Σ3 Grain and Twin Boundaries in FCC Materials
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The atomic structures of both coherent {111} Σ3 and incoherent {112} Σ3 CSL (coincidence site lattice) boundaries have been experimentally [4 - 6] and theoretically [7 - 9] studied. The grain boundary in FCC structure, e.g. Cu materials, can be an asymmetrical tilt boundary of the Σ3 misorientation. The bicrystals with this grain misorientation correspond to coherent twins when the boundary is parallel to {111} planes in both grains. The geometry in Figure 4737a shows the angle of tilt with respect to a common {111} plane of the two half crystals. The rotation angles about <110> and <211> tilt axes are Φ110 and Φ211, receptively. It was proposed that the energy of Σ3 <211> tilt boundaries has a minimum at Φ211 = 84° [1] as shown in Figure 4737a (d).

Crystallography of Σ3 tilt boundaries in Cu. (a) <110> tilt axis, (b) <211> tilt axis,

Figure 4737a. Crystallography of Σ3 tilt boundaries in Cu. (a) <110> tilt axis, (b) <211> tilt axis,
(c) 82° <110> boundary [2], (d) 84° <211> boundary [1].

Incoherent {112} Σ3 CSL boundary shows unique relaxation with or without relative crystal translation between each grains, i.e. rigid-body displacement. [10 - 12] It was proposed that Si atom with an extra bond is presented at the {112} Σ3 CSL boundary without the rigid-body displacement. [13, 14]

Figure 4737b shows a typical HRTEM image of {112} and {111} Σ3 CSL grain boundaries and their junction in polycrystalline silicon (poly-Si) observed in <110> direction. The arrows point some pairs of two parallel {111} Σ3 CSL boundaries. {112} Σ3 CSL junction exists between the terminations of a pair of parallel {111} Σ3 CSL boundaries.

typical HRTEM of {112} and {111} Σ3 CSL grain boundaries and their junction in polycrystalline silicon

Figure 4737b. A typical HRTEM of {112} and {111} Σ3 CSL grain boundaries and their junction in polycrystalline silicon. [15]

In many cases, the deep level states in semiconductors can be analyzed by EELS measurements. For instance, the pronounced shoulder below 100 eV indicated by the arrow in Figure 4737c presents a deep level state, above Fermi level in band gap, produced by symmetric segment a 5-fold coordinated atom in CSL junction in polycrystalline silicon. The shoulder in the Si-L2,3 ELNES was detected only from the symmetric segment of the {112} Σ3 CSL boundary near the CSL junction, but not from the bulk, {112} and {111} Σ3 CSL boundaries. The CSL junction would be electrically active and affects the electrical conductivity in polycrystalline silicon.

energy-loss near-edge spectra (ELNES) of Si-L23 edge acquired from a bulk, {112} and {111} Σ3 CSL boundaries, and their junction

Figure 4737c. The energy-loss near-edge spectra (ELNES) of Si-L2,3 edge acquired from a bulk, {112} and {111} Σ3 CSL boundaries, and their junction. [15]

Table 4737. Examples of CSL (coincident site lattice) translation vectors and angles of
misorientation (θ) at Σ3 <110> FCC tilt grain and twin boundaries.

CSL translation vectors Angle of misorientation (θ)    
Misorientated planes
70.53°
   
Misorientated planes Sigma 3
109.47°
   
       

Electron beam induced current (EBIC) measurements demonstrated that shallow states exist at Σ3 coincidence site lattice (CSL) grain boundaries. [3]

 

 

 


 

 

 

 

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