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]
01.7812716712514E-10
-0.51.4136946652437E-10
-11.2077435576078E-10
-1.51.0716390909904E-10
-29.731376053375E-11
-2.58.9760290336106E-11
-38.3730496346182E-11
-3.57.8772582588369E-11
-47.4602495330654E-11
-4.57.1031502323733E-11
-56.7928652394058E-11
-5.56.5199855205082E-11
-66.2775531167785E-11
-6.56.0602969200526E-11
-75.8641408542492E-11
-7.55.685876677738E-11
-85.5229400138945E-11
-8.55.3732532044312E-11
-95.2351126335216E-11
-9.55.1071063762341E-11
-104.9880529754016E-11