2 pages,
M A S S A C H U S E T T S I N S T I T U T E O F T E C H N O L O G Y
Closed book
3.155J/6.152J
Microelectronics Processing Technology
Spring Term,2003
Quiz 1 90 min/ 90 points total March 19 2003
Note,Be brief and relevant in your answers,and use sketches,Show your work,
k
B
= 1.38 10
-23
J/K = 8.62 10
-5
eV/K
40 1,Film deposition,CVD
a) Discuss briefly what factors affect the microstructure of a film grown on a substrate [15]
b) A CVD process is used to deposit P-doped silica at 1200 K,The reactions are,
SiH
4
--> Si (s) + 2H
2
(g) k = 0.1 exp (-E/ k
B
T) cm/s where E = 1.0eV
-3
D
silane
= 10
-5
cm
2
/s c
silane
= 10
21
cm
PH
3
(g) ---> P (s) + 3/2 H
2
(g) k = 2 exp (-E/ k
B
T) cm/s where E = 1.2eV
-3
D
phosphine
= 10
-6
cm
2
/s c
phosphine
= 10
20
cm
In the reactor,the average boundary layer thickness is 2 mm,N = 5x10
22
cm
-3
for the film,
Calculate the film’s growth rate and composition,[15]
c) Suppose the flow velocity of the gases is doubled,What happens to the answer to part (b)? [5]
d) CVD processes such as the one in part b) are often run at fairly high pressures,e.g,several
Torr,Speculate briefly on what might be different if the process is instead run at a very low
pressure,e.g,in the mTorr range,[5]
25 2,Diffusion
a) A thin layer of As is deposited onto the surface of a Si wafer containing a uniform
concentration of 10
18
cm
-3
of B,The As layer is only 10 nm thick,
If the sample is annealed for 1 hour at 1000 K,calculate the profile of the As,(Assume Si and
As atoms are the same size,1 cm
3
of Si contains 5x10
22
cm
-3
) [15]
b) Write down the assumptions you used in reaching this answer,and discuuss how valid they
are,[10]
For As,D
o
o
= 0.066 cm
2
/s; E
o
= 3.4 eV D
-
o
= 12 cm
2
/s; E
-
= 4.0 eV
For B,D
o
o
= 0.037 cm
2
/s; E
o
= 3.4 eV D
+
o
= 0.4 cm
2
/s; E
+
= 3.4 eV
25 3,Lithography and Etch
a) Define in one or two sentences the differences between the following,[10]
i,Depth of focus,Resolution of imaging system and Resolution of resist
ii,Positive and negative resist
iii,Proximity and projection printing
b) For plasma etching,explain concisely how selectivity and anisotropy can be controlled by
choice of etching parameters,[7]
c) If you are etching the following sample,sketch what profiles you
fSi (100)
Nitride mask
might expect from these three etch processes,and explain why,[8]
i,etching in KOH solution
ii,etching in an HF and nitric acid mixture
iii,Ion milling
Useful equations
k
B
= 1.38 10
-23
J/K = 8.62 10
-5
eV/K
Gas kinetics,Pressure P = nk
B
T 1 atm = 760 torr ≈ 10
5
Pa
Average speed c
ave
= (8k
B
T/πm)
0.5
Mean free path λ = 1/(πd
2
n√2)
Arrival rate at a surface J = P/(2πk
B
T m)
0.5
= 3.5 10
22
P(torr)/(MT (g/mol.K))
0.5
m = mass of a molecule,M = molar mass,
Oxidation,thickness x
o
after time t x
o
2
+ A x
o
= B (t + τ)
or (x
o
2
– x
i
2
) + A(x
o
– x
i
) = Bt
B/A = c
o
k
s
/N,B = 2D
ox
c
o
/N
c
o
= conc,of oxidant at surface,k
s
= rate constant for oxidation,D
ox
= diffusivity of oxidant in
oxide,N = number of oxidant molecules needed to make unit volume of oxide,τ = time offset,
x
i
= initial oxide thickness,
Chemical vapor deposition
film growth rate v = (c
g
/ N)(h
g
k/(h
g
+ k))
Reaction flux F
r
= k c
s
Transport flux F
d
= h
g
(c
g
-c
s
)
Gas phase transport coefficient h
g
= 3/2 (D
g
/L) (ρ u L/η)
0.5
= D
g
/δ
ave
Boundary layer thickness δ = (x η/ρ u )
0.5
Reaction coefficient k = k
o
exp (-?G/k
B
T)
c
g
is concentration of reactant species in bulk of gas; c
s
is concentration on the surface,N is
density of film (atoms/cm
3
),D
g
is the diffusivity in the gas,L is a characteristic length,x is
distance along wafer,ρ is gas density,η is viscosity,u is gas velocity,k
B
= 1.38 10
-23
J/K,=
8.62 10
-5
eV/K
Semiconductor conductivity σ = (μ
n
n + μ
h
p)e
μ
n
= electron mobility,μ
h
= hole mobility,n = number of electrons,p = number of holes,e =
electronic charge 1.6 10
-19
C,
Difffusion,
Source with constant surface concentration,C(z,t) = C
surf
erfc (-z/(2√(Dt)))
This introduces dose Q Q = 2C
surf
√(Dt)/√π
Fixed amount of dopant diffusing into wafer,C(z,t) = Q/√(πDt) exp (-z
2
/4Dt)
z = distance,t = time,C = concentration(atoms/cm
3
),C
surf
= conc,at surface,Q = dose
(atoms/cm
2
)
Effective Intrinsic Diffusivity D
eff
= D
o
+ D
-
+ D
=
+ D
+
…
where D
o
= D
o
o
exp (-E
o
/kT),D
+
= D
+
o
exp (-E
+
/kT),etc
2
D
=
Extrinsic Diffusivity D
eff
= D
o
+ (n/n
i
)D
-
+ (n/n
i
) + (p/n
i
)D
+
…
Name,___________________________
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
Department of Materials Science and Engineering
6.152J/3.155J
IN-CLASS QUIZ
16 September 2002
(5 problems/9 pages total)
1) Defects (20 points)
The equilibrium concentration of oxygen in Si is given by
C
OX
= 5 × 10
22
exp (-2.6 eV / k
B
T) (cm
-3
) and that for vacancies is given by
C
VAC
= 2 × 10
22
exp (-1.06 eV / k
B
T) (cm
-3
),Recall k
B
= 8.62 x 10
-5
eV/K,
a) At what temperature are C
VAC
and C
OX
equal?
b) Which defect,oxygen impurities or vacancies,would have a greater
equilibrium concentration at the melting temperature (1417 °C) of Si?
1
Name,___________________________
c) Sketch ln [C] vs 1000 / T (i.e.,an Arrhenius plot) identifying the slope
and intercept for each plot,
ln [C]
1000/T
2
Name,___________________________
2) Vacuum Systems (20 points)
The Knudson number is defined as N
K
= λ / L,where λ is the molecular mean
free path and L is a characteristic dimension of the chamber (reaction vessel),
a) Write the numbers 1 to 7 corresponding to the terms below in the
appropriate column,N
K
> 1,N
K
< 1,
1) Molecular flow
2) Viscous flow
3) P > 10 mT
~
4) P < 0.1 mT
~
5) Atoms strike surface with a velocity that traces linearly back to the source
6) Gas diffusion regime
7) Atoms strike surface with a variety of angles of incidence,
N
K
> 1 N
K
< 1
3
Name,___________________________
b) Select TWO steps that occur in film growth,as numbered below,and describe the
physical process in one or two short,concise sentences,
1) 3)
5)
2)
4) 6)
4
C
Name,___________________________
3) Oxidation (20 points)
a) Describe why SiO
2
grows on Si at the Si / SiO
2
interface,not at the SiO
2
/ gas
interface,
b) (i) Briefly describe the physical processes occurring at J
1
,J
2
and J
3
in the
figure below,
Dead
J
1
layer
J
3
SiSiO
2
gas
J
2
C
5
Name,___________________________
c) Oxide growth on Si is described by the Deal-Grove quadratic equation
t
2
+ At = B(t +τ) with τ = ( t
0
2
+ At
0
) / B
ox ox
Write the expression for growth rate dt
ox
/ dt in ONE of the limits below,
I) thin oxide t
ox
2
<< At
ox
OR
II) thick oxide t
ox
2
>> At
ox
d) Give a physical reason why oxide growth is generally faster on doped
Si than on pure Si,
6
Name,___________________________
4) Chemical vapor deposition (CVD) [20 points]
You want to deposit a p+ doped gate oxide for a MOSFET using CVD,
You chose for the SiO
2
reaction:
SiH
4
(g) + O
2
Si O
2
(s) + 2H
2
(g),
a) Circle one of the following reactions that will give you p+ doping of
your gate oxide,
i. 2PH
3
(g)? 2 P (s) + 3H
2
(g) or
ii. B
2
H
6
(g)? 2B (s) + 3H
2
(g)
b) Define the terms in the CVD growth equation and give the
dimensions,e.g,number/(sec-area),of each,
C /N
v =
g
1 1
+
h k
g s
c) Write the equation for the film growth rate in the regime where it is
limited by reaction kinetics,
7
Name,___________________________
d) Use one of the figures below to answer the following questions for
reaction rate-limited growth of a p-doped gate oxide,
i. Circle the reaction rate-limited regime on each of the figures
below,
ii. Will the dopant concentration in the gate oxide be likely to be
affected by the gas flow rate? Why?
iii. What processing parameter would be best to control the ratio
of dopant to SiO
2
concentration in the gate oxide layer?
iv. Sketch on the appropriate figure below how that processing
variable in part iii would change the figure (assume the figures
as given to you apply to the SiO
2
parameters),
ln (v)
ln (v)
1 / T
u
0
T
1000 K 400
K
8
Name,___________________________
5) Lithography (20 points)
i) What is the,critical resist modulation transfer function (CMTF)”?
ii) What is the,modulation transfer function (MTF)”? What affects MTF?
iii) Using an aligner in the Technology Research Laboratory at MIT,you
determine that the modulation transfer function is 0.35,whereas the critical
resist modulation transfer function for your process is determined to be 0.45,
Will you or will you not be able transfer your pattern? Why or why not,
please explain,
9
M A S S A C H U S E T T S I N S T I T U T E O F T E C H N O L O G Y
Closed book
3.155J/6.152J
Microelectronics Processing Technology
Spring Term,2003
Quiz 1 90 min/ 90 points total March 19 2003
Note,Be brief and relevant in your answers,and use sketches,Show your work,
k
B
= 1.38 10
-23
J/K = 8.62 10
-5
eV/K
40 1,Film deposition,CVD
a) Discuss briefly what factors affect the microstructure of a film grown on a substrate [15]
b) A CVD process is used to deposit P-doped silica at 1200 K,The reactions are,
SiH
4
--> Si (s) + 2H
2
(g) k = 0.1 exp (-E/ k
B
T) cm/s where E = 1.0eV
-3
D
silane
= 10
-5
cm
2
/s c
silane
= 10
21
cm
PH
3
(g) ---> P (s) + 3/2 H
2
(g) k = 2 exp (-E/ k
B
T) cm/s where E = 1.2eV
-3
D
phosphine
= 10
-6
cm
2
/s c
phosphine
= 10
20
cm
In the reactor,the average boundary layer thickness is 2 mm,N = 5x10
22
cm
-3
for the film,
Calculate the film’s growth rate and composition,[15]
c) Suppose the flow velocity of the gases is doubled,What happens to the answer to part (b)? [5]
d) CVD processes such as the one in part b) are often run at fairly high pressures,e.g,several
Torr,Speculate briefly on what might be different if the process is instead run at a very low
pressure,e.g,in the mTorr range,[5]
25 2,Diffusion
a) A thin layer of As is deposited onto the surface of a Si wafer containing a uniform
concentration of 10
18
cm
-3
of B,The As layer is only 10 nm thick,
If the sample is annealed for 1 hour at 1000 K,calculate the profile of the As,(Assume Si and
As atoms are the same size,1 cm
3
of Si contains 5x10
22
cm
-3
) [15]
b) Write down the assumptions you used in reaching this answer,and discuuss how valid they
are,[10]
For As,D
o
o
= 0.066 cm
2
/s; E
o
= 3.4 eV D
-
o
= 12 cm
2
/s; E
-
= 4.0 eV
For B,D
o
o
= 0.037 cm
2
/s; E
o
= 3.4 eV D
+
o
= 0.4 cm
2
/s; E
+
= 3.4 eV
25 3,Lithography and Etch
a) Define in one or two sentences the differences between the following,[10]
i,Depth of focus,Resolution of imaging system and Resolution of resist
ii,Positive and negative resist
iii,Proximity and projection printing
b) For plasma etching,explain concisely how selectivity and anisotropy can be controlled by
choice of etching parameters,[7]
c) If you are etching the following sample,sketch what profiles you
fSi (100)
Nitride mask
might expect from these three etch processes,and explain why,[8]
i,etching in KOH solution
ii,etching in an HF and nitric acid mixture
iii,Ion milling
Useful equations
k
B
= 1.38 10
-23
J/K = 8.62 10
-5
eV/K
Gas kinetics,Pressure P = nk
B
T 1 atm = 760 torr ≈ 10
5
Pa
Average speed c
ave
= (8k
B
T/πm)
0.5
Mean free path λ = 1/(πd
2
n√2)
Arrival rate at a surface J = P/(2πk
B
T m)
0.5
= 3.5 10
22
P(torr)/(MT (g/mol.K))
0.5
m = mass of a molecule,M = molar mass,
Oxidation,thickness x
o
after time t x
o
2
+ A x
o
= B (t + τ)
or (x
o
2
– x
i
2
) + A(x
o
– x
i
) = Bt
B/A = c
o
k
s
/N,B = 2D
ox
c
o
/N
c
o
= conc,of oxidant at surface,k
s
= rate constant for oxidation,D
ox
= diffusivity of oxidant in
oxide,N = number of oxidant molecules needed to make unit volume of oxide,τ = time offset,
x
i
= initial oxide thickness,
Chemical vapor deposition
film growth rate v = (c
g
/ N)(h
g
k/(h
g
+ k))
Reaction flux F
r
= k c
s
Transport flux F
d
= h
g
(c
g
-c
s
)
Gas phase transport coefficient h
g
= 3/2 (D
g
/L) (ρ u L/η)
0.5
= D
g
/δ
ave
Boundary layer thickness δ = (x η/ρ u )
0.5
Reaction coefficient k = k
o
exp (-?G/k
B
T)
c
g
is concentration of reactant species in bulk of gas; c
s
is concentration on the surface,N is
density of film (atoms/cm
3
),D
g
is the diffusivity in the gas,L is a characteristic length,x is
distance along wafer,ρ is gas density,η is viscosity,u is gas velocity,k
B
= 1.38 10
-23
J/K,=
8.62 10
-5
eV/K
Semiconductor conductivity σ = (μ
n
n + μ
h
p)e
μ
n
= electron mobility,μ
h
= hole mobility,n = number of electrons,p = number of holes,e =
electronic charge 1.6 10
-19
C,
Difffusion,
Source with constant surface concentration,C(z,t) = C
surf
erfc (-z/(2√(Dt)))
This introduces dose Q Q = 2C
surf
√(Dt)/√π
Fixed amount of dopant diffusing into wafer,C(z,t) = Q/√(πDt) exp (-z
2
/4Dt)
z = distance,t = time,C = concentration(atoms/cm
3
),C
surf
= conc,at surface,Q = dose
(atoms/cm
2
)
Effective Intrinsic Diffusivity D
eff
= D
o
+ D
-
+ D
=
+ D
+
…
where D
o
= D
o
o
exp (-E
o
/kT),D
+
= D
+
o
exp (-E
+
/kT),etc
2
D
=
Extrinsic Diffusivity D
eff
= D
o
+ (n/n
i
)D
-
+ (n/n
i
) + (p/n
i
)D
+
…
Name,___________________________
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
Department of Materials Science and Engineering
6.152J/3.155J
IN-CLASS QUIZ
16 September 2002
(5 problems/9 pages total)
1) Defects (20 points)
The equilibrium concentration of oxygen in Si is given by
C
OX
= 5 × 10
22
exp (-2.6 eV / k
B
T) (cm
-3
) and that for vacancies is given by
C
VAC
= 2 × 10
22
exp (-1.06 eV / k
B
T) (cm
-3
),Recall k
B
= 8.62 x 10
-5
eV/K,
a) At what temperature are C
VAC
and C
OX
equal?
b) Which defect,oxygen impurities or vacancies,would have a greater
equilibrium concentration at the melting temperature (1417 °C) of Si?
1
Name,___________________________
c) Sketch ln [C] vs 1000 / T (i.e.,an Arrhenius plot) identifying the slope
and intercept for each plot,
ln [C]
1000/T
2
Name,___________________________
2) Vacuum Systems (20 points)
The Knudson number is defined as N
K
= λ / L,where λ is the molecular mean
free path and L is a characteristic dimension of the chamber (reaction vessel),
a) Write the numbers 1 to 7 corresponding to the terms below in the
appropriate column,N
K
> 1,N
K
< 1,
1) Molecular flow
2) Viscous flow
3) P > 10 mT
~
4) P < 0.1 mT
~
5) Atoms strike surface with a velocity that traces linearly back to the source
6) Gas diffusion regime
7) Atoms strike surface with a variety of angles of incidence,
N
K
> 1 N
K
< 1
3
Name,___________________________
b) Select TWO steps that occur in film growth,as numbered below,and describe the
physical process in one or two short,concise sentences,
1) 3)
5)
2)
4) 6)
4
C
Name,___________________________
3) Oxidation (20 points)
a) Describe why SiO
2
grows on Si at the Si / SiO
2
interface,not at the SiO
2
/ gas
interface,
b) (i) Briefly describe the physical processes occurring at J
1
,J
2
and J
3
in the
figure below,
Dead
J
1
layer
J
3
SiSiO
2
gas
J
2
C
5
Name,___________________________
c) Oxide growth on Si is described by the Deal-Grove quadratic equation
t
2
+ At = B(t +τ) with τ = ( t
0
2
+ At
0
) / B
ox ox
Write the expression for growth rate dt
ox
/ dt in ONE of the limits below,
I) thin oxide t
ox
2
<< At
ox
OR
II) thick oxide t
ox
2
>> At
ox
d) Give a physical reason why oxide growth is generally faster on doped
Si than on pure Si,
6
Name,___________________________
4) Chemical vapor deposition (CVD) [20 points]
You want to deposit a p+ doped gate oxide for a MOSFET using CVD,
You chose for the SiO
2
reaction:
SiH
4
(g) + O
2
Si O
2
(s) + 2H
2
(g),
a) Circle one of the following reactions that will give you p+ doping of
your gate oxide,
i. 2PH
3
(g)? 2 P (s) + 3H
2
(g) or
ii. B
2
H
6
(g)? 2B (s) + 3H
2
(g)
b) Define the terms in the CVD growth equation and give the
dimensions,e.g,number/(sec-area),of each,
C /N
v =
g
1 1
+
h k
g s
c) Write the equation for the film growth rate in the regime where it is
limited by reaction kinetics,
7
Name,___________________________
d) Use one of the figures below to answer the following questions for
reaction rate-limited growth of a p-doped gate oxide,
i. Circle the reaction rate-limited regime on each of the figures
below,
ii. Will the dopant concentration in the gate oxide be likely to be
affected by the gas flow rate? Why?
iii. What processing parameter would be best to control the ratio
of dopant to SiO
2
concentration in the gate oxide layer?
iv. Sketch on the appropriate figure below how that processing
variable in part iii would change the figure (assume the figures
as given to you apply to the SiO
2
parameters),
ln (v)
ln (v)
1 / T
u
0
T
1000 K 400
K
8
Name,___________________________
5) Lithography (20 points)
i) What is the,critical resist modulation transfer function (CMTF)”?
ii) What is the,modulation transfer function (MTF)”? What affects MTF?
iii) Using an aligner in the Technology Research Laboratory at MIT,you
determine that the modulation transfer function is 0.35,whereas the critical
resist modulation transfer function for your process is determined to be 0.45,
Will you or will you not be able transfer your pattern? Why or why not,
please explain,
9
