Elastic Softening of Surface Acoustic Wave Caused by Vacancy Orbital in Silicon Wafer

Abstract

We have performed surface acoustic wave (SAW) measurements to examine vacancies in a surface layer of a boron-doped silicon wafer currently used in semiconductor industry. A SAW with a frequency of fs = 517 MHz was optimally generated by an interdigital transducer with a comb gap of \(w=2.5\) µm on a piezoelectric ZnO film deposited on the (001) silicon surface. The SAW propagating along the [100] axis with a velocity of \(v_{\text{s}}=4.967\) km/s is in agreement with the Rayleigh wave, which shows an ellipsoidal trajectory motion in the displacement components ux and uz within a penetration depth of λp = 3.5 µm. The elastic constant Cs of the SAW revealed the softening of ΔCs/Cs = 1.9 × 10−4 below 2 K down to 23 mK. Applied magnetic fields of up to 2 T completely suppress the softening. The quadrupole susceptibilities based on the coupling between the electric quadrupoles Ou, Ov, and Ozx of the vacancy orbital consisting of Γ8–Γ7 states and the symmetry strains εu, εv, and εzx associated with the SAW account for the softening and its field dependence on Cs. We deduced a low vacancy concentration N = 3.1 × 1012/cm3 in the surface layer within λp = 3.5 µm of the silicon wafer. This result promises an innovative technology for vacancy evaluation in the fabrication of high-density semiconductor devices in industry.