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Simulation of proximity printing
Microelectronic Elsevier
Engineering
127
10 (1990) 127-152
Simulation of proximity printing W. Henke,
M. Weiss
Fraunhofer-Imtitut Rep. Germar~~
f‘iir Mikrostrukturtechnik.
Diller~hurger Str. .53. 1000 Berlin 33. Fed.
R. Schwalm BASF AC,
Carl-Bosch-Str.
-18. 6700 Ldwigshaferl.
Fed. Rep. Getmarl!
J. Pelka Fraltnhofer-lnstilrt Germany Received Accepted
fiir Mikrostruktlrrtechrlik.
Dillerlhurger.~tr. 5.1. 1000 Berlin 33, Fed. Rep.
19 April 1989 August 7, 1989
Abstract. A simple and easy to apply model is presented for contact and proximity lithographic steps. A first order approximation to the wave propagation inside a resist layer during exposure is provided. including diffraction and standing wave interference effects. This model takes refraction at the air-resist interface into consideration. as well as the depthwise change of the distance from the diffracting mask feature. The algorithm is easy to implement since the data structures of simulators such as SAMPLE are preserved. thus requiring only a modest increase in computational effort. A comparison of simulated resist profiles with those obtained from experiments shows that the model qualitatively explains the shape of profiles which arise under various lithographic conditions. The question of profile degradation, caused by exceeding certain limits for the proximity distance, is discussed. Computed irradiance distributions inside the resist layer at the beginning of the exposure, when the optical properties of the resist material are still isotropic, are used.
Keywords. Lithography.
simulation,
diffraction,
refraction.
proximity
printing
Wolfgang Henke was born in Berlin in 1955. He received his diploma on physics from the Technical University Berlin in 1984. His work dealt with thin film optics and ellipsometry. He joined the staff of the Federal Institute for Materials Testing and Research (BAM) in 1984. working on the field of optical surface roughness analysis. In June 1986 he joined the Fraunhofer Institute of Microstructure Technique and worked since then on process simulation in optical microlithography.
0167-9317/90/$3.50
0
1990. Elsevier
Science
Publishers
B.V.
Manfred Weiss obtained the Diplom degree in mathematics in 1978 and the Dr. degree in physics in 1Y8-1both from the Freic Univcrsitiit Berlin. He worked there on group theory and theoretical low temperature physics. In 1986 he joined the staff of the Fraunhofer Institute of Microstructure Technique in Berlin. His current research interests are modelling and simulation of X-ray and optical lithography and of dry etching processes.
Reinhold Schwalm received his Ph.D. in Polymer Chemistry (lY83) from the University of Marburg. Fed. Rep. Germany. From 19X.1 to 1983 he was a postdoctoral fellow at IBM Research Laboratory. San Jose. California, where he was engaged in the design and synthesis of new. radiation sensitive. dry developable polymers for resist applications. His furthel research activities include 5ynthesix of thermoplastic and liquid crystalline polymers. tclechelics and oligomers. radiation sensitive compounds. etc. In 1985 he joined BASF company. West Germany and currently hc is investigating novel photosensitive resist materials for mid and deep UV lithography. Joachim Pelka was born in Berlin, on March 25. 1954. He received the Dipl.-Ing. degree in electrical engineering in 1978 from the Technical University of Berlin and the Dr.-Ing. degree in lY83. From 1978 to 1083 he was with the Institute of Electrotechnical Materials at the University of Berlin. investigating the blocking capabilities of semiconductor power devices. Since 1983 he has been with the Fraunhofer Institute of Microstructure Technique, Berlin. where he is responsible for the process modeling activities.
1. Introduction Contact or proximity lithography cannot be considered a prime candidate for the mass production of highly integrated memory chips. Nevertheless, it has widespread applications, in areas such as large area flat panel display fabrication or custom chip production. Traditional application areas for contact/proximity aligners are the fabrication of GaAs devices and advanced silicon sensors. Additionally, in deep-UV lithography, where projection printers for exposure wavelengths around 250 nm are still hardly available, contact or proximity printing often serves as a valuable tool in research and development for evaluation of resist systems, or in the investigation of different radiation sources. In the last few years, several authors have discussed various aspects of this lithographic technique, concentrating mostly on diffraction induced image degradation, which occurs most drastically under inappropriate process conditions. For several technological reasons. for example, the size of the proximity
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gap cannot be kept stable over the entire wafer. In contact printing, variable distances between the photomask and the resist film occur due to the lack of wafer flatness or because of dust particles between the mask and the resist layer [7,10] Variable proximity distances can also be caused by a nonplanar wafer surface, which results from preceding lithographic and etch processes. Kundu et al. [14] for example, have determined the 2-dimensional irradiance distribution for different proximity distances, the mask consisting of a set of contact holes. They suggest a method for optimizing the exposure parameters. Similar research has been done by White [20] who computed aerial image shapes of isolated contact holes using the Fresnel diffraction theory. Arshak et al. [2] have shown that, for the 2-dimensional aerial images of arbitrary mask features, the distance between single apertures is an important factor in that this separation contributes significantly to image degradation. The resolution of the lithographic process is determined by the minimum line or space widths which are to be printed, the wavelength of the exposing radiation and the size of the proximity gap. For a given wavelength, the proximity distance should not exceed a certain limit, in order to obtain properly resolved resist profiles after development. According to Novotny [17] who suggested a simple method for estimation of the proximity distance, the gap between mask and wafer typically ranges from 0 to 3 km for hard contact lithography where the mask is held in ‘contact’ to the wafer by a vacuum, from 0 to 15 km for soft contact where ‘contact’ is produced by a small partial vacuum or a small mechanical force, and from about 9 to 25 km for proximity printing. Proximity gap variations of such magnitude critically affect the dimensions of the minimum printable feature sizes on the wafer. The conditions under which minimum feature sizes can be attained using contact or proximity lithography have been determined experimentally by Weill et al. [19], Jain [12] and Massetti et al. [15]. Initial modelling and simulation approaches have been discussed by Bogdanov et al. [3] and Meyerhofer and Mitchell [16]. An effort is made in this article to fill the need for comprehensive modeling of the proximity printing process step. A good understanding of the physical effects involved is desirable in order to separate chemical from physical properties of the resist material during exposure. Therefore, an approximation of the wave propagation in the resist layer during exposure is suggested using a straightforward simulation model, thus allowing computation of the concentration of the photoactive compound (PAC) and simulation of the development step, resulting finally in actual resist profiles. This is essential since the resist profile is virtually the only feature accessible for evaluation. Aerial image shapes, for example, are not suitable because they are only roughly comparable to experimental results. The usual approach for simulation of lithographic process steps, in the process simulator sample [18] for instance, is based on the elementary model introduced by Dill [6]. The elementary or vertical propagation model assumes that the incident radiation is transmitted vertically through the resist layer after crossing the air-resist interface. In such a case the aerial image Z(X) and the
standing wave interference pattern i(z) may be calculated total irradiance inside the resist layer is then 1(X, z) = I(s) * i(z),
independently.
The
(1)
where z is the depth into the resist. This model is insufficient for both contact or proximity and projection lithography, since the proximity distance in proximity printing varies depending on the depth into the resist (see Fig. 9) and the defocus position in the resist layer changes in projection printing. In this article, an effort is made to overcome the deficiency of the elementary model. A short introduction into the theoretical background of the problem is presented in part two of this report. The third section includes an approximative model for the determination of the irradiance distribution in the resist layer. The validity of this model is discussed in the fourth section by comparison with a more rigorous approach. Some simulation and experimental results are presented in the fifth section.
2. The diffraction-refraction
approach
For the formulation of a simulation model of irradiance distribution inside a resist layer in a proximity printing step, a number of physical effects have to be taken into account. Some of the major phenomena which influence the exposure of the resist material are: (1) diffraction of the incident radiation at the mask features, (2) refraction of the radiation at the resist surface, (3) reflection of the indicent radiation at resist/substrate or underlying thin film boundary layers, (4) interference of the reflected wave frontals with the incoming radiation, resulting in a standing wave interference pattern. An influence of scattered radiation is neglected, since neither rigorous nor approximative physical approaches to the problem exist. Scattering has a significant impact, however, since microroughness of the resist surface and/or boundary layers is much better ‘resolved’ by the short wavelength radiation of the deep-UV region, giving rise to a wider angular spread of the stray light. Consequently, the scattered radiation contributes substantially to the exposure of the resist material. The basic purpose of the model to be presented is to determine the distribution of the wave frontals behind the mask and to investigate the refraction effect on the wave propagation afterwards. Finally, the interference effect must be incorporated into the model. The model described here is 2-dimensional, assuming a l-dimensional transparency distribution of the mask, which should be infinitely thin (see Fig. 1). The mask features are considered to be infinitely extended in the y-direction. The simulation of the diffraction phenomena is based on the scalar Kirchhoff diffraction theory, neglecting any polarization effects which might occur while
W. Henke et al. I Sirndntior~ of proxirniry prin/itzg R
L
131
mask
d / O_
c
IIT \ 2
P
plane
of observation
r-1
Fig. 1. Diffraction
at a single space in a mask.
the radiation propagates through mask features, having dimensions similar to those of the wavelength. This approximation seems justified if one considers the results of [S] The scalar field in a point P(x, z) on the plane of observation lying behind the diffracting mask feature can be expressed through the Fresnel-Kirchhoff diffraction integral, from which the following formula can be derived
u(x, p) = u,, . eikP . -~~
.
The position of the coordinate system and the notation are shown in Fig. 1. In this equation, p is the size of the proximity gap and x represents the x-coordinate of a point in the plane of observation, and x is the coordinate in the plane of the diffracting aperture. The wave number is
and f(t),
the transparency
f(5) = { Equation
function
1
in transparent
0
in opaque
(2) consists
of the mask, is areas,
areas.
of two major parts:
a plane wave
having an amplitude
U(x,p)
U,,, and a disturbance
in (2) re d uces
to the incoming
f(5). ei(XI*/O(~-_v)2
h
=
m
wave if f(l)
.
= 1 in --x s 5 s ix,
since
J g.
(7)
k
For the transparency function of a mask space (Fig. expressed using the complex Fresnel-function
1) the scalar field can be
A straightforward calculation now gives the scalar field (2) in the plane observation which is at distance p behind the mask of the form
of
(9)
The phase
4(x, p) of the scalar field can be determined
and the irradiance
can be obtained
I(& p> = IU(.Gp)12.
using the relation
from (9) by
(11)
By evaluating (9) using a rational approximation for the Fresnel-function given in [l] and by varying the proximity distance, the phase distribution behind a diffracting aperture can be computed. Figure 2 shows the contour plot of the phase values C#J(X, p) = 0 directly behind the mask feature. The space is chosen to be 0.5 km wide and the wavelength of the incident radiation is A = 248.0 nm. which corresponds to the commonly used excimer laser line. The proximity distance or the distance of the plane of observation from the mask is varied between 0.5 and 1.0 pm. If a semi-infinite refractive medium is placed at a distance behind the mask, and the phase or irradiance distribution is to be determined, the wavelength has to be scaled while maintaining phase relations inside the medium. The wavelength inside the medium is:
W. He&e et al. I Simrlation of proximity printing
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--
Fig. 2. Contour
plot of planes of equal phase behind a 0.5 )J-m wide space in a mask. wavelength A = 248.0 nm: the position of the mask feature is shown above.
A2 = Al/n,
(12)
where A, corresponds to the wavelength in air and n is the refractive index of the medium. The computation of the scalar field inside the refractive medium is done in two steps. First, the field distribution on the surface boundary plane of the refractive medium for the wavelength A, of the radiation in air and for the given proximity gap pi is determined. In a second step, the mask plane is vertically shifted (Fig. 3) in such a way that the same field distribution results at the interface between air and the refractive medium. The space behind the mask is assumed to be homogeneously filled with the refractive medium, and the propagation of the field inside the refractive medium is now treated as if there were no step in the refraction index behind the mask. In this way, diffraction and refraction effects can be handled simultaneously. Formally, the scalar field before shifting the mask results from (9), giving for O
(13)
The scalar field inside the refractive is for z >pl:
p2 -pl
medium
after shifting the mask by a distance
Fig. 3. In the diffraction-refraction wavelength A2 the space behind
approach the mask is vertically shifted, the mask can hc considered homogeneously rcfractivc medium.
.Y -
-c
‘\‘(z -PI with the respective numbers
proximity
distances
so that for the tilled with the
R
(14)
fp,)AJ2
p , and p?. and the respective
wave
k, = 25-l/I,
(15)
k, = 21~lh,.
(16)
and
Since the field at the interface u,(~,p,)
= LL(.LP,)
must be continuous,
from
at17 =PI.
two conditions for equality of the scalar refractive medium are achieved:
(17) fields
in the surface
plane
of the
W. Henke et ul. I Sirndutiot~
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and kz.pz+6=k,-p,. From (18), the following
(19) proximity
pz=n.p,. Condition
distance
can be calculated: (20)
(19) leads to a phase shift
(21) which avoids phase discontinuities at the surface plane. Condition (20) is most important for the computation of the diffraction pattern inside the refractive medium. It simply means that wavelength and proximity distance have to be scaled by the refractive index n in order to obtain the irradiance distribution due to diffraction at the mask feature inside the refractive medium. We call the approach summarized by (20) and (21) the diffraction-refraction approach. It must be emphasized that the’ proximity distance p2 is only of theoretical interest; the size of the physically relevant proximity gap is of course pt. Figure 4 shows an example of the effect of a refractive medium on the phase distribution. The refractive index is chosen to be n = 1.6 and the mask to surface plane separation is 0.75 pm. Figure 4 shows that the planes of equal phase are continuous at the interface between air and the refractive medium. For media with very high refractive indices, the validity of the Snell’s law of refraction can be verified graphically at the boundary plane of the medium (see for example Fig. 5a). Additionally, it shows that the planes of equal phase become increasingly flatter as the refractive index increases. This fact is consistent with geometric optics considerations. The considerations in this section were limited to the case of a single space in an opaque mask. Nevertheless, they can easily be extended to the case of arbitrary mask features.
3. The separation model The basic idea of a model is presented in this section, allowing the computation of the irradiance distribution as well as the amount of decomposed photoactive compound in a resist layer during a proximity printing process step. The effects of diffraction and of interference phenomena are separated. The individual irradiance distribution for each single effect is determined. The diffraction computation is performed for several sublayers of the resist film using the diffraction-refraction approach, in order to take both effects into account. The condition expressed in (21) is not necessary in this case since only
136
Fig. 3. Contour
plot of planes of equal phase inside a refractive
a 0.5 pm wide space in a mask. wavelength position
1.50
x [uml
0.00
medium of index II =
h = 238.0 nm, proximity
of the mask feature is shown above: the surface of the medium is symbolized line
I .6 behind
distance 17= 0.75 km:
the
by a straight
in the middle of the plot.
the irradiation distribution is of interest. The standing wave interference pattern is calculated assuming normal incidence of the incoming radiation. Finally, the two distributions are superimposed, giving the basic formula of the so-called separation model:
(22) where I[,(x, z) is the irradiance distribution due to the diffraction at the mask features as described in Section 2. and i(z) is the irradiance that exists at a depth I when a plane wave of unit flux is incident normal to the surface of the resist. Thus, the separation model can be considered as a combination of the diffraction-refraction approach with an extended elementary model. The funcFor a nonreflecting substrate, i(z) tion i(z) includes absorption and reflection. is given approximately by Beer’s Law i(z) = i,, . exp {-
where
CI is the absorption
J1: cu(z’) dr’i coefficient
(z ‘o),
of the resist material.
(23) Since the optical
137
W. Hmke et ~1. / Sirndntiot~ of proxirni~ printing
properties of the resist are modified by exposure, it is usually divided into sublayers thin enough to be treated as if they had isotropic optical properties Consequently, i(z) in the resist sublayers can conveniently be treated using the thin film optics algorithms as described in [6]. Absorption is incorporated into the separation model (22) even though oblique rays contribute to the image at depth z, with such rays undergoing polarization dependent surface reflection and enhanced absorption. The primary effect is contained in the normal and near normal rays. The fact that the absorption is included in the function i(z) enables the calculation of bleaching of the resist material during exposure and then the determination of the photoactive compound as described in [5]. This model is easily simulated because its representation is closely similar to that of the vertical propagation model (1). Note that the time-dependence in the problem arising from the time dependent photoproduct concentration is still limited to the function i(z).
4. Comparison
of the separation
model with a more rigorous model
To check the validity of the separation model, a more rigorous approach is taken and the results from both models are compared for several cases. For the ‘rigorous’ model. the range of variation for the proximity distance is twice as large as the thickness of the resist layer DR. With the diffraction-refraction approach of Section 2, the scalar field is computed for the range 0 < z < 2. DR. Then the reflected image of the region DR d z ZG2 * DR is coherently superimposed with the range 0 s z G Dn, considering possible amplitude attenuation and phase shift at the resist substrate interface. In Fig. 5, the situation for planes of equal phase is shown. The complex reflection R is introduced here and has the following form: (24) The reflection coefficient following [9] :
R
=
at the resist (R)/substrate
(S) interface
is given by the
(h - i&d - (ns- ik.)
(25)
(nR - ikn) + (ns - iks)
assuming normal incidence of the radiation. n, k represent the refractive index and the extinction coefficient of the resist and the substrate respectively. Thus, both the reflected scalar field and the reflected irradiance within the range DR d z d 2. DR can be calculated from Urr&,
z) = R . U(x, 2&
In the same manner
as described
(26)
- z). above,
multiple
reflections
inside
the resist
138
z =
2 * DR
Fig. 5. (a) For determination of the irradiance distribution in a resist layer: enlargement of the proximity range 0 < : < 2 DR. (b) For determination of the irradiance distribution in a resist layer: construction of the reflected image above ; = DR.
layer and the influence of underlying thin films can be computed. Note that only layers having isotropic optical properties can be simulated using the socalled rigorous approach; bleaching effects of the resist material are, therefore, excluded from the investigation when using this approach. The basic premise of the rigorous model, superposition of wave frontals propagating in opposite directions, can be summarized in the following formula:
W. Henke et 01. I Sirndntion of proximity prirltiq
I(& z) =
ICu
1
(x, z) +
2 u t (x3z)12,
139
(27)
where m is the number of reflections taken into account in the calculation, and up and downward pointing arrows have been added to indicate the direction of propagation. Thus, the so-called rigorous model in this section is based on three major assumptions. First, wave propagation in the resist layer is assumed to be a strictly scalar phenomenon. Second, the reflection R is calculated under the normal incidence assumption and third, the number of propagation calculations through the resist layer or computations of reflected images is finite. The second assumption is justified since only the reflection coefficients for large angles of incidence vary significantly compared to those for normal incidence. The influence of multiple reflections inside the resist layer can be neglected since even after a small number of reflections, the amplitude of the radiation will drop to an insignificant fraction. Note that usually only about 5% of the incident radiation will be reflected back into the resist layer at the resist/air boundary plane. In the results shown here, five reflections were considered (three at the resist/substrate interface and two at the resist/air interface). Figures 6 and 7 show examples of contour plots of the irradiance distribution inside a resist layer as a result of both the ‘rigorous’ and the ‘separation’ approaches, for comparison. All computations were done using a wavelength A = 248.0 nm and a refractive index of the resist layer of n = 1.6, with silicon as substrate. The resist material was taken to be nonabsorbing and the thickness of the resist film was set at the relatively low value of DR = 0.5 nm. Both these conditions served to make the plots easy to survey and to compare. All contour plots present contours for irradiance values of 0.3 and 1.3, where the irradiance is normalized to a value of one in the mask plane. There is very good agreement between results from both models, as shown in Figs 6 and 7. The agreement even increases with increasing proximity gap size, due to the fact that far field wave frontals are flatter than those in near field. The conditions for assuming normal incidence for the interference pattern calculation are, therefore, more likely satisfied in far field. This shows that the separation model can be used to simulate the irradiance distribution inside a resist layer taking into account the depthwise change of the diffraction image, which is due to the change of the proximity distance (Fig. 9) and refraction effects. The difference in size or position of corresponding contours of both models can be considered a measure of error for the separation model. From a series of calculations, this error was found to be less than 10% of the feature size for the 0.3 contour. For the contours of higher values, the error is even less. This agreement between the results from both models shows that the separation model is applicable if one neglects the change of wave propagation inside the resist layer during exposure, which is due to the dynamic response of the resist material (bleaching).
140
Fig. 6. Comparison of results of the rigorous model (top) and the separation model (bottom). wavelength h = 248 nm, feature size d = 0.5 km. proximity distance p = 0.75 pm. resist thickness DR = 0.5 pm. refractive index II = I .6, extinction coefficient li = 0.0.
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Fig. 7. Comparison of results of the rigorous model (top) and the separation model (bottom), wavelength A = 248.0 nm, feature size d = 0.5 km, proximity distance p = 1.0 (*rn. resist thickness DR=0.5 )J-m, refractive index n=1.6, extinction coefficient k=O.O.
142
0.0
Fig. 8. Irradiance 1.0 (*m, proximity
2.0
h = 248.0 nm. feature size C/= distribution inside a resist layer. wavelength index II = 1.6. distance p = 0.5 pm, resist thickness DK = 1.0 km. refractive extinction coefficient I, = 0.0.
c
mask
_..__b
x
proximity
gap
resist
Fig. 9. In proximity
printing,
the proximity distance varies between resist thickness DR.
p and P,,,;,, = p -t D,. with a
W. Henke et al. I Sirndation Table 1 Basic formulae
of the models
Model
143
discussed Formula
Elementary
model
Separation Rigorous
of proximity printing
model model
(1) (22)
(27)
1(x, z) = I(x). i(z) I(x, z) = I&, I(x,z)=
z) . i(z)
CLQ(x.,‘)+ ,,I
c Ur(..r)~z ,,1 I
In the absence of interference effects, which is the case when the resist is placed on a non-reflecting substrate, both models give identical results. In this case, the irradiance distribution reduces to the well known pattern shown in Fig. 8. Finally, the basic formulae of the various models discussed in Sections 1, 3 and 4, are summarized in Table 1.
5. Results
The separation model, as described in section three, has been implemented in our revised SAMPLE version (1.6a, 1985) [X3]. This now allows simulation of proximity printing process steps with typical Novolac resist systems for which the resist model of Dill. [5] is applicable. In this section several simulations as well as .experimental results are presented and discussed, using an HPR 204 positive resist. A production type mask aligner in the hard contact mode, from the K. Siil3 Company, was used for exposures. The mean wavelength of the exposing radiation was approximately A = 404.7 nm. The simulation parameters for the resist were taken from [13] ( see Table 2). Unfortunately, the data for the LSI developer (Olin Hunt) used in the experiments were not available, so the data for the HPRD-429 developer were used instead. To partially compensate for this parameter substitution the exposure dose has been adjusted freely in the simulation. The resist was spun on a bare silicon wafer, resulting in a final resist thickness of DR = 1.4 km after a hotplate pre-bake. No post-exposure bake was performed in order to avoid wipe out of the diffraction image and the standing wave interference pattern ‘written’ into the resist material during the exposure step. For similar reasons we have chosen relatively large mask features in the forthcoming examples, since lateral diffraction dependent irradiance oscillations are more pronounced in this case. The development time was chosen to be relatively short, t,, = 5 s, in order to preserve the diffraction and interference dependent resist profile which, of course, vanishes if the resist is completely developed. The exposure dose was approximately 120 mJ/cm*. Figure 10a represents a SEM-photograph of a 4 pm wide resist space. It shows,
Table 2 Parameters Resist:
used for experiments
HPR 204Developer:
and simulations
HPRD-429
(Olin Hunt)
(Optical Parameters) A: Parameter for photobleachable component B: Parameter for nonblcachable component C: Speed of bleaching of the photoactive compound
0.57 km ’ 0.08 p.m ’ 0.010 cm’/mJ
(Chemical Parameters) R,: Dissolution rate of fully exposed resist X2: Dissolution rate of unexposed resist R,: Fitting coefficient for dissolution rate curves
0.537 km/s 0.040 km/s 7.9
Lithographic
Conditions:
Substrate: Resist thickness:
silicon II,, = I.4 pm
(Optics) Equipment: Exposure dose:
K. Sup. MA 56 Mask aligner. I20 mJ/cm’
(Development) Development
5s
time:
h = 304.7 nm
as a consequence of the well-known standing wave interference pattern, ripples in the the side-walls of the profile. Additionally, the influence of diffraction becomes clear in the middle of the pattern, where the resist has not been developed as fast as in the areas lying closer to the edges of the profile. Especially in the corners of the profile, the effect of diffraction induced irradiante variations becomes obvious. Two irradiance maxima can be observed here, corresponding to results obtained by White [20] in 2-dimensional modeling of aerial images in proximity printing. Figure lob shows the results of a simulation in which the cross section of the developed resist profile is at a sufficient distance from the corners of the resist pattern. This restriction is significant since influences due to diffraction at the corners of the 2-dimensional mask feature are not included in the separation model. Because a l-dimensional transparency function of the mask was assumed for the formulation of the separation model, simulation of such 2-dimensional effects would require a 3-dimensional simulation model. In such a case. the separation approach could easily be extended to apply. For the profile shown in Fig. lOb, the entire resist film was divided into 160 sublayers for computation. The diffraction dependent irradiance distribution in each individual sublayer was calculated for approximately 120 points. In addition, the extended exposure dose table which was implemented in our revised SAMPLE version was used. The development section of our SAMPLE version had to be modified in order to make it capable of handling strong lateral oscillations of the PAC-concentration which are caused by diffraction. A single
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simulation run took about 4-5 CPU minutes on a DEC MicroVax 11 with a VAX/VMS operating system. The distance p between the mask and the resist surface was chosen to be approx. 4.5 pm. Changes in p within the range of kO.3 brn leave the resist profile essentially unaltered. Comparison of experimental results (Fig. 10a and simulation (lob) show satisfying qualitative agree-
-1.600
lb 0.000 x
Cum1
Fig. 10. Developed profiles of a nominally 4.0 pm wide space distance p = 4.5 Frn; (a) experimental result, (b) simulation; summarized in Table 2.
6 000
in HPR 204 resist. proximity lithographic conditions are
ment of both, so that the separation model can be considered a practical first order approximation to the propagation of radiation inside a resist film during a proximity printing process step. Residual discrepancies between experiment and simulation in, for example, the side wall angle are very likely due to improper developer simulation data. Figure 11 shows a contour plot of the irradiance distribution inside the resist film for the situation displayed in Fig 10 at the start of the exposure, when the resist material can still be considered optically isotropic. The data taken to calculate this distribution were the same as those used for the simulation in Fig lob. Figures 12a and 12b show another comparison of a proximity printed resist profile and the corresponding simulation. The mask pattern in this case was a line/space combination consisting of 1:l lines with a width of d = 3.5 pm. The lithographic conditions were the same as those mentioned above. The proximity distance had to be adjusted, however, to a value of 2.5 pm. Again. Fig 13 shows a contour plot of the irradiance distribution at the start of exposure for the same lithographic conditions as in Figure 12b. Simulations using the elementary model of (1) and the separation approach are shown in Fig 14 (a) and (b) respectively. Here. the conditions are the same as those given in Table 2 except that an index matched substrate is used. the
Fig. 11. Contour
plot of the irradiance distribution at the beginning correspond to those of Fig. 1Ob.
of the exposure.
conditions
W. Henke et 01. I Sirndation of proximity printing
147
1 000
T L
N
-1600 0.000 x
Cum1
5 000
Fig. 12. Developed profiles of a nominally 3.5 km wide line/space pattern in HPR proximity distance p = 2.5 km; (a) experimental result, (b) simulation; lithographic are summarized in Table 2.
204 resist. conditions
proximity distance is set to p = 1.0 pm and multiple development contours are plotted. As shown in Fig 14, the elementary model predicts that the developer breaks earlier through the resist layer than the separation model does. The increase in development time to achieve a break through in the separation model is caused by the fact that the degradation of the aerial image for various depths into the resist layer is taken into account. The irradiance distribution
W. Henke et al. 1 Si~nillationof proximity printing
Fig. 13. Contour plot of the irradiance distribution at the beginning of exposure, conditions correspond to those of Fig. 12b.
maximum lowers through the resist film and the image is laterally spread. As a result, this effect is readily observed in the near field (small proximity distance). It can be neglected, however, in the far field (large proximity distance), where the irradiance distribution changes only insignificantly through the resist. The degradation of the aerial image, on the other hand, is not considered at all in the elementary model. It should be noted that the phenomenon just mentioned
Fig. 14. Comparison of results of the elementary model (a) and the separation model (b); proximity distance p = 1.0 pm; mask feature: space d = 1.0 km; development contour times: 2.0, 3.5 and 5.0 s, other conditions are given in Table 2. Note that for both simulations an exposure dose of 120 mJlcm2 was used.
W. Henke et al. I Simulation of proximity printing
149
occurs only if small mask features are used. For large feature sizes, where the diffraction image changes only insignificantly across the resist layer, both models give identical results. Using the separation model, an image reversal [ll] inside the resist layer can be simulated. This phenomenon can occur if the mask consists of periodic line/space combinations. The lithographic conditions under which an image reversal occurs can be constructed using the structural factor [ 111. The proximity distance necessary for this effect to occur can be determined using the definition of the structural factor u:
(28)
u=d-e.
The structural factor UrR for the diffraction pattern on the bottom side of the resist film in the case of an image reversal has been determined in [II] to be u ,R =
0.7.
(29)
According to (20), the scaled proximity distance has to be put into (28) with the addition of the thickness of the resist film &, giving (30) where hn is the wavelength of the radiation inside the resist material and n is its refractive index. This results in the proximity distance between mask and resist surface in the case of an image reversal inside the resist layer 2 PIR
=
DR
d2
A H UIR
--
n
’
(31)
Note that the structural factor for the diffraction pattern occurring at the top of the resist must be significantly greater than one. If not, then no image reversal inside the resist film can be observed. Figure 15 shows a contour plot of the irradiance distribution inside a relatively thick resist layer with DR = 3.0 km. The size of the single mask feature is d = 0.5 km, the wavelength of the exposing radiation is A = 248.0 nm, the refractive index is n = 1.5 and the proximity distance is p = 1.0 pm. To facilitate the surveying of the plot, only contour lines for a value of 1.0 of the normalized irradiance were plotted. For the same reason, the resist layer was assumed to be nonabsorbing. The existence of a critical proximity distance at which an image reversal occurs is obvious from (31). Especially for very small feature sizes, the proximity distance should be kept well below that critical value. Otherwise it is very likely that the mask feature will not be transferrable into the resist material at all. A large refractive index of the resist material slightly shifts this critical distance to larger values. If one allows a structural factor of u = 1.0, for instance, as the
Fig. 15. Contour plot of the irradiancc distribution inside a resist layer in the case of an image reversal: mask feature: line/space rl= 0.5 km. A = 248.0 nm, refractive index II = 1.5. proximity distance p = I .Okm.
Fig. 16. Dependence of the proximity distances for which a structural factor of u = 1.0 on the bottom side of the resist layer is obtained: mask feature: line/space. resist thickness DK = I .Opm. A = 248.0 nm.
W. Her&e et al. I Sirndnriorl
of proximity
printing
151
worst possible value for the diffraction pattern on the bottom side of the resist film, the critical proximity distance depends mainly on the size of the mask features. Figure 16 shows the dependence for three different refractive index values. It is obvious that very tight restrictions on the size of the proximity gap have to be made for submicron mask features.
6. Conclusions The separation model which has been presented and examined in this article provides a practical first order approximation for the wave propagation inside a resist layer during a proximity printing process step. The model was implemented in our revised SAMPLE version, allowing for computation of the diffraction and interference induced irradiance variations inside a resist film. Since the physical effects of diffraction and interference are treated separately and the interference phenomena are assumed to be due to normally incident radiation, the bleaching of the resist material can easily be introduced. This allows simulation of the decomposition of the photoactive compound and the development process step. Consequently, the properties of the resist profiles which can be obtained under particular lithographic conditions can be predicted using this model. The model is limited to a description of coplanar layers. Satisfying agreement of both proximity printed resist profiles and simulations shows that the model is applicable to simulation of such processes. The simulations give a good qualitative explanation for resist profiles which arise after exposure and during the development of the resist material. Using the structural factor along with the separation model, the influences of certain wavelength/feature size/proximity distance margins can be investigated. It has been shown that under particular lithographic conditions, image reversals inside the resist layer can occur, making a proper transfer of patterns into the resist film virtually impossible. This requires that a certain critical proximity distance is not exceeded if, for example, submicron feature sizes are to be printed.
References [l] M. Abramowitz and I. A. Stegun. Handbook of Mnthernaticnl Functions (Dover. New York. 1972) 302. [2] K. I. Arshak, N. N. Kundu and S. N. Gupta, Simulation of proximity printing. Proceedings SPIE OpticaNLnser Microlithogrphy, Vol. 922 (1988) 241-246. [3] A. L. Bogdanov, A. A. Polykov. K. A. Valiew. L. V. Velikov and D. Y. Zaroslov. Computer simulation of the percolational development and pattern formation in pulsed laser exposed positive photoresists. Proceedings SPIE Advances in Resist Technology nnd Processing IV. Vol. 771 (1987) 167-172. [4] M. Born and E. Wolf, Principles of Optics (Pergamon, sixth edition. 1987) Chapter 8.8.3, 382-383.
152
W. Henke
et al. I Simulation
of proximiv
printing
[S] F. H. Dill, W. P. Hornberger, P. S. Hauge and J. S. Shaw, Characterization of positive photoresist. IEEE Tram. Electr. Der,. ED-22(7) (July lY75) 445-156. [6] F. H. Dill. A. R. Neureuther, J. A. Tuttle and E. J. Walker, Modeling projection printing of positive photoresist, IEEE Trwzs. Elect,-. Del, ED-22 (7) (July lY75) 356-464. [7] G. Geikas and B. Ables, Contact printing - associated problems. Proceedilzgs Kotfrrk :l~ic~roelectrorlics Semirwr lY68. Vol. 11 (1068) 47-54. [8] W. E. Haller and A. R. Neureuther. Polarization dependence of diffraction by high resolution masks, Proceediqs SPIE OpticuIILrwr ,~licrolitl7ograI,l7!,. Vol. 922 ( lYX8) 165--l 77. [9] 0. S. Heavens. Opticrd Properties of Thin Solid Films (Butterworths. London. lY55) Chapter 4, 46-55. [ 101 R. C. Heim. Practical aspects of contact/proximity. photomasklwafcr exposure. P~mwlir7gs SPIE Semiconductor Microlithography II. Vol. 100 ( lY77) 104-l l-1. [ll] W. Henke, R. Schwalm. M. Weiss and J. Pelka. Diffraction effects in submicron contact/proximity printing. Microelectrolzic E,zgineeriq 10 (lY89). [12] K. Jain, Advances in excimer laser lithography. Proceedings SPIE Losers i/7 Microlithoglophy,
Vol.
774 (1987)
115-123.
[13] T. Kokubo, Z. Idemoto. Y. Kawabe and K. Ucnishi. Design of a positive photoresist for submicron imaging assisted by SAMPLE simulation. Proceediq.r SPIE Ad\wce.s ir7 resi.\t technology arut’ processing V. Vol. 920 (1988) 3X-363. [14] N. N. Kundu, S. Goel, S. N. Gupta and B. P. Mathur. Image intensity distribution of double spaced contact holes, Proceedings SPIE Optical Microlithogrq&v Vol. 633 (lY86) 245-252. [lS] D. 0. Massetti. M. A. Hockey. and D. L. McFarland. Evaluation of deep UV proximit) mode printing. Proceedirlgs SPIE Semiconductor Microlithogrr~I?h~ V. Vol. 221 ( 1980) 32-38. [16] D. Meyerhofer and J. Mitchell, Proximity printing of chrome masks. RCA Rel, 43 (April 1982) 608-625. [17] D. B. Novotny. Measurement of the separation distance in contact and proximity lithography, J. Electrochem. Sot.. Solid-state science and technology. 133 (12) (December 1986) 260&2605. [IS] W. G. Oldham. S. N. Nandgaonkar, A. R. Neureuther and M. O‘Toole. A general simulator for VLSI lithography and etching processes, IEEE Trans. Elcctr. Del,. ED-26 (4) (1979) 717-722. [19] A. Weill, J. M. Francou and J. P. Panabiere, Subhalfmicronic contact printing lithograph! using microwave powered deep UV source. Procerdir7g.s SPIE 0pticalILa.w Microlithogrrrphy Vol. 992 (1988) 236-240. [20] L. K. White, Positive and negative tone near-contact printing of contact hole maskings. RCA Rev. 43 (June 1982) 391311.
Engineering
127
10 (1990) 127-152
Simulation of proximity printing W. Henke,
M. Weiss
Fraunhofer-Imtitut Rep. Germar~~
f‘iir Mikrostrukturtechnik.
Diller~hurger Str. .53. 1000 Berlin 33. Fed.
R. Schwalm BASF AC,
Carl-Bosch-Str.
-18. 6700 Ldwigshaferl.
Fed. Rep. Getmarl!
J. Pelka Fraltnhofer-lnstilrt Germany Received Accepted
fiir Mikrostruktlrrtechrlik.
Dillerlhurger.~tr. 5.1. 1000 Berlin 33, Fed. Rep.
19 April 1989 August 7, 1989
Abstract. A simple and easy to apply model is presented for contact and proximity lithographic steps. A first order approximation to the wave propagation inside a resist layer during exposure is provided. including diffraction and standing wave interference effects. This model takes refraction at the air-resist interface into consideration. as well as the depthwise change of the distance from the diffracting mask feature. The algorithm is easy to implement since the data structures of simulators such as SAMPLE are preserved. thus requiring only a modest increase in computational effort. A comparison of simulated resist profiles with those obtained from experiments shows that the model qualitatively explains the shape of profiles which arise under various lithographic conditions. The question of profile degradation, caused by exceeding certain limits for the proximity distance, is discussed. Computed irradiance distributions inside the resist layer at the beginning of the exposure, when the optical properties of the resist material are still isotropic, are used.
Keywords. Lithography.
simulation,
diffraction,
refraction.
proximity
printing
Wolfgang Henke was born in Berlin in 1955. He received his diploma on physics from the Technical University Berlin in 1984. His work dealt with thin film optics and ellipsometry. He joined the staff of the Federal Institute for Materials Testing and Research (BAM) in 1984. working on the field of optical surface roughness analysis. In June 1986 he joined the Fraunhofer Institute of Microstructure Technique and worked since then on process simulation in optical microlithography.
0167-9317/90/$3.50
0
1990. Elsevier
Science
Publishers
B.V.
Manfred Weiss obtained the Diplom degree in mathematics in 1978 and the Dr. degree in physics in 1Y8-1both from the Freic Univcrsitiit Berlin. He worked there on group theory and theoretical low temperature physics. In 1986 he joined the staff of the Fraunhofer Institute of Microstructure Technique in Berlin. His current research interests are modelling and simulation of X-ray and optical lithography and of dry etching processes.
Reinhold Schwalm received his Ph.D. in Polymer Chemistry (lY83) from the University of Marburg. Fed. Rep. Germany. From 19X.1 to 1983 he was a postdoctoral fellow at IBM Research Laboratory. San Jose. California, where he was engaged in the design and synthesis of new. radiation sensitive. dry developable polymers for resist applications. His furthel research activities include 5ynthesix of thermoplastic and liquid crystalline polymers. tclechelics and oligomers. radiation sensitive compounds. etc. In 1985 he joined BASF company. West Germany and currently hc is investigating novel photosensitive resist materials for mid and deep UV lithography. Joachim Pelka was born in Berlin, on March 25. 1954. He received the Dipl.-Ing. degree in electrical engineering in 1978 from the Technical University of Berlin and the Dr.-Ing. degree in lY83. From 1978 to 1083 he was with the Institute of Electrotechnical Materials at the University of Berlin. investigating the blocking capabilities of semiconductor power devices. Since 1983 he has been with the Fraunhofer Institute of Microstructure Technique, Berlin. where he is responsible for the process modeling activities.
1. Introduction Contact or proximity lithography cannot be considered a prime candidate for the mass production of highly integrated memory chips. Nevertheless, it has widespread applications, in areas such as large area flat panel display fabrication or custom chip production. Traditional application areas for contact/proximity aligners are the fabrication of GaAs devices and advanced silicon sensors. Additionally, in deep-UV lithography, where projection printers for exposure wavelengths around 250 nm are still hardly available, contact or proximity printing often serves as a valuable tool in research and development for evaluation of resist systems, or in the investigation of different radiation sources. In the last few years, several authors have discussed various aspects of this lithographic technique, concentrating mostly on diffraction induced image degradation, which occurs most drastically under inappropriate process conditions. For several technological reasons. for example, the size of the proximity
W. Herlke
et al.
I Sirnulatio~~
of proxirniy
printing
129
gap cannot be kept stable over the entire wafer. In contact printing, variable distances between the photomask and the resist film occur due to the lack of wafer flatness or because of dust particles between the mask and the resist layer [7,10] Variable proximity distances can also be caused by a nonplanar wafer surface, which results from preceding lithographic and etch processes. Kundu et al. [14] for example, have determined the 2-dimensional irradiance distribution for different proximity distances, the mask consisting of a set of contact holes. They suggest a method for optimizing the exposure parameters. Similar research has been done by White [20] who computed aerial image shapes of isolated contact holes using the Fresnel diffraction theory. Arshak et al. [2] have shown that, for the 2-dimensional aerial images of arbitrary mask features, the distance between single apertures is an important factor in that this separation contributes significantly to image degradation. The resolution of the lithographic process is determined by the minimum line or space widths which are to be printed, the wavelength of the exposing radiation and the size of the proximity gap. For a given wavelength, the proximity distance should not exceed a certain limit, in order to obtain properly resolved resist profiles after development. According to Novotny [17] who suggested a simple method for estimation of the proximity distance, the gap between mask and wafer typically ranges from 0 to 3 km for hard contact lithography where the mask is held in ‘contact’ to the wafer by a vacuum, from 0 to 15 km for soft contact where ‘contact’ is produced by a small partial vacuum or a small mechanical force, and from about 9 to 25 km for proximity printing. Proximity gap variations of such magnitude critically affect the dimensions of the minimum printable feature sizes on the wafer. The conditions under which minimum feature sizes can be attained using contact or proximity lithography have been determined experimentally by Weill et al. [19], Jain [12] and Massetti et al. [15]. Initial modelling and simulation approaches have been discussed by Bogdanov et al. [3] and Meyerhofer and Mitchell [16]. An effort is made in this article to fill the need for comprehensive modeling of the proximity printing process step. A good understanding of the physical effects involved is desirable in order to separate chemical from physical properties of the resist material during exposure. Therefore, an approximation of the wave propagation in the resist layer during exposure is suggested using a straightforward simulation model, thus allowing computation of the concentration of the photoactive compound (PAC) and simulation of the development step, resulting finally in actual resist profiles. This is essential since the resist profile is virtually the only feature accessible for evaluation. Aerial image shapes, for example, are not suitable because they are only roughly comparable to experimental results. The usual approach for simulation of lithographic process steps, in the process simulator sample [18] for instance, is based on the elementary model introduced by Dill [6]. The elementary or vertical propagation model assumes that the incident radiation is transmitted vertically through the resist layer after crossing the air-resist interface. In such a case the aerial image Z(X) and the
standing wave interference pattern i(z) may be calculated total irradiance inside the resist layer is then 1(X, z) = I(s) * i(z),
independently.
The
(1)
where z is the depth into the resist. This model is insufficient for both contact or proximity and projection lithography, since the proximity distance in proximity printing varies depending on the depth into the resist (see Fig. 9) and the defocus position in the resist layer changes in projection printing. In this article, an effort is made to overcome the deficiency of the elementary model. A short introduction into the theoretical background of the problem is presented in part two of this report. The third section includes an approximative model for the determination of the irradiance distribution in the resist layer. The validity of this model is discussed in the fourth section by comparison with a more rigorous approach. Some simulation and experimental results are presented in the fifth section.
2. The diffraction-refraction
approach
For the formulation of a simulation model of irradiance distribution inside a resist layer in a proximity printing step, a number of physical effects have to be taken into account. Some of the major phenomena which influence the exposure of the resist material are: (1) diffraction of the incident radiation at the mask features, (2) refraction of the radiation at the resist surface, (3) reflection of the indicent radiation at resist/substrate or underlying thin film boundary layers, (4) interference of the reflected wave frontals with the incoming radiation, resulting in a standing wave interference pattern. An influence of scattered radiation is neglected, since neither rigorous nor approximative physical approaches to the problem exist. Scattering has a significant impact, however, since microroughness of the resist surface and/or boundary layers is much better ‘resolved’ by the short wavelength radiation of the deep-UV region, giving rise to a wider angular spread of the stray light. Consequently, the scattered radiation contributes substantially to the exposure of the resist material. The basic purpose of the model to be presented is to determine the distribution of the wave frontals behind the mask and to investigate the refraction effect on the wave propagation afterwards. Finally, the interference effect must be incorporated into the model. The model described here is 2-dimensional, assuming a l-dimensional transparency distribution of the mask, which should be infinitely thin (see Fig. 1). The mask features are considered to be infinitely extended in the y-direction. The simulation of the diffraction phenomena is based on the scalar Kirchhoff diffraction theory, neglecting any polarization effects which might occur while
W. Henke et al. I Sirndntior~ of proxirniry prin/itzg R
L
131
mask
d / O_
c
IIT \ 2
P
plane
of observation
r-1
Fig. 1. Diffraction
at a single space in a mask.
the radiation propagates through mask features, having dimensions similar to those of the wavelength. This approximation seems justified if one considers the results of [S] The scalar field in a point P(x, z) on the plane of observation lying behind the diffracting mask feature can be expressed through the Fresnel-Kirchhoff diffraction integral, from which the following formula can be derived
u(x, p) = u,, . eikP . -~~
.
The position of the coordinate system and the notation are shown in Fig. 1. In this equation, p is the size of the proximity gap and x represents the x-coordinate of a point in the plane of observation, and x is the coordinate in the plane of the diffracting aperture. The wave number is
and f(t),
the transparency
f(5) = { Equation
function
1
in transparent
0
in opaque
(2) consists
of the mask, is areas,
areas.
of two major parts:
a plane wave
having an amplitude
U(x,p)
U,,, and a disturbance
in (2) re d uces
to the incoming
f(5). ei(XI*/O(~-_v)2
h
=
m
wave if f(l)
.
= 1 in --x s 5 s ix,
since
J g.
(7)
k
For the transparency function of a mask space (Fig. expressed using the complex Fresnel-function
1) the scalar field can be
A straightforward calculation now gives the scalar field (2) in the plane observation which is at distance p behind the mask of the form
of
(9)
The phase
4(x, p) of the scalar field can be determined
and the irradiance
can be obtained
I(& p> = IU(.Gp)12.
using the relation
from (9) by
(11)
By evaluating (9) using a rational approximation for the Fresnel-function given in [l] and by varying the proximity distance, the phase distribution behind a diffracting aperture can be computed. Figure 2 shows the contour plot of the phase values C#J(X, p) = 0 directly behind the mask feature. The space is chosen to be 0.5 km wide and the wavelength of the incident radiation is A = 248.0 nm. which corresponds to the commonly used excimer laser line. The proximity distance or the distance of the plane of observation from the mask is varied between 0.5 and 1.0 pm. If a semi-infinite refractive medium is placed at a distance behind the mask, and the phase or irradiance distribution is to be determined, the wavelength has to be scaled while maintaining phase relations inside the medium. The wavelength inside the medium is:
W. He&e et al. I Simrlation of proximity printing
133
--
Fig. 2. Contour
plot of planes of equal phase behind a 0.5 )J-m wide space in a mask. wavelength A = 248.0 nm: the position of the mask feature is shown above.
A2 = Al/n,
(12)
where A, corresponds to the wavelength in air and n is the refractive index of the medium. The computation of the scalar field inside the refractive medium is done in two steps. First, the field distribution on the surface boundary plane of the refractive medium for the wavelength A, of the radiation in air and for the given proximity gap pi is determined. In a second step, the mask plane is vertically shifted (Fig. 3) in such a way that the same field distribution results at the interface between air and the refractive medium. The space behind the mask is assumed to be homogeneously filled with the refractive medium, and the propagation of the field inside the refractive medium is now treated as if there were no step in the refraction index behind the mask. In this way, diffraction and refraction effects can be handled simultaneously. Formally, the scalar field before shifting the mask results from (9), giving for O
(13)
The scalar field inside the refractive is for z >pl:
p2 -pl
medium
after shifting the mask by a distance
Fig. 3. In the diffraction-refraction wavelength A2 the space behind
approach the mask is vertically shifted, the mask can hc considered homogeneously rcfractivc medium.
.Y -
-c
‘\‘(z -PI with the respective numbers
proximity
distances
so that for the tilled with the
R
(14)
fp,)AJ2
p , and p?. and the respective
wave
k, = 25-l/I,
(15)
k, = 21~lh,.
(16)
and
Since the field at the interface u,(~,p,)
= LL(.LP,)
must be continuous,
from
at17 =PI.
two conditions for equality of the scalar refractive medium are achieved:
(17) fields
in the surface
plane
of the
W. Henke et ul. I Sirndutiot~
of proxirni~
printing
13s
and kz.pz+6=k,-p,. From (18), the following
(19) proximity
pz=n.p,. Condition
distance
can be calculated: (20)
(19) leads to a phase shift
(21) which avoids phase discontinuities at the surface plane. Condition (20) is most important for the computation of the diffraction pattern inside the refractive medium. It simply means that wavelength and proximity distance have to be scaled by the refractive index n in order to obtain the irradiance distribution due to diffraction at the mask feature inside the refractive medium. We call the approach summarized by (20) and (21) the diffraction-refraction approach. It must be emphasized that the’ proximity distance p2 is only of theoretical interest; the size of the physically relevant proximity gap is of course pt. Figure 4 shows an example of the effect of a refractive medium on the phase distribution. The refractive index is chosen to be n = 1.6 and the mask to surface plane separation is 0.75 pm. Figure 4 shows that the planes of equal phase are continuous at the interface between air and the refractive medium. For media with very high refractive indices, the validity of the Snell’s law of refraction can be verified graphically at the boundary plane of the medium (see for example Fig. 5a). Additionally, it shows that the planes of equal phase become increasingly flatter as the refractive index increases. This fact is consistent with geometric optics considerations. The considerations in this section were limited to the case of a single space in an opaque mask. Nevertheless, they can easily be extended to the case of arbitrary mask features.
3. The separation model The basic idea of a model is presented in this section, allowing the computation of the irradiance distribution as well as the amount of decomposed photoactive compound in a resist layer during a proximity printing process step. The effects of diffraction and of interference phenomena are separated. The individual irradiance distribution for each single effect is determined. The diffraction computation is performed for several sublayers of the resist film using the diffraction-refraction approach, in order to take both effects into account. The condition expressed in (21) is not necessary in this case since only
136
Fig. 3. Contour
plot of planes of equal phase inside a refractive
a 0.5 pm wide space in a mask. wavelength position
1.50
x [uml
0.00
medium of index II =
h = 238.0 nm, proximity
of the mask feature is shown above: the surface of the medium is symbolized line
I .6 behind
distance 17= 0.75 km:
the
by a straight
in the middle of the plot.
the irradiation distribution is of interest. The standing wave interference pattern is calculated assuming normal incidence of the incoming radiation. Finally, the two distributions are superimposed, giving the basic formula of the so-called separation model:
(22) where I[,(x, z) is the irradiance distribution due to the diffraction at the mask features as described in Section 2. and i(z) is the irradiance that exists at a depth I when a plane wave of unit flux is incident normal to the surface of the resist. Thus, the separation model can be considered as a combination of the diffraction-refraction approach with an extended elementary model. The funcFor a nonreflecting substrate, i(z) tion i(z) includes absorption and reflection. is given approximately by Beer’s Law i(z) = i,, . exp {-
where
CI is the absorption
J1: cu(z’) dr’i coefficient
(z ‘o),
of the resist material.
(23) Since the optical
137
W. Hmke et ~1. / Sirndntiot~ of proxirni~ printing
properties of the resist are modified by exposure, it is usually divided into sublayers thin enough to be treated as if they had isotropic optical properties Consequently, i(z) in the resist sublayers can conveniently be treated using the thin film optics algorithms as described in [6]. Absorption is incorporated into the separation model (22) even though oblique rays contribute to the image at depth z, with such rays undergoing polarization dependent surface reflection and enhanced absorption. The primary effect is contained in the normal and near normal rays. The fact that the absorption is included in the function i(z) enables the calculation of bleaching of the resist material during exposure and then the determination of the photoactive compound as described in [5]. This model is easily simulated because its representation is closely similar to that of the vertical propagation model (1). Note that the time-dependence in the problem arising from the time dependent photoproduct concentration is still limited to the function i(z).
4. Comparison
of the separation
model with a more rigorous model
To check the validity of the separation model, a more rigorous approach is taken and the results from both models are compared for several cases. For the ‘rigorous’ model. the range of variation for the proximity distance is twice as large as the thickness of the resist layer DR. With the diffraction-refraction approach of Section 2, the scalar field is computed for the range 0 < z < 2. DR. Then the reflected image of the region DR d z ZG2 * DR is coherently superimposed with the range 0 s z G Dn, considering possible amplitude attenuation and phase shift at the resist substrate interface. In Fig. 5, the situation for planes of equal phase is shown. The complex reflection R is introduced here and has the following form: (24) The reflection coefficient following [9] :
R
=
at the resist (R)/substrate
(S) interface
is given by the
(h - i&d - (ns- ik.)
(25)
(nR - ikn) + (ns - iks)
assuming normal incidence of the radiation. n, k represent the refractive index and the extinction coefficient of the resist and the substrate respectively. Thus, both the reflected scalar field and the reflected irradiance within the range DR d z d 2. DR can be calculated from Urr&,
z) = R . U(x, 2&
In the same manner
as described
(26)
- z). above,
multiple
reflections
inside
the resist
138
z =
2 * DR
Fig. 5. (a) For determination of the irradiance distribution in a resist layer: enlargement of the proximity range 0 < : < 2 DR. (b) For determination of the irradiance distribution in a resist layer: construction of the reflected image above ; = DR.
layer and the influence of underlying thin films can be computed. Note that only layers having isotropic optical properties can be simulated using the socalled rigorous approach; bleaching effects of the resist material are, therefore, excluded from the investigation when using this approach. The basic premise of the rigorous model, superposition of wave frontals propagating in opposite directions, can be summarized in the following formula:
W. Henke et 01. I Sirndntion of proximity prirltiq
I(& z) =
ICu
1
(x, z) +
2 u t (x3z)12,
139
(27)
where m is the number of reflections taken into account in the calculation, and up and downward pointing arrows have been added to indicate the direction of propagation. Thus, the so-called rigorous model in this section is based on three major assumptions. First, wave propagation in the resist layer is assumed to be a strictly scalar phenomenon. Second, the reflection R is calculated under the normal incidence assumption and third, the number of propagation calculations through the resist layer or computations of reflected images is finite. The second assumption is justified since only the reflection coefficients for large angles of incidence vary significantly compared to those for normal incidence. The influence of multiple reflections inside the resist layer can be neglected since even after a small number of reflections, the amplitude of the radiation will drop to an insignificant fraction. Note that usually only about 5% of the incident radiation will be reflected back into the resist layer at the resist/air boundary plane. In the results shown here, five reflections were considered (three at the resist/substrate interface and two at the resist/air interface). Figures 6 and 7 show examples of contour plots of the irradiance distribution inside a resist layer as a result of both the ‘rigorous’ and the ‘separation’ approaches, for comparison. All computations were done using a wavelength A = 248.0 nm and a refractive index of the resist layer of n = 1.6, with silicon as substrate. The resist material was taken to be nonabsorbing and the thickness of the resist film was set at the relatively low value of DR = 0.5 nm. Both these conditions served to make the plots easy to survey and to compare. All contour plots present contours for irradiance values of 0.3 and 1.3, where the irradiance is normalized to a value of one in the mask plane. There is very good agreement between results from both models, as shown in Figs 6 and 7. The agreement even increases with increasing proximity gap size, due to the fact that far field wave frontals are flatter than those in near field. The conditions for assuming normal incidence for the interference pattern calculation are, therefore, more likely satisfied in far field. This shows that the separation model can be used to simulate the irradiance distribution inside a resist layer taking into account the depthwise change of the diffraction image, which is due to the change of the proximity distance (Fig. 9) and refraction effects. The difference in size or position of corresponding contours of both models can be considered a measure of error for the separation model. From a series of calculations, this error was found to be less than 10% of the feature size for the 0.3 contour. For the contours of higher values, the error is even less. This agreement between the results from both models shows that the separation model is applicable if one neglects the change of wave propagation inside the resist layer during exposure, which is due to the dynamic response of the resist material (bleaching).
140
Fig. 6. Comparison of results of the rigorous model (top) and the separation model (bottom). wavelength h = 248 nm, feature size d = 0.5 km. proximity distance p = 0.75 pm. resist thickness DR = 0.5 pm. refractive index II = I .6, extinction coefficient li = 0.0.
W. Henke
et al. I Sirndatio/~
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141
Fig. 7. Comparison of results of the rigorous model (top) and the separation model (bottom), wavelength A = 248.0 nm, feature size d = 0.5 km, proximity distance p = 1.0 (*rn. resist thickness DR=0.5 )J-m, refractive index n=1.6, extinction coefficient k=O.O.
142
0.0
Fig. 8. Irradiance 1.0 (*m, proximity
2.0
h = 248.0 nm. feature size C/= distribution inside a resist layer. wavelength index II = 1.6. distance p = 0.5 pm, resist thickness DK = 1.0 km. refractive extinction coefficient I, = 0.0.
c
mask
_..__b
x
proximity
gap
resist
Fig. 9. In proximity
printing,
the proximity distance varies between resist thickness DR.
p and P,,,;,, = p -t D,. with a
W. Henke et al. I Sirndation Table 1 Basic formulae
of the models
Model
143
discussed Formula
Elementary
model
Separation Rigorous
of proximity printing
model model
(1) (22)
(27)
1(x, z) = I(x). i(z) I(x, z) = I&, I(x,z)=
z) . i(z)
CLQ(x.,‘)+ ,,I
c Ur(..r)~z ,,1 I
In the absence of interference effects, which is the case when the resist is placed on a non-reflecting substrate, both models give identical results. In this case, the irradiance distribution reduces to the well known pattern shown in Fig. 8. Finally, the basic formulae of the various models discussed in Sections 1, 3 and 4, are summarized in Table 1.
5. Results
The separation model, as described in section three, has been implemented in our revised SAMPLE version (1.6a, 1985) [X3]. This now allows simulation of proximity printing process steps with typical Novolac resist systems for which the resist model of Dill. [5] is applicable. In this section several simulations as well as .experimental results are presented and discussed, using an HPR 204 positive resist. A production type mask aligner in the hard contact mode, from the K. Siil3 Company, was used for exposures. The mean wavelength of the exposing radiation was approximately A = 404.7 nm. The simulation parameters for the resist were taken from [13] ( see Table 2). Unfortunately, the data for the LSI developer (Olin Hunt) used in the experiments were not available, so the data for the HPRD-429 developer were used instead. To partially compensate for this parameter substitution the exposure dose has been adjusted freely in the simulation. The resist was spun on a bare silicon wafer, resulting in a final resist thickness of DR = 1.4 km after a hotplate pre-bake. No post-exposure bake was performed in order to avoid wipe out of the diffraction image and the standing wave interference pattern ‘written’ into the resist material during the exposure step. For similar reasons we have chosen relatively large mask features in the forthcoming examples, since lateral diffraction dependent irradiance oscillations are more pronounced in this case. The development time was chosen to be relatively short, t,, = 5 s, in order to preserve the diffraction and interference dependent resist profile which, of course, vanishes if the resist is completely developed. The exposure dose was approximately 120 mJ/cm*. Figure 10a represents a SEM-photograph of a 4 pm wide resist space. It shows,
Table 2 Parameters Resist:
used for experiments
HPR 204Developer:
and simulations
HPRD-429
(Olin Hunt)
(Optical Parameters) A: Parameter for photobleachable component B: Parameter for nonblcachable component C: Speed of bleaching of the photoactive compound
0.57 km ’ 0.08 p.m ’ 0.010 cm’/mJ
(Chemical Parameters) R,: Dissolution rate of fully exposed resist X2: Dissolution rate of unexposed resist R,: Fitting coefficient for dissolution rate curves
0.537 km/s 0.040 km/s 7.9
Lithographic
Conditions:
Substrate: Resist thickness:
silicon II,, = I.4 pm
(Optics) Equipment: Exposure dose:
K. Sup. MA 56 Mask aligner. I20 mJ/cm’
(Development) Development
5s
time:
h = 304.7 nm
as a consequence of the well-known standing wave interference pattern, ripples in the the side-walls of the profile. Additionally, the influence of diffraction becomes clear in the middle of the pattern, where the resist has not been developed as fast as in the areas lying closer to the edges of the profile. Especially in the corners of the profile, the effect of diffraction induced irradiante variations becomes obvious. Two irradiance maxima can be observed here, corresponding to results obtained by White [20] in 2-dimensional modeling of aerial images in proximity printing. Figure lob shows the results of a simulation in which the cross section of the developed resist profile is at a sufficient distance from the corners of the resist pattern. This restriction is significant since influences due to diffraction at the corners of the 2-dimensional mask feature are not included in the separation model. Because a l-dimensional transparency function of the mask was assumed for the formulation of the separation model, simulation of such 2-dimensional effects would require a 3-dimensional simulation model. In such a case. the separation approach could easily be extended to apply. For the profile shown in Fig. lOb, the entire resist film was divided into 160 sublayers for computation. The diffraction dependent irradiance distribution in each individual sublayer was calculated for approximately 120 points. In addition, the extended exposure dose table which was implemented in our revised SAMPLE version was used. The development section of our SAMPLE version had to be modified in order to make it capable of handling strong lateral oscillations of the PAC-concentration which are caused by diffraction. A single
W. Her&e
et cd. I Simrlrrtion
of proxirniy
printing
145
simulation run took about 4-5 CPU minutes on a DEC MicroVax 11 with a VAX/VMS operating system. The distance p between the mask and the resist surface was chosen to be approx. 4.5 pm. Changes in p within the range of kO.3 brn leave the resist profile essentially unaltered. Comparison of experimental results (Fig. 10a and simulation (lob) show satisfying qualitative agree-
-1.600
lb 0.000 x
Cum1
Fig. 10. Developed profiles of a nominally 4.0 pm wide space distance p = 4.5 Frn; (a) experimental result, (b) simulation; summarized in Table 2.
6 000
in HPR 204 resist. proximity lithographic conditions are
ment of both, so that the separation model can be considered a practical first order approximation to the propagation of radiation inside a resist film during a proximity printing process step. Residual discrepancies between experiment and simulation in, for example, the side wall angle are very likely due to improper developer simulation data. Figure 11 shows a contour plot of the irradiance distribution inside the resist film for the situation displayed in Fig 10 at the start of the exposure, when the resist material can still be considered optically isotropic. The data taken to calculate this distribution were the same as those used for the simulation in Fig lob. Figures 12a and 12b show another comparison of a proximity printed resist profile and the corresponding simulation. The mask pattern in this case was a line/space combination consisting of 1:l lines with a width of d = 3.5 pm. The lithographic conditions were the same as those mentioned above. The proximity distance had to be adjusted, however, to a value of 2.5 pm. Again. Fig 13 shows a contour plot of the irradiance distribution at the start of exposure for the same lithographic conditions as in Figure 12b. Simulations using the elementary model of (1) and the separation approach are shown in Fig 14 (a) and (b) respectively. Here. the conditions are the same as those given in Table 2 except that an index matched substrate is used. the
Fig. 11. Contour
plot of the irradiance distribution at the beginning correspond to those of Fig. 1Ob.
of the exposure.
conditions
W. Henke et 01. I Sirndation of proximity printing
147
1 000
T L
N
-1600 0.000 x
Cum1
5 000
Fig. 12. Developed profiles of a nominally 3.5 km wide line/space pattern in HPR proximity distance p = 2.5 km; (a) experimental result, (b) simulation; lithographic are summarized in Table 2.
204 resist. conditions
proximity distance is set to p = 1.0 pm and multiple development contours are plotted. As shown in Fig 14, the elementary model predicts that the developer breaks earlier through the resist layer than the separation model does. The increase in development time to achieve a break through in the separation model is caused by the fact that the degradation of the aerial image for various depths into the resist layer is taken into account. The irradiance distribution
W. Henke et al. 1 Si~nillationof proximity printing
Fig. 13. Contour plot of the irradiance distribution at the beginning of exposure, conditions correspond to those of Fig. 12b.
maximum lowers through the resist film and the image is laterally spread. As a result, this effect is readily observed in the near field (small proximity distance). It can be neglected, however, in the far field (large proximity distance), where the irradiance distribution changes only insignificantly through the resist. The degradation of the aerial image, on the other hand, is not considered at all in the elementary model. It should be noted that the phenomenon just mentioned
Fig. 14. Comparison of results of the elementary model (a) and the separation model (b); proximity distance p = 1.0 pm; mask feature: space d = 1.0 km; development contour times: 2.0, 3.5 and 5.0 s, other conditions are given in Table 2. Note that for both simulations an exposure dose of 120 mJlcm2 was used.
W. Henke et al. I Simulation of proximity printing
149
occurs only if small mask features are used. For large feature sizes, where the diffraction image changes only insignificantly across the resist layer, both models give identical results. Using the separation model, an image reversal [ll] inside the resist layer can be simulated. This phenomenon can occur if the mask consists of periodic line/space combinations. The lithographic conditions under which an image reversal occurs can be constructed using the structural factor [ 111. The proximity distance necessary for this effect to occur can be determined using the definition of the structural factor u:
(28)
u=d-e.
The structural factor UrR for the diffraction pattern on the bottom side of the resist film in the case of an image reversal has been determined in [II] to be u ,R =
0.7.
(29)
According to (20), the scaled proximity distance has to be put into (28) with the addition of the thickness of the resist film &, giving (30) where hn is the wavelength of the radiation inside the resist material and n is its refractive index. This results in the proximity distance between mask and resist surface in the case of an image reversal inside the resist layer 2 PIR
=
DR
d2
A H UIR
--
n
’
(31)
Note that the structural factor for the diffraction pattern occurring at the top of the resist must be significantly greater than one. If not, then no image reversal inside the resist film can be observed. Figure 15 shows a contour plot of the irradiance distribution inside a relatively thick resist layer with DR = 3.0 km. The size of the single mask feature is d = 0.5 km, the wavelength of the exposing radiation is A = 248.0 nm, the refractive index is n = 1.5 and the proximity distance is p = 1.0 pm. To facilitate the surveying of the plot, only contour lines for a value of 1.0 of the normalized irradiance were plotted. For the same reason, the resist layer was assumed to be nonabsorbing. The existence of a critical proximity distance at which an image reversal occurs is obvious from (31). Especially for very small feature sizes, the proximity distance should be kept well below that critical value. Otherwise it is very likely that the mask feature will not be transferrable into the resist material at all. A large refractive index of the resist material slightly shifts this critical distance to larger values. If one allows a structural factor of u = 1.0, for instance, as the
Fig. 15. Contour plot of the irradiancc distribution inside a resist layer in the case of an image reversal: mask feature: line/space rl= 0.5 km. A = 248.0 nm, refractive index II = 1.5. proximity distance p = I .Okm.
Fig. 16. Dependence of the proximity distances for which a structural factor of u = 1.0 on the bottom side of the resist layer is obtained: mask feature: line/space. resist thickness DK = I .Opm. A = 248.0 nm.
W. Her&e et al. I Sirndnriorl
of proximity
printing
151
worst possible value for the diffraction pattern on the bottom side of the resist film, the critical proximity distance depends mainly on the size of the mask features. Figure 16 shows the dependence for three different refractive index values. It is obvious that very tight restrictions on the size of the proximity gap have to be made for submicron mask features.
6. Conclusions The separation model which has been presented and examined in this article provides a practical first order approximation for the wave propagation inside a resist layer during a proximity printing process step. The model was implemented in our revised SAMPLE version, allowing for computation of the diffraction and interference induced irradiance variations inside a resist film. Since the physical effects of diffraction and interference are treated separately and the interference phenomena are assumed to be due to normally incident radiation, the bleaching of the resist material can easily be introduced. This allows simulation of the decomposition of the photoactive compound and the development process step. Consequently, the properties of the resist profiles which can be obtained under particular lithographic conditions can be predicted using this model. The model is limited to a description of coplanar layers. Satisfying agreement of both proximity printed resist profiles and simulations shows that the model is applicable to simulation of such processes. The simulations give a good qualitative explanation for resist profiles which arise after exposure and during the development of the resist material. Using the structural factor along with the separation model, the influences of certain wavelength/feature size/proximity distance margins can be investigated. It has been shown that under particular lithographic conditions, image reversals inside the resist layer can occur, making a proper transfer of patterns into the resist film virtually impossible. This requires that a certain critical proximity distance is not exceeded if, for example, submicron feature sizes are to be printed.
References [l] M. Abramowitz and I. A. Stegun. Handbook of Mnthernaticnl Functions (Dover. New York. 1972) 302. [2] K. I. Arshak, N. N. Kundu and S. N. Gupta, Simulation of proximity printing. Proceedings SPIE OpticaNLnser Microlithogrphy, Vol. 922 (1988) 241-246. [3] A. L. Bogdanov, A. A. Polykov. K. A. Valiew. L. V. Velikov and D. Y. Zaroslov. Computer simulation of the percolational development and pattern formation in pulsed laser exposed positive photoresists. Proceedings SPIE Advances in Resist Technology nnd Processing IV. Vol. 771 (1987) 167-172. [4] M. Born and E. Wolf, Principles of Optics (Pergamon, sixth edition. 1987) Chapter 8.8.3, 382-383.
152
W. Henke
et al. I Simulation
of proximiv
printing
[S] F. H. Dill, W. P. Hornberger, P. S. Hauge and J. S. Shaw, Characterization of positive photoresist. IEEE Tram. Electr. Der,. ED-22(7) (July lY75) 445-156. [6] F. H. Dill. A. R. Neureuther, J. A. Tuttle and E. J. Walker, Modeling projection printing of positive photoresist, IEEE Trwzs. Elect,-. Del, ED-22 (7) (July lY75) 356-464. [7] G. Geikas and B. Ables, Contact printing - associated problems. Proceedilzgs Kotfrrk :l~ic~roelectrorlics Semirwr lY68. Vol. 11 (1068) 47-54. [8] W. E. Haller and A. R. Neureuther. Polarization dependence of diffraction by high resolution masks, Proceediqs SPIE OpticuIILrwr ,~licrolitl7ograI,l7!,. Vol. 922 ( lYX8) 165--l 77. [9] 0. S. Heavens. Opticrd Properties of Thin Solid Films (Butterworths. London. lY55) Chapter 4, 46-55. [ 101 R. C. Heim. Practical aspects of contact/proximity. photomasklwafcr exposure. P~mwlir7gs SPIE Semiconductor Microlithography II. Vol. 100 ( lY77) 104-l l-1. [ll] W. Henke, R. Schwalm. M. Weiss and J. Pelka. Diffraction effects in submicron contact/proximity printing. Microelectrolzic E,zgineeriq 10 (lY89). [12] K. Jain, Advances in excimer laser lithography. Proceedings SPIE Losers i/7 Microlithoglophy,
Vol.
774 (1987)
115-123.
[13] T. Kokubo, Z. Idemoto. Y. Kawabe and K. Ucnishi. Design of a positive photoresist for submicron imaging assisted by SAMPLE simulation. Proceediq.r SPIE Ad\wce.s ir7 resi.\t technology arut’ processing V. Vol. 920 (1988) 3X-363. [14] N. N. Kundu, S. Goel, S. N. Gupta and B. P. Mathur. Image intensity distribution of double spaced contact holes, Proceedings SPIE Optical Microlithogrq&v Vol. 633 (lY86) 245-252. [lS] D. 0. Massetti. M. A. Hockey. and D. L. McFarland. Evaluation of deep UV proximit) mode printing. Proceedirlgs SPIE Semiconductor Microlithogrr~I?h~ V. Vol. 221 ( 1980) 32-38. [16] D. Meyerhofer and J. Mitchell, Proximity printing of chrome masks. RCA Rel, 43 (April 1982) 608-625. [17] D. B. Novotny. Measurement of the separation distance in contact and proximity lithography, J. Electrochem. Sot.. Solid-state science and technology. 133 (12) (December 1986) 260&2605. [IS] W. G. Oldham. S. N. Nandgaonkar, A. R. Neureuther and M. O‘Toole. A general simulator for VLSI lithography and etching processes, IEEE Trans. Elcctr. Del,. ED-26 (4) (1979) 717-722. [19] A. Weill, J. M. Francou and J. P. Panabiere, Subhalfmicronic contact printing lithograph! using microwave powered deep UV source. Procerdir7g.s SPIE 0pticalILa.w Microlithogrrrphy Vol. 992 (1988) 236-240. [20] L. K. White, Positive and negative tone near-contact printing of contact hole maskings. RCA Rev. 43 (June 1982) 391311.