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 0.008 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]
04.8476864143761E-10
-0.53.9012769449041E-10
-13.3547736529663E-10
-1.52.9880260500222E-10
-22.7201090769616E-10
-2.52.5133592083067E-10
-32.347561811591E-10
-3.52.2107676281263E-10
-42.0954004286473E-10
-4.51.9963934820613E-10
-51.9102129314355E-10
-5.51.8343088385847E-10
-61.7667888457062E-10
-6.51.706215069781E-10
-71.6514727579661E-10
-7.51.6016825440845E-10
-81.5561401723181E-10
-8.51.5142740725167E-10
-91.4756148574888E-10
-9.51.4397729749773E-10
-101.4064220570552E-10