fd8029fa-17a7-4ac1-a5a6-d75f28053f13 24 Alvaro Diaz Falconi 4 15 false false 0 decimal

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Elementary charge

q.e 1.602 1019 -^* C * :

ni 1.5 1010^* :

Vacuum permittivity

ε.r 11.9 :

ε.0 8.854 1012 -^* F m / * :

Doping concentration on P-side

Temperature :

Na 81015^* :

T 300 K * :

Doping concentration on N-side

Nd 21016^* :

SMath built in constants:

Boltzmann constant :

ε.0 8.85418781762039 1012 -^* F m / *

kb 1.38 1023 -^* J K / * :

k 1.3807 1023 -^* J K / *

Permittivity :

ε ε.0 ε.r * : 1.0536 1010 -^* F m / *

Built-in voltage, contact potential:

Vbi kb T * q.e / Nd Na * ni 2^/ ln * m 3^* : 0.7052 m 3^* V *

Depletion width (no external bias)

W 2 ε * Nd Na + (* Vbi * q.e Nd * Na * / sqrt : 0.0004029 m *

Depletion width in the p-region:

Wp Nd W * Nd Na + / : 0.0002878 m *

Depletion width in the n-region:

Wn Na W * Na Nd + / : 0.0001151 m *

From this point on, I don't know how to proceed.

l 0 :

On figure 4, this is point x=0

Equation given:

y x 2 diff Pnet qe e0 * / + 0 ≡

Boundary condition:

E 1 ε / ≡ ρ x Wp - Wn int *

Vo q.e 2 ε * / Wp Wn + (2^* Na Nd * Na Nd + / * 1 m 3^/ * : 0.7052 V *

this is Vbi

Charge density, electric field an potential

x ρ q.e Na * - x Wp - 0 ltlt q.e Nd * x 0 Wn ltlt 0 cases :

x m * ρ

x E q.e Na * ε / x Wp + (* - x Wp - 0 ltlt q.e Nd * ε / x Wn - (* x 0 Wn ltlt 0 cases :

x m * E

x V q.e Na * 2 ε * / x Wp + (2^* - x Wp - 0 ltlt Vbi q.e Nd * 2 ε * / x Wn - (2^* - x 0 Wn ltlt 0 cases :

x m * V