Microstructure dependence of low-temperature elastic properties in amorphous diamondlike carbon films

We have studied the internal friction and the relative change in the speed of sound of amorphous diamondlike carbon films prepared by pulsed-laser deposition from $0.3\mathrm{K}$ to room temperature. Like most amorphous solids, the internal friction below $10\mathrm{K}$ exhibits a temperature independent plateau. The values of the internal friction plateaus, however, are slightly below the universal glassy range where the internal frictions of almost all amorphous solids lie. Similar observations have been made in our earlier studies in the thin films of amorphous silicon and amorphous germanium, and the behavior could be well accounted for by the existence of the low-energy atomic tunneling states. In this work, we have varied the concentration of $s{p}^3$ vs $s{p}^2$ carbon atoms by increasing the laser fluence from $1.5\text{to}30\mathrm{J}∕{\mathrm{cm}}^2$. Our results show that both the internal friction and the speed of sound have a nonmonotonic dependence on an $s{p}^3∕s{p}^2$ ratio with the values of the internal friction plateaus varying between $6\times {10}^{-5}$ and $1.1\times {10}^{-4}$. We explain our findings as a result of a possible competition between the increase of atomic bonding and the increase of internal strain in the films, both of which are important in determining the tunneling states in amorphous solids. In contrast, no significant dependence of laser fluence is found in shear moduli of the films, which vary between 220 and $254\mathrm{GPa}$. The temperature dependence of the relative change in speed of sound, although it shows a similar nonmonotonic dependence on laser fluence as the internal friction differs from those found in thin films of amorphous silicon and amorphous germanium, which we explain as having the same origin as the anomalous behavior recently observed in the speed of sound of thin nanocrystalline diamond films.

Figure 1

Outline of the double-paddle oscillator. The left side shows the front view, and the right side shows the back view. The hatched area in the front view is the amorphous diamondlike carbon film deposited through a stainless steel mask. On the back side of the paddle a thin Cr and Au film is covered in the gray area. The dashed circles indicate the position of electrodes for capacitive drive and detection.

Figure 2

The internal frictions of double-paddle oscillators carrying $a\text{−}\mathrm{C}$ films with different laser fluences labeled in the figure, and a $350\mathrm{nm}$ thick nanocrystalline diamond film taken from Ref. 32. The background internal friction of a bare double-paddle oscillator is shown as a solid line.

Figure 3

The internal frictions of $a\text{−}\mathrm{C}$ films with different laser fluences labeled in the figure, and of a $350\mathrm{nm}$ thick nanocrystalline diamond film taken from Ref. 32. The internal friction of bulk $a\text{−}\mathrm{Si}{\mathrm{O}}_2$, measured at $4500\mathrm{Hz}$ from Ref. 33, is shown for comparison. The double arrow denotes the glassy range explained in the text.

Figure 4

The internal friction of $a\text{−}\mathrm{C}$ films at $1\mathrm{K}$ representing the plateau $Q_0^{-1}$ (left $Y$ axis) and residual compressive stress in the films after deposition (right $Y$ axis) versus laser fluence. The residual stress data are taken from Ref. 23 measured on a series of similarly prepared $a\text{−}\mathrm{C}$ films. The vertical dashed line indicates the structural transition at $f_t=5\mathrm{J}∕{\mathrm{cm}}^2$ from primarily disordered graphitic glass to a tetrahedrally bonded amorphous solid.

Figure 5

The relative changes in the speed of sound for the six $a\text{−}\mathrm{C}$ films with different laser fluences labeled in the figure. The data for a $350\mathrm{nm}$ thick nanocrystalline diamond film, taken from Ref. 32, are shown for comparison. It is shifted upward for clarity purpose. The data for bulk $a\text{−}\mathrm{Si}{\mathrm{O}}_2$, measured at $4500\mathrm{Hz}$ from Ref. 33, are also shown for comparison. The two straight lines indicate the linear temperature dependence discussed in the text.