# Chapter 11: Film Formation¶

## Example 11.1 Page 371¶

In [1]:
#initialisation of variable
from math import *
M1=28.9;#mass
M2=60.08;#mass
d1=2.33;#density of Si
d2=2.21;#density of SiO2

#calculation
V1=M1/d1;#volume
V2=M2/d2;#volume
T=V1/V2;#thickness

#result
print"thickness of Si consumed per 100nm of SiO2 layer is",round(T*100,2),"nm"
print"(answer differ slightly due to approximation)"

thickness of Si consumed per 100nm of SiO2 layer is 45.63 nm
(answer differ slightly due to approximation)


## Example 11.2 Page 386¶

In [2]:
#initialisation of variable
from math import *
a=.5;#width
l=1;#length
K=2.7;#dielectric constant
t=.5;#thickness
R=2.7;#resistivity
E=8.85*10**-14;#constant

#calculation
Rc=R*l/a**2*E*K*l/t/2;#intrinsic RC

#result
print"intrinsic RC is",round(Rc*10**12,2),"ps"

intrinsic RC is 2.58 ps


## Example 11.3 Page 387¶

In [11]:
#initialisation of variable
from math import *
C=40;#capacitance
A=1.28;#cell size
k1=3.9;#dielectric constant
k2=25;#dielectric constant

#calculation
Ae=k1/k2*A;#cell size

#result
print"equivalent cell size is",round(Ae,2),"micro-m^2"

equivalent cell size is 0.2 micro-m^2


## Example 11.4 Page 394¶

In [6]:
#initialisation of variable
from math import *
T=500;#temperature
t=30;#min
ZL=16;
Z=5;
H=1;
D=2*10**-8;#cm^2/sec
S=.8;#%
Dr=1.16;#density ratio

#calculation
d=2*(D*t*60)**.5*Z*H/ZL*S*Dr;#depth

#result
print"depth is",round(d*100,2),"micro-m"

depth is 0.35 micro-m


## Example 11.5 Page 396¶

In [7]:
#initialisation of variable
from math import *
k1=3.9;#dielectric constant for SiO2
k2=2.6;#dielectric constant for CuAl
r1=2.7;#resistivity of Al
r2=1.7;#resistivity of Cu

#calculation
P=r2/r1*k2/k1*100;

#result
print"reduction of RC time is",round(P,0),"%"

reduction of RC time is 42.0 %


## Example 11.6 Page 398¶

In [25]:
#initialisation of variable
from math import *
R1=1;
R2=.1;
T=5.5;#time
t1=1;#layer1
t2=.01;#layer2

#calculation
r=((t1/R1)+(t2/R2))/T;#removal rate

#result
print"removal rate is",round(r,2),"micro-m/min"

removal rate is 0.2 micro-m/min


## Example 11.7 Page 400¶

In [3]:
#initialisation of variable
from math import *
R=.6;#resistance
r=18;#resistivity

#calculation
t=r/R;#thickness

#result
print"film thickness is",round(t*10,2),"nm"

film thickness is 300.0 nm