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Crystal Defects

Semiconductor Physics

Abstract

Semiconducting properties of most interest are predominantly caused by crystal defects. They are classified into point, line, and planar defects. Some defects are beneficial, such as donors, acceptors, or luminescence centers. These defects determine the desired electronic and optical properties of the semiconductor. Other defects promote nonradiative carrier recombination, carrier trapping, or excessive carrier scattering and are detrimental to device performance.

Native point defects and associates of these defects are formed at elevated temperature and may be frozen-in with decreasing temperature. Their creation is interrelated – among each other and also to the presence of extrinsic (impurity) defects – and governed by the conservation of particles and quasi-neutrality. The mobility of defects is provided by various diffusion mechanisms and affected by their charge. Line defects involve rows of atoms. Most important are edge and screw dislocations, which affect crystal growth and accommodate strain in semiconductors. Dislocations are characterized by their Burgers vector and its angle to the dislocation line, and their mobility is provided by glide and climb processes. Planar defects comprise stacking faults, grain and twin boundaries, inversion-domain boundaries, and interfaces between different semiconductors or between a semiconductor and a metal.

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Notes

  1. 1.

    These comprise divacancies, an impurity associated with an intrinsic defect, and two impurities associated with each other.

  2. 2.

    An isocoric P in a Si lattice can be thought of as “created” by adding to a lattice atom a proton, i.e., a point charge, and an extra electron (the donor electron), thereby creating the most ideal hydrogen-like defect. Any other hydrogen-like donor, e.g., As or Sb in Si, is of different size, causing more lattice deformation and a substantially different core potential (see Sect. 1 of chapter “Shallow-Level Centers”).

  3. 3.

    That is, a defect that can act as a donor or acceptor depending on the chemical potential of the lattice (influenced, e.g., by optical excitation or other doping).

  4. 4.

    The notation of charges with respect to the neutral lattice was introduced by Kröger, Vink, and Schottky (see Schottky and Stockmann 1954). This notation allows to distinguish from the charge identification used in an ionic lattice, e.g., Na+Cl−. Inclusion of a Cd++ instead of a Na+ ion makes the cadmium ion singly positively charged with respect to the neutral lattice.

  5. 5.

    In contrast, purification can be accomplished by diffusion of impurities into a sink. With the solubility of impurities being a function of the temperature, a temperature gradient can be used as a driving force for purification. A more effective means is the use of the boundary between the liquid and solid phase, using the fact that the solubilities in these two phases are substantially different (a measure of which is the segregation coefficient). Zone refining is a well-established technique to achieve such purification (see de Kock 1980).

  6. 6.

    For simplicity, we have neglected here the vibrational part of the entropy (S = S config + S vib). These contributions are considered later in this section. The vibrational part results in an increase of the intrinsic defect density.

  7. 7.

    This simple model of a pair-wise defect formation maintaining stoichiometry will be modified later (Sect. 2.5) to permit slight changes in the stoichiometry, thereby making the crystal n- or p-type. Inversely, the creation of such intrinsic defects can be enhanced or suppressed depending on the position of the Fermi level, i.e., depending on doping.

  8. 8.

    In materials in which two types of defects need to be considered, two different freezing-in temperatures appear, and, because of conservation and neutrality considerations, a more complex behavior is expected (Hagemark 1976).

  9. 9.

    Often, the enthalpy H Schottky is cited rather than the energy; however, with \( \Delta {H}_{\mathrm{Schottky}}=\Delta {E}_{\mathrm{Schottky}}+P\Delta V \) and negligible volume changes in the solid, both are almost identical at room temperature. Near the melting point, a \( \Delta V/V\cong \left(1/3\right)\left(\Delta l/l\right)\cong 2\kern0.5em \% \) change in volume (Eq. 17 of chapter Phonon-Induced Thermal Properties) may be considered.

  10. 10.

    In Sect. 2.1, the Helmholtz free energy F was used, which is related to the Gibbs free energy G by G = F+PV. Since some of the reactions involve an interaction with a gas atmosphere, the more general notation is used here.

  11. 11.

    Or, for an A n B m compound, we have \( 0\overleftarrow{\to}n{\mathrm{V}}_A^0+m{\mathrm{V}}_B^0 \) with \( {\left[{\mathrm{V}}_A^0\right]}^n{\left[{\mathrm{V}}_B^0\right]}^m={K}_{\mathrm{Schottky}} \).

  12. 12.

    With proper charging, these dimers could be regarded as equivalent to a nonmetal molecule B 2 sitting on a lattice site of a cluster of four vacancies. Such molecules are often covalently bound and therefore have a substantial binding energy; hence, they have a high probability of occurring.

  13. 13.

    In order to avoid exact compensation, we must also consider some extrinsic donors to make the donors predominant (see Sect. 2 of chapter “Equilibrium Statistics of Carriers”).

  14. 14.

    When a mirror-symmetry plane exists normal to the dislocation line, an arbitrariness in the sense of this line cannot be avoided. There are hence different conventions to define the sign of the dislocation line and the Burgers circuit (clockwise or reverse), yielding different signs for the Burgers vector (see Hirth and Lothe 1982). For a finish-start/left-hand (FS/LH) convention with a counterclockwise circuit, l pointing from surface to bulk and b drawn from the finish to the start point to close the circuit, the screw dislocation in Fig. 13b is defined left-handed.

  15. 15.

    Electron beam-induced conductivity is used in a scanning electron microscope (Heydenreich et al. 1981).

  16. 16.

    The 60° dislocation in Fig. 19a is drawn for zincblende structure; to obtain this defect for the diamond structure of silicon, consider all atoms to be identical.

  17. 17.

    The terms glide and slip are generally used to describe, respectively, the motion of a single dislocation and many dislocations.

  18. 18.

    Along [0001] in the hexagonal wurtzite lattice, corresponding to the [111] direction of the cubic zincblende lattice

  19. 19.

    An example is the well-lattice-matched InP/Si(001), a prominent material for integrating optoelectronics of InP-based devices with the established Si electronics.

  20. 20.

    On Si(001) substrates, such double steps can be achieved applying ~6° offcut orientation to create single-step terraces and a thermal treatment for double-step formation.

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  1. 138 Moorings Park Rd. O 301, Naples, FL, USA

    Karl W. Böer

  2. Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstr. 36, 10623, Berlin, Germany

    Udo W. Pohl

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Böer, K.W., Pohl, U.W. (2015). Crystal Defects. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_15-1

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    Crystal Defects
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    Crystal Defects
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    DOI: https://doi.org/10.1007/978-3-319-06540-3_15-1

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