({e_s^{\prime }}^{\perp }\right)$ component, rotated back to $e_s^{″}$ $(\equiv e_i)$ $(\Vert )$ or ${e_s^{″}}^{\perp }$ $(\equiv e_i+{90}^{°})$ $(\perp )$, respectively. $\theta$ is the inclination of the $c$ axis with respect to the $Z$ axis, the (laboratory-fixed) normal to the substrate. Inset: $\mathrm{GaN}$ wurtzite structure (Ga=gray circles and $\mathrm{N}=\mathrm{black}$ circles) with the $\left(10\overline{1}0\right)$ and $\left(0001\right)$ planes denoted in light gray and dark gray, respectively.

Figure 2

A series of parallel $(\Vert )$ and perpendicularly $(\perp )$ polarized Raman spectra measured as a function of the polarization direction of the incident light for a $500\mathrm{nm}$ diameter nanowire shown by electron diffraction (TEM) to be $c^{*}$ directed.

Figure 3

Polar plots (filled and open circles are for $\perp$ and $\Vert$ configurations, respectively), which summarize the Raman intensities of various bands from the $c^{*}$—directed nanowire as a function of the angle $\left({\psi }_L\right)$ between the $X$ axis and the direction of the electric vector of the incident light. Relative intensities calculated as a function of the polarization direction are also shown.

Figure 4

The best value of ${\varphi }_{ac}=\pi ∕2$ for both $\Vert$ and $\perp$ polarization configurations as determined graphically by comparing the measured Raman intensities ($\Vert$ open circles and $\perp$ filled circles) with Raman intensities calculated as a function of ${\varphi }_{ac}$ and ${\psi }_L$ using Eqs. (2). The best fit was determined after subtracting a small background from $I_{\perp }$ that probably arises from depolarization.

Figure 5

The photoluminescence (PL) spectrum of a bundle of $\mathrm{GaN}$ nanowires excited at $300\mathrm{K}$ by a $\mathrm{He}\text{−}\mathrm{Cd}$ laser operated at $325\mathrm{nm}$.

Figure 6

(a) Raman spectra of a single, $a^{*}$-directed nanowire at the excitation energies indicated; (b) same as (a) but for a $c^{*}$-directed nanowire; (c) the intensity ratio dependences as a function of excitation energy that clearly show a resonance profile for both nanowires.

Figure 7

The complete anti-Stokes and Stokes spectrum for a single $120\mathrm{nm}$ nanowire excited at a photon energy of $2.71\mathrm{eV}$. The spectrum of Silicon (at a similar power density) is included for comparison. For clarity, the anti-Stokes spectrum multiplied by $F$ $\left(490\mathrm{K}\right)$ is shown in gray; where $F\left(T\right)=[E_l-E_{ph}∕E_l+E_{ph}{]}^4\exp (E_{ph}∕kT)$ ($E_l$ is the incident laser energy and $E_{ph}$ is the phonon energy). This procedure estimates the temperature of the nanowire and indicates the enhancement in the anti-Stokes side of the $A_1\left(\mathrm{LO}\right)$ mode.

Figure 8

(Color online) Polar plots of the $E_2^{\mathrm{H}}$ and the $A_1\left(\mathrm{TO}\right)$ bands for two nanowires. The nanowires shown in (a) and (b), referred to as $w_1$ and $w_2$, have $\sim 200\mathrm{nm}$ and $\sim 150\mathrm{nm}$ diameters, respectively. Electron diffraction images and the crystallographic disposition of the nanowires deduced from them are also shown. (c) a series of parallel $(\Vert )$ polarized Raman spectra measured as a function of the polarization direction of the incident light for $w_1$. (d) a plot the Raman intensity for the $E_2^{\mathrm{H}}$ and $A_1\left(\mathrm{TO}\right)$ bands calculated for $\underset{̣}{\theta }=32°$, $59°$ for the $\Vert$ (solid line) and $\perp$ (dashed line) configurations (the higher intensities correspond to $\theta =59°$).

Figure 9

A series of parallel $(\Vert )$ and perpendicularly $(\perp )$ polarized Raman spectra measured as a function of the polarization direction of the incident light for a $\sim 300\mathrm{nm}$ diameter nanowire [as determined by scanning electron microscopy (SEM)] with unknown crystallographic orientation.

Figure 10

Polar plots (filled and open circles are for $\perp$ and $\Vert$ configurations, respectively), summarizing the Raman intensities of various bands as a function of ${\psi }_L$, the angle between the $X$ axis and the direction of the electric vector of the incident light, for the nanowire shown in Fig. 9. Also shown are relative intensities calculated for values of $\theta$ calculated in $10°$ intervals with the contours corresponding to $\theta \underset{̣}{=}90$, 60, 30, and 0 degrees emphasized by using thicker lines.