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Photoresist Development Model for Linewidth Control in the Fabrication of MCM and Customised ASICs
E. Saint-Christophe, H. Fremont, M. Fathi, Y. Danto
To cite this version:
E. Saint-Christophe, H. Fremont, M. Fathi, Y. Danto. Photoresist Development Model for Linewidth Control in the Fabrication of MCM and Customised ASICs. Journal de Physique III, EDP Sciences, 1996, 6 (11), pp.1507-1526. �10.1051/jp3:1996199�. �jpa-00249542�
J. Phys. III France 6 (1996) 1507-1526 NOVEMBER1996, PAGE 1507
Photoresist Development Model for Linewidth Control in the
Fabrication of MCM and Customised ASICS
E. Saint-Christophe (*), H. Fremont, M. Fathi and Y. Danto
Laboratoire de Micro61ectronique, IXL, [iniversitA Bordeaux 1, 351 cours de La Lib6ration, 33405 Talence Cedex, France
(Received 21 December1995, revised 12 April 1996, accepted 6 August 1996)
PACS.42.62.Ht Laser applications (other applications) PACS.78.20.Bh Theory, models and numerical simulation PACS.81.65.Cf Surface cleaning, etching, patterning PACS.85.40.Hp Lithography, masks and pattern transfer
Abstract. The authors present an analytical approach of the line width control in photore-
sist sensitized using a laser beam lithography bench. They take into consideration parameters of the photoresist such as the Dill parameters, the absorbance and the reflection factor as well
as parameters of the etching process such as the speed and the intensity of the laser beam. They give a large study of the time and spatial dependence of the absorbance during the passage of the laser beam spot on the photoresist surface and present experimental results in accordance with their theoretical approach.
1. Introduction
Prediffused Asics of Multi-Chip Module (MCM) require several levels of metallisation within
a high level of integration. To create new prototypes or test structures in a development phase, the rapidity of processing is of minor importance in comparison with the simplicity of
implementation and the cost of physical masks. To make these complex interconnections, an original direct patterning system has been set-up using a laser beam bench [1j the sensitization
resolution matches the micrometric range, this kind of laser is cheaper than an electron beam
etching station and does not require vacuum.
CAD created masks are used to drive the laser beam, in a vectorial mode, upon a photoresist deposited on an aluminium layer to be patterned. In order to get the best resolution in the aluminium line width, the width of the photoresist sensitized by the laser beam must be controlled with precision.
The width of the line sensitized by the laser beam can not be directly deduced from the di- ameter of the laser beam spot just at the photoresist surface. The reflections on the substrate play an important role if the substrate is highly reflective (case of a metal). The speed V of
the spot while sensitizing the photoresist is an important parameter: the greater V is, the less sensitized the photoresist is. Other parameters such as the Dill parameters, the absorbance of the resist and the intensity of the beam are involved as well. Every variation of one of these
(*) Author for correspondence
© Les llditions de Physique 1996
1508 JOURNAL DE PHYSIQUE III N°11
parameters leads to a new set of experiments and makes akward the use of a laser beam bench.
Thus we have developed a theoretical model to predict the line width etched in the photoresist after its exposure by the laser beam, and its development.
In order to establish this model, several steps must be conducted:
. Determination of the light intensity It received by the photoresist. This intensity depends,
among other parameters, on the absorbance of the resist.
. Geometric simulation of the laser beam on the surface, depending on the spatial distri- bution and time evolution of the resist absorbance as well as on the speed of the spot.
. Geometric simulation of the laser beam on the surface, depending on the spatial distri- bution and time evolution of the resist absorbance as well as on the speed of the spot.
. The value of It, combined with the geometric simulation, leads to the determination of the energy absorbed within the photoresist thickness during the spot scan.
. From this energy, one deduces the linewidth etched in the photoresist.
This study follows the one which presented the main advantages of the direct ~vriting of interconnections with a laser beam [1j. This study allows to improve the model of laser beam and photoresist interaction proposed there, by a precise time and spacial comportment of the photoresist absorbance. After a short description of the bench, this paper presents the
theoretical model of line width control. This model can be applied for every kind of laser beam and photoresist. It is supported by our experimental conditions.
2. The Laser Lithography Machine
The main part of the laser lithography bench 11,2], is a Hecd laser of wavelength1 = 442 nm,
emitting in the visible range (blue), and having a nominal power of16 mW (Fig. I). An
optical microscope works as a filtering and focusing system and allows a spot of about 0.9 ~lm to be focused on the wafer. The power of sensitization P can be adjusted. To do that, an
attenuator is realized with two polarizers, whose angular difference (also called aperture angle) can be varied. They are located, as shown in Figure I, on the optical path of the beam.
The relationship between the nominal pol~<er Po and the effective pol~>er of sensitization P is a function of 6 (R varies from 0° to 90°):
P = Po cos~R. (I)
The power of the laser beam intensity under the microscope lens was measured as a function of 6 and is outlined in Figure 2. It confirms the validity of relation (1) 1~>hen the laser beam
reaches the photoresist surface.
During the patterning sequence, the beam can be split by an acousto-optic modulator. The z-axis is used to focus the laser beam. A diode laser of wavelength 1
= 780 nm is used for
focusing during the patterning sequence, thus avoiding defects due to the wafer topography. A
micropositionner is used to control the movement of the wafer in the z, y and z directions. It has a resolution of o.1 ~lm and a programmable velocity from 0.5 mm s~~ to 8 mm s~~ with
a
resolution of10 ~lm s~~ The whole bench is controlled by a PC, while work stations are used to produce CAD masks (OPUS software) that are transferred to the PC via and ETHERNET
network.
N°11 LINEWIDTH CONTROL MODEL IN THE FABRICATION OF MCM, ASICS 1509
Pe÷iscopical
Afocal system objec~ive
lens
~'~~~'~~~'~ Poianze×s Diaphragn~
~"°'°~~~~"
o Diaphragrn
0 250 260 460 660
' z(mm)
0.145 0,283 0.005 5,~87 5.487 #$~$,
u÷f~~e ~~~~~~
R(z)(mm)
~
393 ~10.3
~
200 o~
~ ~
Fig. I. Schematic diagram of the laser beam used. Evolution of the laser beam dimensions along
its path.
m m
m
I
m
m
~
, o(o)
0 20 40 60 80 100
Fig. 2. Power of the laser beam
as a function of the polarizing angle 6. Measured values.
As the spatial resolution of the patterning must be known as precisely as possible, the design
rules will be determined as a function of the photoresist and of the power and the speed of the laser beam.
3. Laser Beam Description
The schematic diagram of the laser beam path is shown in Figure i. In this figure, the origin of z is the laser tube, uJ(z) is the radius of the beam and R(z) its curve radius. uJ(z) and R(z)
are calculated along the path of the laser beam, in a medium of refraction n, by the following
1510 JOURNAL DE PHYSIQUE III N°il
relations [3-5j:
uJ~(z) = uJ(
i
+ ~ (2)
zo
R(z) = z1+(~°)~ (3)
z
where uJo is the beamwaist radius, z taken from the former beamwaist and zo
=
~"~°°
l
~
The role of the afocal system is to purify the laser beam obtaining a quasiplane beam before entering the objective lens of the periscopical system and to increase its surface section to the
diameter size of the objective lens (10 mm).
In laser optic experiments, sharp instrumentation and measurements are required. Precise
alignment of the bench is of most importance as is the position z of the diaphragm of the afocal system: a variation of i% of its position would lead to a reduction of 98% of the radius curve.
The beam would no longer be considered as a quasiplane when entering the objective lens, and distortion and diffraction effects would appear.
After the passage through the objective lens, the light intensity of the laser beam has been measured in order to determine the focused spot size ii.e. the diameter 2uJo of the beamwaist).
Various measurements were taken at three different positions of z (Figs. 3a, 3b and 3c). One notices that the shorter z is, the stronger the light intensity is. No secondary light intensity peak is discernable on the curves. It confirms the absence of diffraction and the high purity of the laser beam when it reaches the photoresist.
Depending on the type of application, two different photoresists from SHIPLEY were used.
Their main features are summarized in Table1 [6j. Dill parameters: A and B characterize the value of the absorbance coefficient of the photoresist which is comprised between A+B and B.
C is linked with its time evolution. With the greater thickness of the 1400-31-Di, one obtains
a wider line width at the aluminium surface since the laser beam diameter increases with the thickness h(see Fig. 4). Thus, the evolution of the laser beam path within the thickness h of the photoresist must be taken into account and because of the very high reflectivity of aluminium, the path of the laser beam during its return to the very high reflectivity of aluminium. the
Table 1. Characteristic8 of the two photore818ts 1t8ed for1
= 442 nm fsj.
Type of Photoresist
Characteristics SHIPLEY SHIPLEY
1400-27 1400-31-Di
Recommended thickness 1.5 /Jm 2.i /Jm
Dill parameters A
= 0.612 pm~~ A
= 0.608 /Jm~~
B
= o.ioi /Jm~~ B = 0.238 /Jm~~
C = o.o145 cm~ mJ~~ C
= o.0153 cm2 mJ~~
Index of refraction n
= 1.68 n
= 1.68
Reflection rate RI
" o.064 RI " o.064
~~~~~~°~~ ~~~~~Y 4° nlJ Cnl~~ 32 mJ cm-2
N°li LINEWIDTH CONTROL MODEL IN THE FABRICATION OF MCM, ASICS lsll
1(~A) ~
4
O=350
3
z=663 p m
0
r @m)
aj ~I500 -Iooo -500 o 500 loco lsoo
15 1(pA)
lo
o =220
5 z=308 p m
o
roun)
b) ~800 -600 -4~© ~200 0 200 400 600 800
20 1wA>
is
lo a=200
194 p m 5
r 0
c)-800
Fig. 3. Experimental intensity points superimposed to best fitted theoretical Gaussian
curves.
a) z
= 663 ~tm; b) z
= 308 /Jm; c) z
= 194 ~tm.
1512 JOURNAL DE PHYSIQUE III N°11
lLaser bwim
Air '
RI
Photoresist
layer
h
R2 to(h)
Aluminiumlayer
Fig. 4. Pattern of the laser beam going through the photoresist. Beam widening after one reflection.
Fig. 5. Illustration of the laser beam widening within the photoresist.
N°li LINEWIDTH CONTROL MODEL IN THE FABRICATION OF MCM, ASICS 1513
path of the laser beam during its return to the surface must also be considered. The threshold energy Ets is the lowest one needed to sensitize the photoresist throughout its whole thickness.
Figure 4 schematically shows the exposure of a photoresist of thickness h deposited on
an aluminium substrate. The laser beam comes perpendicularly along the z-axis onto the
photoresist surface, described by the x and g axes. The laser beam, considered as Gaussian,
is focused at the surface of the resist, I.e. the beamwaist of the beam is at the surface. Then the spot radius at the bottom of the resist is uJ(h) and, after the reflection, ~videns on the way back until uJ(2h) at the resist surface. Moreover photo of Figure 5 shows the edges widened
shape obtained on the way back in accordance with Figure 4.
One can also see undulations on the shape of the edge resolution. They come from the standing
waves due to the reflections. Their influence on the mean line width is negligible [7].
The index of refraction of both photoresists is n
= 1.68. Applying the matricial method [3,4]
to uJo and Ro, one deduces the values of uJre~ (size of the beam under the surface) and of Rres (curve radius of the beam under the surface):
l°res 0 Ldo
j~ ~ l j~ ~~
res l.68 °
Hence uJres
= uJo and Rre~
=
~°
The size of the spot stays unchanged when crossing the
1.68
surface. Moreover, Ro is considered as infinite since the laser beam is at its beamwaist on the resist surface. Thus Rres can be considered as infinite as well. Then the laser beam stays at its beamwaist under the surface, when crossing it. The variations of uJ(z) and R(z) within the
photoresist layer are given by relation (2) and (3).
4. Light Intensity Received by the Pl~otoresist
The basic law of absorption (Lambert-Beer law) is given by:
~~)~~ -alit, z) 15)
where I(r, z) is the intensity of light travelling in the z-direction at the distance r jr is defined
as r2
=
x2 +g~) of the optical axis through photoresist medium. a is the absorption coefficient of this medium. It varies during the insolation. In the general case, I(r, z) is given by relation
(6) where the absorbance q(z) is given by expression (7).
~iT,Z) " ~trans~XPI~QIZ)) 16)
with
qlz) = /~ Olz')dz' 17)
and
Itrans " I(r,o)
= ii Ri)I;nc (8)
where Ri is the reflection factor of the photoresist and I;n~ the light intensity arriving at the surface of the resist. The expression ofI;n~ is given by 11,2]:
1;n~ = lo exp ~~ with lo
"
~~ ~~ ~ (9)
Ji
7ruJ~
~
1514 JOURNAL DE PHYSIQUE III Soil
~inc
R~
~trms ~left,I ~l~left,I ~left,3
4 4 Qt 4
~~°'°~~~~~~
~ ~left,0 ~2~left,0 ~left,2 ~2~left,
Aiuminium subs'ra<e
Fig. 6. The three reflections of the light intensity within the photoresist thickness taken into account for the model.
Since the medium can be considered as homogeneous [6], a is independent of z. Thus, when
integrating along this axis, q(z) is equal to oz and at a depth z one has:
~iT,Z) " ~trans ~XPI~°Zi i~°)
We represent diagrammatically in Figure 6 the beam travelling through the photofesist along
the z-axis and reflected by the substrate. The reflection factor of the substrate is R2. In order to determine precisely the line width etched in the photoresist as a function of 9, high values of R2 (for instance, in aluminium R2
" 0.998) mean the second reflection on the substrate must
be considered, I-e- the first reflection under the photoresist surface is not neglected. It is not necessary to take into account further reflections under the resist surface since they represent only o.3% of the total light intensity. Considering Figure 6, the total absorbed light intensity by the resist is:
3
it " ~ jabs,i (11)
1=0
At the bottom of the resist layer (z
= h), with the assumption that the medium is homogeneous, equation (10) becomes:
placing Itrans by - RI and It is given by:
In the general case, the absorbance depends on the depth z, (Eq. (6)). One can still use equation (16) by replacing oh by q(z).
Let us assume Eabs(z, g) the energy absorbed within the thickness of the photoresist. Figure 7
shows the light intensity scanning the photoresist surface, along x-axis, at a speed V. Curve I represents the distribution of the total intensity along g and curve 2 the distribution of the
N°11 LINEWIDTH CONTROL MODEL IN THE FABRICATION OF MCM. ASICS 1515
y (2)
P(x,y)
x
(1>
Fig. 7. Evolution of the light intensity. i) Distribution along the ~-axis; 2) Total light intensity absorbed by a point P during the passage of the spot.
intensity absorbed by a point Fix, g) during the passage time of the spot at a speed V. It depends on r
=
fi. Then It
= Itlx, g) and:
dEabs(x, g)
= It(x, g)dt
= It(x, g)dz. (17)
Expression ii?) has to be integrated along the x-axis. Along this axis, the beam is considered
as coming from infinity and going to infinity. Hence:
El§) " /~~ dEabs = ) /~~Itlx,gjdx. j18j
The result depends on the value of It(x,g) and hence on the value of the absorbance o. The value of this absorbance changes when the spot is moving along the x-axis. One has to take this evolution into consideration.
5. Time Evolution and Spatial Distribution of the Absorbance
The time evolution of the absorbance depends on Dill parameters given in Table I. From these parameters, the two limits of the absorbance value are defined as:
. when the photoresist is still unexposed, the value of the absorbance is the initial one:
a = an = A + B,
. when the photoresist is fully sensitized, its value is: a = ae
= B.
The variation of o comes from the variation of the relative concentration of photoactive compound m(t) within the layer of the photoresist. One has [8, 9]:
nit)
= Amjtj+B j19j
~~ijj~'~~ = -mjr,z,tjljr,zjc j20j
m(t) decreases from i at t = o (the photoresist is not exposed, a
= an to o at t = -oo (the
photoresist is fully sensitized, o = ae).
1516 JOURNAL DE PHYSIQUE III N°li
point stalling
to be affected
spot of rue p /
Q
laser bemn .
~
point still not affected
x~ x
~ v
Fig. 8. Schematization of the laser beam. Definition of xo, yo and ah.
Equation (20) shows the rate of decrease of the absorbance from an to oe. It shows as well that the time dependence of the absorbance leads to a spatial distribution as a function of the
distance r from the beam axis.
Because of the reflection of the laser beam on the substrate, the total light intensity at a depth
z is due to the incoming light ItIT, z, t) superposed with the outcoming light ItIT, 2h z, t).
The evolution of a will be considered, in a first approach, at the depth h, where the patterning
must be realized. Since the spot moves along the x-axis, r depends on time.
5.I. SizE OF THE LASER BEAM. In order to solie equations (19) and (20), it is
necessary to give a shape and a size to the laser beam. They are given by the fact that 98% of the
light intensity of the Gaussian beam is comprised within the circle of radius uJ(h) = ah hence any point of the photoresist surface will see its absorbance affected by the laser beam, moving along the x axis, as soon as this point will be ah away from the center of the spot (see Fig. 8).
In this case, x can be expressed by:
z = xo Vt (21)
x( + g( = Q( (22)
One replaces (21) and (22) into equations (8), (9) and (10) including the time t:
~~~~ ~~~~ ~~~~~ ~~~~ ~~~~(t ~~° j ~-Ahm(t)
-Bh
~°° V ~ j~~~
~~~~ ~ ~~~~~~ ~
F = Ii + R2)Ii RI ~i
exp ~~~
~~~
7r°Jo 1°0
