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]
04.935380620819E-10
-0.53.9465494858924E-10
-13.3834307665533E-10
-1.53.0082210717929E-10
-22.7353178820804E-10
-2.52.5253422363278E-10
-32.3573174868074E-10
-3.52.2189095872453E-10
-42.102329206426E-10
-4.52.0023830440291E-10
-51.9154578258579E-10
-5.51.8389515250917E-10
-61.77093634861E-10
-6.51.7099495567232E-10
-71.6548584993887E-10
-7.51.6047706309623E-10
-81.5589717982213E-10
-8.51.5168828692076E-10
-91.4780285905142E-10
-9.51.4420147966637E-10
-101.4085114472448E-10