1. CV Measurements Diode junction capacitance C j =  A/w Depletion depth np+p+ w VaVa reverse bias:  =  r  o (static dielectric constant). For Si,  r = 11.7. for N a >> N d

2. Differential Capacitance What is actually being measured is the differential capacitance C = dQ/dV a as a function of V a. ~ n-typep-type w + dw VaVa dV a dc adjusted by user ac supplied by C- meter dQ = N d ( w+  w ) – N d ( w )

3. Measurement of N d Boonton meter: dV a = 1 MHz, 15 mV dQ: ionized dopants in depletion region w C is determined by N d in the region dw. The depth w is determined by V a. So a measure of the capacitance at V a corresponds to a measurement of N d at w. ~ n-typep-type w + dw VaVa dV a

4. 1/C j 2 – V a Plot Depletion depth Junction capacitance If N d is constant, we can plot a straight line to find V o and N d.

5. Diode CV Data The “raw” CV data looks something like the following. The capacitance C ~ V a -1/2 if the doping density is constant.

6. Doping a Semiconductor n-type semiconductor (in cross-section) Addition of p-type dopants (B) diffusion implantation B B B B B B B B B B B BB B B B B B B B B B NANA x

7. Doping Density Profile n-type background concentration

8. Net Doping Density |N A – N D | n-type background concentration p-type n-type p-type dopant

9. Data Analysis VoVo Slope ~ 1/N D For doping density N D constant with depth, 1/C 2 vs. V a is a straight line. The doping density in this sample is not constant.

10. General Doping Density We can show that the doping profile N B (x) is given by… …and that the distance x is…

11. Data Analysis There is “noise” from the numerical differentiation, but we can do some “curve fitting”.

12. Curve-fitting Region p-typen-type This plot shows where in the sample we are “looking”.

13. Diode Connection The diagram shows how to connect the diode to the capacitance meter. Connecting with the wrong polarity will forward-bias the diode, resulting in a very large capacitance. Test Place device to be measured here. Diff (difference) A capacitance placed here will be subtracted from “Test”. HighLow Test Diff