Scanning tunneling microscopy on unpinned $\text{GaN}\left(1\overline{1}00\right)$ surfaces: Invisibility of valence-band states

We investigated the origins of the tunnel current in scanning tunneling microscopy (STM) and spectroscopy experiments on $\text{GaN}\left(1\overline{1}00\right)$ surfaces. By calculating the tunnel currents in the presence of a tip-induced band bending for unpinned $n$-type $\text{GaN}\left(1\overline{1}00\right)$ surfaces, we demonstrate that only conduction-band states are observed at positive and negative voltage polarities independent of the doping concentration. Valence-band states remain undetectable because tunneling out of the electron-accumulation zone in conduction-band states dominates by four orders of magnitude. As a result band-gap sizes cannot be determined by STM on unpinned $\text{GaN}\left(1\overline{1}00\right)$ surfaces. Appropriate band-edge positions and gap sizes can be determined on pinned surfaces.

Figure 1

(Color online) Schematic of the bending of the conduction-band $\left(E_{\text{C}}\right)$ and valence-band $\left(E_{\text{V}}\right)$ edges and the resulting electron occupation in the presence of a tip. (a) Flat band conditions in the absence of a metallic tip. The energy positions of the conduction-band $\left(E_{\text{CS}}\right)$ and valence-band $\left(E_{\text{VS}}\right)$ edges at the surface are identical with those in the bulk $\left(E_{\text{C}},E_{\text{V}}\right)$. No surface states are present within the fundamental band gap. (b) Electron accumulation at negative sample voltages in the conduction band. (c) Situation at positive sample voltages without carrier inversion. $I_{\text{V}}$, $I_{\text{C}}$, and $I_{\text{acc}}$ denote the different tunnel current contributions.

Figure 2

(Color online) Calculated band bending at the unpinned $n$-type GaN surface as a function of the sample voltage for three different carrier concentrations indicated on the right side of each curve. The calculation based on a metal–vacuum–GaN system assumed that due to carrier dynamics no inversion can persist. Only accumulation of majority carriers occurs. Inset: band bending as a function of the depth for different selected voltages. The carrier concentration used for this set is $3\times {10}^{18}{\text{cm}}^{-3}$. The surface is at the depth 0.

Figure 3

(Color online) Calculation of the conduction-band (marked $E_{\text{CS}}$) and valence-band (marked $E_{\text{VS}}$) edge energies at the unpinned GaN surface as a function of the applied sample voltage. The band-edge positions are shown for three different doping levels (shown as solid, dashed, and dotted pairs of lines, respectively). The upper and lower solid, dashed, and dotted lines of these pairs of lines represent the conduction-band (marked $E_{\text{CS}}$) and valence-band (marked $E_{\text{VS}}$) edge energies, respectively. The Fermi level of the tip $\left(E_{\text{F},\text{tip}}\right)$ lies on the dashed-dotted gray diagonal line. All energies are given relative to the Fermi level of the sample (at 0 eV).

Figure 4

(Color online) Calculated tunneling currents for the metal tip–vacuum–GaN tunneling junction for three different $n$-type free-carrier concentrations (solid lines, unpinned GaN) and a pinned GaN surface (dashed lines) as a function of the sample bias voltage. $I_{\text{C}}$ denotes the electron current from the tip in to empty conduction-band states of the semiconductor (solid curves at positive voltages). $I_{\text{acc}}$ is the tunnel current arising from the electron accumulation in the conduction-band states due to the tip-induced band-bending [upper solid (blue) curves at negative voltages, see schematic in Fig. 1]. $I_{\text{V}}$ denotes the tunnel current from the valence-band states into the tip [lower solid and dashed (red) curves at negative voltages]. Note, the current contributions $I_{\text{acc}}$ and $I_{\text{V}}$ are essentially independent of the doping level for unpinned GaN (because the band bending shown in Fig. 2 is at negative voltages independent of the doping level) and thus the respective three curves calculated for the indicated three different doping levels overlap at negative voltages. Note the large domination of the valence-band current $I_{\text{V}}$ by the accumulation current $I_{\text{acc}}$ in case of unpinned GaN surfaces. As a result only conduction-band states are visible in scanning tunneling images of unpinned GaN surfaces. The dashed spectrum (marked “pinned”) shows the tunnel current originating in the valence (negative voltages) and conduction bands (positive voltages), respectively, calculated for a nonpolar GaN surface pinned by a defect level 1 eV below the conduction-band edge. For pinned GaN no accumulation current exists.