Silicon Photonics: Fundamentals and Devices

7.4 Thermo-Optic Effects in Si

For proper design of the devices, it is necessary to have knowledge of the thermal behavior of silicon, especially the effect of temperature on absorption and refraction near the fundamental absorption edge.

Cocorullo et al. 11 undertook a detailed measurement of the TO coefficient of a number of silicon samples with different crystallographic orientations and thicknesses at 1.55 µm. The values of dn/dT have been obtained from room temperature to 550 K.

The authors also provided the following polynomial interpolation of the experimental data:

(7.11)

Example 7.1

At 300 K, the value of dn/dT is 1.86 × 10⁻⁴ K⁻¹ from Eq. (7.11).

A theoretical paper on physical modeling of the TO effect has been published 12. The essential points in the theory are now described.

The optical properties of matter are usually determined by considering coupling between various types of oscillators and the electromagnetic radiation field. The amplitude of these oscillations depends on (1) the frequency of the incident electromagnetic field, (2) the oscillator eigenfrequencies, (3) the different coupling strengths f between the electromagnetic field and the oscillators, and (4) their damping functions. In a simplified model to analyze the RI of a material in its transparency region, only the real part of the dielectric function may be considered, obtaining

(7.12)

where is ...