A Practical Guide to Optical Metrology for Thin Films by Michael Quinten

By Michael Quinten

A one-stop, concise advisor on opting for and measuring skinny movie thickness by means of optical methods.

This functional e-book covers the legislation of electromagnetic radiation and interplay of sunshine with topic, in addition to the idea and perform of thickness size, and glossy functions. In so doing, it indicates the features and possibilities of optical thickness selection and discusses the strengths and weaknesses of size units besides their overview methods.

Following an advent to the subject, bankruptcy 2 offers the fundamentals of the propagation of sunshine and different electromagnetic radiation in house and subject. the most subject of this publication, the selection of the thickness of a layer in a layer stack via measuring the spectral reflectance or transmittance, is taken care of within the following 3 chapters. the colour of skinny layers is mentioned in bankruptcy 6. eventually, in bankruptcy 7, the writer discusses a number of commercial functions of the layer thickness dimension, together with high-reflection and anti-reflection coatings, photolithographic structuring of semiconductors, silicon on insulator, obvious conductive motion pictures, oxides and polymers, skinny movie photovoltaics, and seriously doped silicon.

Aimed at business and educational researchers, engineers, builders and brands keen on all parts of optical layer and skinny optical movie size and metrology, technique keep watch over, real-time tracking, and applications.

Chapter 1 creation (pages 1–5):
Chapter 2 Propagation of sunshine and different Electromagnetic Waves (pages 7–57):
Chapter three Spectral Reflectance and Transmittance of a Layer Stack (pages 59–80):
Chapter four The Optical size (pages 81–119):
Chapter five Thin?Film Thickness choice (pages 121–140):
Chapter 6 the colour of skinny movies (pages 141–147):
Chapter 7 functions (pages 149–185):

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Then, the maxima of the GF obey the grating equation l sin bÀsin e ¼ m ; g m ¼ 0; Æ1; Æ2; Æ3; . . 12 Diffraction by a grating with angle of incidence e 6¼ 0. ð2:64Þ j25 j 2 Propagation of Light and Other Electromagnetic Waves 26 The negative sign of the angle of incidence results from the sign convention for angles: right-handed angles have a negative sign and left-handed angles have a positive sign. All components of light corresponding to m ¼ 0 follow a straight line given by b ¼ e. It is not possible to separate the wavelengths for this order.

In the following, we give an overview of the most common empiric formulas for the refractive index. One of the most widely used formula is the Sellmeier formula [42]: n2 À1 ¼ N X Aj l2 j¼1 l2 ÀBj : ð2:119Þ This formula corresponds to the sum over j ¼ 1, . , N undamped harmonic pffiffiffiffiffi oscillators with eigenfrequencies vj ¼ 2pc= Bj and oscillator strengths pffiffiffiffiffi vPj ¼ vj Aj . 7 Dielectric Function and Refractive Index This formula is nowadays used by glass manufacturers like SCHOTT AG (since 1992) or OHARA Inc.

1 vÀvk 2 ck ðvÞ ¼ ck exp À : ck 1 þ s2k ð2:100Þ The parameter s k ! 0 is used to switch between a Gaussian or a Lorentzian shape of ck(v). For s k ¼ 0, a pure Gaussian shape is obtained, and for s k > 5 a Lorentzian shape is obtained. In metals, semimetals, and semiconductors, an important contribution to the dielectric function stems from unbound charge carriers, the so-called free electrons. Within the harmonic oscillator model, their contribution is obtained when assuming the eigenfrequency vfe ¼ 0, corresponding to moving in a potential V(r) ¼ 0.

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