10.1 Strain and Stress at Heterointerfaces

The simplest description of a bulk crystalline semiconductor is that it exhibits perfect or nearly perfect translational symmetry. In other words，suitable translations of the basic unit cell of a crystal restore the crystal back into itself. Implicit in this definition is the assumption that the atoms within the crystal are regularly spaced throughout the entire bulk sample. This assumption is generally true for bulk materials. However，two important exceptions can arise. The first is that a bulk crystal can include impurities and dislocations such that the perfect periodicity of the material is disrupted locally. The crystal can still retain its overall highly ordered structure，yet contain local regions in which perfect periodicity is disrupted by impurities or dislocations. These impurities and dislocations can significantly affect the properties of the material. The second situation arises in multilayered structures. Using exacting crystal growth procedures，heterostructures can be grown with atomic layer precision. A very thin layer of material can be grown on top of or sandwiched between layers grown with a different type of semiconductor material，even materials in which the lattice constant is different.

When a thin layer of material is grown either on or between layers of a different semiconductor that has a significantly different lattice constant，the thin，epitaxial layer will adopt the lattice constant of the neighboring layers provided that the lattice mismatch is less than about 10%. As can be seen from Fig.10.1（a），when the thin，epitaxial layer adopts the lattice constant of the surrounding layers，it becomes strained，i. e.，it is either compressed or expanded from its usual bulk crystal shape. There exists a maximum thickness of the thin layer below which the lattice mismatch can be accommodated through strain. For layer thickness above the critical thickness，the lattice mismatch cannot be accommodated through strain，dislocations are produced and the strain relaxes as is seen in Fig.10.1（b）. The strain within the layer is homogeneous. The strained layer can be in either compressive or tensile strain. If the lattice constant of the strained layer is less than that of the surrounding layers the system is in tension. Conversely，if the lattice constant of the strained layer is greater than that of the surrounding layers，the strained layer is in compression.

Fig.10.1（a）Thin epitaxial layer strained to accommodate the various latticeconstants of the underlying semiconductor layer and（b）a thicker epitaxial layer thathas relaxed. In part（b）the epitaxial layer is thicker than the critical thickness anddislocations appear at the interface.