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How to Calculate Misalignment in Anisotropic Etching

Identifying misalignment ̵2; or mismatch of cells ̵2; in anisotropic etching requires a method of calculation called ̶0;time compensation.̶1; This can be seen when you are solving an algorithm used when simulating the etching process of silicon in a EDP, KOH or TMAH solution. When the Cellular Automata (CA) method for the etching simulation is used, the substrate is represented by individual cells that are contained inside of a crystalline lattice structure.

Instructions

- 1
  Write out the equation to determine the number of etch steps. This is expressed as N(t) = [M/E(s)T]t. A default value of 1 is used for T. The value of M is a multiple of E(s)T. The value of E(s) is [0,1].
- 2
  Write out the equation to determine the equivalent etch rate of the surface material. This is expressed as:
  
  E(s) = M/N(t)T = M/(M/E(s)T)T = E(s).
  
  If M is not a multiple of E(s)T, then a mismatch will occur because the etching of the next cell does not start immediately.
- 3
  Make a note for ̶0;k,̶1; which is used to identify an etch step. The next etch step in the process is labeled as k + 1. Note the time balance for an etch step as Tb(k).
- 4
  Write out the equation used to compute the time compensation. This equation is expressed as:
  
  M(k) > E(s)(T + Tb(k-1)
  
  then
  
  T(k) = T + Tb(k-1)
  
  M(k+1) = M(k) ̵1; E(s)T(k)
  
  Tb(k) = 0
  
  else
  
  T(k) = M(k)/E(s)
  
  M(k+1) = 0
  
  Tb(k) = T ̵1; T(k)
  
  The end result of the time compensation method results in an equation that is expressed as:
  
  E(s) = M(k)/T(k) = E(s) for an etch step k.

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