- Until the early 1980s, mathematical algorithms, not derived from first principles, such as the
Cauchy equations, were used to determine the refractive index (n) and the extinction coefficient
(k) as a function of wavelength, and were thought to be adequate representations for all films.
- Such equations were valid only for a very limited range of wavelengths, and became
difficult to apply as technology advanced.
- Dr. Rahim Forouhi, President and co-founder of n&k, starting from first principles, deduced
physically valid equations for the calculations of n and k.
- The equations are referred to, in current scientific literature, as Forouhi-Bloomer Equations,
as n&k co-founder Dr. Iris Bloomer was simultaneously working with Dr. Forouhi to develop the
physical significance of the equations.
- The Forouhi-Bloomer model is a physically valid universal set of equations for n and k as
functions of wavelengths.
- The Forouhi-Bloomer Equations require far fewer parameters than any other model to fit
experimental data over any wavelength, from the Extreme Ultra-Violet (EUV) to Infra-Red regime.
- These equations are applicable to all thin film materials and substrates, even
- It was obvious to Dr. Forouhi and Dr. Bloomer that even with their discovery of universal
equations for n and k, unless the measured raw data had excellent signal-to-noise ratio, poor
results would be obtained. They solved the problem by introducing their patented all-reflective
optics. With all-reflective optics, there are no light absorbing components such as refractive
lenses and beam splitters. Most of the collected light reaches the detector to produce the
strongest signal-to-noise ratio available in the industry today.
- With the Forouhi-Bloomer Equations for n and k combined with innovative all-reflective optics,
it became possible for the first time in history, to accurately analyze measured reflectance of thin films, data collected over the entire DUV-Vis-NIR regime, with one single set of equations, and simultaneously determine film thickness and n and k spectra, from 190nm to 1000 nm.
- Recognizing the potential market opportunity that their discovery created, Forouhi and Bloomer
founded n&k Technology in 1992.