Chapter 6 - Light Matter Interaction

Question 1

How can one use optical microscopy to see even monolayer flakes of 2D materials?

Answer 1

By so-called contrast engineering. By carefully engineering the sequence of layers with respect to thickness and refractive index, we can get contrast maxima between the underlying substrate and the 2D Material. The relative contrast is also dependent on the number of layers, which means we essentially can count the number of layers.

Question 2

Which parameters is the contrast dependent on?

Answer 2

Thickness of layers, refractive indices, wavelength.

Question 3

What do you measure in an ellipsometry experiment?

Answer 3

The change in polarization state of the reflected light.

Question 4

What is the equation for the change in polarization state of the reflected light?

Answer 4

rho = r_p / r_s = tan psi exp[i∆],

psi and ∆ are the ellipsometric angles.

Question 5

What is nulling ellipsometry?

Answer 5

The polarizer and analyzer are adjusted such that reflected light is linearly polarized and intensity minimized. Angle between the polarizer and analyzer determines the ellipsometric angles.

Question 6

Which interesting parameters are spectroscopic ellipsometry sensitive to?

Answer 6

Film thickness, interfaces, optical functions (complex dielectric function and complex refractive index).

Question 7

Which quantities are measured in spectroscopic ellipsometry?

Answer 7

The relative amplitude X/Y = tan psi

The relative phase ∆

Question 8

What can be said from just the data measured in a SE measurement?

Answer 8

Nothing. Modelling the near-surface region is required to get useful information.

Question 9

Are the ellipsometric angles (psi and ∆) dependent on the number of layers for 2D materials?

Answer 9

Of course…..

Question 10

How does one do a regression analysis of data obtained through an SE experiment?

Answer 10

• Construct a model that describes the sample reasonably well (layer sequence, thickness, optical constants, roughness of individual layers etc.)
• Use model to calculate predicted response from Fresnel’s equations.
• Compare to experimental data.
• Adjust unknown paramters to improve fit.
• Repeat until convergence.

Question 11

What could go wrong when doing a fit in an SE experiment?

Answer 11

The fit could converge to unphysical quantities.