# Electrostatic Clamps Using Dielectrics

1. Nov 3, 2009

### jmtome2

b]1. The problem statement, all variables and given/known data[/b]
Electrostatic clamps are used for holding workpieces while they are being machined, for holding silicon wafers during electron beam microfabrication, etc. They comprise an insulated conducting plate maintained at a potential of several thousand volts and covered with a thin insulating sheet. The workpiece or the wafer resets on the sheet and is grounded. It is advisabled to apply a film of oil to the sheet to prevent sparking.

One particular type operates at 300 volts and has holding power of 2 atmospheres. If the insulator is Mylar (Class-A; $$\epsilon_r=3.2$$, what is its thickness?

2. Relevant equations

$$F=-\frac{dW}{dx}$$

$$W=\frac{1}{2}CV^{2}$$

$$Q=CV$$

3. The attempt at a solution
Can I treat this system as a parallel plate conductor with a dielectric in the center? I don't see how to extract the thickness from this.

$$F==-\frac{dW}{dx}=\frac{1}{2}\frac{Q^2}{C^2}\frac{dC}{dx}=\frac{1}{2}V^2\frac{dC}{dx}$$

But the capacitance is constant $$C=\frac{Q}{\Delta V}$$ meaning F becomes zero... which does not makes sense...

Is there another way to calculate the capacitance?

Last edited: Nov 3, 2009
2. Nov 3, 2009

### jmtome2

I know the capacitance of a parallel plate configuration with dielectric filling the middle is $$C=\frac{A\epsilon_0\epsilon_r}{d}$$, but I also know that the grounded "plate" on top throws this off.... I'm just not sure how