Contacts Between Materials

When two crystals of different materials first make contact there will be a flow of electrons from one to another. This is because the electrons meeting the junction from one side will generally have more energy than those meeting if from the other side.


If the work function of material A (φ_A) is less than the work function of material B (φ_B) electrons will move from material A to material B because the amount of energy required to release electrons in material A is lesser than that of material B. Also note that the work function of a material determines the depth of the conduction band of metals.
The release of electrons in material A makes it positively charged and material B negatively charged because it receives the electrons. The flow of electrons continues until the fermi levels of material A and material B are equal and then the flow can be either from material A to B or material B to A.Potential Difference, V_AB = φ_B - φ_A volts. This is also known as the contact potential. This potential has to be surpassed in order to move electrons from material A to material B.




Metal to Semiconductor Contacts

n - type Semiconductor with φ_m < φ_s

If the work function of the metal is less than the work function of the semiconductor (φ_m < phis), it implies that electrons flow from the metal to the semiconductor and this type of contact is popularly known as the ohmic contact. Note that the contact potential (φ_s - φ_m) is unaffected by the applied voltage and the height of the conduction band of the semiconductor is denoted by x also known as the electron affinity.

n - type semiconductor with φ_m > φ_s

If the work function of the metal is greater than the work function of the semiconductor (φ_m > φ_s), it implies that electrons flow from the semiconductor to the metal. In this case current flow depends on the magnitude and polarity of the applied voltage (V). I_f is the current from the semiconductor to the metal. I_o is the current from the metal to the semiconductor. I = I_f - I_o, for zero bias where V = 0, there is no net current therefore I_f = I.
If the contact is forward biased, the semiconductor is biased negatively with respect to the metal. The energy of all the electrons in the semiconductor is raised and the potential barrier is reduced (φ - V). Thus, the depletion layer is reduced, more electrons can now diffuse from the semiconductor to the metal and If becomes greater than Io.
If the contact is reverse biased, the semiconductor is biased positively with respect to the metal. The energy of the electrons in the semiconductor is lowered and the potential barrier is raised to φ + V. This greatly reduces the diffusion of electrons from the semiconductor and If tends to zero. Electrons are drawn away from the junction so that more donor atoms are uncompensated and the depletion layer increases. However φ_m - x is still unaffected so that Io remains unchanged. The junction is said to be reverse biased and when I_f tends to zero, I = -T_o. This junction therefore acts as a rectifying contact. The application of rectifying contact is in the fabrication of schottky barrier diode or 'hot carrier' used in microwave.

n⁺ - type semiconductor with φ_m > φ_s

This is a special case of n - type semiconductor with φ_m > phis. If the n - region is so heavily doped that it becomes degenerate with the fermi level within conduction band just as a metal, the metal - n⁺ contact becomes similar to the contact between two metals and is therefore ohmic even when φ_m > φ_s. This feature is used in fabricating the contact used for making connections to integrated circuits.

p - type semiconductor with φ_m < φ_s

The initial flow of electrons is from metal to semiconductor so that a positive charge is formed on the metal and a negative charge is formed on the semiconductor. The electrons are captured by acceptor atoms near the junction and a depletion layer of width is formed. This contact is rectifying and forward bias occurs with the semiconductor positive which reduces the potential barrier, φ - V. Reverse bias occurs with the semiconductor negative which increases the potential barrier, φ + V. so that If (current from semiconductor to metal) tends to zero and Io (current from metal to semiconductor) remains constant

p - type semiconductor with φ_m > φ_s

The initial flow of electrons is from the semiconductor to the metal. This results in a surface charge of electrons in the metal and a surface charge of holes in the semiconductor. In this case, there is no depletion layer and external bias does not affect the contact potential, φ_m - φ_s. Finally when the two materials have ascertained an equal fermi level, there is a free flow of holes in either direction. After all said and done, this contact is ohmic.


For material contacts between both n - type and p - type materials, I_o increases with temperature since it is due to thermally generated carriers.

A pn junction is formed by allowing a group III material to diffuse into an n - type region at high temperatures.
An np junction would be formed by diffusion of a group V material into a p - region.