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The Structure of Semiconductors

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Semiconductor Physics

Abstract

The bonding forces and atomic sizes determine the arrangement of the atoms in equilibrium in crystals. The crystal structure is determined by the tendency to fill a given space with the maximum number of atoms under the constraint of bonding forces and atomic radii. Crystal bonding and crystal structure are thus intimately related to each other and determine the intrinsic properties of semiconductors. Nonequilibrium states can be frozen-in and determine the structure of amorphous semiconductors. In an amorphous structure the short-range order is much like that in a crystal, while long-range periodicity does not exist. Quasicrystals are solids with an order between crystalline and amorphous. These quasiperiodic crystals have no three-dimensional translational periodicity, but exhibit long-range order in a diffraction experiment. A quasicrystalline pattern continuously fills all available space; unlike regular crystals space filling requires an aperiodic repetition of (at least) two different unit cells.

Superlattices and low-dimensional structures like quantum wires and quantum dots, created by alternating thin depositions of different semiconductors, show material properties which can be engineered by designing size and chemical composition. This opens the feasibility for fabricating new and improved devices.

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Notes

  1. 1.

    However, there is not always a unique way to define this coordinate system - see Sect. 1.1.3 below. For mathematical reasons, an orthogonal system is preferred when possible.

  2. 2.

    For example, from Na to Na in a NaCl crystal, and not from Na to the next Cl ion. “Equivalent” refers to the neighborhood of this atom, which must be identical to the atom at the origin.

  3. 3.

    Since each corner is shared by eight adjacent cells, only 1/8 of each corner atom belongs to each cell. Therefore, with eight corners one has 8 × 1/8 = 1 atom per primitive cell.

  4. 4.

    Each surface is shared by two neighbor cells; for example, with six surfaces, there are 6 × 1/2 = 3 surface atoms per unit cell.

  5. 5.

    A is the face spun between b and c, B between a and c, and C between a and b.

  6. 6.

    Thus, (r + s)/4 is a quarter of a face diagonal.

  7. 7.

    The general expression for the distance between two planes is given by

    $$ {d}_{hkl}^2=\frac{\left|\begin{array}{ccc}1& \cos \gamma & \cos \beta \\ {}\cos \gamma & 1& \cos \alpha \\ {}\cos \beta & \cos \alpha & 1\end{array}\right|}{\frac{h}{a}\left|\begin{array}{ccc}h/a& \cos \gamma & \cos \beta \\ {}k/b& 1& \cos \alpha \\ {}l/c& \cos \alpha & 1\end{array}\right|+\frac{k}{b}\left|\begin{array}{ccc}1& h/a& \cos \beta \\ {}\cos \gamma & k/b& \cos \alpha \\ {}\cos \beta & l/c& 1\end{array}\right|+\frac{l}{c}\left|\begin{array}{ccc}1& \cos \gamma & h/a\\ {}\cos \gamma & 1& k/b\\ {}\cos \beta & \cos \alpha & l/c\end{array}\right|} $$
  8. 8.

    This description is more convenient than an equivalent description, which in one direction reads ϕ(x) = A exp{2πi(x/λ − νt)}.

  9. 9.

    There are other modifications possible. For example, seven for Si, of which four are stable at room temperature and ambient pressure (see Landoldt-Börnstein 1982, 1987). Only Si I and α-Si are included in this book. Si III is face-centered cubic and a semimetal; Si IV is hexagonal diamond and is a medium-gap semiconductor (see Besson et al. 1987).

  10. 10.

    Aliphatic (from Greek aleiphar, “oil”) designates organic compounds in which the carbon atoms are linked in open chains.

  11. 11.

    An oligomer (from Greek oligos, “a few,” and meros “part”) is a molecule consisting of a small number of the repeat units of a polymer; a polymer (from Greek poly “many” and meros “part”) is a large molecule composed of many repeated subunits.

  12. 12.

    The organic semiconductors listed in Table 3 are widely used particularly due to their high carrier mobility and stability. Highest hole mobilities at room temperature were reported for pentacene (35 cm2/Vs; Jurchescu et al. 2004) and rubrene crystals (40 cm2/Vs; Takeya et al. 2007); CuPc, known as blue dye in artificial organic pigments, is used in organic FETs, and Alq3 is commonly applied in organic LEDs.

  13. 13.

    In thin films the tilt of the long molecule axis with respect to the a–b plane is much smaller (3° instead of 22° for pentacene); see Ambrosch-Draxl et al. 2009.

  14. 14.

    Poisson’s ratio denotes the negative quotient of transverse strain/longitudinal strain for uniaxial stress, generally yielding a positive quantity (typically 0.25 … 0.3): transverse tensile strain leads to longitudinal compressive strain and vice versa; see also Sect. 1.1 in chapter “Elasticity and Phonons.”

  15. 15.

    Nanocrystals of 2–10 nm diameter (corresponding to 10–50 atom diameters) contain some 102–105 atoms.

  16. 16.

    The surface of glasses, even at very high magnification, does not show any characteristic structure; after fracture, glasses show no preferred cleavage planes whatsoever.

  17. 17.

    The “chemical formula” using Tel/2 shows the symmetry of the Te binding and indicates that on the other side of each of the Te atoms another Ge atom is bound.

  18. 18.

    The largest unit cell experimentally found so far corresponds to the Al60.3Cu30.9Fe9.7 compound comprising nearly 5,000 atoms.

  19. 19.

    A natural quasicrystal, an Al63Cu24Fe13 alloy termed icosahedrite, has been found in a meteorite (Bindi et al. 2011).

  20. 20.

    For many quasicrystals a transition from brittle to ductile behavior was found at ~3/4 of the melting temperature (Dubois et al. 2000).

  21. 21.

    The relation is τ:1, τ:1, τ:1 for an icosahedral quasicrystal and, e.g., 2:1, 2:1, 2:1 for a cubic approximant (Pay Gómez and Lidin 2001).

  22. 22.

    Since the theoretical treatment of quasicrystals is challenging, often large approximants which are found to have similar properties are modeled instead.

  23. 23.

    To obtain a quasiperiodic instead of a just random tiling, matching rules for the arrangement of the two different tiles must be obeyed.

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    Karl W. Böer

  2. Institut für Festkörperphysik, EW5-1, Technische Universität Berlin, Berlin, Germany

    Udo W. Pohl

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  2. Udo W. Pohl
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Böer, K.W., Pohl, U.W. (2018). The Structure of Semiconductors. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-69150-3_3

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