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]
01.3108231147589E-11
-0.51.0246919256896E-11
-18.6947035879714E-12
-1.57.685057243361E-12
-26.9612634246896E-12
-2.56.4097376879867E-12
-35.9714576331342E-12
-3.55.6123143527656E-12
-45.3110412810026E-12
-4.55.0535990774722E-12
-54.8302963448986E-12
-5.54.6341986634789E-12
-64.4601957927793E-12
-6.54.3044277090901E-12
-74.1639169786125E-12
-7.54.0363251691202E-12
-83.9197866922649E-12
-8.53.8127925740671E-12
-93.7141073397074E-12
-9.53.6227084109215E-12
-103.5377411471614E-12