Influence of surface band bending on a narrow band gap semiconductor: Tunneling atomic force studies of graphite with Bernal and rhombohedral stacking orders

Tunneling atomic force microscopy (TUNA) was used at ambient conditions to measure the current-voltage ($I$-$V$) characteristics clean surfaces of highly oriented graphite samples with Bernal and rhombohedral stacking orders. The characteristic curves measured on Bernal-stacked can be understood an ordinary self-consistent semiconductor modeling quantum mechanical tunneling current derivations. We show that absence a voltage region without measurable in $I$-$V$ spectra is not proof lack energy band gap. It induced by surface bending due finite contact potential between tip sample surface. Taking this into account model, we succeed obtain quantitative agreement simulated tunnel for gaps $(12 \ldots 37)$\,meV, those extracted from exponential temperature decrease longitudinal resistance order. In contrast, relatively thick reveals existence maximum first derivative $dI/dV$, behavior compatible flat band. are comparable obtained low temperatures similar techniques.