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Figure (1.55) in SSPD_Chapter 1_Part 11_Soild state of Matter_Crystalline Nature of Solid depicts the three cubic crystal systems: simple, bcc and fcc.

Silicon and Germanium are Diamond lattice structures. Diamond structure has been described in SSPD_Chapter 1_Part 11_Soild state of Matter_Crystalline Nature of Solid in Figure 56.

  • Diamond lattice structure belongs to cubic- crystal family.
  • Diamond structure is two interpenetrating fcc sub-lattices with one sub-lattice displaced with respect to the other along the diagonal of the cube by one quarter of the diagonal length i.e. by a√3/4 as shown in Figure(1.56.A).
  • We can better visualize the diamond structure by dividing one major cube (a×a×a) into 8 sub- cubes (a/2×a/2×a/2) by the name A,B,C,D in the upper half of the major cell and E,F,G,H in the lower half of the major cell as shown in Figure(1.56.B). Subcell E is hidden from sight.
  • The perspective view of the major cell is shown in Figure (1.56.B)
  • The plan view is shown in Figure (1.56.C) .
  • Each major cell has 4 subcells A,C,F,H containing tetrahedral structures of silicon or germanium atoms.
  • A tetrahedral structure is shown in Figure(1.56.D). A tetrahedral structure lies in a subcube.
  • There is one atom at the center of the subcube.
  • This body center atom time-shares its 4 valence electrons with 4 valence electrons of the corner atoms of the subcube.
  • The 4 corner atoms forming the covalent bonds with the body centered atom are the two diagonally opposite corner atoms on the upper plane and two diagonally opposite corner atoms on the lower plane but this time it is the other diagonal.
  • That is the two sets of diagonally opposite corner atoms comprise two orthogonal diagonals.
  • Thus in plan view we see, as in Figure (1.56.C), each Si(or Ge) time sharing its 4 valence electrons with 4 valence electrons of the four corner neighboring atoms and in the process each central atom is fulfilling its octave condition.
  • This is 100% covalent bond as the center of positive charge and the center of negative charge are coincident.
  • Each atom in the bulk is sharing the 4 valence electrons with 4 neighboring corner atoms hence octave condition and thereby covalent bond is fulfilled every where except at the surface of the crystal.
  • Hence at the surface we have unfulfilled covalent bonds or dangling bonds.

These dangling bonds are responsible for the surface states which if not properly controlled and passivated will lead to serious flicker noise problem as well as to the failure of the devices. At the initial stages of MOS fabrication there was serious Na impurity problem coupled with surface states problem which was leading to very low yields. Andy Grove, who was the cofounder of INTEL along with Gordon Moore and Robert Noyce , came into grip of this problem and gave a permanent solution of the low yields which enabled MOS Technology to take off. MOS Technology is the key to the fabrication of microprocessors.

GaAs has zincblende lattice which is identical to diamond lattice except that one fcc sublattice consists of Ga and the other fcc sublattice consists of As. So in Plan View we see Ga atom surounded by four As atoms and similarly As atom is surrounded by four Ga atoms thereby each atom is fulfilling the octave condition by time sharing the electrons from the 4 neighboring atoms. The plan view of GaAs tetrahedral structure is shown in Figure(1.61).

Figure 1.61. Zincblende structure of GaAs.


Crystals are anisotropic because of different pattern of arrangement of atoms in different directions. Hence etching rate of the crystal is different in different directions. This property is utilized in Integrated Circuit Technology. Therefore crystal orientation is important in device fabrication and hence needs to be clearly defined.

The basis in which we define the planes and directions of a crystalline lattice is made possible by Miller Indices. This is derived from the Cartesian Coordinates in the following manner:

  1. Any atom in the crystalline lattice is taken as the origin;
  2. Reference coordinate axes are set up in the direction of basis vectors;
  3. Consider a system of parallel planes. Find the intercepts made by one of the planes. Express them as multiples of unit basis vectors;
  4. Take their reciprocals and reduce them to the smallest triad of integers h,k and l having the same ratio.(hkl) is the Miller Index of that system of parallel planes and<hkl>is the direction normal to the plane;
  5. Suppose a plane has intercepts 2a, 3b and 4c where a, b and c are unit basis vectors along X, Y and Z axes. Then reciprocal is (1/2,1/3,1/4). These reciprocals are reduced to the smallest triad having the same ratio. The Miller index is (6,4,3). This has been obtained by multiplying the reciprocals with lowest common multiple of the denominator terms. The denominator terms are 2,3,4. The LCM is 12. Miller Index has been obtained by multiplying the reciprocals by 12.
  6. (6,4,3) is the Miller Index of the given plane and<6,4,3>is the orientation vector of the plane.

The normal to the plane along which the crystals cleave is the crystal cleavage plane.. Generally they cleave along<1,1,1>plane. The cleavage plane is the plane of highest atomic density. If the surface of the Si wafer, known as major flat, is parallel to<111>plane then the crystal orientation is<111>. Different planes of a crystal structure is shown in Figure (1.62).

If the surface of the wafer is parallel to YZ plane then the crystal orientation is<100>. For MOS fabrication crystals with orientation<100>is utilized. For other applications<111>crystal orientations are preferred.

Figure. 1.62. Different Planes of a crystal.

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Source:  OpenStax, Solid state physics and devices-the harbinger of third wave of civilization. OpenStax CNX. Sep 15, 2014 Download for free at http://legacy.cnx.org/content/col11170/1.89
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