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Gaertner 117 Manual Null Ellipsometer



Polarized light

The ellipsometer works on the principle of reflection of polarized light from a surface.  Light can be polarized either in the plane of incidence or parallel to it, and the amount of reflection and phase shift given to the incident light depends upon its orientation.  If the index of refraction (n) and extinction coefficient (k) for a material are known, one can measure the thickness of a film of the material on top of a bulk substrate or even another film.  By using different angles of incidence, it is possible to determine the film thickness without knowing the index of refraction or extinction coefficients.  When considering the effects of reflection on incident light, the magnetic portion of the wave is usually ignored.  Now consider an electromagnetic wave propagating in the positive z direction.  The electric field vector will oscillate in a plane perpendicular to the direction of propagation, or the x-y plane.  If the light is linearly polarized, this oscillation will take place in only one direction in that plane.

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In the drawing below,  two waves are incident upon a plane surface.   The electric field labeled Ep oscillates in a plane parallel to the plane of incidence (the subscript p stands for parallel).  The electric field labeled Es oscillates in a plane perpendicular to the plane of incidence (the subscript s stands for 'senkrecht', or German for perpendicular.  Remember - this component stands out of the plane of incidence).

epes2.jpg (21169 bytes)

Ellipsometric Parameters

There are two phenomena that happen at the reflecting surface which will provide information.   First, the amount of attenuation of a light beam at the surface depends on its orientation to the plane of incidence.  If a linearly polarized light beam with equal Ep and Es components strikes the surface, the reflected beam will not have the same ratio of Ep and Es components.  Click here to see the Fresnel equations for reflection at an interface.

The second phenomenon that happens at the surface is a phase shift of the Es component.  This phase shift depends on the nature of the surface and of the angle of incidence.

Once the light beam hits the surface, its components will undergo attenuation and a phase shift.  As a result, the reflected beam will NOT be linearly polarized.   Instead, the two components, Ep and Es, will be out of phase such that, at any given point in time, the sum of the two components will not be zero.  Remember that for linearly polarized light, the electric field is zero in between any given maximum and minimum.  This is not true for the reflected light in this case.  This light is referred to as elliptically polarized light (see diagram below).   The electric field vector, instead of being confined to a single direction (as in the case of linearly polarized light), will rotate in the x-y plane (perpendicular to the direction of travel for the wave), and the tip of the vector will trace out an ellipse.   In the case where the phase shift is exactly 90 degrees, and if the two components have the same magnitude, the light is referred to as circularly polarized light.

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The reflected light therefore carries information about the nature of the surface.  Different materials and different film thicknesses will yield different amounts of attenuation and phase shifts for the incident beam.  Furthermore, these effects also depend on wavelength.  To see more details, go to the Interaction of Light With Matter page.

Ellipsometer Operation

Manual Null Ellipsometer

To see a diagram of the ellipsometer parts, click here.

Ellipsometry is a type of optical probe, which means it uses photons to probe the surface.  To begin with, a quasimonochromatic light source (in our case a 632.8nm HeNe laser) is first linearly polarized

After being linearly polarized, the light beam travels through a quarter wave plate.  Essentially, this quarter wave plate (QWP) imparts a 90 degree phase shift between the components striking its two axes, referred to as the "fast" and "slow" axes.  Electric fields that oscillate along the fast axis will not be affected as they travel through the QWP.  Electric fields that oscillate along the slow axis will be retarded, and when they emerge from the other end, they will be lagging behind the electric fields that traveled along the fast axis ( the QWP has to be a certain thickness to get 90 degree retardation). 

If the angle between the polarizer and QWP changes, this will change the ratio of light traveling along the fast and slow axes.  Rotating the polarizer changes the "ellipticity" of the emerging beam.  To visualize how this works, imagine that all the linearly polarized light is traveling along the fast axis.   Then the emerging light will still be linearly polarized.  But if you rotate the QWP, a portion of the incident beam will travel along the slow axis, and it will experience a phase shift by slowing down inside the QWP (the fast axis component also slows down, but not as much).  If you continue to rotate the polarizer until half of the linearly polarized light strikes the fast axis and half strikes the slow axis, you will get circularly polarized light.

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When the beam strikes the surface, the components of the electric field perpendicular and parallel to the plane of incidence, i.e.  Ep and Es, each get attenuated, but by different amounts.  The ratio of the reflected components can be measured.  The equation that describes these two reflections is:

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where Rp is the total reflection coefficient for the p component, and Rs is the total reflection coefficient for the s component, as follows:

rp_def.jpg (5536 bytes)rs_def.jpg (6395 bytes)

The straight lines around the two values indicate the modulus of the values contained.  The value "psi" in the first equation is also defined from the following equation:

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Not only do the beams get attenuated, but they also experience a phase shift upon reflection.  The phase shift for each component will be different.  We can measure the difference between the p component phase shift and the s component phase shift.  The equation for this is:

D = dp - ds = arg(Rp)-arg(Rs)

where dp is the phase shift upon reflection of the p component, and ds is the phase shift upon reflection of the s component.  The value defined here is called delta or "del".  The reflection can, theoretically, completely compensate for the original orientation of the beam, making the reflected light linearly polarized.  This is kind of like working backwards from the previous description. 

Now, since the reflected beam is linearly polarized, it can be extinguished by another linear polarizer.  The positions of the polarizer and "analyzer", or second linear polarizer, contain information about the film.   These positions are related to del and psi by the following equations:

psi_fromA1-A2.jpg (3980 bytes)

del_fromP1+P2.jpg (3256 bytes)

The values A2 and A1 are the two positions of the analyzer.  The values P1 and P2 are the two positions of the polarizer.  By using these values along with the Fresnel equations for reflection, the thickness of the film can be found.

Step by Step Operation Procedure (from Gaertner manual)