Determine the dielectric thickness and determine the sheet

Question

Problem 1. The optical transmittance T of a semiconductor wafer of thickness d is shown in Figure 1. Replicate this figure and draw the T- 1/λ curve where the semiconductor wafer is thinned, i.e. d is reduced. Justify your answer. The reflectance remains the same:

T = (1 - R)²e^-∝d/(1 - R)²e^-2∝d

Problem 2. Light is incident perpendicular on a Si wafer covered with a dielectric of thickness d and refractive index n. The reflectance versus wavenumber is shown Figure 2.

Determine the dielectric thickness. Where n= 2

And the following may be useful:

d = λ₀λ₁/2n(λ₁-λ₀)

Problem 3. Consider an n-type wafer containing small n⁺ regions. A four-point probe is placed on the wafer so that probe 1 of a conventional in-line four-point probe is placed on one of the n⁺ regions. The other three probes are on the n-portion of the wafer. In this four-point probe, current enters probe 1 and leaves probe 4; the voltage is measured across probes 2 and 3. There are no n+ regions between probes 2 and 4. Is the correct sheet resistance measured in this case? Explain your answer

Problem 4. A transmission line measurement structure below gives R_T values as shown in the graph (Figure 3). The doping density N_D in the n⁺ layer is uniform.

Determine the sheet resistance R_SH (ohms/square), the contact resistance RC (ohms) and the doping density ND (cm-3). Z (n⁺ layer width = 100µm, L= 25 µm, t = 2.5x10^-4 cm, µ_n = 50 cm²/Vs).