Physics of Semiconductor Devices

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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 0.002 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]
06.1586655024601E-11
-0.54.9277822027351E-11
-14.2258814255676E-11
-1.53.7578811298045E-11
-23.4173463695857E-11
-2.53.1552603785827E-11
-32.9454938600768E-11
-3.52.7726753222792E-11
-42.6270935541571E-11
-4.52.5022720206616E-11
-52.3937035840996E-11
-5.52.2981419051241E-11
-62.2131814520608E-11
-6.52.1369967508438E-11
-72.0681741118588E-11
-7.52.0055994154216E-11
-81.9483811426707E-11
-8.51.8957962741745E-11
-91.8472514375948E-11
-9.51.8022544719749E-11
-101.7603932612242E-11