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 0.009 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]
06.0670192173088E-10
-0.54.8911229970922E-10
-14.2094989253731E-10
-1.53.7511651206854E-10
-23.4159329371874E-10
-2.53.1570215472474E-10
-32.9492698388642E-10
-3.52.7777823923331E-10
-42.6331044937624E-10
-4.52.5089076765709E-10
-52.4007750183582E-10
-5.52.3055175805526E-10
-62.220767674083E-10
-6.52.1447255226246E-10
-72.0759953283939E-10
-7.52.0134756969052E-10
-81.956284327135E-10
-8.51.9037049835382E-10
-91.8551493556967E-10
-9.51.8101291053886E-10
-101.7682350339063E-10