Atomic and electronic structure of the nonpolar $\text{GaN}\left(1\overline{1}00\right)$ surface

We present a cross-section scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS) and ab initio density-functional theory simulations study of the cleaved nonpolar $\left(1\overline{1}00\right)$ surface ($m$-plane) of $n$-type HVPE GaN free-standing quasisubstrates. Atomically resolved empty and filled states STM topographies show that no reconstruction occurs upon cleavage, as predicted by theory. STS measurements on clean and atomically flat cleaved surfaces (defect concentration ${\sigma }_d\le 2\times {10}^{12}{\text{cm}}^{-2}$) show that the Fermi energy is not pinned and the tunneling current flows through Ga-like electronic states lying outside the fundamental band gap. On surface areas with defect concentration ${\sigma }_d\ge 3\times {10}^{13}{\text{cm}}^{-2}$, the Fermi energy is pinned inside the band gap in defect-derived surface states and tunneling through filled (empty) N-like (Ga-like) states takes place.

Figure 1

(Color online) Experimental empty states STM topographies on the clean cleaved $\text{GaN}\left(1\overline{1}00\right)$ surface: (a) $\text{area}=40\times 40{\text{nm}}^2$, $U_{\text{bias}}=+2.5\text{V}$, and $I=0.05\text{nA}$; (b) $\text{area}=10\times 10{\text{nm}}^2$, $U_{\text{bias}}=+2.9\text{V}$, and $I=0.1\text{nA}$. Gray scaled with black denoting minimal and white denoting maxima STM-tip height with the $\left[11\overline{2}0\right]$ direction along $x$ and the [0001] along $y$. The $z$ range varies between (a) 0 and $+110\text{pm}$ and (b) 0 and $+260\text{pm}$, respectively. The surface unit cell is highlighted in red (dark gray) and its stick-ball model is magnified at the center of the image: the different planes sketched are the first surface layer and the second layer in the slab. Outermost N and Ga atoms are indicated with blue (small) and green (large) spheres, respectively, while atoms in the underlayer are represented with sticks of the same colors.

Figure 2

(Color online) Experimental filled (a, b) and empty (c, d) states STM topographies: (a) $U_{\text{bias}}=-2.2\text{V}$, $I=0.1\text{nA}$, (b) $U_{\text{bias}}=-1.3\text{V}$, $I=0.1\text{nA}$, (c) $U_{\text{bias}}=+1.5\text{V}$, $I=0.05\text{nA}$, and (d) $U_{\text{bias}}=+3.6\text{V}$, $I=0.1\text{nA}$. Gray scaled with black denoting minimal and white denoting maxima STM-tip height (the $z$ range is different in the images) with the $\left[11\overline{2}0\right]$ direction along $x$ and the [0001] along $y$. The surface unit cell is highlighted in red (dark gray).

Figure 3

(Color online) Differential conductivity $dI/d{U}_{\text{bias}}$ STS spectra measured on the clean cleaved $\text{GaN}\left(1\overline{1}00\right)$ surface at constant bias $U_{\text{bias}}=+1.7\text{V}$ and different current set points $I$: $I=150\text{pA}$ (short-dashed red), $I=300\text{pA}$ (long-dashed blue), $I=500\text{pA}$ (dash-dotted orange), $I=700\text{pA}$ (dotted green), and $I=900\text{pA}$ (solid brown). Each spectrum is measured at different tip-sample distance $d=d_0+\Delta d$, where $d_0$ is the distance at set point $\left(U_{\text{bias}}=+1.7\text{V},I=150\text{pA}\right)$.

Figure 4

(Color online) Differential conductivity STS spectra on (a) clean and (b) defect-rich cleaved $\text{GaN}\left(1\overline{1}00\right)$ surface areas taken on a line scan along the [0001] direction. Each spectrum is acquired at constant tip-sample distance according to the starting $I{U}_{\text{bias}}$ set point [(a) $U_{\text{bias}}=+2.4\text{V}$ and $I=0.05\text{nA}$, (b) $U_{\text{bias}}=+2.5\text{V}$ and $I=0.1\text{nA}$]. The vertical yellow (light gray) lines identify the position of the empty states maxima.

Figure 5

(Color online) Upper images: top view of the (a) truncated and (b) relaxed supercell considered. Bottom images: side view of the (c) truncated and (d) relaxed supercell considered. The different planes sketched are the first surface layer, the second, and third layer in the slab. The buckling angle between the Ga-N surface bond and the surface plane is indicated with ${\omega }_b$. Outermost N and Ga atoms are indicated with blue (small) and green (large) spheres, respectively, while atoms in the underlayer are represented with sticks of the same colors. The surface unit cell is highlighted in red (dark gray).

Figure 6

Surface band structure of the relaxed $\text{GaN}\left(1\overline{1}00\right)$ surface. The shaded areas show the projected bulk band structure. In the inset the projected 2D BZ is shown.

Figure 7

(Color online) Representative simulated STM topographies for (a) filled and (b) empty states present complementary localization in space, since they are localized, respectively, on N and Ga atoms. The filled (empty) states STM topography is calculated at the $\overline{\Gamma }$ point of the BZ at $E=E_{\text{V}}-1.6\text{eV}$ $\left(E=E_{\text{C}}+0.3\text{eV}\right)$. $E_{\text{V}}$ and $E_{\text{C}}$ correspond to the energy of the valence-band maximum (VBM) and conduction-band minimum (CBM), respectively. Outermost N (Ga) atoms are indicated with blue (green) spheres, while atoms in the first underlayer are represented with sticks of the same colors. The surface unit cell is highlighted in red (dark gray).

Figure 8

(Color online) Bias-dependent scheme of the tunneling experiment on the clean cleaved $\text{GaN}\left(1\overline{1}00\right)$ surface. The position of the vacuum level at equilibrium is fixed according to the work function of tungsten STM tip ${\varphi }_T\approx 4.5–4.8\text{eV}$ and work function of $n$-type HVPE GaN quasisubstrates ${\varphi }_S\approx {\chi }_S\approx 4.1\text{eV}$, where ${\chi }_S$ represents the GaN(0001) electron affinity. The Fermi level of the tip and sample is denoted with $E_{\text{FT}}$ and $E_{\text{FS}}$, respectively. $E_{\text{C}}$ and $E_{\text{V}}$ indicate the energy of the CBM and VBM of the sample surface, respectively. The LDOS of the sample surface is displayed in blue color (dark gray). $I_{\text{cb}}^{\text{fs}}$ and $I_{\text{cb}}^{\text{es}}$ represent the tunneling current flowing through filled and empty states of the sample conduction band, respectively.

Figure 9

(Color online) IVCHAR simulated $I{U}_{\text{bias}}$ characteristic of the tunneling experiment on the clean cleaved $\text{GaN}\left(1\overline{1}00\right)$ surface: $I_{\text{cb}}^{\text{es}}$, $I_{\text{cb}}^{\text{fs}}$ and $I_{\text{vb}}^{\text{fs}}$ are the contributions to the current due to tunneling through CB empty states, CB filled states and VB filled states, respectively. $I_{\text{tot}}^{\text{fs}}$ is the sum of the two contributions $I_{\text{vb}}^{\text{fs}}$ and $I_{\text{cb}}^{\text{fs}}$ to tunneling current from filled states.

Figure 10

(Color online) Bias-dependent scheme of the tunneling experiment on cleaved $\text{GaN}\left(1\overline{1}00\right)$ surface areas with defect concentration ${\sigma }_d\ge 3\times {10}^{13}{\text{cm}}^{-2}$. The Fermi level is pinned at the surface in defect-derived surface states. The work function of the STM-tip and sample is indicated with ${\varphi }_T$ and ${\varphi }_S$, the Fermi level of the STM-tip and sample with $E_{\text{FT}}$ and $E_{\text{FS}}$, respectively. $E_{\text{C}}$ $\left(E_{\text{V}}\right)$ denotes the energy of the CBM (VBM) of the sample. The LDOS of the sample surface is displayed in blue color (dark gray). $I_{\text{vb}}^{\text{fs}}$ and $I_{\text{cb}}^{\text{es}}$ indicate the tunneling current flowing through VB filled states and CB empty states, respectively.