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 0.006 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]
02.8129254080171E-11
-0.52.189001375379E-11
-11.8537455695596E-11
-1.51.6366720965783E-11
-21.481477352977E-11
-2.51.3634319483171E-11
-31.2697447357695E-11
-3.51.1930472797965E-11
-41.1287562035886E-11
-4.51.0738511954133E-11
-51.0262503059731E-11
-5.59.8446558464221E-12
-69.4740156163966E-12
-6.59.1423144665831E-12
-78.8431793791849E-12
-7.58.5716080943814E-12
-88.3236119361003E-12
-8.58.095966174609E-12
-97.8860316442603E-12
-9.57.6916247633571E-12
-107.5109211632314E-12