Nano-regime Length Scales Extracted from the First Sharp Diffraction Peak in Non-crystalline SiO(2) and Related...

This paper distinguishes between two different scales of medium range order, MRO, in non-crystalline SiO(2): (1) the first is ~0.4 to 0.5 nm and is obtained from the position of the first sharp diffraction peak, FSDP, in the X-ray diffraction structure factor, S(Q), and (2) the second is ~1 nm and is calculated from the FSDP full-width-at-half-maximum FWHM. Many-electron calculations yield Si-O third- and O-O fourth-nearest-neighbor bonding distances in the same 0.4-0.5 nm MRO regime. These derive from the availability of empty Si dpi orbitals for back-donation from occupied O ppi orbitals yielding narrow symmetry determined distributions of third neighbor Si-O, and fourth neighbor O-O distances. These are segments of six member rings contributing to connected six-member rings with ~1 nm length scale within the MRO regime. The unique properties of non-crystalline SiO(2) are explained by the encapsulation of six-member ring clusters by five- and seven-member rings on average in a compliant hard-soft nano-scaled inhomogeneous network. This network structure minimizes macroscopic strain, reducing intrinsic bonding defects as well as defect precursors. This inhomogeneous CRN is enabling for applications including thermally grown ~1.5 nm SiO(2) layers for Si field effect transistor devices to optical components with centimeter dimensions. There are qualitatively similar length scales in nano-crystalline HfO(2) and phase separated Hf silicates based on the primitive unit cell, rather than a ring structure. Hf oxide dielectrics have recently been used as replacement dielectrics for a new generation of Si and Si/Ge devices heralding a transition into nano-scale circuits and systems on a Si chip.