Correlation between plasma dynamics and porosity of Ge films synthesized by pulsed laser deposition

To improve the signal-to-noise ratio, all the emission signals were integrated over a $100ns$ exposure time and averaged over an accumulation of 100 laser shots. The background signal was systematically subtracted from the measured data.

The hard-sphere model described in Ref. 15 is briefly summarized as follows. Assuming hard-sphere collisions between heavy plume and light gas background, the loss of directed velocity of the heavy plume atoms/ions varies as the square of the velocity. The main approximations of the model are (1) $mGe⪢mHe$⁠, (2) $vGe⪢vHe$⁠, and (3) all the collisions are elastic. $mGe$ and $mHe$ and $vGe$ and $vHe$ are the masses and the velocities of Ge and He atoms, respectively. Despite its rather strong assumptions, this simplified model works quite well. Improvements would require significant kinetic modeling.

In addition, the vertical resolution $Rv$ of the spectrometer in TOF measurements is typically $10mm$⁠. As a consequence, the measured emission signal is due to ablated species located at different flight distances (all the flight distances between $x$ and $x2+Rv$⁠). Clearly, the vertical resolution is negligible only for distances significantly larger than $Rv$⁠.

Below the critical angle $θ⩽θc$⁠, total reflection occurs, whereas at $θ⩾θc$⁠, x rays are partially absorbed by the sample. The critical angle $θc,film$ can thus be determined from the sharp changes in reflected x-ray intensity. $θc,film$ is related to the film density $ρfilm$ using the following expression: $ρfilm=(θc,film2∕θc,bulk2)ρbulk$⁠, where $ρbulk$ and $θc,bulk$ are the density and the critical angle of bulk material, respectively.