Impact of series resistance on the measured capacitance
The Model 410 C-V meter assumes the device being measured is a capacitor with a small leakage current through the oxide. It assumes the device can be modeled by a capacitance in parallel with a conductance.
The admittance of this simple circuit is
The 410 measures the magnitude and phase of the admittance and determines the capacitance from the imaginary part. (It can also determine the conductance from the real part by properly setting the C/G button.)
The actual device being measured is better modeled by the circuit
For this circuit
The measured capacitance (C') is then
Typically the oxide is a pretty good insulator so for simplicity we will assume G ® 0.
This shows that the series resistance will cause the measured capacitor to be less than the actual capacitance by an amount that depends on the capacitance, the series resistance and the measuring frequency.
The 410 C-V plotter operates at f = 1 MHz and we have w = 2pf.
As an example let's look at what series resistance does to the measurement if the actual capacitance is 30 pf. You can easily check the effect for the expected value of your capacitor.
|
RS (W) |
C' (pf) |
|
100 |
30.0 |
|
1 K |
29.0 |
|
2 K |
26.3 |
|
5 K |
15.9 |
|
10 K |
6.6 |
|
20 K |
2.0 |
Where is your substrate contact resistance in this range?