  The interrelation between spin and charge in semiconductors leads to
interesting effects, e.g., the Rashba-type spin-orbit splitting or the exchange
enhancement. These properties are proposed to be used in applications such as
spin transistors or spin qubits. Probing them on the local scale with the
ultimate spatial resolution of the scanning tunneling microscope addresses
their susceptibility to disorder directly. Here we review the results obtained
on two-dimensional semiconductor systems (2DES). We describe the preparation
and characterization of an adequate 2DES which can be probed by scanning
tunneling microscopy. It is shown how the electron density and the disorder
within the 2DES can be tuned and measured. The observed local density of states
of weakly and strongly disordered systems is discussed in detail. It is shown
that the weakly disordered 2DES exhibits quantum Hall effect in magnetic field.
The corresponding local density of states across a quantum Hall transition is
mapped showing the development from localized states to extended states and
back to localized states in real space. Decoupling the 2DES from screening
electrons of the bulk of the III-V semiconductor leads to a measurable exchange
enhancement of up to 0.7 meV which depends on the local spin polarization of
the 2DES. At stronger confinement potential, i.e. larger doping, the Rashba
spin splitting with $\alpha$ as large as $7\cdot 10^{-11}$eVm is observed as a
beating in the density of states in magnetic field. The Rashba spin splitting
varies with position by about $\pm 50$% being largest at potential hills.
