Tolansky method

The Tolansky method , named after the physicist Samuel Tolansky , is a method for measuring layer thickness. It is based on the principle of interference . When viewing an interference pattern under monochromatic light, the distance between the interference fringes and the offset of the interference fringes at one edge of the layer are measured in order to determine the layer thickness.

principle

Sketch of the origin of the interference fringes and their offset on one edge

A glass plate is tilted slightly and placed on a layer. The normals of the plate and the layer enclose a small angle . Looking at the arrangement under monochromatic light, e.g. B. a sodium vapor lamp , a characteristic image of equidistant interference fringes can be seen at a distance . The rays of light are extinguished when the distance between the glass plate and the layer is a multiple of half the wavelength. This pattern is now offset by the length at one edge of the layer . The reason for this is that light rays now also have to cover the distance , the thickness of the upper layer. However, this is not a multiple of half the wavelength. The light beam only interferes again when the distance has just been compensated by an offset. As can be seen in the sketch, the important relationships result from this in order to draw conclusions about the layer thickness. ${\ displaystyle {\ alpha} <{1 ^ {\ circ}}}$ ${\ displaystyle a}$ ${\ displaystyle l}$ ${\ displaystyle d}$ ${\ displaystyle d}$

{\ displaystyle \ tan \ alpha = {\ frac {\ lambda / 2} {a}} \ quad {\ text {and}} \ quad \ tan \ alpha = {\ frac {d} {l}}}

The equation gives the formula for the layer thickness.

{\ displaystyle d = {\ frac {l \ cdot \ lambda} {2a}}}

Thick layers

With monochromatic illumination, layer thicknesses of up to half the wavelength can be clearly determined. In the case of thicker layers, however, it is necessary to identify which is the corresponding interference line beyond the jump in order to be able to determine the length correctly. This requires lighting with several spectral lines, e.g. from a mercury vapor lamp. The more complex interference pattern that then arises continues beyond the jump edge and makes it possible to determine the corresponding interference line. In the case of a gradual change in the layer thickness, it is sometimes also possible with monochromatic illumination to identify the corresponding interference line based on its course. If the orientation of the direction of the air wedge between the support plate and the sample is known, it can also be seen whether it is a rising or falling step in the material. ${\ displaystyle \ lambda / 2}$ ${\ displaystyle l}$

Optimizations

A significant improvement in the interference contrast is achieved if the glass plate on top is provided with a semi-transparent mirror layer. For example with a 10 nm thick aluminum or chrome layer. It is also helpful if this glass plate is very thin: thickness about 0.2 mm. This makes it somewhat flexible and you can make the air wedge narrower by pressing it on, so that low interference orders occur and a short coherence length of the light source is sufficient - as when lighting with a high-pressure gas discharge lamp (xenon, mercury or sodium vapor lamp). The observation can be done with a simple incident light microscope. The measurement of the interference lines is usually realized with a measuring eyepiece. It is of course also possible using image data.

The achievable measurement accuracy depends on the quality of the lighting, the image and the sharpness of the interference lines. It is typically in the range of 5–10 nm. As the glass plate becomes more reflective ( ), the interference lines become narrower and the achievable resolution becomes higher, down to 1 nm. See HK Pulker under literature. It should be noted that a high-resolution lens with a high numerical aperture can degrade the contrast, since the light hits the interference wedge from a wider angular range and the interference pattern is smeared. ${\ displaystyle {R}> {90 \, \%}}$

Web links

Practical experiment: Structure and mode of operation of the Tolansky microscope (University of Düsseldorf)
Practical experiment: Structure and mode of operation of the Tolansky microscope (University of Düsseldorf, pdf; 64 kB)

literature

Alfred Recknagel: Physics, Volume Optics . 3rd edition, Verlag Technik Berlin, Berlin 1963, section 5.10. Interferometer, pp. 169f
HK Pulker: Simple interchangeable interference lens for microscopes for thickness measurement according to Fizeau-Tolansky . Natural Sciences Volume 53, Issue 9, p. 224, 1966. doi : 10.1007 / BF00633891