Physics of Semiconductor Devices

Return to
problem list

      

Capacitance-Voltage Characteristics

The capacitance of a pn junction depends on the width W of the depletion layer.

If the junction is heavily p-doped then it will be an asymmetric p+n junction where Na >> Nd. In this case the total depletion width is approximately equal to the depletion width on just the n-side of the junction.

To experimentally characterize a pn-junction, often the capacitance is measured as a function of the applied voltage. For an abrupt p+n junction, a plot of 1/Cj² versus V is a straight line. The formula can be determined from the above two equations. The slope and intercept of this line give the doping concentration and built-in potential.

The capacitance-voltage characteristic of a silicon p+n-junction with an area of 0.005 cm² is measured. The results of this measurement are shown in the table on the right.

What is the doping concentration and the built-in potential?

Nd = 1/cm³

Vbi = V

The dielectric constant of silicon is εr = 11.9.

     
voltage [V]  capacitance [F]
03.6769443454761E-10
-0.52.9685949203256E-10
-12.5566838051631E-10
-1.52.2792499874447E-10
-22.0761234549817E-10
-2.51.9191328817038E-10
-31.7930995237705E-10
-3.51.6890263156502E-10
-41.6011971354387E-10
-4.51.5257831526862E-10
-51.4601105048744E-10
-5.51.4022477951554E-10
-61.3507604528791E-10
-6.51.3045576370531E-10
-71.2627931137735E-10
-7.51.2247989709712E-10
-81.1900400430147E-10
-8.51.1580818084114E-10
-91.1285672931084E-10
-9.51.1012001383546E-10
-101.0757319784665E-10