Validating Surface Energy Measured by Three Liquid Contact Angle Analysis with Computed Gibbs Energy for LiNbO$_{\mathrm{3}}$/$\alpha $-Quartz SiO$_{\mathrm{2}}$ for Direct Wafer Bonding

LiNbO$_{\mathrm{3}}$ is a ferro-electric with the most significant electro-optical, piezo-electric properties, and a near perfect linear response. Hence, LiNbO$_{\mathrm{3}}$ is an ideal material to integrate piezoelectrics monolithically to Si. But lattice and thermal expansion mismatches between LiNbO$_{\mathrm{3}}$ and Si/SiO$_{\mathrm{2}}$ are incompatible with hetero-epitaxy and Direct Wafer Bonding (DWB). This work investigates DWB at RT via Nano-Bonding$^{\mathrm{TM,\thinspace 1\thinspace }}$(NB). NB nucleates bonding inter-phases via complementary 2D- Precursor Phases (2D- PP) instead of thermal activation. 2D-PP relies on Surface Energy Engineering (SEE), which characterizes and then modifies hydro-affinity and surface energy into far-from-equilibrium states. SEE finds that $\Delta $Gs for interaction between LiNbO$_{\mathrm{3}}$ and Si/SiO$_{\mathrm{2}}$ are both positive and do not favor NB. Hence, SEE on LiNbO$_{\mathrm{3}}$ and Si/SiO$_{\mathrm{2}}$ needs to change $\Delta $G to negative at RT. Experimental results show that SEE of ?-quartz SiO$_{\mathrm{2}}$ and LiNbO$_{\mathrm{3}}$ yield NB at RT. $^{\mathrm{1}}$ Herbots et al. US Pat. 6613677 (2003), 7,851,365 (2010), 9,018,077 (2015), 9,589,801 (2017), and pending (2020)