As discussed in Section 2.2.3, because all semiconductors have high refractive indices, according to the Fresnel formulas, reflection loss at the semiconductor-air interface is significant.
The solution, that is, antireflection coatings, were invented in early twenteenth century and has been applied to reduce the reflection of lenses in eyeglasses, cameras, telescopes, and microscopes. The concept of antireflection coatings is shown in Fig. 9.13. Without antireflection coatings, the reflection coefficient at the interface of two media with refractive indices ni and n2 is determined by the Fresnel formula 2.78,
For example, for silicon, where n = 3.8, R = 0.34, which is very high. By coating the
surface with a film of thickness equal to a quarter wavelength in that medium, the two reflected light waves should have a phase difference of 180°. If the intensities of the two reflected light waves are equal, complete cancellation can take place. The condition of cancellation is then
(П1 ~ П2У =(. (9.53)
ni + П2 П2 + П3
It can happen only when n1/n2 = n2 /n3, or
П2 = V nin3. (9.54)
In other words, the reflection can be completely eliminated when the refractive index of the thin film is the geometric mean of the refractive indices of air and the bulk medium. Obviously, it only works for a single wavelength. As shown in Fig. 9.13(c), by using multiple coatings, two or more reflection minima can be created, and the wavelength range for almost zero reflection can be extended.
The above argument based on interference is intuitive but not accurate. Multiple reflections take place in the film. The simple interference argument does not work for multiple antireflection coatings. The standard treatment is based on a matrix method, as presented in the next section.