Work function of the semiconductor and metal and the relation which give us ohmic contact and which gives us rectifying contact?

The work function of a semiconductor is the minimum energy required to remove an electron from the Fermi level to the vacuum level, while the work function of a metal is the energy needed to do the same for electrons in the metal. Ohmic contact occurs when the work function of the metal is close to that of the semiconductor, allowing for efficient charge carrier injection and a linear current-voltage relationship. In contrast, rectifying contact is formed when there is a significant difference in work functions, leading to a potential barrier that allows current to flow more easily in one direction than the other, resulting in a diode-like behavior. This difference creates a Schottky barrier, which is essential for rectification.