Energy Band Structure of Open Circuited PN Junction

ENERGY BAND STRUCTURE OF OPEN CIRCUITED PN JUNCTION

Consider the unbiased PN junction and to know the energy band structure, we have to analyze the Fermi level of the semiconductor material. Fermilevel is defined as the particular energy level where the probability of occupation is 50%. For an n- type semiconductor, there are more electrons in the conduction band than there are holes in the valence band. This implies that the probability of finding an electron near the conduction band is larger than that of finding a hole at the valence band. So, the Fermilevel is closer to the conduction band in an n-type semiconductor.

For p-type semiconductor, there are more holes in the valence band than the electrons in the conduction band. Thus probability of finding an electron near the conduction band is smaller than the probability of finding a hole at the valence band. Therefore, the Fermilevel is closer to the valence band in a P-type semiconductor.

When a PN junction is formed, the energy levels of these regions will undergo a relative shift to make the Fermilevel constant throughout the diode. This equalization is similar to equalization of levels of water in two containers i.e., when two semiconductor materials are joined, the flow of charge carriers occur until the fermilevels in the two materials are equalized. We know that Fermilevel E_F is closer to the conduction band E_CN in n type semiconductor and it is closer to the valence band E_VP in P-type semiconductor as shown in Fig. 1.19.

The Fermilevel E_F is constant throughout the region in PN diode.

The conduction band edge E_CP in P-type is higher than the conduction band edge ECN in n-type. The valence band E_VP in P material is also higher than the valence band E_VN in n-type material. The shifts in the Fermilevel from the intrinsic conditions in p -type and n-type material are represented as E₁ and E₂ respectively. Thus the total shift in energy level E_o is given by

E_o is the potential energy of the electrons in the PN junction, E_o = q V_o, where V_o is barrier potential

From Fig. 1.19,

Substitute the above equation in (3)

Substitute in equation (4)