# Al-n Si contact barrier

Consider a contact between Al and n Si doped at $N_d = 10^{16}$ $(cm^{-3})$ . T = 300 K.

(a) Draw the energy-band diagrams of the two materials before the junction is formed.

(b) Draw the ideal energy band at zero bias after the junction is formed.

(c) Calculate Schottky barrier and  electron affinity of Si for part b)

Work function for Al is $W =4.08 eV$

Position of Fermi level in Si with $Nd =10^{16} cm^-3$ (with reference to the valence band)

b,c)

$E_f = E_g/2 + KT*ln(N_d/N_i)$

$N_i =1.5*10^{10} cm^{-3}$ is the electron concentration for intrinsic silicon

$N_d = 10^{16} cm^{-3}$

$E_g = 1.12 eV$ (for Silicon)

$KT =0.0256 eV$ at T=300 K

$E_f = 1.12/2 +0.0256*ln(10^{16}/1.5*10^{10}) =0.903 eV$

Thus the $E_c-E_f=1.12-0.903 = 0.2167 eV$

($E_f$ lies 0.2167 eV under the conduction band)

For Silicon energy difference between BC (conduction band) and vacuum level is

electron affinity

$chi = 4.05 eV$

(http://www.siliconfareast.com/sigegaas.htm)

The barrier potential $phi$ (see the figure) is the difference between the Fermi level in Si and the metal upper band.

$phi(b) = 0.2167 +(4.08-4.05) =0.2167+0.03 =0.2467 eV$ 