1.
2.
origin of the x′ axis (x′ := −x) is set at the edge of the depletion region in the n-type
semiconductor and denoted as b in Fig. B.1. Here, we use the approximation of infinite
thickness for the n-type semiconductor. The constants A′ and B′ can be determined from
the boundary conditions
At x′ = 0, p n (b) = p n0 exp(qV a /k B T).
p − n is finite at x′ → ∞, therefore A′ = 0.
We thus find the concentration profile of holes in the quasi-neutral region of the n-type
semiconductor to be
When substituting the corresponding concentration profiles of minority carriers Eqs.
(B.8) into Eqs. (B.2) we obtain for the current densities
Under the assumptions that the effect of recombination and thermal generation of carriers
in the depletion region can be neglected, which means that the electron and hole current
densities are essentially constant across the depletion region, one can write for the current
densities at the edges of the depletion region
The total current density flowing through the p-n junction at the steady state is constant
across the device therefore we can determine the total current density as the sum of the
electron and hole current densities at the edges of the depletion region,
Using Eqs. (8.1b) and (8.2b), Eq. (B.11) can be rewritten as
where J 0 is the saturation current density of the p-n junction which is given by
2.
origin of the x′ axis (x′ := −x) is set at the edge of the depletion region in the n-type
semiconductor and denoted as b in Fig. B.1. Here, we use the approximation of infinite
thickness for the n-type semiconductor. The constants A′ and B′ can be determined from
the boundary conditions
At x′ = 0, p n (b) = p n0 exp(qV a /k B T).
p − n is finite at x′ → ∞, therefore A′ = 0.
We thus find the concentration profile of holes in the quasi-neutral region of the n-type
semiconductor to be
When substituting the corresponding concentration profiles of minority carriers Eqs.
(B.8) into Eqs. (B.2) we obtain for the current densities
Under the assumptions that the effect of recombination and thermal generation of carriers
in the depletion region can be neglected, which means that the electron and hole current
densities are essentially constant across the depletion region, one can write for the current
densities at the edges of the depletion region
The total current density flowing through the p-n junction at the steady state is constant
across the device therefore we can determine the total current density as the sum of the
electron and hole current densities at the edges of the depletion region,
Using Eqs. (8.1b) and (8.2b), Eq. (B.11) can be rewritten as
where J 0 is the saturation current density of the p-n junction which is given by