  Kelvin probe force microscopy (KPFM) is a popular tool for studying
properties of semiconductors. However, the interpretation of its results is
complicated by the possibility of so-called band bending and the presence of
surface charges. In this work we study two different interpretations for KPFM
on semiconductors: the contact potential difference (CPD) interpretation, which
interprets the measured potential as the work function difference between the
sample and the probe, and a newer, alternative, interpretation proposed by
Baumgart, Helm and Schmidt (BHS). By performing model calculations we
demonstrate that these models generally lead to very different results. Hence
it is important to decide which one is correct. We demonstrate that BHS
predictions for the Kelvin voltage difference between the $p$ and $n$ parts of
a $pn$-junction are inconsistent with a set of experimental results from the
literature. In addition, the BHS interpretation predicts an independence from
the probe material as well as from surface treatments, which we both find to
disagree with experiment. On the other hand, we present a theoretical argument
for the validity of the CPD interpretation and we show that the CPD
interpretation is able to accommodate all of these experimental results. Thus
we posit that the BHS interpretation is generally not suitable for the analysis
of KPFM on semiconductors and that the CPD interpretation should be used
instead.
