What is the difference in intensity of X-rays penetrating a pure Si wafer 0.05 cm thick relative to this same wafer that is patterned with a 1 μm thick Au bond pad? Assume that the operating X-ray voltage is 20 kV. Is the contrast better at 100 kV?

Question

What is the difference in intensity of X-rays penetrating a pure Si wafer 0.05 cm thick relative to this same wafer that is patterned with a 1 [latex]\mu m[/latex] thick Au bond pad? Assume that the operating X-ray voltage is 20 kV. Is the contrast better at 100 kV?

Accepted Answer

Using Eq. 11-1, for the Si wafer alone [latex]I/I_{o}=\exp\left[ -10.2\left( 0.05 \right) \right]=0.60[/latex]. For the Si/Au combination, [latex]I/I_{o }=\exp\left(-[10.2\left( 0.05 \right)+\left( 1510 \right) 10^{-4}\right]=0.52[/latex]. This intensity difference of over [latex]13\%[/latex] is detectable on film. At 100 kV the corresponding intensity ratios are [latex]I/I_{o}=\exp\left[ -0.429\left( 0.05 \right) \right]=0.979[/latex] and exp [latex]\left( -\left[ 0.429\left( 0.05 \right)+\left( 98.8 \right)10^{-4} \right] \right)=0.969[/latex]. The more penetrating, high-energy X-rays are thus seen to considerably reduce the contrast.

[latex]I\left(x\right)=I_{o} \exp \left[ -\mu x \right][/latex] (11-1)

Question 11.1: What is the difference in intensity of X-rays penetrating a ...