The intrinsic carrier concentration and the fraction of ionized atoms of silicon at -55℃, 0℃, 20℃, 75℃, 125℃ is calculated below.
The intrinsic carrier concentration in intrinsic material is the number of electrons found in the conduction band or holes in the valence band. This quantity of carriers is determined by the material's band gap as well as its temperature.
Because the number of holes equals the number of electrons, the concentration of each is equal to some amount, ni, and this quantity is known as the intrinsic carrier concentration, and the pure semiconductor material is referred to as intrinsic material.
Given:
B = 5.4 x [tex]10^{31}[/tex]
[tex]E_G[/tex] = 1.12 ev for silicon
K = 8.62 x [tex]10^{-5}[/tex]
Silicon crystal = 5 x [tex]10^{22}[/tex] atoms/[tex]cm^3[/tex]
To find:
Intrinsic carrier concentration, ni = ?
Fraction of ionized atom = ?
Formula:
[tex]ni^2 = BT^3 e^{\frac{-E_G}{KT}[/tex]
Fraction of ionized atom = ni / 5 x [tex]10^{22}[/tex]
Calculations:
(a) For -55℃:
T = -55 + 273 = 218K
ni = [tex]5.4 * 10^{31} * 218^3 * e^{(\frac{-1.12}{8.62 * 10^{-5} * 218})}[/tex]
ni = 2.7018 x [tex]10^6[/tex] carriers/[tex]cm^3[/tex]
Fraction of ionized atom = 2.7018 x [tex]10^6[/tex] / 5 x [tex]10^{22}[/tex]
Fraction of ionized atom = 5.403 x [tex]10^{-17}[/tex] atoms/[tex]cm^3[/tex]
(b) For 0℃:
T = 0 + 273 = 273K
ni = [tex]5.4 * 10^{31} * 273^3 * e^{(\frac{-1.12}{8.62 * 10^{-5} * 273})}[/tex]
ni = 1.53 x [tex]10^9[/tex] carriers/[tex]cm^3[/tex]
Fraction of ionized atom = 1.53 x [tex]10^9[/tex] / 5 x [tex]10^{22}[/tex]
Fraction of ionized atom = 3.07 x [tex]10^{-14}[/tex] atoms/[tex]cm^3[/tex]
(c) For 20℃:
T = 20 + 273 = 293K
ni = [tex]5.4 * 10^{31} * 293^3 * e^{(\frac{-1.12}{8.62 * 10^{-5} * 293})}[/tex]
ni = 8.65 x [tex]10^9[/tex] carriers/[tex]cm^3[/tex]
Fraction of ionized atom = 8.65 x [tex]10^9[/tex] / 5 x [tex]10^{22}[/tex]
Fraction of ionized atom = 1.73 x [tex]10^{-13}[/tex] atoms/[tex]cm^3[/tex]
(d) For 75℃:
T = 75 + 273 = 348K
ni = [tex]5.4 * 10^{31} * 348^3 * e^{(\frac{-1.12}{8.62 * 10^{-5} * 348})}[/tex]
ni = 3.724 x [tex]10^{11}[/tex] carriers/[tex]cm^3[/tex]
Fraction of ionized atom = 3.724 x [tex]10^{11}[/tex] / 5 x [tex]10^{22}[/tex]
Fraction of ionized atom = 7.449 x [tex]10^{-12}[/tex] atoms/[tex]cm^3[/tex]
(e) For 125℃:
T = 125 + 273 = 398K
ni = [tex]5.4 * 10^{31} * 398^3 * e^{(\frac{-1.12}{8.62 * 10^{-5} * 398})}[/tex]
ni = 4.75 x [tex]10^{12}[/tex] carriers/[tex]cm^3[/tex]
Fraction of ionized atom = 4.75 x [tex]10^{12}[/tex] / 5 x [tex]10^{22}[/tex]
Fraction of ionized atom = 9.51 x [tex]10^{-11}[/tex] atoms/[tex]cm^3[/tex]
The complete question is in the image given below.
Learn more about Intrinsic carrier concentrations of silicon here:
https://brainly.com/question/15078086
#SPJ4
