Picosecond Laser Ultrasonics Metrology Lab

1. Opto-Acoustic Strain Wave Generation

Absorption of a sub-picosecond pump pulse elevates electron temperatures in the metal skin depth $\delta \sim 15\text{ nm}$. Subsequent electron-phonon thermalization generates localized thermoelastic expansion:

where $B$ is the bulk modulus and $\beta$ is the linear thermal expansion coefficient. This mechanical stress launches a longitudinal acoustic strain wave $\eta_{zz}(z, t)$ propagating into the wafer at speed $v_s = \sqrt{C_{11} / \rho}$.

2. Acoustic Impedance & Interface Reflections

At material interfaces, acoustic wavepackets split into transmitted and reflected waves governed by acoustic impedance $Z = \rho \cdot v_s$:

When encountering a denser/stiffer layer ($Z_2 > Z_1$), the reflected strain retains polarity ($r > 0$). When reflecting off a softer low-$k$ dielectric or delamination void ($Z_2 < Z_1$), the echo undergoes a $180^\circ$ phase inversion ($r < 0$).

3. Photoelastic Detection & Echo Transit Times

When the reflected acoustic pulse returns to the metal surface, it modulates the optical dielectric permittivity through the photoelastic tensor:

The round-trip delay $\tau_i$ corresponds directly to layer thickness $d_i = (1/2) v_{s,i} \tau_i$, providing picosecond time-of-flight metrology without requiring optical transparency.

4. CMP Dishing & Interfacial Void Detection

In chemical mechanical planarization (CMP), over-polishing causes copper dishing and erosion, increasing line resistance. Picosecond ultrasonics monitors thickness reduction in real time. Furthermore, interfacial micro-voids in direct hybrid bonding act as acoustic free surfaces ($Z \approx 0$), generating inverted echo signals that detect bond defects.