Q1:
a.
R=dM/dA=MecosΦcosθ/πr2 cosΦ=h/r Φ=θ cosθ=h/r cosΦcosθ=h2/r2 r2=h2+l2
R=Meh2/(h2+l2)/π(h2+l2)
R=Meh2/π(h2+l2)2
b.
Highest deposition rate
When the l=0, the cosΦ and cosθ both equal to 1,the point is right above the source ,it's at the highest deposition rate.

Lowest deposition rate
When the r=∞, the cosΦ and cosθ both equal to 0, the point is farthest from the source, it's at the lowest deposition rate.
c.
d/d0=R/R0 R0=Me/πh2 d/d0= (MecosΦcosθ)/πr2/Me/πh2 d/d0=1/(1+l2/h2)2 d. d/d0=1/(1+(l/h) 2)2

Table in excel Q1

See the graph above, it shows that when the source is farther from the wafer the d/d0 is increased. If choose the higher value of h, we will get more uniform thinkness. If we put the wafer far from the source, the deposition time will be longer.
e.
r0=r0 Φ=θ cosθ=cosΦ=r/2/r0 R=MecosΦcosθ/πr2
R=Me(r/2/r0)2/πr2
R=Me/4πr0
Q2a: Pre-deposition t=100 x t x/(4Dt)^0.5 Cs
1.00E-10
100
1.58E-02
9.82E+19
3.00E-10
100
0.047434
9.47E+19
6.00E-10
100
0.094868
8.93E+19
9.00E-10
100
0.142302
8.41E+19
1.00E-09
100
0.158114
8.23E+19
3.00E-09
100
0.474342
5.02E+19
6.00E-09
100
0.948683
1.80E+19
9.00E-09
100
1.423025
4.42E+18
1.00E-08
100
1.581139
2.53E+18
3.00E-08
100
4.743416
1.97E+09
6.00E-08
100
9.486833
4.85E-21
9.00E-08
100
14.23025
4.49E-70 t=300 x t x/(4Dt)^0.5 Cs
1.00E-10
300
0.009129
9.90E+19
3.00E-10
300
0.027386
9.69E+19
6.00E-10
300
0.054772
9.38E+19
9.00E-10
300
0.082158
9.08E+19
1.00E-09
300
0.091287
8.97E+19
3.00E-09
300
0.273861
6.99E+19
6.00E-09
300
0.547723
4.39E+19
9.00E-09
300
0.821584
2.45E+19
1.00E-08
300
0.912871
1.97E+19
3.00E-08
300
2.738613
1.08E+16
6.00E-08
300
5.477226
9.49E+05
9.00E-08
300
8.215838
3.30E-11 t=600 x t x/(4Dt)^0.5 Cs
1.00E-10
600
0.006455
9.93E+19
3.00E-10
600
0.019365
9.78E+19
6.00E-10
600
0.03873
9.56E+19
9.00E-10
600
0.058095
9.35E+19
1.00E-09
600
0.06455
9.27E+19
3.00E-09
600
0.193649
7.84E+19
6.00E-09
600
0.387298
5.84E+19
9.00E-09
600
0.580948
4.11E+19
1.00E-08
600
0.645497
3.61E+19
3.00E-08
600
1.936492
6.17E+17
6.00E-08
600
3.872983
4.32E+12
9.00E-08
600
5.809475
2.11E+04

Total drive in
Saturation concentration: 1.00E+20
Diffusion coeffcient: 1.00E-19
Assumed D>D1 t>t1
D1= 1.00E-19 D= 1.00E-17 t1= 300 t= 600
Then change t equal to 1200, 1800. t=600 x Q0
Q0/((πDt)^1/2)
"-x^2/4Dt exp(-x^2/4Dt) C(x,t)
1.00E-08
1.91E+03
1.39E+10
-4.17E-03
9.96E-01
1.39E+10
3.00E-08
1.91E+03
1.39E+10
-3.75E-02
9.63E-01
1.34E+10
6.00E-08
1.91E+03
1.39E+10
-1.50E-01
8.61E-01
1.20E+10
9.00E-08
1.91E+03
1.39E+10
-3.38E-01
7.14E-01
9.93E+09
1.00E-07
1.91E+03
1.39E+10
-4.17E-01
6.59E-01
9.18E+09
3.00E-07
1.91E+03
1.39E+10
-3.75E+00
2.35E-02
3.27E+08
6.00E-07
1.91E+03
1.39E+10
-1.50E+01
3.06E-07
4.26E+03
9.00E-07
1.91E+03
1.39E+10
-3.38E+01
2.20E-15
3.06E-05
1.00E-06
1.91E+03
1.39E+10
-4.17E+01
8.02E-19
1.12E-08
3.00E-06
1.91E+03
1.39E+10
-3.75E+02
1.38E-163
1.92E-153
6.00E-06
1.91E+03
1.39E+10
-1.50E+03
0.00E+00
0.00E+00
9.00E-06
1.91E+03
1.39E+10
-3.38E+03
0.00E+00
0.00E+00

t=1200 x Q0
Q0/((πDt)^1/2)
"-x^2/4Dt exp(-x^2/4Dt) C(x,t)
1.00E-08
1.91E+03
9.84E+09
-2.08E-03
9.98E-01
9.82E+09
3.00E-08
1.91E+03
9.84E+09
-1.88E-02
9.81E-01
9.66E+09
6.00E-08
1.91E+03
9.84E+09
-7.50E-02
9.28E-01
9.13E+09
9.00E-08
1.91E+03
9.84E+09
-1.69E-01
8.45E-01
8.32E+09
1.00E-07
1.91E+03
9.84E+09
-2.08E-01
8.12E-01
7.99E+09
3.00E-07
1.91E+03
9.84E+09
-1.88E+00
1.53E-01
1.51E+09
6.00E-07
1.91E+03
9.84E+09
-7.50E+00
5.53E-04
5.44E+06
9.00E-07
1.91E+03
9.84E+09
-1.69E+01
4.69E-08
4.62E+02
1.00E-06
1.91E+03
9.84E+09
-2.08E+01
8.96E-10
8.82E+00
3.00E-06
1.91E+03
9.84E+09
-1.88E+02
3.71E-82
3.66E-72
6.00E-06
1.91E+03
9.84E+09
-7.50E+02
0.00E+00