MSE 630 - IC Processing

CZ processing

Ingot diameter varies inversely with pull rate:

r

T

LNV mmp 3

21 5

max

L = latent heat of fusion

N = density

= Stephan-Boltzman constant

m = thermal conductivity at Tm

Tm = melt temperture (1417 oC for Si)

o = 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)(o-1)

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

o: initial L: liquid and s: solid

Float Zone Processing

L

xk

oos

o

CxC exp11)(

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

Concentration

Liquid

Tem

pera

ture

Solid

CoCs CL

Typical defects in crystalsTypical 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)

Thermal stresses cause dislocations. Thermal stress is: = ET

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

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