Method for extracting a transverse magneto-optic effect signal

A method for extracting a transverse magneto-optic Kerr effect (T-MOKE) signal in an ellipsometric measurement procedure upon a sample, the method employing an apparatus comprising a light source intended to emit a light beam that is to follow an optical path, the sample having a reflecting surface arranged to reflect, at least partially, the light beam in an optical plane of incidence, the apparatus further comprising:

• a first linear polarizer having an axis and being located on the optical path between the light source and the reflecting surface;
• a device to produce a magnetic field at a sample location, the device being configured to direct the magnetic field perpendicularly to the optical plane of incidence and to reverse the direction of the magnetic field;
• a rotatable quarter-wave plate having an axis and being located after the reflecting surface on the optical path of the reflected light beam;
• a second linear polarizer that is rotatable and is located after the quarter-wave plate on the optical path of the reflected light beam, the quarter-wave plate having an axis;
• a photo-detector located after the second linear polarizer on the optical path of the reflected light beam, the photo-detector being configured to measure an intensity of the light beam that reaches it;
• and
• the sample is represented by a Jones reflection matrix of the form
• [
• r
• s
• 0
• 0
• r
• p
• +
• β
• ]
• ,
• where rs is a complex Fresnel reflection coefficient for s-polarization, rp is the complex Fresnel reflection coefficient for p-polarization and β is a complex coefficient that represents the component of light reflected on the reflecting surface due to the magnetic-field induced magnetization of the sample in a direction perpendicular to the optical plane of incidence, whereby {tilde over (β)}=β/rp is a relative T-MOKE coefficient;
• the method comprising the steps of:
• a) defining a grid of at least six angle pairs, each angle pair being formed by an orientation angle φ for the quarter-wave plate and a polarization angle θ for the second linear polarizer, the orientation angle φ being an angular distance between the quarter-wave plate axis and the optical plane of incidence, and the polarization angle θ being an angular distance between the second linear polarizer axis and the optical plane of incidence;
• b) setting the first linear polarizer at a fixed polarization angle α that is neither 0° nor 90°, the fixed polarization angle α being the angular distance between the first linear polarizer axis and the optical plane of incidence;
• c) setting the quarter-wave plate at the orientation angle φ of an angle pair;
• d) setting the second linear polarizer at the polarization angle θ of the same angle pair of step (c);
• e) testing the set angle pair by making the light source to emit the light beam along the optical path, whereby the light beam is transmitted through the first linear polarizer, is reflected, at least partially, by the reflecting surface of the sample, is transmitted through the quarter-wave plate, is transmitted through the second linear polarizer and reaches the photo-detector;
• f) recording a measurement of the light intensity from the photo-detector;
• g) recording a measurement of the light intensity from the photo-detector upon a magnetic-field reversal with respect to the measurement of step (f);
• h) computing and recording a relative change in the light intensity (ΔI/I) due to magnetization reversal upon the magnetic-field reversal of step (g);
• i) setting the quarter-wave plate at the orientation angle of another angle pair;
• j) setting the second linear polarizer at the polarization angle of the same angle pair of step (i),
• k) repeating steps (e) to (j) until at least six of the angle pairs of the grid have been tested;
• and
• l) determining numerical values of real free fit parameters B1, B2, B3, B4, B5 and B6 by matching the collection of the recorded relative changes in the light intensity to equation ΔI/I=f(α, φ, θ, B1, B2, B3, B4, B5, B6), where f is a function mathematically derived for the relative change in the light intensity.