Internal mechanical dissipation mechanisms in amorphous silicon

Using activation-relaxation technique nouveau (artn), we search for two-level systems (TLSs) in models of amorphous silicon ($a$-Si). The TLSs are mechanisms related to internal mechanical dissipation and represent the main source of noise in the most sensitive frequency range of the largest gravitational wave detectors as well as one of the main sources of decoherence in many quantum computers. We show that in $a$-Si, the majority of the TLSs of interest fall into two main categories: bond-defect hopping, where neighbors exchange a topological defect, and Wooten-Winer-Weaire bond exchange. The distribution of these categories depends heavily on the preparation schedule of the $a$-Si. We use our results to compute the mechanical loss in amorphous silicon, leading to a loss angle of ${10}^{-3}$ at room temperature, decreasing to ${10}^{-4}$ at 150 K in some configurations. Our modeling results indicate that multiple classes of events can cause experimentally relevant TLSs in disordered materials and therefore multiple attenuation strategies might be needed to reduce their impact.

Figure 1

Potential energy landscape representation of a two-level system. Minima 1 and 2 are connected by a saddle point, point S. The mean barrier is $V$, and the asymmetry is $\mathrm{\Delta }$.

Figure 2

Barrier and asymmetry of events found by artn. The gray dashed lines show the asymmetry cutoff.

Figure 3

Square root of squared atomic displacement in each TLS as a function of the energy barrier for the events plotted in Fig. 2. Symbols are color-coded according to the number of active atoms during the event (scale at right).

Figure 4

Example of a bond-defect-hopping event (type 1) showing the system at both minima and at the saddle point. The central atom is in red. The atoms in yellow change their bonding status with the main atom. The green lines show the trajectory of the atoms between the frames.

Figure 5

Example of a bond-exchange TLS (type 2). The red atoms are the main atoms. The yellow atoms break a bond with one red atom and form a new bond with the other red atom. The green lines show the trajectory of the atoms between the frames.

Figure 6

Barrier distribution of bond-defect -hopping (cyan bars) and bond-exchange TLSs (bars outlined in black).

Figure 7

Smoothed distribution of the bond lengths (top) and the bond angles (bottom) of the main active atom in the bond-defect-hopping (blue dashed curves) and bond-exchange TLSs (red dash-dotted curves). The black solid curves represent the first peak and bond-angle distribution of the RDF of our $a$-Si configurations. A raw histogram (blue, top) is also shown to illustrate the effect of the smoothing.

Figure 8

Energy barrier distribution for the TLSs in models obtained by the melt-quench and NHN preparation methods (described in the text).

Figure 9

Density of the three types of TLSs in quenched $a$-Si (gray) and NHN $a$-Si (black).

Figure 10

Internal mechanical dissipation computed for quenched $a$-Si (black) and NHN $a$-Si (red). The pale curves show the contributions from individual TLSs. Blue circles and blue diamonds are experimental data in $a$-Si deposited at 45 and 200 ${}^{\circ }\mathrm{C}$, respectively, from Ref. [14].