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

摘要

We have performed surface acoustic wave (SAW) measurements to examine vacancies in a surface layer of a borondoped silicon wafer currently used in semiconductor industry. A SAW with a frequency of f_s = 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 υ_s = 4.967km/s is in agreement with the Rayleigh wave, which shows an ellipsoidal trajectory motion in the displacement components u_x and u_z within a penetration, depth of λ_p = 3.5 μm. The elastic constant C_s of the SAW revealed the softening of ?C_s/C_s= 1.9 × 10~(-4) below 2K 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 O_u, O_v, and O_(zx) of the vacancy orbital consisting of Γ_8-Γ_7 states and the symmetry strains ε_u, ε_v, and ε_(zx) associated with the SAW account for the softening and its field dependence on C_s. We deduced a low vacancy concentration N=3.1 ×x 10~(12)/cm~3 in the surface layer within λ_p = 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.