Effect of Carbon on the Lattice Parameter of Silicon

Abstract

A correlation between the lattice parameter and the carbon concentration in otherwise pure samples of silicon has been observed. Carbon content has been determined by mass spectrometry, infrared, and lattice parameter measurements. Typical values of the carbon concentration are given for some float-zoned silicon crystals and for a series of intentionally carbon-doped crystals.

Diffusion Engineering by Carbon in Silicon

“…1. In contrast to interstitially dissolved oxygen, carbon contracts the silicon lattice as much as the volume of about one atomic volume of silicon for each carbon atom [20,21]. After electron irradiation at low temperature radiation-induced silicon self-interstitials push carbon atoms from their lattice site forming thereby a carbon-silicon split interstitial, which has been investigated by EPR and infrared absorption [22].…”

A simple Bragg-spacing comparator

“…It is interesting to recall that Baker, Tucker, Moyer & Buschert (1968) found that six of their PERFX crystals had a fractional range of lattice parameter of only 8 + 3 x 10 -8 with a mean deviation of only 2 x 10 -8 over the six samples. We may assume that our sample of PERFX has the same lattice parameter as theirs to better than one part in ten million.…”

“…It is well established that carbon is the main cause of this variation and that in carbon-free material (Baker et al, 1968) the differences between crystals grown by the same manufacturer may vary by only 0.08 p.p.m. The time is almost ripe for a new survey of the so called 'swirl free' material which has become available in the last year or two though, if sample 16 is typical, we may well find that the lattice parameter of this material is less reproducible than that of hyper-pure material such as PERFX and perhaps even less reproducible than the standard float-zoned material has been.…”

“…Following Baker et al (1968) we may conclude that the high-purity PERFX crystals were extremely con-sistently prepared. The standard deviation of six crystals was approximately _+0.012 p.p.m.…”

“…Since this precision is far below the reproducibility of PERFX and is comparable with the range of lattice parameters measured in Table 1 for float-zoned silicon, it would seem that any source of such silicon could be used to access the absolute value of lattice spacing. IR absorption measurements can be used to measure the carbon concentration and the necessary correction is (Baker et al, 1968) dd/d = -6.5 × 10-24n c where n c is the number of carbon atoms per cm a.…”