8.3 Junction Capacitance

Since we have a separation of positive and negative charges in the depletion region，a capacitance is associated with the pn junction. Fig.8.3 shows the charge densities in the depletion region for applied reverse-bias voltages of VR and VR+dVR. An increase in the reverse-bias voltage VR will uncover additional positive charges in the n region and additional negative charges in the p region. The junction capacitance is defined as Cj=dQ/dVR and the following expression can be derived：

where is the capacitance at zero applied voltage.

It is seen that the junction capacitance decreases as the bias becomes more negative. When Vbi1|Va|，Cj decreases roughly as the inverse square root of the reverse voltage.7. When Vbi|Va|，Cj decreases roughly as the inverse square root of the reverse voltage. 提示：roughly表示“约为”、“近似为”，不要机械地翻译为“粗略”；square root of…表示“平方根”、“二分之一次方”，前面加inverse表示平方根的倒数，也可翻译为“负二分之一次方”。

The junction capacitance Cj can also be expressed in terms of the depletion layer thickness，and we find that we can write

Fig.8.3 Illustrating the variation of depletion layer charge and width with junction voltage.

So the junction capacitance is identical with that of an ordinary capacitor of the same size，shape，and permittivity as the depletion layer. Keep in mind that the depletion layer width is a function of the reverse bias voltage so that the junction capacitance is also a function of the reverse bias voltage applied to the pn junction. This fact can be put to good use in a variety of ways，since it represents a voltage-controlled capacitance. A diode specifically designed for such an application is called a varactor diode