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 0.002 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]
01.14061525232E-11
-0.58.8998596569026E-12
-17.5455567369627E-12
-1.56.6663041181724E-12
-26.0366909595552E-12
-2.55.5572857841155E-12
-35.1765188953185E-12
-3.54.8646275716196E-12
-44.6030730645745E-12
-4.54.3796259627013E-12
-54.1858492675073E-12
-5.54.0157090194905E-12
-63.8647603402461E-12
-6.53.7296469203666E-12
-73.6077806135169E-12
-7.53.4971292353424E-12
-83.3960718738866E-12
-8.53.3032977126945E-12
-93.2177337018998E-12
-9.53.1384918347053E-12
-103.0648300432571E-12