Quantized Electron Accumulation States in Indium Nitride Studied by Angle-Resolved Photoemission Spectroscopy

Electron accumulation states in InN have been measured using high resolution angle-resolved photoemission spectroscopy (ARPES). The electrons in the accumulation layer have been discovered to reside in quantum well states. ARPES was also used to measure the Fermi surface of these quantum well states, as well as their constant binding energy contours below the Fermi level $E_F$. The energy of the Fermi level and the size of the Fermi surface for these quantum well states could be controlled by varying the method of surface preparation. This is the first unambiguous observation that electrons in the InN accumulation layer are quantized and the first time the Fermi surface associated with such states has been measured.

Figure 1

ARPES spectra from InN. (a) Series of normal emission spectra ($\theta =0°$) for $h\nu$ from 51 to 92 eV. (b) Series of spectra where $h\nu$ and $\theta$ are simultaneously varied to measure states along the $\Gamma \mathrm{TK}$ direction (parallel to the film surface) in the bulk Brillouin zone. Sample was annealed to 400 °C in UHV for (a) and 500 °C for (b). Spectra were recorded with the sample at room temperature. Inset: experimental geometry (${\theta }_i=45°$ in all cases), and symmetry labels for the bulk Brillouin zone.

Figure 2

ARPES photocurrent intensity map of states within 1.5 eV of $E_F$. $h\nu =69\mathrm{eV}$ and sample temperature was 177 K. Sample was annealed to 300 °C in UHV for 30 min. The false color intensity reflects the photocurrent, with lighter intensity indicating higher current. The momentum direction is along $\Gamma \Sigma \mathrm{M}$, in the surface plane.

Figure 3

(a) ARPES photocurrent intensity map of states within 1.2 eV of $E_F$. $h\nu =70\mathrm{eV}$, and sample temperature was 60 K. Sample was prepared by two cycles of 500 eV ${\mathrm{Ar}}^{+}$ ion bombardment and annealing in UHV to 300 °C (10 min for each ion bombardment and annealing step). The momentum direction is the same as in Fig. 2. (b) The calculated downward bending of the CBM and VBM (solid black curves) with respect to $E_F$. Optimum agreement between calculations and the experimental data was obtained using a bulk free electron density of $4\times {10}^{19}{\mathrm{cm}}^{-3}$ and band bending of 1.3 eV. An exponential approximation to the surface potential well is also shown with the corresponding subband minima, $E_1$ and $E_2$ at 0.511 and 0.797 eV, respectively.

Figure 4

Fermi surface and constant binding energy contours extracted from the data of Fig. 3. The photocurrent is plotted as $k_x$ and $k_y$ are varied, while the binding energy relative to $E_F$ is kept constant at 0 (Fermi surface), 0.2, 0.5, and 0.7 eV. $h\nu =70\mathrm{eV}$ and sample temperature was 60 K. The diameter of the outer Fermi surface is $0.4{\AA }^{-1}$.