Abstract
No crystal is perfect. Various point defects and their thermodynamics, diffusion and distribution effects are discussed. Also dislocations and extended defects such as cracks, stacking faults, grain boundaries and antiphase domains are covered.
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Notes
- 1.
At higher temperatures a silicon atom can occasionally acquire sufficient energy from lattice vibrations to leave its lattice site and thus an interstitial and a vacancy are generated.
- 2.
The positive charge state is stable, the neutral charge state is metastable since the defect is a negative-U center (see Sect. 7.7.5).
- 3.
Mass preservation of the impurities can be written at any time \(c_{\mathrm {m}}(1-x)+\int _0^x c(x')\, \mathrm {d}x'=c_0\), where \(c_{\mathrm {m}}\) is the (remaining) concentration in the melt. At the beginning \(c_{\mathrm {m}}(0)=c_0\). At the interface \(c(x)=k\, c_{\mathrm {m}}(x)\). Putting this into the mass preservation, building \(c'(x)\) and solving the resulting differential equation \(c'=c(1-k)/(1-x)\) with \(c(0)=k\,c_0\) leads to (4.18).
- 4.
When the float zone moves through the crystal, the change of mass of impurities \(m_{\mathrm {m}}=c_{\mathrm {m}}z\) in the liquid is \(m_{\mathrm {m}}'=c_0-k c_{\mathrm {m}}\). The first term stems from the melting of the polycrystalline part, the second from the solidification of the crystal. Solving the resulting differential equation \(c_{\mathrm {m}}'=(c_0-k c_{\mathrm {m}})/z\) with \(c_{\mathrm {m}}(0)=c_0\) and using \(c(x)=k c_{\mathrm {m}}(x)\) yields (4.20).
- 5.
We note that during directed solidification of Si:(B,P) a pn-junction forms due to the different distribution coefficients of boron and phosphorus. This has been used in [79].
- 6.
The mean path length is the distance integrated along the ion trajectory until its direction deviates by more than 4\(^{\circ }\) from the incident direction.
- 7.
Eight atoms per cubic unit cell of length \(a_0=0.543\) nm.
- 8.
We note that in elasticity theory a continuous deformation is assumed. Obviously the separation (fracture) into two unstrained blocks is the lowest strain energy state of a stressed piece of material.
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© 2016 Springer International Publishing Switzerland
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Grundmann, M. (2016). Defects. In: The Physics of Semiconductors. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-23880-7_4
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DOI: https://doi.org/10.1007/978-3-319-23880-7_4
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