= Linearly graded junction capacitance
{title2=$C/A=\varepsilon_s/w$}
For a <linearly graded p-n junction>, the signed p-side depletion charge per area is $Q_p=-e\alpha w^2/8$. Differentiating with respect to positive p-side voltage $V$, using the <linearly graded junction depletion width>, gives the positive differential <junction capacitance> per area
$$
C_A=\frac{dQ_p}{dV}=\frac{\varepsilon_s}{w}
=\left[\frac{e\alpha\varepsilon_s^2}{12(V_b-V)}\right]^{1/3}.
$$
Thus $C_A^{-3}$ is linear in $V$. If stored charge denotes the positive n-side magnitude $Q_n=-Q_p$, its derivative with respect to $V$ is negative; the positive capacitance is instead $-dQ_n/dV=dQ_n/dV_R$ for reverse-voltage magnitude $V_R=-V$. Neither definition uses the zero net charge of the whole depletion layer.
Back to article page
