Ultrasonic-Wave Propagation in Pure Silicon and Germanium

Abstract

Ultrasonic attenuation and velocity measurements have been made in pure germanium and silicon (doping <1014 impurity atoms per cc) and in doped n-type germanium and p-type silicon. The attenuation in pure materials shows a continuous decrease as the temperature is decreased and a very low attenuation below 20°K. These results indicate that the energy losses are accounted for entirely by phonon-phonon interactions. A calculation has been made of these losses, using a model based on the Akheiser effect and incorporating the recently measured third-order elastic moduli of silicon and germanium. For both materials, the calculated values predict correctly the large difference between longitudinal and shear waves and agree quantitatively within 50% with the measured values over the whole temperature range.

What is the Young's Modulus of Silicon?

“…This is called "doping." The volumetric effect of adding the mass of the dopant atoms to the crystal lattice is negligible, but the effect of doping on crystalline semiconductor elastic behavior through electrical interaction can be predicted from the strain energy of the crystal using the standard "many-valleys" model, and measurements align well with the theoretical predictions [11], [12], [22]- [24]. The changes are typically a 1%-3% decrease for heavy doping levels and are usually ignored for engineering calculations.…”

Akhiezer damping in nanostructures

“…where β is a numerical coefficient, τ (q, j), λ(q, j) and C(q, j) are the relaxation time, the Grüneisen parameter and specific heat capacity of the phonon branch labelled as q, j. Q is related to α t as Q = ω 2αt and, hence, Eqn (17) shows that Q scales as ω −1 . This explains the trend as has been observed for the case of 7.1 × 7.1 nm 2 cross-sectional area.…”

Ultrasonics: A Technique of Material Characterization

“…The process is entropy producing, which results absorption. The concept of modulated thermal phonons provides following expression for the absorption coefficient of ultrasonic wave due to phonon-phonon interaction in solids (α) Akh (Bhatia, 1967;Mason, 1950Mason, , 1958Mason, , 1964Mason, , 1965) . …”