Calculate the approximate donor binding energy

Calculate the approximate donor binding energy for Si (r = 11.7,m^x_n= 1.18 m₀)

Solution: From E= m^*_nq⁴ / 2(4 πε₀ε_r)² [h/(2 π)]² we have

= 1.867 x 10^-20 J = 0.117 eV.

Note:  The  effective  mass  used  here  is  an  average  of  the  effective  mass  in  different crystallographic directions, and is termed as the "conductivity effective mass" with values of 1.28 m₀ (at 600 K), 1.18 m₀ (at 300 K), 1.08 m₀ (at 77 K), and 1.026 m₀  (at 4.2 K).

1. In III-V compounds, column VI impurities (e.g., S, Se, Te) that occupying column V sites act as donors. Similarly, column II impurities (e.g., Be, Zn, Cd) that occupying column III sites act as acceptors.
2. When a column IV material (e.g., Si, Ge) is used to dope III-V compounds, then they might substitute column III elements (and act as donors), or substitute column V elements   (And act as acceptors) => amphoteric dopants.
3. Doping  creates a  large change  in  the electrical  conductivity,  e.g.,  with a doping  of 10¹⁵/cm³ , the resistivity of Si changes from 2 x 10⁵ Ω-cm to 5 Ω -cm.