X-ray reflectivity is a powerful
tool for determining the physical properties of thin films supported
on solid substrates. Several important thin film characteristics can
be determined by measuring, as a function of incident angle, the specularly
reflected intensity of a well-collimated, monochromatic beam of x-rays.
Among them are film thickness, the change in film thickness due to
temperature (and hence, the coefficient of thermal expansion (CTE)),
the change in thickness due to solvent uptake and the electron density
profile, which can be converted to a mass density profile provided
the chemical composition of the film is given.
Method
A highly collimated and monochromated
x-ray beam is shined on the sample surface at low grazing incident
angles and the specularly reflected beam intensity is recorded and
analyzed. A typical measurement is conducted over an angular range
between zero to 5 degrees. Measurements can be conducted in ambient
air, under vacuum, or in the prospect chemical vapors of interest.
For CTE measurements the sample is placed in vacuum to ensure the
evenness of the temperature. The temperature range available is 15
C to 185 C . A typical measurement takes about 30 minutes to an hour
depending the sample dimension.
Sample
Thin films supported on flat solid
substrates are the commonly accepted sample geometry. Limited success
has been obtained from free standing thin films. Samples with a thickness
ranging from 5 nm to 1 micron can be measured by this x-ray technique.
The lateral dimensions of samples need to be 0.5 cm x 3.0 cm or larger
but not to exceed 10 cm x 10 cm. There is another central requirement
for the sample - its flatness. It must be optically flat on both a
long wavelength (centimeters) and short wavelength (nanometers) scales.
This requirement is necessary to insure strong specular reflection.
Typical substrates used are polished silicon single crystal wafers
and float glass.
Limits of Accuracy
The accuracy of film thickness
determination is typically a few angstroms. The electron density of
the films can be determined within one percent. Flatness of the film
and its substrate dictates the accuracy of this measurement.