Hi could someone check my answer?

The question asks for a pn junction, calculate the total bending through energy at zero bias of the conduction band edge passing from neutral n-type section to the neutral p-type section.

Additional info:

Band gap of silicon Eg = 1.1 eV

Density of states at conduction band (Nc) = 2.8e19 states/cm^3

Density of states at valence band (Nv) = 1e19 states/cm^3

p-type contains 5e16 holes/cm^3 (p)

n-type contains 1e19 electrons/cm^3 (n)

Boltz constant k = 8.614e-5 eV/K

temperature = 300K

My ans:

qV_bi = Eb - ∂1 - ∂2, where ∂1 = (Ef-Ev) and ∂2 = (Ec-Ef)

if holes p = Nv*exp[-(Ef-Ev)/KT] = Nv*exp[-∂1/KT]

and electrons n = Nc*exp[-(Ec-Ef)/KT] = Nc*exp[-∂2/KT]

then ∂1 = KT*ln[Nv/p]

and ∂2 = KT*ln[Nc/n]

therefore qV_bi = EG - {KT*ln[Nv/p]} - {KT*ln[Nc/n]} = 0.62V

Is this correct?

The question asks for a pn junction, calculate the total bending through energy at zero bias of the conduction band edge passing from neutral n-type section to the neutral p-type section.

Additional info:

Band gap of silicon Eg = 1.1 eV

Density of states at conduction band (Nc) = 2.8e19 states/cm^3

Density of states at valence band (Nv) = 1e19 states/cm^3

p-type contains 5e16 holes/cm^3 (p)

n-type contains 1e19 electrons/cm^3 (n)

Boltz constant k = 8.614e-5 eV/K

temperature = 300K

My ans:

qV_bi = Eb - ∂1 - ∂2, where ∂1 = (Ef-Ev) and ∂2 = (Ec-Ef)

if holes p = Nv*exp[-(Ef-Ev)/KT] = Nv*exp[-∂1/KT]

and electrons n = Nc*exp[-(Ec-Ef)/KT] = Nc*exp[-∂2/KT]

then ∂1 = KT*ln[Nv/p]

and ∂2 = KT*ln[Nc/n]

therefore qV_bi = EG - {KT*ln[Nv/p]} - {KT*ln[Nc/n]} = 0.62V

Is this correct?

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