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Silicon has a diamond crystal lattice. The lattice constant is 10^-5 m. Determine the surface density of atoms for silicon on:

(a) the (100) plane

(b) the (110) plane

(c) the (111) plane

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(a) the (100) plane

Atoms: 4*1/4+1=2

Area=a2

(a=5.43*10-10m for Si)

Density= 2/a2=6.78*1018 atoms/m2

(b) the (110) plane

Atoms: 4*1/4+2*1/2+2=4

Surface area: sqrt(2) *a2

Density= [4/ sqrt(2)]* a2 = 9.59*1018 atoms/m2

(c) the (111) plane

(111) Atoms: 3*1/6+3*1/2=2

Surface area: sqrt(3)* a2 / 2

Density= [4/ sqrt(3)]* a2= 7.83*1018 atoms/m2

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The silicon cell's (100) plane surface density

2/(0.543x10^-7)^2 =6.78 x10^14 atom/cm^2

The silicon cell's (110) surface density:

=4/(0.543x0.543x sqrt 2 x 10^-14)=9.6 x10^14 atom/cm^2

The silicon cell's (111) surface density: 7.8*10^14 atom/cm^2

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