  Scanning Tunneling Microscopy (STM) is a powerful technique that utilizes
quantum tunneling to visualize atomic surfaces with high precision. This study
presents detailed topographic maps and evaluates the local density of states
(LDOS) for three distinct materials: Highly Oriented Pyrolytic Graphite (HOPG),
gold, and silicon. By meticulously measuring the tunneling current from a
finely pointed tip positioned nanometers above the sample, we successfully
image the surface topography of HOPG, revealing a lattice constant of $0.28 \pm
0.01$ nm. Additionally, we determine the local work functions for gold and
graphite to be $0.7 \pm 0.1$ eV and $0.5 \pm 0.1$ eV, respectively. Employing
scanning tunneling spectroscopy, this work further investigates the LDOS for
gold (a metal), graphite (a semi-metal), and silicon (a semiconductor),
providing valuable insights into their electronic properties at the atomic
level.
