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18 Fall

The slide #13 for Ch. 1., there are compression and tension on the right figure to describe the yellow-shaded area. Those words indicate the stress(same unit with pressure, appied to crystal=force/area). 

 

The tension/compression indicates the different direction of atomic displacement under "internal" pressure (a response to external pressure, with opposite sign) to induce tensile/compressive strain.  And the strain is the term for representing misalginment or displacements of atomic position. When the lattice constants got bigger, then, we describe it as tensile strain. The strain is a parameter to describe the crystal while the state of matter with strain is called as distortion. 

 

So, let's say the original lattice constant is "a0", and it is changed into "a". Then, the strain is calculated as "( a-a0 )/a0". If the strain sign is positive, we call it tensile. If the sign is negative, we call it compressive.

 

The stress is proportional to strain in most of semiconductors. So, stress=C*strain. And "C" is the elastic coefficient or stiffness.  

 

So, stress ( those compression and tension) are "coupled with strain". Please note it is similar to Hook's law of physics, with "F=-kx".

In this case of "-"sign, however, F is external force and x is the internal length change. So, the external and internal terms are mixed. Please note that if there is externally tension, then, the inside of medium should have compression to balance the structure. So, we should be careful about the description of conditions. Most of physics problems mix the external force (action) with internal force (reaction). But in semiconductor, we only formulate the internal  stress and strain.  

 

Now, semiconductor defects are internal change (and let's say we don't know the external force or external origin, just to keep the formalism)

In this case, the force "F=kx", with internal force F and internal length chang x. The figure of slide 13 are all described based on internal force and internal atomic position changes. So, you will realize that C is positive in this case, similarly to "k". And that's the convention for crystal studies.  

 

Also, in realistic case, when the interfaces are formed between different materials (we call this as hetero-interface), there are almost always strain.In the yellow-shaded area, a line of atoms are missing in the bottom side, and it is called as dislocation in a crystal or line defect. 

 

In semiconductor device, we often see dislocation near hetero-interface. And the distance between different dislocations are around ~ 100 nm.

Also the strain is reduced as the atoms are away from the interface. Interestingly the strain amplitude always decays exponentially from the interface within 100-400 nm. 

 

This topic is not discussed fully in our textbook but one of the most important issues of semiconductor materials. 

 

 

 

 

 

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