1. Lecture 21 QCM and Ellipsometry

2. Quartz Crystal Microbalance
The Quartz Crystal Microbalance (QCM) is an extremely sensitive mass sensor, capable of measuring mass changes in the nanogram range. QCMs are piezoelectric devices fabricated of a thin plate of quartz with electrodes affixed to each side of the plate. .

3. Quartz crystal microbalance
Quartz crystals have piezoelectric properties, that is they develop an electric potential upon the application of mechanical stress. The frequency of oscillation of the quartz crystal is partially dependent on the thickness of the crystal. During normal operation, all the other influencing variables remain constant; thus a change in thickness correlates directly to a change in frequency. As mass is deposited on the surface of the crystal, the thickness increases; consequently the frequency of oscillation decreases from the initial value. With some simplifying assumptions, this frequency change can be quantified and correlated precisely to the mass change using Sauerbrey's equation.

4. Sauerbrey equation
f0 – Resonant frequency(Hz) Δf – Frequency change (Hz) Δm – Mass change (g) A – Piezoelectrically active crystal area (Area between electrodes, cm2) ρq – Density of quartz (ρq = g/cm3) μq – Shear modulus of quartz for AT-cut crystal (μq = 2.947x1011 g/cm.s2) νq – Transverse wave velocity in quartz (m/s)

5. MODE OF OPERATION
In ring-down, one measures the voltage between the electrodes after the exciting voltage has suddenly been turned off. The resonator emits a decaying sine wave, where the resonance parameters are extracted from the period of oscillation and the decay rate.
QCMs make use of oscillator circuits, ring-down and impedance analysis.

6. MODE OF OPERATION
In impedance analysis, the electric conductance as a function of driving frequency is determined by means of a network analyzer. By fitting a resonance curve to the conductance curve, one obtains the frequency and bandwidth of the resonance as fit parameters.

7. Ellipsometry
Ellipsometry is a method that enables the determination of the optical properties of surfaces. The principle of this method is based on the change in polarization state of light reflected from the surface of a sample.

8. Experimental Setup
Electromagnetic radiation is emitted by a light source and linearly polarized by a polarizer.
After reflection the radiation passes a compensator (optional) and a second polarizer, which is called analyzer, and falls into the detector.

9. Theory
Ellipsometry measures the ratio of rs and rp, which is described by the fundamental equation of ellipsometry:
tanΨ is the amplitude ratio upon reflection, and Δ is the phase shift.
Ψ and Δ values are calculated using the Fresnel equations.

10. Advantages of Ellipsometry
It measures the ratio of two values so is highly accurate and reproducible, does not need a reference sample, and is not so susceptible to light source fluctutation
Since it measures phase, it is highly sensitive to the presence of ultrathin films (down to submonolayer coverage).
It provides two pieces of data at each wavelength. More film properties can be determined.

11. Types of Ellipsometer
Ellipsometers may be single wavelength or spectroscopic
They may be single- or multiple- angle of incidence
They may operate as rotating element or as nulling ellipsometers
They may be single point or imaging

12. Spectroscopic Ellipsometer SOPRA GESP5
SOPRA variable angle spectroscopic ellipsometer GESP5

13. Rotating polariser ellipsometer