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MSE 630 - IC Processing. CZ processing. k o = C s /C o increases as ingot grows The dopant concentration is given by: I L =I o (1+V s /V o ) ko and C s = -dI L /dV s = C o k o (1-f) ( k o-1). Ingot diameter varies inversely with pull rate:. L = latent heat of fusion N = density

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Cz processing
CZ processing

ko = Cs/Co increases as ingot grows

The dopant concentration is given by:

IL=Io(1+Vs/Vo)ko and

Cs = -dIL/dVs = Coko(1-f)(ko-1)

Ingot diameter varies inversely with pull rate:

L = latent heat of fusion

N = density

s = Stephan-Boltzman constant

km = thermal conductivity at Tm

Tm = melt temperture (1417 oC for Si)

C, I and V are concentration, number of impurities and volume when

o: initial L: liquid and s: solid


Float zone processing
Float Zone Processing

Liquid

Temperature

Solid

Cs

Co

CL

Concentration

In Float Zone refining, solid concentration varies with initial concentration as follows:


Typical defects in crystals
Typical defects in crystals

Typical defects are:

Point defects – vacancies & interstitials

Line defects – dislocations

Volume defects – stacking faults, precipitates

The equilibrium number of vacancies varies with temperature:

nv = noexp(-Ev/kT)

O and C are also defects with concentrations of 1017-1018 cm-3 and 1015-1016 cm-3

Other impurities are in the ppb range

Thermal stresses cause dislocations. Thermal stress is: s = EaDT

s = stress, E = Young’s modulus, a = thermal expansion coefficient (mm/m/oC)


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