Optimal Design of Channel Doping for Fully
Depleted SOI MOSFETs
by
Dennis Okumu Ouma
Submitted to the Department of Electrical Engineering and
Computer Science
in partial fulfillment of the requirements for the degree of
Er699
Master of Engineering in Electrical Engineering and Computer
Science
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OF TECHNOLOGY
at the
JAN 2 9 1996
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
LIBRARIES
June 1995
@ Massachusetts Institute of Technology 1995. All rights reserved.
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Department of Electrical Engineering and Computer Science
May 1, 1995
C ertified by ......
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Accepted by.... ...... .
...............................
Dimitri Antoniadis
Professor
Thesis Supervisor
bP
. . ........
Leonard A. Gould
Chairman, Departmental Committee on Graduate Students
Optimal Design of Channel Doping for Fully Depleted SOI
MOSFETs
by
Dennis Okumu Ouma
Submitted to the Department of Electrical Engineering and Computer Science
on May 1, 1995, in partial fulfillment of the
requirements for the degree of
Master of Engineering in Electrical Engineering and Computer Science
Abstract
Fully-depleted SOI devices are being considered for low power applications due to
their threshold voltage, sub-threshold slope and capacitance advantages over other
technologies. However, the threshold voltage of a fully-depleted SOI device is a strong
function of the silicon film and sacrificial oxide thicknesses. Thus, to fully realize
the advantages of fully-depleted SOI devices in commercial products, the threshold
voltage sensitivity to sacrificial oxide and silicon film variations must be minimized.
Using one dimensional numerical simulations, the threshold voltage variation for
long channel SOI devices is explored over a range of thickness errors related to silicon
film and sacrificial oxide. It is found that the threshold voltage variation is minimized
when the peak of the implanted profile is near the center of the silicon film. High
variations in sacrificial oxide thickness shift the optimal profile towards the buried
oxide while high silicon film thickness variations shift it away from the buried oxide.
Thesis Supervisor: Dimitri Antoniadis
Title: Professor
Acknowledgments
Completion of any educational phase at M.I.T is by no means easy. I must therefore
thank God fbr making it possible that this moment would ever come true. Many
people have been of great help to me over the years and foremost on the list is
Professor Antoniadis who has guided me through the thesis project. I appreciate his
patience as I was trying to master the basics of device physics. Great appreciation is
also due to Professor Jesus del Alamo, my academic advisor. Professor Alamo is not
only a great teacher but also one of the best advisors I've ever had. His continuous
encouragement just kept me going and I always remember smiling after every chat
we had. On the same rank, I must thank Jarvis Jacobs for showing me how to wade
around process simulators. I think I would have given up on modifying SUPREM III
if it was not for his encouragement. He was always there to listen to my incessant
whinings!
Working
in building 39 has been great fun. My office-mate, Mark Armstrong,
made life quite easy. I must confess he made it hard for me to leave the office early
since I would always feel that I was working less. Melanie's friendliness must also be
appreciated. She was always willing to share a thing about SOI. Many thanks also go
to Andy Wei, Keith Jackson and Isabel Yang, the other members of "device" group,
for being great buddies. Special thanks to Andy Tang and Jeff Thomas, my 6.720
buddies. I hope you guys have fun in industry.
Let nobody lie to you that MIT is just about books! In this regard I must express
my gratitude to my High School buddies, Omondi Orondo, John Gachora and Victor
Owuor. Christine Odero and Jane Wahome, I hereby induct you into this fraternity.
You guys are great. I've enjoyed every moment we've spent together. I must also
thank the entire African fraternity at MIT for being so special. It's sad we never won
the Soccer Tournament but you guys could play! Shela and Setumo, rumor has it
that we would've won if you guys had no dreadlocks! Many thanks to my St. Paul
College fellowship members: Monica Coleman, Kevin, Bonnie James and the others.
Bonnie, thanks for being so sweet! Special thanks are due to Joy, my Wellesley buddy
for always checking on me late at night! The phone calls made pulling all-nighters
a worthy past-time. Patricia Muthaura, thanks for allowing us to be a nuisance in
the "Valley." To Lillian Ouko, I must say that your comments that you admired my
determination meant everything to me!
Lastly, I'd like to thank my family for their support over the years. I would
certainly not be here had it not been for their love and kindness. In deed this thesis
is dedicated to them.
Contents
1 Introduction
1.1
2
Thesis Goals .
2.1
General Process Structure .
2.2
General Grid Structure ........
2.3
Diffusion Modelling in SUPREM-III ..............
2.3.1
2.4
3
.... .
..............
.............
. . . . .
14
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14
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16
18
Numerical implementation of impurity Redistribution
Grid Refinement for SOI simulation .
......
.......
. . . . .
21
Ion Implantation and Diffusion in SOI structures
24
3.1
24
Ion Implantation
3.1.1
3.2
4
14
SUPREM-III Grid Structure For SOI
.
. . . . . . . . . . . . . . . . . . . .
Implant Models Applicable for SOI . ..............
Diffusion .......................
..........
28
32
3.2.1
Fick's M odel of Diffusion . . . . . . . . . . . . . . . . . . . . .
32
3.2.2
Atomistic models of Diffusion in Silicon . ............
34
3.2.3
Non-equilibrium Diffusion . . . . . . . . . . . . . . . . . . . .
36
3.2.4
Effect of the buried Oxide on Impurity Diffusion ........
39
3.2.5
Interstitial Vacancy Supersaturation Level . ..........
42
3.2.6
Experimental Verification of the Effect of the buried Oxide ..
43
Process Flow Design of a Fully Depleted SOI NMOSFET
44
4.1
Problem Statem ent ............................
44
4.2
Threshold Voltage Expression ......................
44
4.3
4.4
D esign . . . . . . . . . . . . . . . . . . . .
4.3.1
Design Space for Energy and Dose
4.3.2
Design Flow .............
4.3.3
Design Implementation .......
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Results and Discussion ...........
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A SUPREM III Process File
B Scripts and Source Files
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List of Figures
1-1
Pictorial Drawings of Bulks MOSFETs .............
1-2
Cross-sectional view of an SOI NMOSFET
2-1
Spaces less than number required for uniform distribution
2-2
Spaces greater than number required for uniform distribution
. . . .
16
2-3
Space Discretization
. . . .
19
2-4
Illustration of the cell structure .
. . . .
21
2-5
Silicon Film Retained Dose vs Film Thickness . . . . . . . .. . . . .
22
2-6
Grid spacing, dx, vs Depth from top of Layer
23
3-1
Boron implanted atom distributions, comparing measured data points
.
. . . . . .
. .. . . . . . . . . . . . .
. . . . . .
.
.. .
. . . . .
.
. . . .
with four-moment (Pearson IV) and Gaussian fitted distributions. The
boron was implanted into amorphous silicon without annealing.
3-2
Experimental profiles of boron implanted into < 111 > (closed circles) and < 100 > (open circles) silicon. The solid lines represent the
Pearson IV distribution and the dashed lines the exponential tail.
3-3
Boron profile separation for channelled and none channelled components
3-4
BF2 Implant into an SOI structure .
3-5
Silicon Intrinsic Carrier Concentration as a Function of Temperature
3-6
Vacancy and Interstitial Diffusion models..
4-1
Design Tree ................................
4-2
Module dependency diagram
..................
...............
15
4-3
As implanted profile for 15 keV and 56 keV
4-4
Implant Dose vs Energy
4-5
% Retained Implant Dose vs Energy
4-6
..
..
54
..
55
..
55
VT Error due to Film Thickness variation . . .
..
56
4-7
VT Error due to Oxide thickness Variation
..
57
4-8
VT Error due to Oxide and Film variation.
4-9
Signed VT error for variation of Film and Oxide thicknesses.
.. . . . . . . . . . . .
.. . . . .
4-10 Average VT error for film thickness variation
Chapter. 1
Introduction
It is projected that as Metal Oxide Semiconductor(MOS) technologies are scaled
to the point where critical device dimensions are well into the deep sub-micron
regime, silicon-on-insulator(SOI) technology may replace bulk technology in mainstream Complementary Metal Oxide Silicon (CMOS) applications [17]. Fig 1-1 shows
pictorial drawings of the complementary bulk Metal Oxide Semiconductor Field Effect Transistors (MOSFETs) employed in CMOS while Fig 1-2 is a cross-sectional
view of an SOI NMOSFET. For a complete understanding of the operation of an
MOSFET, the reader may consult any standard semiconductor devices text book
such as Muller and Kamins [15].
Correspondingly, a detailed discussion of CMOS
design and applications may be found in such texts as Weste and Eshraghian [14].
As MOS device dimensions are scaled down, substrate dopings must be increased
to control short channel effects and drain-induced barrier lowering (DIBL). For bulk
devices, the increased substrate doping results in higher parasitic source and drain
capacitances which limit device speeds. These capacitances are drastically reduced
in SOI devices because the source and drain junction depths are controlled by the
thickness of the silicon film. SOI devices are thus characterized by almost constant
parasitic junction capacitance. The perfect dielectric isolation of devices in SOI also
results in the elimination of latch-up, a parasitic phenomena that occurs in bulk
devices due to a bipolar action between the source, drain and substrates of adjacent
devices. Other advantages attributed to SOI devices are radiation hardness, and, for
Gate
Drain
©
0
Source
'Lj
conductor
gate
drain
n
-
source
in
substrate
p-doe- semiconductor sucstrate
n-trans!stor
Schematic Icon
Gate
Drain
-'
Source
CO!cuctor
cate
nsuiaior
drain
I
source
/
substrate
n-doped semiconductor substrate
p-transistor
Schematic Icon
Figure 1-1: Pictorial Drawings of Bulks MOSFETs
Gate
Figure 1-2: Cross-sectional view of an SOI NMOSFET
fully-depleted devices, increased transconductance and steeper subthreshold slope.
A fully-depleted SOI device results when the silicon film thickness is less than the
substrate depletion depth at the onset of inversion. For a uniformly doped substrate,
the critical film thickness for full depletion is given by
Xd =
(1.1)
where NA is the substrate doping and 4Q, is given by
k,q In NA
D = kT(
ni
(1.2)
where, T is the temperature, k is the Boltzmann constant and ni is the intrinsic
carrier concentration in silicon.
1.1
Thesis Goals
The advantages of fully depleted SOI devices are underscored by their threshold voltage sensitivity to silicon film thickness. As will be shown in chapter 4, the threshold
voltage of a fully depleted uniformly doped SOI device is linearly dependent on the
film thickness. Given that it is difficult to obtain a uniform film thickness across a
wafer, attempts must be made to employ design strategies which result in the minimization of threshold voltage variation across a wafer given some variation in silicon
film thickness. The goal of this work is therefore to design an optimal channel implant
profile that minimizes threshold voltage variation given the intrinsic variation in silicon film thickness. Using SUPRE-M III, a 1-D process simulator, a design strategy
is proposed and implemented. The design also accounts for variations in sacrificial
oxides used to reduce channeling during ion implantation. A complete statement of
the design problem is presented in chapter 4.
The thesis is divided into four chapters and three appendices.
Chapter 2 describes how SUPREMN III models the physical processes resulting
in the actual devices. Emphasis is placed in the appropriate grid structure that must
be employed for proper simulation of SOI processing. A new algorithm which sets an
appropriate grid structure for SOI is described.
Chapter 3 describes how the buried oxide layer in SOI modifies ion implantation
and diffusion modelling for SOI.
Chapter 4 presents the complete design for channel implant energy and dose
that results in minimization of threshold voltage variation.
Appendix A presents the SUPREM III process file used in the design for channel
implant dose and energy.
Appendix B is a listing of programs and scripts used in chapter 4.
Institute Archives and Special Collections
Room 14N-118
The Ubraries
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139-4307
This is the most complete text of the thesis
available. The following page(s) were not included
in the copy of the thesis deposited in the Institute
Archives by the author: 13
Telephone: (617) 253-5690 * reference (617) 253-5136
Chapter 2
SUPREM-III Grid Structure For
SOI
2.1
General Process Structure
SUPREM-III simulates the physical processes of a one dimensional structure which
may comprise up to ten layers of material. Current versions of the program allow for
simulation of layers of single crystalline silicon, polycrystalline silicon, silicon nitride,
silicon dioxide, aluminum and photo-resist. A material can be in more than one layer
and the layers are identified by their index with the first layer having an index of
unity.
2.2
General Grid Structure
The physical processes are modelled by numerical solution of finite difference equations. The processes modelled include oxidation of silicon, ion implantation, diffusion,
material deposition, epitaxial growth and etching. To facilitate the modelling of these
continuous processes, the layers are further divided into one dimensional cells defined
by nodes in a one dimensional grid. Each cell in the interior of a layer is centered
about a single node. The cells at the ends of a layer have one cell boundary at the
end node and the other boundary halfway between the end node and the adjacent
grid
spacing
DX2
D
x
0
A
THICKNES
Figure 2-1: Spaces less than number required for uniform distribution
interior node. In the current version of the program there can be up to 500 nodes.
The physical coefficients and impurity concentrations within each cell are assumed
constant.
The grid spacings, or distance between adjacent nodes, can be independently set
by the user for each laver within the simulation structure. This can be done at any
point in the simulation. To minimize the simulation time, the user may set sparse
nonuniform grids within a layer provided dense grids are used in areas with rapid
spatial variations in impurity distribution.
To generate dense grids at a particular distance from the top of a layer, the user has
to specify the nominal grid spacing required and the depth at which this is required.
Let the distance at which the nominal grid is required be xdx. The program then
generates grid spacings which vary with the distance from xdx. Depending on the
thickness of the layer and the maximum number of spaces allowed for the layer, the
grid spacings will follow the pattern in either Fig 2-1 or Fig 2-2. For Fig 2-1 the
allowed spaces are less than the number needed for a uniform distribution so that
(spaces * dx < thickness of layer) where dx in the nominal grid spacing required at
xdx. Fig 2-2 arises when the number of spaces allowed is greater than that required
for uniform distribution of grids. In this case (spaces * dx > thickness of layer).
grid
SDacing
D:
D
DX2
x
YVIY
rurrk'NES
Figure 2-2: Spaces greater than number required for uniform distribution
2.3
Diffusion Modelling in SUPREM-III
Of the physical processes modelled by SUPREM-III, high temperature impurity redistribution is most sensitive to grid spacings. It is therefore necessary to review
the nature of the diffusive fluxes as modelled by SUPREM-III in order to determine
the appropriate grid structure for SOI simulation. A complete analysis of the diffusive fluxes can be found in [7]. Impurity redistribution during thermal processing is
governed by the following continuity equation:
-i
CdV =
(g - l)dV -
F.ndS
where
C =the impurity concentration(atoms per unit volume),
S(t) =closed surface area at time t,
V(t) = Volume enclosed by S(t),
F =impurity flux vector,
n =outward unit normal to S(t),
g =impurity generation rate per unit volume, and
l=impurity loss rate per unit volume.
(2.1)
If we consider a 1-D system in direction x perpendicular to the simulation structure
and we assume (g-l)=0, Equation 2.1 may be written as:
Q(x1,2)
[F( 2) - F(xi)]
(2.2)
C(x)dx.
(2.3)
where
Q(x 1 ,x 2 ) =
1
The flux is considered positive in the x direction. Diffusive flux, FD, at any depth x
is given by Fick's first law which assumes the general form:
FD(X) = -fE(C)D(C) c
(2.4)
D(C) is the concentration dependent diffusivity and fE is an electric field enhancement
factor due to the electric field arising from ionized impurities.
At static material
interfaces, Equation 2.1 is replaced by
F,= h (C,-
C2
(2.5)
where F, is defined positive from region 1 to 2. C, and C2 are the interface concentrations in region 1 and 2 respectively; meq,1-2 is the equilibrium segregation of the
diffusing species in the two regions and is defined by:
meq,1-2 =
(\(C21
)
(2.6)
equilibrium
and h is the surface mass transfer coefficient which has units of velocity. For a moving
boundary another impurity flux Fb arises. For oxidation, it is given by:
Fb = -voX(C
1
- cC 2 )
(2.7)
where vox is the oxide growth rate and a is the ratio of oxidized silicon to resulting
oxide thickness (0.44).
2.3.1
Numerical implementation of impurity Redistribution
The division of the process structure into discrete cells facilitates the solution of the
continuity equation ( 2.2). The impurity concentration C(x) is evaluated at nodes
lying in the middle of of each cell. Fig 2-3 illustrates the space reader . For any cell
i not at any boundary, the continuity equation becomes
d
Qi = -[FD(xi+/ 2 ) - FD(xT~1/2)]
(2.8)
and FD is evaluated at the cell boundary using Equation ( 2.4) while Qi is given by:
Qi=
(2.9)
-1/2Cidx.
i- 1/2
The spatial derivative in Equation ( 2.4) and the integration in Equation ( 2.9) are
approximated by difference equations and midpoint integrations respectively. FD is
therefore given by
FD(Xi+1/2 ) = -fE(Ci+1/ 2 )D(Ci+1/2 ) Ci+1
Xi+I -
Xi
(2.10)
where i = 1,2,..., (n - 1) and Ci+1/2 = (C 1, + Ci)/2. n is the number of discrete
cells. Similarly, Qi is given by:
- x+
2
Qi = Ci
(2.11)
where i is not an interface node. The general continuity equation has to be modified
for cells at the boundaries. For the first cell it is given by:
d
dtQi = -[FD(Xl+l/ 2) - F,(0)]
where F,(0) is the interface flux as given by Equation ( 2.5)
Q1
= C1
2
-(2.13)
2
(2.12)
GAS
Figure 2-3: Space Discretization
while for the last cell it becomes:
d
-Qn
dt
= FD(Xn•
Qn -
Cmn I
1/2)
(2.14)
where
n
(2.15)
-- Xn-1
For an interior boundary located at node I and separating regions 1
and 2, there are
two corresponding continuity equations given by:
d
(XI-1/2) ]
(2.16)
d QI,2 = -[FD(+1 /2) - F,
(2.17)
d
where Q1,1 and QI,2 are given by:
QI,i
QI, 2
S I1 - XI-1
2
CI+1 -
CI,2
2
IT
(2.18)
(2.19)
All these continuity equations are of the form
Hi(t) = dQ
where the left hand side represents the flux difference.
(2.20)
In SUPREM-III they are
solved by time discretization. If the concentration is known at time to and the fluxes
are assumed constant for the time interval tl - to, the concentration at time ti is
given by solving the following equation:
Hi(t1 )=
[Qi(tl) - Qi(to)]
tl - to
(2.21)
(2.21)
There are as many equations of this form as there are cells. The flux function Hi
is evaluated at a future time t, thus it helps to couple the concentrations of the
adjacent cell at t 1 . The resulting equations are solved by Gaussian elimination for
small simulated time increments.
If the system is nonlinear due to concentration
dependence of diffusivity then Newton-Raphson iterations are used till convergence
(of concentrations) is attained.
The situation is very complex for an oxidizing interface. The details are provided
in [7]. It should be mentioned that in this case one has to deal with at least three
fluxes, namely, FD, Fs and Fb. The non unity volumetric ratio of silicon dioxide and
silicon also imposes time discretization conditions which do not arise when a static
boundary is involved.
The main point behind this discussion is to identify the areas where it is mandatory
to have very dense grids. From the description of the nature of fluxes it should be clear
that boundary conditions are areas of high profile variation thus they should always
have dense grids. Confirmation of this observation is dramatically demonstrated in
Fig 2-5 which shows plots of the retained dose vs the thickness of the SOI silicon
film. The plots are generated by running the SUPREM-III NMOS process file shown
in Appendix A. The silicon film is deposited and subsequently thinned to the required
thickness then implanted with BF 2 through a sacrificial oxide of 53A. The sacrificial
oxide is then etched away and the gate oxide grown. The noisy plots results when no
special care is taken to ensure that the grids at the interfaces is sufficiently dense.
2.4
Grid Refinement for SOI simulation
As was shown at the beginning of this chapter, SUPREM-III provides a way of varying
grid spacing at any depth of any layer. However the grids may only be set at one
point. This is inadequate for SOI simulations since dense grids are required at both
the back gate interface and the front gate interface. To alleviate this problem, I have
developed and implemented an algorithm which allows for the simultaneous setting
of grid spacing at the two edges of a layer.
For simplicity we will assume that the number of allowed spaces is even. The
algorithm is as follows:
Define the following variables:
n = Number of spaces allovwed for the layer
t 2
m
n
t_ = Thickness of the laver
dz =Required nominal spacing at either side of the layer
'2
SF2, Energy = 30 keV, Dose = 3e12
x 10
1.9 -
1.8
E1.7 -
,1.6 -
-o
1.5 1.4-
1.3
1.2
1.1
200
400
600
1000
1200
800
Film Thickness /Angstroms
1400
1600
1800
Figure 2-5: Silicon Film Retained Dose vs Film Thickness
x[] = Array of spacings for this layer
set
for i = 1 to m
do
z = (1- d)(2i - 1)t 2 + d t
x[i] = z *
x[2m - i + 1] = z *
w-
end
Fig 2-6 shows a demonstration of this algorithm for various choices of dx. Since
the grid spacing increases (or decreases) linearly from either edge of the layer, it is
possible to calculate a negative value of grid spacing. This occurs when the number of
spaces is too large for the given layer thickness. Whenever this happens SUPREM-III
exit with an error message. Calculation of a negative grid spacing is a consequent of
the requirement that the grid spacings vary linearly from the nominal grid spacing.
Thus, the original algorithm in SUPREM-III often results is the same error since it
also generates spacings with linear variations.
Spaces = 100, Thickness = 500 Angstroms
E
o
C:
Cn
g
c
a
30
Depth from top of Layer /Angstroms
Figure 2-6: Grid spacing, dx, vs Depth from top of Layer
Chapter 3
Ion Implantation and Diffusion in
SOI structures
3.1
Ion Implantation
Ion implantation, the process of introducing impurity atoms into a substrate by ion
bombardment. is currently a standard process in VLSI processing. This is mainly
because the amount and location of the introduced species can be determined with
a higher degree of accuracy than is possible by other methods such as diffusion from
a surface source. Physical modelling of the process has undergone tremendous improvement since the early 1960s when it was first used in device processing and very
accurate profile models can now be realized. The first successful model was developed in 1963 by Lindhard, Scharff and Schiot (LSS) for implantation into amorphous
targets [13]. For a one dimensional system, the resulting profile is Gaussian and the
concentration at depth x is given by
n(x) = n(Rp)exp
-(
)2
(3.1)
where the maximum concentration occurs at x = Rp (the range) and ARp is the
standard deviation or straggle of the distribution. The peak concentration is given
0.4¢
S
n(R,) =
(3.2)
where 0 is the dose or total number of ions implanted per unit area so that
(3.3)
n(x)dx.
S=
ARp and R, are evaluated from the theory due to LSS [13]. This model is found to be
inadequate when compared with experimental profiles for most impurities implanted
into amorphous targets. Experimental profiles are found to be skewed and not completely Gaussian. If the skewness is not excessive an additional third moment may
be used to model such profiles [12]. In this case the profile is modelled by two-half
Gaussians. The resulting concentration is given by
n(x) = i
,X exp
+ARp)
\/7(A/R1
2q
n(x) =
2 )ep
>
2AR
-(x -
~Rm)2
X
Rm
(3.4)
Rm
(3.5)
and ARp, and ARp2 are the straggles for the two Gaussians. The joining range, R.,,.
is given by
Rm = Rp - 0.8(ARpN
- ARp2).
(3.6)
The values of ARp and ARp2 are tabulated in [12]. The joined Gaussian has been
found to model Phosphorus and Arsenic implants into amorphous silicon.
For boron implants, it was found that a Pearson IV distribution produces excellent
agreement with experimental results [10]. Later work showed that the distribution
could also model other species. A Pearson distribution function is described by four
moments, namely, range, Rp, straggle, o, skewness, y, and kurtosis, P. Qualitatively,
skewness measures the asymmetry of the distribution-positive skewness places the
peak of the distribution closer to the surface than R,. Kurtosis measures how flat
the top of the distribution is. If the kurtosis is not known it may be approximated
by [18]
S- 2.8 + 2.4y2 .
(3.7)
A Pearsop distribution is defined by the differential equation [18]
df(y)
(y- a)f(y)
dy
bo + ay + b2y 2
(3.8)
where
y = x-Rp
a·- = -Y(.
+ 3)
- 3/ 2)
_ 2(4
b2
-
A
=
(3.9)
(3.10)
-20 + 372 + 6
A
100 - 127/2-
18.
(3.11)
(3.12)
(3.13)
A Pearson IV distribution result when the value of d, given by
d = a2 - 4bob 2 ,
(3.14)
is negative. The distribution decays smoothly to zero on either side of a single maximum at y = a. f(x) is a normalized distribution function such that
S+00
f(x)dx = 1.
(3.15)
-00
The moments are defined as follows:
~+00
Rp
=
/0
+-00
xf(x)dx
(3.16)
Rp) 2 h(x)dx
(3.17)
Jfc (x - Rp) h(x)dx
(3.18)
_OO (x -
S3
fi
(x - Rp)4h(x)dx
(3.19)
E
E
O
2CI
4-z
0
U
DEPTH (,um)
Figure 3-1: Boron implanted atom distributions, comparing measured data points
with four-moment (Pearson IV) and Gaussian fitted distributions. The boron was
implanted into amorphous silicon without annealing.
Fig 3-1 shows how good Pearson IV distribution fits experimental profile of boron
implant into amorphous silicon.
The above models are only appropriate for implant into a single layer of amorphous
targets. For multiple layers or implants into crystalline targets, the models have to
be modified or new ones used. For implants into single crystalline silicon the wafer
is normally tilted at 70 in which case the lattice presents a dense orientation to the
incident ion beam. This reduces but does not eliminate channeling which occurs
when the implant ions redirect themselves such that they follow a lattice channel or
direction with no target atoms on the ions' paths. Implants into crystalline silicon
can be modelled using Pearson IV distributions with an added exponential tail to
account for channelling. It has been empirically found that the tail should be added
at a fixed characteristic length (0.045p/m) which is independent of energy and surface
orientation [5]. The tail is appended to the shoulder of the distribution where the
concentration has decreased to 50% of the peak value.
Fig
3-2 shows how the
inclusion of the exponential tail results in close modelling of boron implant profiles
C,
EE
U
C
0
U
C
U0
Depth, pm
Figure 3-2: Experimental profiles of boron implanted into < 111 > (closed circles) and
< 100 > (open circles) silicon. The solid lines represent the Pearson IV distribution
and the dashed lines the exponential tail.
into crystalline silicon.
3.1.1
Implant Models Applicable for SOI
Implant into crystalline silicon is invariably done through a sacrificial oxide thus
practical implantation normally involves more than one layer. An SOI structure is,
of course, multi-layered hence the above models are not sufficient. For implants into
single crystal silicon through a sacrificial oxide, implant models into single crystal
silicon may be used with minor modification provided the sacrificial oxide is not very
thick [5]. However, accurate evaluation of impurity profiles in multi-layered structures
requires either the numerical solution of the Boltzmann transport equation (BTE) or
Monte Carlo simulation. BTE is limited since it can only be used for amorphous
layers so we need not consider it any further. In Monte Carlo simulation, the history
of an energetic ion is followed as the ion goes through successive collisions with target
atoms. Binary collision of the ion and target atom is assumed. Calculation of each
trajectory begins with a given energy, position, and direction. A large number of ion
trajectories are calculated and the depth at which each ion stops is determined. The
predicted profile is generated by plotting histograms of the number of ions stopped
within a depth interval. For an amorphous material, the position of the target atoms
follows a Poisson distribution while in crystalline materials.
The atom positions
are specified to correspond to positions that they would assume on a lattice [19].
Monte Carlo simulation is extremely time consuming and thus hardly applicable in
the simulation of actual integrated circuits (IC) processing. It is however very valuable
in some applications as it provides knowledge of distribution of recoil atoms such as O
from SiO 2 . Recoil atoms are often involved in unwanted device effects like excessive
junction leakage thus knowing their resulting distribution is important [5].
Dual-Pearson Model
The main shortcoming of the traditional implant models (excluding Monte Carlo) is
that they include only explicit dependence on energy. No explicit dependence on other
parameters such as dose, tilt and rotation angles, and mask thickness are included.
Research at the University of Texas at Austin (UT) has adequately addressed these
shortcomings [1]. Implant into single crystal silicon can be divided into channelled
and non-channelled components. The approach taken by UT is to model each of these
components by separate Pearson IV distribution functions. The resulting model is
called Dual-Pearson and is thus described by eight moments, four moments for each
component. Fig 3-3 shows a typical separation of an implant profile into channelled
and non-channelled components. Currently UT has developed Double-Pearson models
for Boron, BF 2 and Arsenic implant into crystalline silicon. The model explicitly
accounts for sacrificial oxide (mask) thickness of up to 500A apart from including
explicit dependence on implant dose, energy and tilt and rotation angles.
Dual-Pearson is a semi-empirical model and the moments are extracted from actual experimental profiles. To provide a physical understanding of the semi-empirical
model, UT has used a modified version of MARLOWE (UT-MARLOWE), a Monte
Carlo simulator developed at Oak Ridge National Laboratories. In this way, the benefits of Monte Carlo are used to generate models which are less time intensive. In
1018
E
1017
U
a
a
oa
ob
o
10o
Q..•
Depth (-M.n)
Figure 3-3: Boron profile separation for channelled and none channelled components
some cases where experimental data was not available, UT-MARLOWE was used to
generate the moments.
I have implemented the Dual-Pearson model in the M.I.T version of SUPREM
III. The model has also been implemented in most other versions of SUPPREM III
including a commercial one from Technology Modelling Associates (TMA).
SOI Application
Dual-Pearson model should be adequate for low energy implant into thick film SOI
structures. For implant into thin film SOI, the model is not applicable. This is a
serious concern since for practical applications SOI films are very thin. New models
must be developed for this case. It should be noted that the Monte Carlo simulation
can still be used for any SOI film thickness.
To help understand the effect of the buried oxide on the implant profile for an SOI
structure, we asked Prof. Al Tasch of UT to kindly use UT-MARLOWE to model
BF2 implant into an SOI structure. Fig 3-4 shows the resulting profiles. As can be
seen from the plot, the buried oxide almost eliminates the channelled components as
1e-
8f2 - 30keV, 3e12, 7/25, nodamage
II
1e-
le-
le-
1÷e-
0
0.05
0.1
0.15
0.2
Figure 3-4: BF2 Implant into an SOI structure
0.25
0.3
would be expected but it does not drastically affect the impurity distribution in the
silicon film if one compares the resulting profile to that of bulk silicon without the
buried oxide. This is an important result as it shows that the buried oxide does not
reflect the ions back into the silicon film away from the buried interface. This means
that modification of the Dual-Pearson distribution for SOI structure should be quite
simple since the fraction of the implant dose that results in the silicon film can be
determined independent of the buried oxide. One can just assume an implant into
bulk substrate then consider the implant that end up in the section corresponding to
the film thickness. Modelling of the implant into the buried oxide can then be done
by considering an appropriately scaled energy (to account for energy loss in the film)
and then using the fractional dose that was not included in the film.
3.2
Diffusion
The goal of this section is to develop an understanding of the effects of the buried
oxide on impurity diffusion in thin film SOI structures.
The development begins
with a review of Fick's continuum theory of diffusion followed by a presentation of
currently accepted atomistic diffusion models. The atomistic models are then used
to elucidate on the effects of the SOI buried oxide on impurity diffusion.
3.2.1
Fick's Model of Diffusion
Solid state diffusion is a thermally activated process by which a species moves as a
result of the presence of a chemical gradient. In modern VLSI processing, the chemical
gradient invariably results from doping via ion implantation of an impurity species
into silicon. Depending on the impurity concentrations and processing temperature,
immobile precipitates or clusters of impurities form and this fraction must be excluded
from the diffusion equation presented below. Clustering is a thermally controlled
kinetic process which is very well understood [5].
For the mobile fraction of any impurity, the concentration over time and space is
described by the general continuity equation which is presented in integral form as
di(t)CAdV =
J
(g- )dV -
J ndS
(3.20)
where CA is the mobile impurity concentration in atoms per unit volume, t the time,
S(t) the closed surface area as a function of time, V(t) the volume enclosed by S(t), J
the impurity flux vector, n the outward unit normal to S(t), g the impurity generation
rate per unit volume, and 1 is the impurity loss rate per unit volume.
The diffusive flux J and the concentration gradient CA are further related by
Fick's first law of diffusion
J = -DAVCA
(3.21)
where DA is the diffusion coefficient or diffusivity. These two equations form the
foundation of all diffusive analyses.
Rewriting Equation ( 3.20) in differential form and ignoring the generation-loss
term then using Equation ( 3.20) results in Fick's second law,
CA = DA V 2CA,
at
(3.22)
in the limit of constant diffusion coefficient.
Fick's second law is generally adequate in evaluating diffusive migration under
low impurity concentrations. The limit of application is the intrinsic semiconductor
carrier concentration ni(T) where T is the processing temperature. Morin and Moita
[5] give an empirical expression for ni(T) as:
ni(T) = 3.87 * 1016T 3 / 2 exp[-(.605 + .5AE)/kT]
(3.23)
where AE = 7.1 * 10- 10 (ni/T)1/ 2 . A plot of this expression is shown if Fig 3-5. From
the plot it should be clear that the application of Fick's second law is not that limited
since doping levels are rarely higher than intrinsic concentrations at typical processing
temperatures. Silicon with an impurity concentration lower than the intrinsic carrier
concentration (at the processing temperature) is known as intrinsic silicon. If the
-opposite is true then the silicon is referred to as extrinsic.
n
E
Y
c
o
c
o
o
c
o
u
L
.r
t
lo
o
.u
c
900
1000
1 00
1200
Temperature ("C)
Figure 3-5: Silicon Intrinsic Carrier Concentration as a Function of Temperature
For extrinsic silicon, Fick's law first law can still be used with concentration dependent diffusivities. To understand the nature of the resulting formulation of concentration dependent diffusivities, examination of atomistic models of diffusion in
necessary.
3.2.2
Atomistic models of Diffusion in Silicon
Most common substitutional impurities in silicon are currently believed to diffuse
by interacting with silicon point defects like vacancies and interstitials generated in
single-crystal silicon at high temperatures. Fig 3-6 shows the two most dominant
models of atomistic diffusion for a two dimensional lattice. Fig 3-6a is the vacancy
model where an impurity atom moves to occupy a vacancy in the silicon lattice while
Fig 3-6b is a display of the interstitialcy model where the diffusing atoms move by
pushing one of its nearest substitutional neighbours into and adjacent interstitial site.
DIFFUSION 171
"---
.-- TRACER ATOM
- -
0M
HOST ATOM
C
-7
0
0
0
0 0 -
C
0
0
(a)
0
0O
0
(b)
0
0
I
I
0
(c)
_T
a-
(d)
Figure 3-6: Vacancy and Interstitial Diffusion models.
In the diffusion model formulation, the vacancies are believed to be charged although no charge states have been identified with self-interstitials at present [5]. The
effect of the point defects is incorporated in the diffusion model by setting the diffusion coefficient to be proportional to concentration of the point defects. The point
defects concentration is affected by processing condition in two basic categories: quasiequilibrium conditions in which the relative population of defects depend on the local
Fermi level in the band gap which intern depend on the doping level when it exceeds
ni; and non-equilibrium conditions in which point defects are generated by the process itself, for example during oxidation, which generates self interstitials, or during
annealing subsequent to in implantation which generates both vacancies and interstitials. The diffusion coefficient when all charged impurities is included is given by
[5]:
DA = D2 + E DcN + ADA
(3.24)
The first two terms of the above equation correspond to the quasi-equilibrium condi-
tions while the last term is a contribution of the non-equilibrium conditions. The first
term, D', is the diffusivity due to the neutral point defects while D' is the diffusivity
of charge state c of impurity defects and Nc is the sum of concentration of vacancies in each charge state normalized to the intrinsic concentration. The normalized
concentration of charged point defects is given by [5]
N = (n/ni)j
(3.25)
where j, = ±1,±2, ... , for acceptor(+) and donor(-) states.
Under intrinsic and quasi-equilibrium conditions the above equation reduces to
D* = Dx + E De
(3.26)
where the asterisk is used to denote that the diffusivity is for quasi-equilibrium case.
This is the situation in which Fick's law is completely applicable. In order to incorporate the non-equilibrium contribution term in Equation ( 3.26) another diffusion
model is presented in the following section.
3.2.3
Non-equilibrium Diffusion
Oxidation has been found to enhance the diffusivity of boron, phosphorus and arsenic [3] while reduced diffusivity has been observed for antimony. According to a
model proposed by Hu [11] and qualified by Antoniadis et al. [3], the phenomena
of oxidation enhanced diffusion(OED) and oxidation-reduced diffusion(ORD), are attributed to the enhancement of silicon self interstitial point defects due to oxidation.
This model invokes a dual diffusion mechanism for impurities via vacancy and interstitialcy mechanisms. According to this model, during oxidation, the interstitialcy
component of diffusivity in enhanced leading to OED while a reduced concentration
of vacancies due to recombination with self interstitials leads to ORD. The situation
after ion implantation (ie during anneal) is similar except that both vacancies and
interstitials are above the equilibrium level thus high diffusivities should be observed
for all the three main impurities mentioned above.
For intrinsic conditions, the model results in the following expression for diffusivity
[5]:
DA- = DI(L
) +D
(3.27)
where D) and DV, are the interstitialcy and vacancy motivated equilibrium diffusivities of the impurity. C, and Cv are the self-interstitial and vacancy concentration
while C7 and C* are the corresponding equilibrium concentrations. The fractional
interstitialcy component is given by
f = D*Al/D
(3.28)
D*A = Dw + D*AV
(3.29)
where
The change in diffusivity over the equilibrium value is given by
A\DA = D (fCI- Cr
.C7
+
(1 - f
- C)
C(3.30)
CI
The application of this equation is very straight forward in case of non-equilibrium
situations arising from ion implantation. In that case, the concentration of interstitials
and vacancies can be easily approximated and Equation ( 3.30) used to determine the
enhancement of diffusivity. It should be pointed out that in this case diffusivity will be
time dependent because the vacancies and interstitials combine and no regeneration
occurs.
The case of surface oxidation is more complicated.
The rate of generation of
interstitials at an oxidizing interface depends on many factors including surface crystal
orientation and oxidation conditions. A detailed surface generation rate formulation
is presented in the next section but for illustrative purposes we will use the generation
rate from [3] which relates the excess interstitials to the surface oxidation rate by
CI - C = KX
•
(3.31)
where is X is the oxide growth rate and K 1 is a reaction constant.
The power
exponent n is fitted accordingly to account for the detailed defect generation process
at the interface.
In order to demonstrate the change in diffusivity resulting from
oxidation, a irelation between vacancies and interstitials is required. Hu [11] presents
a detailed analysis of these parameters but for this section an approximation based
on mass action law will suffice. This yields
Cv/C* = C*/C1
(3.32)
From Equation ( 3.30) it is possible to determine whether oxidation will enhance or
retard diffusion of a particular species. fi, K, and CI must be fitted from OED/ORD
and OSF(oxidation stacking fault) data at the relevant temperature.
The preceding analysis has not considered enhancement in the extrinsic case because the detailed charge contribution to interstitial diffusivity is not well understood.
The above modification can however still be used for extrinsic case because the error
is likely to be small. In any case, as mentioned earlier, the intrinsic concentration
is very high at typical processing temperatures to allow for modelling of practical
impurity concentrations.
In the extrinsic case, another modification needs to be made to the diffusivity to
account for electric field effects. At the processing temperature the impurities are
ionized and the resulting field acts to enhance the motion of the ions. The effective
diffusivity is then given by
Deff = DA(1 ± d
(3.33)
where the plus sign should be used for acceptor atoms and minus sign for donor
atoms. n is the electron concentration given by
n = (N + (N 2 + 4n') 1/ 2 )/2
(3.34)
and N is the net donor concentration at the processing temperature which is given
by the difference between the total ionized donor and acceptor atom concentrations.
The enhancement factor, (1 ± •), has a maximum value of 2.
The diffusive mechanism for most common impurities are now well established.
Phosphorus, boron and arsenic are known to diffuse mainly via interstitial mechanisms
while antimdny diffuses mainly via vacancies. With this knowledge we are prepared
to understand the effect of the buried oxide on diffusivity of these impurities.
3.2.4
Effect of the buried Oxide on Impurity Diffusion
The introduction of a buried oxide layer in SOI structures creates complications in
the modelling of diffusion. From the discussion in the previous section, it should
be clear that the effect of the buried oxide on diffusivity is completely determined
if its effect on interstitial and vacancy migration can be established. In the absence
of the buried oxide, interstitials can readily diffuse from an oxidizing surface where
where they are generated to the substrate. Even in the case of ion implantation, the
resulting vacancies and interstitials generated close to the surface(assuming implantation is close to the surface) can likewise diffuse into the substrate. In this section
surface generation of interstitials will be considered since an extension to include ion
implantation should be straight forward.
The effect of the buried oxide on diffusivity depends on how it modulates the flux
of interstitials at its boundary with the silicon film. The weaker this interface is in
trapping interstitials relative to diffusion in the bulk, the higher the supersaturation
level of interstitials in the film and vice versa. The diffusivity of impurities will
depend on the levels of supersaturation in case of impurities with major interstitial
contribution to diffusivity.
Interstitial recombination or generation rate at oxide boundaries is still an area
of active research. In this section I will present what I believe are the most plausible
models from current literature. The utility of a model is measured by its ability to
explain a wide range of experimental observations and to make valid predictions. In
this respect, the model proposed by Dunham [8] seems most plausible. According to
this model, during oxidation, the oxide acts as the dominant sink for the interstitials
generated at the oxidizing interface. The model therefore invokes segregation and
diffusion of interstitials in silicon and silicon dioxide with preferential segregation
into the oxide. The diffusivity of interstitials is very low but as Dunham explains,
the preferential segregation into the oxide and the fact that interstitials react with
oxidizing species in the oxide results in a very high interstitials gradient in the oxide
such that the interstitial flux into the oxide remains very high. The conclusion that
the oxide is the dominant sink for interstitials is based on experimental observation
that point defect concentrations near an oxidizing interface are not influenced by the
presence of additional sources or sinks of point defects in silicon. This model also leads
to the conclusion that the surface re-growth rate of interstitials near the interface is
negligible.
Using this model, Dunham arrives at two models for interstitial injection rate
into the silicon substrate which depends on the oxidizing conditions. For steam (wet
oxidation) he obtains
C(0O)
C7
_
Ksteam(dxo)1/2
(3.35)
dt
while for dry oxidation he obtains
C,(O)
_
C7
Khdy(dxo/dt)
(72 + dxo/dt)1 / 2 -
(3.36)
7
where Ktseam and Ka,, are reaction constants which include the segregation factor,
dxo/dt is the oxide growth rate and
77= (-/2)(B/A)
2
(3.37)
where B/A is the Grove-Deal linear oxidation growth rate for Dry oxidation and y
is a factor which accounts for the fraction of 02 molecules which breaks up into O
atomic species. This factor can be evaluated from oxidation kinetics.
These expressions may be contrasted with Equation ( 3.31) which can be rewritten
as
C= 1 + K(d
Cfi
)"
(3.38)
dt
which originated from the fits to experimental data obtained from stacking fault
growth experiments. Equation ( 3.38) does not distinguish between the oxidation
process and n is chosen to fit the experimental data but there is no conclusive physical
explanation of its origin. In view of this and the ability of Dunham's model in fitting
a wide range'of experimental data, it is clear that Dunham's model in most plausible.
In this section the goal is to study the effect of the buried oxide but it is clear that
the proper model for interstitial injection at the oxidizing interface is fundamental to
the understanding of the effects of the inert buried interface. Furthermore, the treatment of the oxidizing surface can be modified to model the inert interface. Dunham
has successfully employed this model to explain phosphorus diffusion retardation in
argon in which depletion of a pre-grown oxide is observed [8]. With a little modification, this model could be used for buried oxide in SOI. Current models assume that
the flux of interstitials from the oxidizing surface are balanced by recombination at
the inert oxide interface which leads to surface regrowth. The effect of the buried
oxide is therefore characterized by a constant surface recombination velocity U, such
that
DsA\C, = r[C, - C'0]
(3.39)
where Dj's is the diffusivity of interstitials in silicon. This should be modified to
incorporate the segregation of interstitials into the oxide and subsequent diffusion in
the buried oxide by adding the term
DIsiO2ACSiO2
(3.40)
to the right hand side. An effective recombination velocity which is time dependent
could be used to take care of the segregation term.
It has been observed by Ahn,et al. [2] that silicon interstitial in the oxide react to
form SiO which then becomes the diffusive species. More work needs to be done to
determine the fraction of interstitials which undergo this reaction. This should then
lead to a reformulation of the above equation. The nature of ao is also still not very
well understood. The segregation term should explain why most workers have consistently found different recombination velocities since this term clearly depends on the
experimental conditions. Assuming, like before, that there is preferential segregation
into the oxide, a thinner oxide should result in a higher effective recombination velocity. For thick oxides, the effective recombination velocity in steady state should be
low because ihe diffusivity of Si and SiO in SiO 2 is much lower than Si(interstitial)
diffusivity in silicon. Indeed in this case Equation ( 3.40 needs no modification.
For low temperatures and thick oxides, the effectiveness of the buried oxide in
removing interstitials from the silicon film will depend on a, in Equation ( 3.40).
For the temperature range of 750°C and 8500, extracted and effective recombination
velocity such that [6]
ar/DI = 4.7 * 10 3 exp(+1.34/kT).
(3.41)
At these temperatures, the interface acts as a better sink than bulk thus the supersaturation level of interstitials decreased. From this work it could be concluded that
at higher temperatures there would be increased interstitial supersaturation in the
film.
From the above, it should be clear that it is not possible to emerge with a general
rule on the effect of the buried oxide as a trap for interstitials, and that more work
need to be done to understand the effect of the oxide. Experiments involving varying
buried oxide thicknesses should be adequate to ascertain the need for inclusion of the
segregation term. Work also needs to be done to determine the nature of arI
3.2.5
Interstitial Vacancy Supersaturation Level
Correct implementation of diffusion of the impurities depend on the right relationship
of interstitials and vacancies in supersaturation. Currently the approximation used is
CICv = C7C*
(3.42)
but it is not correct as Hu [11] explains. At an oxidizing interface,
CICv > C7C .
(3.43)
To model oxidation retarded diffusion of antimony this the correction relation must
be used and the reader is referred to [11] for further information.
3.2.6
Experimental Verification of the Effect of the buried
Oxide
Pending the resolution of the above problem, one can experimentally determine the
relative effect of the buried oxide on the interstitial supersaturation level in the silicon film. If the interface interstitial recombination velocity is infinite, diffusion in the
film can be conveniently modelled by switching off the enhanced component. This
is an extreme case but it establishes the lowest bound of impurity diffusivity. An
approximate upper bound can be obtained by assuming the burried oxide interface
is as effective as bulk silicon in removing self interstitials. For this case the normal
bulk diffusion enhancement is employed. It should be noted that the case where the
interstitial supersaturation level is higher than in bulk systems is ignored since experiments have not supported it. Sherony [16] has used the normal enhanced diffusion
mode and found that the simulated threshold voltages are comparable to that obtained from experimental wafers. From this one may conclude that the effect of the
buried oxide is not as important as might have been expected.
Chapter 4
Process Flow Design of a Fully
Depleted SOI NMOSFET
4.1
Problem Statement
Given a nominal threshold voltage,
rTo, a silicon film of thickness, tji, and associated
error, At,., design a fully depleted SOI NMOSFET by selecting channel implant
energy and dose that minimizes the threshold voltage variation. AVTo
and Atj are
constants independent of VTO and ti respectively. The implant is done through a
sacrificial oxide of thickness t,, and associated error At,,.
4.2
Threshold Voltage Expression
Central to this design is the expression for threshold voltage of a fully depleted SOI
NMOSFET. For the case of a uniformly doped film, Lim and Fossum [9] derived
expressions for the front and back gate voltages, VGf and VGf, as follows:
VG
f
VFB+
V,
C
si
Wes
1+
Ox
Ci
2
Cbox
-(
1/ 2 Qd + Qfinv1)
Cbox
4 .1)
where ',1
and
'is2
are the surface potentials at the front and back oxide interfaces
respectively; V~/B and VfB are the front and back gate flat band voltages; Qfin, and
Qbinv are the front and back gate inversion charges; Cf,, and Cbo, are the front and
back gate oxide capacitances; C,j is the silicon-film capacitance, Csb is the substrate
capacitance and Qd is the depletion charge in the silicon film. From these expressions,
three threshold voltage expressions corresponding to whether the back gate surface
is in accumulation, inversion or depletion can be written, namely:
A
VTA
-= V/,f
+
VW
=
V,
+
V7 D
=
1+
2((BQ3
Qd(4.3)
fo
ffox
2
DB
Qd
(4.4)
CsiCbox
A
Cfoz(Csi + Cbo + Csb) (VGb
Gb
(4
where
DB
(4.6)
= kT In (NA\
q
n.
and T is the temperature, k is the Boltzmann constant, q is the electronic charge, AA
is the silicon film doping while ni is the intrinsic electron concentration. VGAB is the
back gate potential when the back interface is in accumulation and is given by:
B = V
C 2B
Cbox
2 Qd
Cbox
(4.7)
In this study, only the condition where the back interface is depleted is examined. It
is further assumed that the back gate is at VFB so that the silicon film is depleted
due to the front gate bias, and Ci > Cbox + Csb, which is true for practical device
technologies. For this condition, the threshold voltage is given by:
D
Y
f -
V
FB
+2 2
Qep
fox
(4.8)
If the approximations are not justified Equation ( 4.5) can be used where VGB = V1B.
In this case, the threshold voltage would be given by:
Df
VTf
F
+2
FB +
+
+
1
CSi
C
Csi + CboX
depl
2Co
Csi + Cbox ,
(4.9)
where Csb is still considered insignificant. This expression reduces to Equation ( 4.8)
when C,i > Cbox.
To derive an expression valid for nonuniform doping profiles, Equation ( 4.8) is
modified. Firstly, V,/, is replaced by VR, which is given by:
f
O(4.10)
VR = Cms
Cf ox
where
(ams= ýmsi + - In
q
NA (tsi)
.
(4.11)
VNA(t~.) is the dopant concentration at the edge of depletion, which is the concentration
at the buried oxide interface, Qfo is the front gate oxide interface charge and Dmsi
is the metal(poly) intrinsic silicon work function difference. 2?B(surface potential at
inversion) is written as:
TS = 2( =
kT
I
yIn
ANA (tsi)
2
(4.12)
where
=
-NA
NA(x)dx
tsi
(4.13)
Antoniadis [4] has successfully used Equations ( 4.10) and ( 4.12 to evaluate threshold
voltages for nonuniformly-doped bulk MOSFETS. It should be noted that 24sB is just
a convenient criteria for surface inversion. We could also use a constant inversion
charge criteria but this value is found to be arbitrary and thus inappropriate for
design. The threshold voltage for a fully-depleted SOI structure with nonuniform
profile is therefore given by:
VTi VR+
V =v+ +
C( )
Csi + CboX
Qdeppt
2Cfoz
1+
C,
Csib)
(4.14)
Csi + Cbox
If the silicon film is fully-depleted, the depletion charge is:
Qdepl
(4.15)
NA(x)dx = qDj
= q
where D, is integrated dopant (or the retained dose).
Full depletion is attained
whenever ts is less Xd the maxim depletion given by
2=esiJs
Xd
qI\A
(4.16)
For a fully depleted SOI NMOSFET, the threshold voltage does not explicitly depend
on the centroid of the dopant profile in the silicon film. This is because at inversion
the surface potential I, is a constant independent of the charge centroid. The surface
potential is composed of a voltage drop across the silicon film and the buried oxide.
The maximum potential drop across the oxide is given by:
Vfilm =
q
f
A (ti
xNA(x)dx
(4.17)
si 0
which is less than the required inversion potential except when t,i = Xd. However,
the centroid of the profile, xc, given by:
S=
fs"i NA(x)dx
(4.18)
will be useful in analyzing the effect of implant energy on the retained dose.
4.3
Design
The process design uses suprem3 and a complete NMOS process file is given in Appendix A. This is the file which will be modified to reflect all changes in the device
structure and process conditions. The SOI film is obtained by thinning of an epitaxially grown silicon layer by oxidation. Silicon film thickness variation if therefore
accomplished by varying the thickness of the original epitaxial layer while maintaining
the thinning oxidizing conditions. The sacrificial oxide thickness variation is accomplished by etching or deposition of oxide after the growth of the nominal thickness.
This is accompanied by deposition or etching of the silicon film. For example, increase
in the sacrificial oxide by an additional 20Aconsumes 0.44*20Aof the silicon film. As
a result the film thickness must be reduced by this amount before the implant step
occurs.
4.3.1
Design Space for Energy and Dose
From Equation ( 4.14) threshold voltage is linear in retained dose since
VR
have relatively low variation. With the given definition of V• and J,, if Ci
and Ts
>
Cbox,
threshold voltage is given by:
VT = ,Omsi+-
d
N "AT
A
+
q i
ni
Cfox
n
(4.19)
We can minimize variation of VT by simply minimizing the variation of retained dose.
This design strategy has been verified by Sherony. et. al [16]. This problem would be
trivial if the implant straggle could be arbitrarily set since a trivial solution would be
attained by ensuring that the peak of the profile was in the middle of the film and the
straggle set such that the entire implanted dose was located far from the interfaces.
Variation of to, and ti would only result in variation of T In ( : - ) through NA which
is relatively small. For typical implant energies, the straggle is comparable to silicon
film thickness so the trivial solution may not be attained and the nominal implant
energy depends on allowed errors in Ato, and Ati. We can however limit the range of
possible energies such that the lowest energy places the profile peak at the sacrificial
oxide and film interface and the largest energy places the profile peak at the interface
of the film and the buried oxide. For any chosen implant energy, the implant dose
is adjusted until the nominal voltage is attained. From the foregoing discussion, it
should be obvious that the low energies will result in higher threshold voltage errors
if the sacrificial oxide film varies while film thickness variation will result in higher
errors at high implant energies.
4.3.2
Design Flow
Fig 4-1 shows the design tree for this problem. The strategy is to iterate through the
entire energy range. For each value of energy, the implant dose is adjusted until the
nominal threshold voltage, VTO, is attained. The nominal film thickness and sacrificial
oxide are used in this case. To obtain the value of implant dose for the next iteration,
the following equations are used:
VTO = VT + Di -- Di-_
Di+1 = D + fAD,
ADi
(4.20)
(4.21)
where
VTO = Nominal VT
VTi= Calculated VT at step i
TV]_1 = Calculated VT at step i - 1
Di = Implant dose at step i
Di- 1 = Implant dose at step i - 1
ADi = Required incremental dose at step i
f = Constant damping factor
It should be noted that the implant dose evaluated above is distinct from retained
dose which is used for the evaluation of threshold voltage. The two are however
almost linearly-related and the above iteration should necessarily converge. Once the
nominal implant dose is attained, Fig 4-1 design tree is followed to the leaves. For
example, leaf 1 results when the film thickness increases to ti + Atsi and the sacrificial
oxide increases to to,, + At,,. It should be noted that the increase in sacrificial oxide
results in lower effective film thicknesses than ti + Ati.
the implementation.
This is accounted for in
Errors in VT are determined at each leaf. For each energy,
ox o
=T
(1)
V
(ii)
ox
x d tox
T (iii)
V
ox +dto
-'
tox
-V•
tox
(iv)
(v)
MAX d VT
T (vi)
ox d tox
tox
MAX d VT
-VT
oxdt
-
VT
(vii)
(viii)
MAX d VT
Figure 4-1: Design Tree
the leaf with maximum error is recorded and the optimal energy is the one whose
corresponding maximum error is least. The following section explains how the errors
are calculated.
4.3.3
Design Implementation
This design has been implemented using UNIX shell scripts and C programs. The
suprem process flow file in Appendix A is embedded in UNIX shell programs so that it
can be automatically generated and modified as required by the design flow. There are
Figure 4-2: Module dependency diagram
three scripts: nmasprog (master program), nprog, and nloop2. The C programs
are threshold.c and nextvalues.c. These are compiled into executables sample
and dosecalc. sample evaluates the threshold voltage while dosecalc evaluates the
next implant dose according to Equation ( 4.21). All these scripts and C programs
are included in Appendix B.
Fig 4-2 shows the module dependency diagram for the complete design. nmasprog
is the main controller and is used to iterate through the entire energy range. Its inputs are the initial value of implant dose iterations and the nominal threshold voltage.
51
The main controller calls nprog. The inputs to nprog are initial dose for iterations,
implant energy and the nominal threshold voltage. It is the script which evaluates
the implant dose required for the nominal threshold voltage ,VTo. It has an embedded
process file which allows for the automatic adjustment of the implant dose when iterations are done to determine the implant dose corresponding to VTO. For each value
of dose, the process file is run and the resulting concentration profile is passed to
sample to calculate the corresponding VT. With the calculated VT, dosecalc is then
called to evaluate the implant dose for the next iteration. Once the nominal dose in
attained nprog calls nloop2 to process conditions in which the sacrificial oxide and
silicon film thicknesses change.
The running time of the entire implementation is controlled by the rate of convergence of Equation ( 4.20). For the current implementation, it takes an average of
three suprem-3 runs to obtain the implant dose for a particular energy. This speed
is attained by varying the damping term in proportion to the difference between the
calculated VT and Vro. The implementation of sample (threshold.c) is very straight
forward and its running time is in order of seconds.
nloop2 is simply a nested loop whose body generates and runs the suprem process
file. The inner loop iterates through the possible film thicknesses (ts, t, - it 8 i, tsi +
Ant,) while the outer loop iterates through the sacrificial oxide thickness(to,, tox Atox, to
0 + Atox). For each of these combinations sample is called to evaluate the
threshold voltage with the implant dose passed to nloop2 from nprog. For each
implant energy there are approximately thirteen suprem-3 runs, nine in nloop and
four in nprog to obtain the nominal implant dose. Each suprem run takes about 30
sec so each energy value takes about seven minutes. For the current implementation
the energy ranges from 15 keV to 56 keV in steps of 1 keV and it takes about 9 hours
to complete the run.
4.4
Results and Discussion
As a demonstration, this design has been tested for the following conditions:
VTO = 0.45, 0.50, 0.55V
ti = 495A
Atsi = 25A = 5% of tj
tox = 53A
Ato
0 = 10A e 20% of tox.
As already mentioned, the error in threshold voltage is a strong function of the
implanted profile. When the implant peak is close to the sacrificial oxide interface,
the variation of the latter results in high variation of threshold voltage. Similarly an
implant peak close to the buried oxide interface results in higher threshold voltage
variation due to film thickness variation.
The variation of threshold voltage can
therefore be minimized by positioning the implant peak close to the middle of the
silicon film. To explore the entire range, implant energies ranging from 15 keV to 56
keV have been examined. Fig 4-3 shows the implanted profiles for these energies. The
implant dose in either case is set such that the nominal threshold voltage is attained
when neither film nor sacrificial oxide thickness varies.
For a nominal threshold
voltage of 0.5 V: Fig 4-4 shows a plot of implanted dose against energy. Fig 4-5
is a complementary plot of the percentage retained dose vs implant energy. These
figures can be readily explained. For low implant energy the fractional implant dose
that is retained in the sacrificial oxide is significant. Similarly, the dose that ends up
in the buried oxide is high for high implant energy. In both cases the implanted dose
must be high since the retained dose is fixed by the choice of the nominal threshold
voltage. Preferential segregation of boron into silicon dioxide and subsequent diffusion
in silicon dioxide also results in significant loss of implanted dose from the silicon film.
This further increases the required implant dose if the implant peaks are close to the
interfaces. For the two oxide interfaces the segregation effect is most severe when the
peak is close to the sacrificial oxide since the loss during the growth of gate oxide
is substantial.
Fig 4-5 confirms this observation as it shows that the percentage
retained dose at 15 keV is lower than at 56 keV yet, in the former case, the peak
is a little displaced from the interface as can be seen in Fig 4-3. To understanding
the nature of the error in threshold voltage, we separate the effect of oxide and film
E
U
r0
o
O
oU
C
0
-0.4
-0.35
-0.3
-0.4
-0.35
Depth from Surface (microns)
Figure 4-3: As implanted profile for 15 keV and 56 keV
-0.3
15
20
25
30
35
40
45
Implant Energy A/eV
50
55
60
Figure 4-4: Implant Dose vs Energy
0
Implant Energy /keV
Figure 4-5: % Retained Implant Dose vs Energy
VTO = 0.50V
60
-,•
.....
: .... ..:......
........
... .
tsi
S
40
....
........
520 Ang.
20
--
+ +-*
+ .
:
W -20
.
-40
.
.
.
.
.
. .
.
..
. ...
........
= 4. 0 AN ....
...
..
. .. ... .. .. .. .. ,. ... .. ... .tsi
.. .
-60
_0f
15
20
25
30
35
40
.
45
50
55
60
Implant Energy /keV
Figure 4-6: VT Error due to Film Thickness variation
thickness.
Film Thickness Variation
Fig 4-6 shows a plot of threshold voltage error vs implant energy for a nominal film
thickness of 495A. The upper curve corresponds to film thickness increase of 255A to
520A. The lower curve corresponds to a decrease in film thickness to 470A. It should
be noted that for each energy value the implant dose is chosen such that nominal
threshold voltage is attained in the absence of film variation. From the plot it can be
seen that low implant energy is required to minimize threshold voltage variations. For
films thinner than the nominal thickness the threshold voltage is consistently below
the nominal while the opposite is true for thicker films. This should be expected
since the retained dose, on which threshold voltage linearly depends, is a near-linear
function of film thickness. The absolute variation for both cases is almost equal.
Sacrificial Oxide Thickness Variation
Fig 4-7 shows a plot of threshold voltage error vs implant energy for for two sacrificial oxide thicknesses. The nominal film thickness of 495A is modified accordingly
for each choice of oxide thickness. The nominal oxide thickness is 53A and is varied
by +10A. This is accompanied by a variation of ±0.44 * 10A in silicon film thickness
du
++++ oxide thickness = 43 Ang.
"" oxide thickness = 63 Ang.
60
40
20
0
-20
-40
-60
-•
.
_on
15
-•
,-
20
I
..
25
30
35
.
40
45
50
55
60
Implant Energy /keV
Figure 4-7: VT Error due to Oxide thickness Variation
since the oxide is thermally grown. We can understand this plot by considering low
and high energies separately. For low implant energy, the VT is less than nominal
for thicker sacrificial oxide. In this case the implant loss into the sacrificial oxide
increases. This together with a thinner silicon film results in the threshold voltage
being below nominal. An apparent anomaly should be observed for very low implant
energies. It was mentioned that for such cases the error should be very high yet this
is not observed. This can possibly be explained by the reduction in diffusion into
the gate oxide because the profile at the film gate oxide interface is flattened. The
threshold voltage error decreases with increasing energy and for an implant energy
above 43 keV the threshold voltage increases above the nominal for thick oxides. To
understand why the error ever goes positive we should note that if the implanted
profile is such that the concentration at the front interface is less than at the back
interface then an increase in the sacrificial oxide thickness can easily result in the
shifting of the peak to the left such that the implant that ends up in the film is
greater than during the nominal case.
For thin sacrificial oxide low implant energy result in high errors. Even in this
case, there is reduced error for very low implant energies. The reduced error is due to
increased loss into the growing gate oxide because of the steepness of the initial profile
in the silicon film The threshold voltage is above nominal because the increased film
thickness and decrease of oxide results in higher dose in the film. The error decreases
with implant energy and at above 43 keV the error becomes negative and starts
increasing in"that direction. What is happening in this case is just the opposite of
what happened in the case of thicker oxide. That is, if the the implant profile in the
nominal case is such that the concentration at the front interface is higher than at the
back interface then an a decrease in the oxide thickness will result in higher loss into
the buried oxide since the peak is shifted to the to the right but the film thickness
does not increase enough to contain the shifted implant.
From this plot is should be observed that for high sacrificial oxide variations the
threshold voltage variation is minimized by implanting at high energies.
The complete Case
In this case we incorporate the variation of both film thickness and sacrificial
oxide. Fig 4-8 shows the complete case. The plot shows the maximum errors for
the three sub branches of the design tree. Fig 4-10 shows the the final results. The
optimal energy can now be read off from Fig 4-4. Up to an energy of 43keV the
maximum error is caused by a condition in which the film thickness increases and the
implant oxide thickness decreases. Above this energy the maximum error results from
a thin silicon film and a thin sacrificial oxide. At this point the worst error changes
from positive to negative. For the demonstrated case, the optimal energy is 32 keV.
VT = 0.50V
Implant Energy /keV
Figure 4-8: VT Error due to Oxide and Film variation.
VT = 0.5V
tin
S11r
60
i-
hick film thir oxide
40
-
/
m...h........
....
....
"Dir
rdk flii thl~kk
6xide '
E
I
0
•-20
-40
-60
t
-du
15
film thick oxide
Shin
*
20
25
30
35
40
Implant Energy /keV
Thirfim thin-oxide-
45
50
55
60
Figure 4-9: Signed VT error for variation of Film and Oxide thicknesses.
59
VT = 0.5V
o
Implant Energy /keV
Figure 4-10: Average VT error for film thickness variation
60
Appendix A
SUPREM III Process File
Title
Suprem3 Doping Profile Simulation for SOI Device
+
with SIMOX
Comment
Obtain Base Structure of SOI Device in the Active
+
Region
Initialize
<100> Silicon, Boron concentration=3el5
+
Thickness=0.5 dx=0.0005 xdx=0.01 min.dx=0.0005
+
Spaces=250
Comment
Grow Oxide and Add the Bonded Silicon Epitaxial Layer
Diffusion
Temperature=900 Time=30 Dry02
Diffusion
Temperature=950 Time=107.32 Wet02
Diffusion
Temperature=950 Time=30 Dry02
Diffusion
Temperature=950 Time=30 Nitrogen
Deposition
<100> Silicon Temperature=900 Thickness=0.2175
+Grid
Boron concentration=3el5
Grid
Layer.3 Spaces=80
Grid
Layer.2 dx = .0001 xdx=0
Print
Layer
Comment
Thin the Bonded Silicon Epitaxial Film
Diffusion
Temperature=950 Time=30 Dry02
Diffusion
Temperature=950 Time=92
Diffusion
Temperature=950 Time=30 Dry02
Diffusion
Temperature=950 Time=30 Nitrogen
Etch
Oxide all
Comment
SRO, Nitride and Field Oxide
Diffusion
Temperature=950 Time=40 Dry02
Diffusion
Temperature=950 Time=30 Nitrogen
Deposition
Nitride Thickness=0.150 Temperature=800
Diffusion
Temperature=950 Time=30 Dry02
Diffusion
Temperature=950 Time=45 Wet02
Diffusion
Temperature=950 Time=30 Dry02
Diffusion
Temperature=950 Time=30 Nitrogen
Comment
Etch to Silicon Surface
Etch
Oxide all
Etch
Nitride all
Etch
Oxide all
Print
Wet02
Layer
Grid
Layer.3 dx=0.0001 xdx=0.006
Comment
Dummy Oxide and Channel Implant
Diffusion
Temperature=800 Time=90 Dry02
spaces=80
Implant
BF2 Dose=4.0664e+12 Energy=15
Save
Structure File=energ.str
Print
Layer
Etch
Oxide all
Print
Layer
Comment
Grow Gate Materials
Diffusion
Temperature=900 Time=20 Dry02
Print
Layer
Deposition
Polysilicon Thickness=0.30 Temperature=625
Comment
Reox
Diffusion
Temperature=900 Time=10 DryO2
Diffusion
Temperature=900 Time=15 Nitrogen
Print
Layer
Comment
Drain Implant, S/D Formation and Silicidation
Implant
Arsenic Dose=4e15 Energy=25
Diffusion
Temperature=900 Time=30 Nitrogen
Comment
LTO, Metal Contacts and Sinter
Comment
Set Data Starting Point at Si02/Si Film Interface
Etch
Oxide All
Etch
Polysilicon All
Etch
Oxide All
Comment
Plot the Doping Profile
Print
Layer
Comment
Save the Channel Doping Structure for Minimos4+
+
Simulation
Save
Structure File=mel.str
Print
Minimos File=chan.sav xmin=0.0 xmax=0.2
Stop
End of Suprem3 file
Appendix B
Scripts and Source Files
B.1
nextvalues.c
#include <stdio.h>
#include <math.h>
main()
{
/* This program calculates the Dose needed to obtain a certain
required threshold voltage
*/
double VTO; /* Norminal Threshold voltage */
double VTi;
/* Calculated VT at present step */
double VTi_1; /* Previous calculated threshold voltage. */
double damp_f; /* Damping factor
double Di;
*/
/* Current Dose*/
double Di_1; /* Previous Dose */
double deltaDi; /* change in Dose that we expect */
double nextDi; /* Next dose */
double vterror; /* error allowed for VT */
FILE *fpVTO, *fp_VTi, *fp_VTi_l,*fopen();
FILE *fpDi, *fp_Di_1;
FILE *fp_E;
int tmp,z;
double y;
char VTOfile[20], VTi_file[20], VTi_l_file[20];
char Di_file[20] , Di_1_file[20],E_file[20];
tmp = 0;
damp_f = 1.0;
/* dampf = .1;*/
vt_error = .001;
sprintf(VTO_file,"VTO");
sprintf(VTi_file,"VT.out");
sprintf(VTi_1_file,"VT.prev");
sprintf(Di_file,"DOSE");
sprintf(Di_ _file,"prev_DOSE");
sprintf(E_file,"ENERGY");
fp_VTO=fopen(VTO_file,"r");
fp_VTi=fopen(VTi_file,"r");
fp_VTi_l=fopen(VTi __file,"r");
fp_Di=fopen(Di_file,"r");
fp_Di_1=fopen(Di__file,"r");
fpE=fopen(E_file,"w");
/* printf("%f \n",vt_error); */
fscanf(fpVTO,
"%lf",
&VTO);
fscanf(fp_VTi, "%lf", &VTi);
fscanf(fp_VTi_1, "/lf",
&VTi_1);
fscanf(fp_Di, "%lf", &Di);
fscanf(fp_Di_1, "/lf", &Di_1);
fclose(fp_Di);
fclose(fp_Di_1);
fpDi=fopen(Di_file,"w");
fp_Di_l1=fopen(Di_1_file,"w");
fprintf(fp_Di_, "%.4e",Di);
if (fabs(VTO-VTi) <= vt_error) {
/* Write 0 to both ENERGY and DOSE files */
fprintf(fp_E, "%d",tmp);
fprintf(fpDi,"%d",tmp);
}
else {
if ((VTi-VTi_1) == 0.0) {
deltaDi = (VTO-VTi)*(Di-0.999*Di_1)/(vt_error);
printf("HERE\n");
}
else
{
deltaDi = (VTO-VTi)*(Di-Di_)/(VTi-VTi_1);
}
if (fabs(VTO-VTi) <= 0.002){
damp_f = 0.1*dampf;
}
nextDi = Di + damp_f*deltaDi;
fprintf(fp_Di, "%.4e",next_Di);
/* printf("%e\n",next_Di); */
fclose(fpVTO);
fclose(fpVTi);
fclose(fpVTi_1);
fclose(fpDi);
fclose(fpDi_);
fclose(fp_E);
printf("\n %.4f %.4f %.4f %.4e %.4e %.4e \n",VTO,
VTi_1, Di, Di_1, nextDi);
I
VTi,
B.2
threshold.c
#include <stdio.h>
#include <math.h>
main()
{
/***This program calculates the threshold voltage given the
concentration array of a fully depleted SOI layer.
The input
concentration file is given in the argument to the excecutable.
The output of the program
is written to a file.
***/
/***
Calculates Vth for range of Tsi
/***
Calculates depletion depth, xd ***/
/***
For Tsi<xd: fully depl -- use L&F model ***/
/***
For Tsi>xd: partial depl -- bulk, Vth constant ***/
/*** same as s_vth.c but have added a shift ***/
/***
in phims of O.iV so model matches simulation
***/
FILE *fp,*fp2,*fp3, *fopen();
char
file.name[20],vt_file[20] ,dose_file [201;
/* input and output
file names */
double
log(),sqrt();
double
q, es, eox, Qff, Qfb, Tfox, Tbox, Tsi, Cfox,
Cbox, Qb, Cb;
double
PhiF, xdf,xdb,Psi_I,VTn, Psi_sbO, Qinvf, Qinvb, Nsb, Csb;
double
Vfbf, Vfbb, Vgb, Vgba, VTfa, VT, Na[6];
double
depth[201];
/* distance from the surface */
double
conc[201];
double
ref,dx[200],midconc[200],dose,Qd;
and grid s
double
/* concentration of dopant */
/*Reference x cordinate
pacing */
VRf,VTnl ; /* equivalent of Flat band for
nonuniform profile */
int i;
int count;
double
/* Maximum index of useful data */
ni, kT, Pmsi, NA;
Pmsi = -.55;
kT = 8.62E-5*300;
ni = 1.45E10;
q = 1.6E-19;
es = 8.85E-14*11.7;
eox = 8.85E-14*3.9;
Tbox = 1E-8*3800;
Nsb = 0;
Qff = 0;
qfb = 0;
count =0;
Tfox = 1E-8*80;
dose=0;
sprintf(file_name, "my.dat");
sprintf(vt_file,"VT.out");
sprintf(dose_file,"ret_dose.dat");
/* printf("%s",file_name); */
Cfox = eox/Tfox;
Cbox = eox/Tbox;
Csb = q*Nsb;
fp = fopen(file_name,"r");
/* Now read in the data
*
for (i=O; i<=200; i++)
{
fscanf(fp, "/ 01f Alf",
&depth[i], &conc[il);
/* printf("%f %e \n",depth[i ],conc[i]);
}
/* get maximum index */
for (i=1; i<=200; i++)
if
(depth[i] == depth[i-1]){
break;
}
else
{
count++;
}
/* printf("\n %f\n",depth[count-1]); */
/* Now go ahead and get integral */
/* Set the coordinates reference properly */
ref = depth[O];
/* printf("%f \n", ref);
*/
for (i=O; i<=count; i++)
{
depth[il -= ref;
depth[i]
= 1E4*depth[i];
for (i=0; i<=count-1; i++){
dx[i] = depth[i+1]-depth[i];
mid_conc[i]
= 0.5*(conc[i+1]
+ conc[il);
dose += mid_conc[i]*dx[i];
}
dose = dose*1E-8;
Qd = dose*q;
/* printf("%e \n",Qd); */
/* Now I can set to calculate the VT */
/* Evaluate some constant for this film */
Tsi = 1E-8*depth[count]; /* silicon film film thickness */
Cb = es/Tsi;
NA = dose/Tsi;
/* Film capacitance
*/
/* Average film doping level */
PhiF = kT*log(NA/ni);
VRf = Pmsi - kT*log(conc[countl/ni) - Qff/Cfox;
Vfbb = 0.347 -kT*log(conc[O]/ni) - Qfb/Cbox;
/* Back gate Flat Band */
Vgb = Vfbb;
Psi_I = PhiF + kT*log(conc[count]/ni);
xdf =
sqrt(2*es*PsiI/(q*NA));
/* maximum depletion */
printf("xdf= %.4e Psi= %.4f NA = %e\n", xdf,Psi_I,NA);
xdb = 0;
VTn1 = 0;
if (xdf + xdb < Tsi) {
Psi_sbO = 0;
VTn1 = VRf + Psi_I + q*NA*xdb/Cfox;
/* Need complete bulk solution */
}
else {
PsisbO=(Vgb - Vfbb + Cb*PsiI/Cbox -
Qd/(2*Cbox))/(l + Cb/Cbox);
if (Psi_sbO<O)
Psi_sbO=O;
VTn = VRf + (1 + Cb/Cfox)*Psi_I -
Cb*PsisbO/Cfox + Qd/(2*Cfox);
VTn = VRf + Psi_I
+ Qd/Cfox; */
}
printf("VT = %.4f
VTn1 = %.4f
\n", VTn,VTnl);
/* Now write out the VT into some file*/
/* But first write the value of previous VT into prev file */
fp2 = fopen(vt_file, "w");
fp3 = fopen(dose_file,"w");
fprintf(fp2,"%.4f",VTn);
fprintf(fp3," % .4e",dose);
fclose(fp);
fclose(fp2);
f close (fp3);
}
B.3
nmasprog
#!/bin/sh
dose=$1
threshold=$2
for energy in {energy}
do
nprog $dose $energy $threshold
done
B.4
nprog
#!/bin/sh
dose=$1
energy=$2
threshold=$3
echo "${dose}" > prev_DOSE
prevenergy=${energy}
prevdose='awk '{print $1 * 0.9}' prev_DOSE'
echo "$prevdose"
> prev_DOSE
echo
"$dose" > DOSE
echo
"$energy" > ENERGY
echo
"$threshold" > VTO
while (test ${energy} -ne 0) do
while (test ${dose} -ne 0) do
##This is the beginning of the suprem3 file.
echo "Title Suprem3 Doping Profile Simulation for SOI Device
+ with SIMOX" > file
echo "Comment Obtain Base Structure of SOI Device in the
+ Active Region" >> file
echo "" >> file
echo "Initialize <100> Silicon, Boron
+
concentration=3el5" >> file
echo "+ Thickness=0.5 dx=0.0005 xdx=0.01 min.dx=0.0005
+ Spaces=250" >> file
echo "" >> file
echo "Comment Grow Oxide and Add the Bonded Silicon
+ Epitaxial Layer" >> file
echo "" >> file
echo "Diffusion Temperature=900 Time=30 DryO2" >> file
echo "Diffusion Temperature=950 Time=107.32 Wet02" >> file
echo "Diffusion Temperature=950 Time=30 Dry02" >> file
echo "Diffusion Temperature=950 Time=30 Nitrogen" >> file
echo "" >> file
echo "Deposition <100> Silicon Temperature=900
+
Thickness=0.2175" >> file
echo "+ Boron concentration=3el5" >> file
echo "" >> file
echo "Grid Layer.3 Spaces=80 " >> file
echo "Grid
Layer.2 dx = .0001 xdx=0 " >> file
echo "" >> file
echo "Print
Layer" >> file
echo "Comment Thin the Bonded Silicon Epitaxial
+ Film" >> file
echo "Diffusion Temperature=950 Time=30 Dry02" >> file
echo "Diffusion Temperature=950 Time=92 Wet02" >> file
echo "Diffusion Temperature=950 Time=30 Dry02" >> file
echo "Diffusion Temperature=950 Time=30 Nitrogen" >> file
echo "" >> file
echo "Etch Oxide all" >> file
echo "" >> file
echo "Comment SRO, Nitride and Field Oxide" >> file
echo "Diffusion Temperature=950 Time=40 Dry02" >> file
echo "Diffusion Temperature=950 Time=30 Nitrogen" >> file
echo "Deposition Nitride Thickness=0.150
+ Temperature=800" >> file
echo "Diffusion Temperature=950 Time=30 Dry02" >> file
echo "Diffusion Temperature=950 Time=45 Wet02" >> file
echo "Diffusion Temperature=950 Time=30 Dry02" >> file
echo "Diffusion Temperature=950 Time=30 Nitrogen" >> file
echo "" >> file
echo "Comment Etch to Silicon Surface" >> file
echo "Etch Oxide all" >> file
echo "Etch Nitride all" >> file
echo "Etch Oxide all" >> file
echo "" >> file
echo "" >> file
echo "Print
echo "Grid
Layer" >> file
Layer.3 dx=0.0001 xdx=0.006
+ spaces=80" >> file
echo "Comment Dummy Oxide and Channel Implant" >> file
echo "Diffusion Temperature=800 Time=90 Dry02" >> file
echo "Implant BF2 Dose=${dose} Energy= ${energy} "
+ >> file
echo "Etch Oxide all" >> file
echo "" >> file
echo "" >> file
echo "Print
Layer" >> file
echo "Comment Grow Gate Materials" >> file
echo "Diffusion Temperature=900 Time=20 Dry02" >> file
echo "Print Layer" >> file
echo "" >> file
echo "Deposition Polysilicon Thickness=0.30
+ Temperature=625" >> file
echo "Comment Reox" >> file
echo "Diffusion Temperature=900 Time=10 Dry02" >> file
echo "Diffusion Temperature=900 Time=15 Nitrogen" >> file
echo "Print Layer" >> file
echo "" >> file
echo "Comment Drain Implant, S/D Formation and
+ Silicidation" >> file
echo "Implant Arsenic Dose=4e15 Energy=25" >> file
echo "Diffusion Temperature=900 Time=30 Nitrogen" >> file
echo " " >> file
echo "Comment LTO, Metal Contacts and Sinter" >> file
echo "Comment Set Data Starting Point at Si02/Si
+
Film Interface" >> file
echo "Etch Oxide All" >> file
echo "" >> file
echo "Etch
Polysilicon All" >> file
echo "Etch Oxide All" >> file
echo " " >> file
echo "Comment Plot the Doping Profile" >> file
echo "Print Layer" >> file
echo "Comment Save the Channel Doping Structure
+ for Minimos4+ Simulation" >> file
echo "Save Structure File=mel.str" >> file
echo "" >> file
echo "Print
Minimos File=chan.sav xmin=0.0
+ xmax=0.2" >> file
echo "Stop End of Suprem3 file " >> file
##This is the end of the suprem file.
##The remaining part of this loop is to evaluate the threshold
##voltage.
##Run suprem
##/u/cad/bin/rsuprem file
/amd/naxos/e/gormahia/w_suprem3/suprem3/run/rsup file
##/u/cad/bin/rsuprem tmp.in
##create a data concentration file.
rpostsup mel.str
awk '$2 !~ /[a-z]/' mel.data > my.dat
## Now run'the program that evaluates the VT.
## First store previous VT is appropriate file.
awk '{print $1}' VT.out > VT.prev
sample
## Now calculate the next dose
dosecalc
## what am I going to try next that get written to DOSE
dose='awk '{print $1}' DOSE'
echo ${dose}
done
energy='awk '{print $1}' ENERGY'
echo ${energy}
done
##awk '{print $1}' VT.out > srun.2175.$2
##awk '{print $1}' prev_DOSE >> srun.2175.$2
awk '{print $1}' ret_dose.dat > dose_$2.dat
awk '{print $1}' VT.out > srun.2175.$2
awk '{print $1}' prev_DOSE >> dose_$2.dat
doseprev='awk '{print $11' prev_DOSE'
nloop2 $doseprev $2 $3
B.5
nloop2
#!/bin/sh
dose=$1
energy=$2
threshold=$3
for tox in 0
1
do
## 1 indicates that oxide is thicker
## 0 indicates that the oxide is thinner
if (test $tox -eq 1)
then
etch="Comment
setch = ''
dep=''
sdep="Comment
else
setch="Comment
sdep=''
etch=''
dep="Comment
fi
for thick in 0.2150 0.2175 0.2200
do
echo "Title Suprem3 Doping Profile Simulation for SOI Device
+ with SIMOX" > file
echo "Comment
Obtain Base Structure of SOI Device in the Active
+ Region" >> file
echo "" >> file
echo "Initialize <100> Silicon, Boron concentration=3el5"
+
>> file
echo "+ Thickness=0.5 dx=0.0005 xdx=0.01 min.dx=0.0005
+
Spaces=250" >> file
echo "" >> file
echo "Comment Grow Oxide and Add the Bonded Silicon
+
Epitaxial Layer" >> file
echo "" >> file
echo "Diffusion Temperature=900 Time=30 Dry02" >> file
echo "Diffusion Temperature=950 Time=107.32 Wet02" >> file
echo "Diffusion Temperature=950 Time=30 Dry02" >> file
echo "Diffusion Temperature=950 Time=30 Nitrogen" >> file
echo "" >> file
echo "Deposition <100> Silicon Temperature=900 Thickness=$thick
+ " >> file
echo "+ Boron concentration=3e15" >> file
echo "${sdep}Deposition <100> Silicon thickness=0.0005
+ Temperature=900">>file
echo "${setch}Etch
Silicon thickness=0.0005
" >> file
echo "" >> file
echo "Grid Layer.3 Spaces=80 " >> file
echo "Grid
Layer.2 dx = .0001 xdx=0 " >> file
echo "" >> file
echo "Print
Layer" >> file
echo "Comment Thin the Bonded Silicon Epitaxial
+ Film" >> file
echo "Diffusion Temperature=950 Time=30 Dry02" >> file
echo "Diffusion Temperature=950 Time=92 Wet02" >> file
echo "Diffusion Temperature=950 Time=30 Dry02" >> file
echo "Diffusion Temperature=950 Time=30 Nitrogen" >> file
echo "" >> file
echo "Etch Oxide all" >> file
echo "" >> file
echo "Comment SRO, Nitride and Field Oxide" >> file
echo "Diffusion Temperature=950 Time=40 Dry02" >> file
echo "Diffusion Temperature=950 Time=30 Nitrogen" >> file
echo "Deposition Nitride Thickness=0.150
+ Temperature=800" >> file
echo "Diffusion Temperature=950 Time=30 Dry02" >> file
echo "Diffusion Temperature=950 Time=45 Wet02" >> file
echo "Diffusion Temperature=950 Time=30 Dry02" >> file
echo "Diffusion Temperature=950 Time=30 Nitrogen" >> file
echo "" >> file
echo "Comment Etch to Silicon Surface" >> file
echo "Etch Oxide all" >> file
echo "Etch Nitride all" >> file
echo "Etch Oxide all" >> file
echo "" >> file
echo "" >> file
echo "Print
echo "Grid
Layer" >> file
Layer.3 dx=0.0001 xdx=0.006
+ spaces=80" >> file
echo "Comment Dummy Oxide and Channel
+ Implant" >> file
echo "Diffusion Temperature=800 Time=90 Dry02" >> file
Oxide thickness=0.O010 " >>file
echo "${dep}Deposition
Oxide
echo "${etch}Etch
thickness=0.O010 " >> file
echo "Implant BF2 Dose=${dose}
+ Energy= ${energy} " >> file
echo "Etch Oxide all" >> file
echo "" >> file
echo "" >> file
Layer" >> file
echo "Print
echo "Comment Grow Gate Materials" >> file
echo "Diffusion Temperature=900 Time=20 Dry02" >> file
echo "Print Layer" >> file
echo "" >> file
echo "Deposition Polysilicon Thickness=0.30
+ Temperature=625" >> file
echo "Comment Reox" >> file
echo "Diffusion Temperature=900 Time=10O Dry02" >> file
echo "Diffusion Temperature=900 Time=15 Nitrogen" >> file
echo "Print Layer" >> file
echo "" >> file
echo "Comment Drain Implant, S/D Formation and
+ Silicidation" >> file
echo "Implant Arsenic Dose=4el5 Energy=25" >> file
echo "Diffusion Temperature=900 Time=30 Nitrogen" >> file
echo " " >> file
echo "Comment LTO, Metal Contacts and Sinter" >> file
echo "Comment Set Data Starting Point at Si02/Si Film
+ Interface" >> file
echo "Etch Oxide All" >> file
echo "" >> file
echo "Etch
Polysilicon All" >> file
echo "Etch Oxide All" >> file
echo " " >> file
echo "Comment Plot the Doping Profile" >> file
echo "Print Layer" >> file
echo "Comment Save the Channel Doping Structure
+ for Minimos4+ Simulation" >> file
echo "Save Structure File=mel.str" >> file
echo "" >> file
echo "Print
Minimos File=chan.sav xmin=0.0
+ xmax=0.2" >> file
echo "Stop End of Suprem3 file " >> file
##This is the end of the suprem file.
##The remaining part of this loop is to evaluate the threshold
##voltage.
##Run suprem
##/u/cad/bin/rsuprem file
/amd/naxos/e/gormahia/w_suprem3/suprem3/run/rsup file
##/u/cad/bin/rsuprem tmp.in
##create a data concentration file.
rpostsup mel.str
awk '$2 !- /[a-z]/'
mel.data > my.dat
## Now run the program that evaluates the VT.
## First store previous VT is appropriate file.
##awk '{print $1}' VT.out > VT.prev
sample
awk '{print $1}' VT.out > crun${thick}.${energy}${threshold}.$tox
done
done
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