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