Determination of the lattice contraction of boron-doped silicon

Abstract

We report a study of the change in lattice constant when single-crystal silicon is substitutionally doped with boron. The measurements were made using lo-pm-thick epilayers with boron concentrations (Ns) in the range 1.7~ 1019-1.2x 102' cm p3. The influence of elastic strain in the epilayers and their substrates was eliminated by including Bragg reflections from planes that were inclined to the (100) surface. We obtained a value for the lattice contraction coefficient fi= (5.19=!=0.09) X1O-24 cm3, where the range is f. one standard error. Specimens with Ns~2 X lOI9 cme3 were strained to give coherent interfaces with their substrates. Evidence for relaxation (presumably by misfit dislocations at the interface) was observed with Nns5 X 1019 cm -3 (corresponding to a lattice mismatch of approximately 2.5 X 10w4), but this occurred in a patchy fashion and remained incomplete while Na was increased to 1.2X lo*' cmh3 [corresponding to a mismatch of 6.5 X 10w4). This partial relaxation occurred at somewhat smaller mismatches than would be expected from reported studies of silicon-germanium alloy epilayers on silicon substrates. Our technique for analyzing a set of Bragg reflections to separate the effects of elastic strain and lattice mismatch appears to be novel and has general applicability to the study of epilayer/substrate combinations.

Lattice parameter measurements of boron doped Si single crystals

“…Numerous studies have been carried out on lattice parameter changes due to impurities, their diffusion as well as on the influence of oxygen micro-precipitations generated during single crystals growing on lattice parameters changes. Several authors measured the effect of boron doping on silicon lattice deformations [3][4][5][6][7][8]. The analysis of data for various boron concentrations in silicon shows that the reported values of the lattice contraction coefficient β lie between 4.5 × 10 -24 cm -3 and 5.5 × 10 -24 cm -3 .…”

“…However, to be studied single crystals should have a high degree of structural perfection. Doping of Si single crystals is known to lead to changes in lattice parameters [3][4][5][6][7][8]. Impuritie atoms of radii smaller than the covalent atomic radius of Si (B or P) cause crystal lattice contraction, while atoms of larger atomic radii (Sb) cause its expansion.…”

Interpretation of phase images of delta-doped layers

“…for a lattice contraction predicted using Eq. (10) for a B concentration N 3D of 3 × 10 21 cm −3 and a layer width w of 1.16 nm, based on a lattice contraction coefficient measured for substitutional B using X-ray diffraction [26]), with all other parameters unchanged. This graph is only indicative, as the average B concentration in each layer is not precisely 3 × 10 21 cm −3 .…”

In-Line Characterization of Heterojunction Bipolar Transistor Base Layers by High-Resolution X-Ray Diffraction

“…In the third application, the sensitivity of HRXRD for the determination of the substitutional boron concentration in SiGe was investigated. The distortion of the silicon lattice due to doping with boron as a substitutional impurity has been studied since the early days of silicon technology, leading to highly accurate measurements of the lattice contraction coefficient (7)(8)(9)(10)(11). In this paper, our aim is to give an estimation of the minimum active boron concentration in SiGe that can be monitored by HRXRD in production environment.…”

“…Smooth epilayers were fabricated by in-situ doping of SiGe grown by reduced pressure chemical vapor deposition (RPCVD) which resulted in highly homogeneous boron concentrations. The high quality of the epitaxially-deposited films allowed to avoid the difficulties that could be encountered in the interpretation of XRD data of diffused materials with non uniform boron contents (11), and to determine the concentration threshold for HRXRD monitoring with good reliability. Finally, this utility of HRXRD can be exploited in other applications like embedded SiGe which is nowadays used in pMOS devices to boost device performance (12).…”