- Lattice constant
The Lattice Constant refers to the constant distance between
unit cell s in acrystal lattice . Lattices in three dimensions generally have three lattice constants, referred to as "a", "b", and "c". However, in the special case of cubic crystal structures, all of the constants are equal and we only refer to "a". Similarly, in hexagonal crystal structures, the "a" and "b" constants are equal, and we only refer to the "a" and "c" constants. A group of lattice constants could be referred to as lattice parameters. However, the full set of lattice parameters consist of the three lattice constants and the three angles between them.For example the lattice constant for a common carbon diamond is "a = 3.57Å at 300k". It is important to note that the structure is equilateral although its actual shape can not be determined from only the lattice constant. Furthermore, in real applications, typically the average lattice constant is given. As lattice constants have the dimension of length, their
SI unit is themeter . Lattice constants are typically on the order of severalangstrom s (i.e. tenths of ananometre ). Lattice constants can be determined techniques such asX-ray diffraction or with anatomic force microscope .In epitaxial growth, the lattice constant is a measure of the structural compatibility between different materials.Lattice constant matching is important for growth of thin layers of materials on other materials; when the constants differ, strains are introduced into the layer, which prevents epitaxial growth of thicker layers without defects.
Lattice matching
Matching of lattice structures between two different
semiconductor material s, allows forming of a region ofband gap change in the material without introducing a change in crystal structure. It allows construction of advancedlight-emitting diode s anddiode laser s.For example,
gallium arsenide ,aluminium gallium arsenide , andaluminium arsenide have almost equal lattice constants, making it possible to grow almost arbitrarily thick layers of one on the other one.Lattice grading
Typically, films of different materials grown on the previous film or substrate are chosen to match the lattice constant of the prior layer to minimize film stress.
An alternative method is to grade the lattice constant from one value to another by a controlled altering the alloy ratio during film growth. The beginning of the grading layer will have a ratio to match the underlying lattice and the alloy at the end of the layer growth will match the desired final lattice for the following layer to be deposited.
The rate of change in alloy must be determined by the weighing of the penalty of layer strain and hence defect density vs. the cost of the time in the epitaxy tool.
For example,
Indium gallium phosphide layers with a band-gap above 1.9 eV can be grown onGallium Arsenide wafers with index grading.References
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