Power loading limitations in soft x-ray projection lithography

JOURNAL OF X-RAY SCIENCE AND TECHNOLOGY 4, 167-181 (1994)

Power Loading Limitations in Soft X-Ray Projection Lithography A. M. HAWRYLUKAND N. M. CEGLIO University of California, Lawrence Livermore National Laboratory, Livermore, California, 94551 Received March 3, 1994; revised April 27, 1994 Soft x-ray projection lithography (SXPL) is an attractive technique for the fabrication of high-speed, high-density integrated circuits. In an SXPL stepper, the x-ray imaging mirrors consist of multilayer coatings deposited onto high precision substrates. The stepper is intended to fabricate ultra-high spatial-resolution structures with a minimum feature size of <0.1 ~m. To achieve this resolution, the imaging mirrors must maintain a very precise surface figure while being exposed to x radiation. Failure to achieve and maintain the mirror surface figure will distort the wavefront propagating through the imaging system and will degrade system resolution. The required surface figure accuracy for each imaging mirror depends upon the required resolution, the wavelength, and the optical design. For conventional SXPL stepper designs, the total (peak-to-valley) surface figure error budget per mirror is approximately + 1 nm. Due to material properties at soft x-ray wavelengths and practical fabrication considerations, x-ray multilayer mirrors have limited reflectivities. A fraction of the incident x radiation is absorbed in the mulfilayer coating. This absorbed radiation constitutes a thermal load on the mirror, thereby distorting its shape and compromising the accuracy of its surface figure. In this paper, we analyze the thermally induced distortion on the imaging optics and conclude that the maximum allowable thermal distortion limits the maximum allowable x-ray power transported to the wafer and limits the minimum acceptable multilayer mirror reflectivity. The penalty for either insensitive xray resists or inefficient mirror reflectivity is a decrease in system throughput which cannot be compensated with increased source power either collected by condenser optics or generated by the source. © 1994AcademicPress,Inc. I. INTRODUCTION

The development of efficient, high-resolution, reflective x-ray optics has renewed interest in soft x-ray projection lithography (SXPL) (also known as extreme ultraviolet, EUV, lithography) as a possible technique for the fabrication of high-speed, highdensity integrated circuits (1-3). The x-ray optics under consideration are x-ray mirrors and consist of multilayer coatings deposited onto ultrasmooth, precisely figured substrates. At soft x-ray wavelengths, multilayer coatings have limited reflectivity due to material properties, substrate roughness, and interlayer mixing. To date, the largest measured normal incidence x-ray mirror reflectivity is 66% at ), = 13 nm (4). The unreflected radiation is absorbed in the multilayer coating and may thermally distort the imaging optic. A SXPL exposure facility (i.e., a "stepper"), Fig. 1, is intended to expose integrated circuit (IC) patterns with a minimum feature size of less than 0.1 #m. Several different imaging systems have been proposed (5) to meet this requirement, including "Step and Scan" and "Step and Repeat" (6) systems. All such SXPL steppers consist of an x-ray source and two distinct optical systems: the condenser optics (which collect the 167

0895-3996/94 $6.00 Copyright© 1994by AcademicPress,Inc. All rightsof reproductionin any formreserved.

168

HAWRYLUK AND CEGLIO

/ P4 \

Reflection Mask

PS

TARGET

Optical Laser Beam

I

-lm

]

FIG. 1. The line drawing illustrates the basic concept for a soft x-ray projection lithography system. A

laser.produced plasma generates soft x rayswhichare collectedby the three-element condenseroptic system and then illuminates the reflection mask. The reflection mask is imaged onto the wafer using a series of imaging optics. In this design, there are three transmission windowsto separate different vacuum chambers, one window between the wafer and the imagingoptics. x-ray emission from the source and illuminate the mask) and the imaging optics (which image the mask pattern onto a resist-coated wafer). While power loading on the condenser optics is likely to be large, the surface figure accuracy requirement for these optics is not critical. In contrast, imaging optics must maintain a very precise surface figure while being exposed to x-ray illumination. Failure to do so will degrade system resolution and blur the IC pattern. We have analyzed the thermal effect of finite x-ray absorption on the imaging mirrors and the consequences for a SXPL stepper. We have derived an expression for the thermal loading and have calculated the associated thermal distortion for a variety of substrate materials. In this manuscript, we show that the m a x i m u m thermal distortion on the imaging mirrors limits the m a x i m u m allowable x-ray power transported to the wafer and limits the maximum throughput that an SXPL stepper can achieve. II. POWER LOADING ON MIRRORS There are two distinct optical systems in an SXPL stepper: the condenser system and the precision imaging system. The thermal loading on the first condenser mirror

SXPL POWER LOADING LIMITATIONS

169

is likely to be high and analyses show that condenser mirrors in a conventional condenser system design can generally tolerate approximately 1 vm of distortion without significantly degrading the resolution or depth of focus of the imaging system (7). Therefore, thermally induced distortions (less than 1 vm in magnitude) should not limit system performance so long as the condenser mirror reflectivity is not degraded. As we shall see in Section V, this requirement can be achieved by fabricating the condenser optics from low-expansion materials and with appropriate cooling of the condenser optics. The thermal loading on the precision imaging mirrors in the SXPL system will be less than the thermal loading on the condenser mirrors, but the imaging mirrors are much more sensitive to thermal distortion. The thermal loading on the imaging mirrors will be dependent upon the x-ray power requirement at the wafer and the number and the reflectivity of the mirrors. In addition, the loading on the imaging mirrors may not be spatially uniform or constant in time. For the SXPL system design shown in Fig. 1, the imaging mirror with the greatest thermal load is mirror MI, the first mirror after the mask. This is because mirror MI must transport sufficient radiation to offset the subsequent absorption losses. The total x-ray power absorbed by mirror M1 can be derived from the total x-ray power at the wafer and the absorption losses in the mirrors and windows between MI and the wafer. The total x-ray power absorbed, q (milliwatts), by mirror M~ for the system illustrated in Fig. 1 is q(milliwatts)

Pw(l - R) -

WR N

,

[I]

where Pw W R N

is the x-ray power delivered to the wafer (milliwatts), is the window transmission, is the mirror reflectivity, is the total number of reflections between the mask and the wafer (N = 4 in Fig. 1).

Note that the absorbed x-ray power depends linearly upon the power requirements at the wafer, Pw, but nonlinearly on the number and reflectivity of the mirrors. The power loading on M1 increases rapidly with decreasing mirror reflectivity; see Fig. 2. Within the constraints of the analysis presented in Section VI, we determine that the maximum allowable thermal loading on an imaging mirror is 63 roW. For a given value of N and Pw, this maximum allowable thermal load defines the minimum acceptable mirror reflectivity. Conversely, the maximum thermal load defines the maximum average power transported to the wafer for a given value of N and mirror reflectivity. III. THERMAL DISTORTION ANALYSIS We have calculated the thermally induced, axial and radial surface distortion and slope error of x-ray mirror substrates using a two-dimensional, axisymmetric, thermal analysis code with finite element heat conduction and finite element structural deformation arrays. The axial and radial distortions for a mirror are defined as the magnitude

170

HAWRYLUK AND CEGLIO

:r

oi\w=O \

4 imagingmirrors

~

-=

\\

;lO

40

45

50

55

60

65

70

75

Mirror Reflectlvity (%)

FIG. 2. The thermal loading on the first imaging mirror, M], for a four-bounce system as a function of mirror reflectivity and power delivered to the wafer.

o f axial and radial displacement for each point on the mirror surface from its original position, Pl(rl, z0, to its thermally distorted position, P2(r2, z2), Fig. 3. Input parameters to the code were the material and thermal properties o f the substrates, b o u n d a r y conditions, mirror geometry, and specific spatial and temporal power loading conditions. In our model, the mirrors were thermally loaded on the front surface by absorbed x radiation and cooled by conduction to a rigid, constant temperature backing plate. Surface distortion o f the mirror was f o u n d to be influenced by the m a n n e r in which the mirror was m o u n t e d to the backing plate. We modeled the rear surface o f the mirror as either "fixed" (where the entire back surface o f the mirror is constrained

P2(r2,z2)

................................ ~i~;T--~-~...~¢. . . . . . . . . j f

Displaced mirror surface

Pl(rl,Zl) DIsplacemen!

Original mirror surface

i<

r

>

Optic Axis

FIG. 3. The axial and radial distortions are defined in this illustration as the magnitude of the shift in the location for each point on the mirror from its original position, Pl, to its distorted position, P2.

171

SXPL POWER LOADING LIMITATIONS

Mirror is free to move ~-~ horizontally

(

(->

Mirror

)

Rear surface of mirror is uncOnstrained

'Fixed' positions

~'i~Backing "" Plate A

e

FIG. 4. The mirror mounting configurations which are under consideration in these analyses. The fixed mounting condition (A) assumes that the back of the mirror is in contact with the backing plate, while the edge-supported condition (B) clamps the mirror at the edges and allows the back surface of the mirror to distort away from the backing plate.

to be in contact with the backing plate but the edges may move laterally) or "edgesupported" (where the back surface of the mirror was constrained to be in contact with the backing plate only along its edges and the center of the mirror was unconstrained). These two mounting configurations, Fig. 4, represent idealized limits. A practical mirror mount will represent a heat transfer boundary condition that is somewhere in between. We calculated the axial and radial surface distortion, slope error, and surface temperature for mirrors made from four different materials (silicon, silicon dioxide, Zerodur-M (9), and ULE (10)) and for many different mirror geometries. The properties of these materials (at 25°C) are listed in Table 1. Mirrors having diameters ranging from 4 to 25 cm, radii of curvature ranging from 6 cm to infinity (i.e., fiat optics), and thicknesses ranging from 1 to 6.25 cm were modeled. Power loading on the mirrors

TABLE 1 Thermal and Material Properties of Silicon, Silicon Dioxide, Zerodur-M, and ULE Silicon (11) Density (g/cc) Heat capacity (J/g-K) Thermal conductivity (W/cm-K) Elastic modulus (N/cm 2) Poisson's ratio Coeff thermal expansion (cm/cm-K) Thermal diffusion (cm2/sec)

Silicon dioxide (11)

Zerodur-M (9)

ULE (10)

2.3

2.2

2.6

2.2

0.71

0.74

0.81

0.77

1.49

0.014

0.016

1.07e7

0.717e7

0.890e7

0.676e7

0.42

0.16

0.25

0.17

2.63e-6

0.55e-6

0.02e-6

0.01 e-6

.0086

.0076

.0077

0.9

.013

172

HAWRYLUK AND CEGLIO 2-

1.S ¸

E

1.2

.~

edge 1.2-

0.9

06

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0.8-

fixed

o

~. I

o

I

0.2

I

I

0.4

I

I

I

0.6

[

I

.¢o E3

0.4"

0

0.8

0.2

Normalized Radius ( r / r )

0.4

0.6

0.8

Normalized Radius (r/ro)

FIG. 5. The thermally induced distortion for a concave, f/1 mirror made with ULE, with an aspect ratio of4:l and with 1 W of total power absorbed by the mirror. The radial distortion is in the plane of the mirror and the axial distortion is normal to the surface of the mirror (see Fig. 3).

was varied from 1-30 m W / c m 2, and the m o u n t i n g condition was modeled as either "fixed" or "edge-supported" as discussed earlier. Calculations verified that radiative cooling to the e n v i r o n m e n t was insignificant (the peak temperature rise on all mirrors was less than a few degrees centigrade for m o s t conditions) and convective cooling was negligible (the mirrors were modeled to be in a v a c u u m environment). Radial and axial distortion plots for f! 1, f/5, and flat mirrors in steady state thermal loading are presented in Figs. 5 - 7 for both "fixed" and "edge-supported" m o u n t i n g conditions. The distortion plots presented are all normalized to a U L E mirror substrate with an aspect ratio o f 4:1 and a power loading o f 1 W distributed uniformly over the entire surface o f the mirror. We used U L E as our baseline material because it exhibits the least thermal deformation o f the four materials studied. To use these normalized plots and determine the distortion on a 4:1 aspect ratio mirror, multiply the horizontal axis by the mirror radius. For example, from Fig. 7, a flat U L E edge-supported optic, 10 c m in diameter (2.5 c m thick), will undergo 0.6 n m o f radial displacement and 1.2 n m o f axial displacement at a distance o f 5 c m from the optic axis. In our analyses, "fixed" m o u n t i n g conditions lead to less distortion on the mirror. While the two-dimensional heat transfer code is necessary to calculate the exact shape and magnitude of the distortion for a particular mirror, it provides little insight

,-... 1.5-

p.

1.2-

o~

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o. 0.3.on a 0

"~ ~ -~ .~_ 121 0.2

0.4

edge

J

edge

"~

1.6-

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E

0.6

0.8

Normalized Radius (r/ro)

o.8o.4-

o

'oi

'oi, 'oi 'oi

'

Normalized Radius (r/re)

FIG. 6. Similar to Fig. 5, except the data are for an f/5 mirror, also made from ULE, with an aspect ratio of 4:l and with 1 W of total power absorbed by the mirror.

SXPL POWER LOADING LIMITATIONS ..-,

1.5-

E

A

1,6-

E

1.2-

.~ '~

173

edge

J

"E

0.9-

edge 1.20.8

06

ca. ._~ r~

fixed

_~ ¢z 0.4

0.3-

.~

.on

0 0.2

0.4

0.6

a

0.8

0

I

0

~

0.2

I

/

0.4

I

I

I

0.6

I

I

0.8

Normalized Radius (dro)

Normalized Radius (r/ro)

FIG. 7. Similar to Fig. 5, except the data are for a fiat optic made from ULE with an aspect ratio of 4:l and with 1 W of total power absorbed by the mirror.

into the distortion under varying conditions. Fortunately, one-dimensional scaling can be used to determine the distortion for different conditions (i.e., materials, power loading, etc.), once the actual distorted shape is calculated for a specific geometry. These one-dimensional scaling relationships are easily derived. Under steady-state conditions, we noted that ~g --

=

e

~AT

[2]

and

aT

=

[31

where 6g £ o~ AT LP

is is is is is is

the the the the the the

distortion (cm), thickness of the optical substrate (cm), linear thermal coefficient of expansion (cm/cm-°K), thermal conductivity of the optic substrate (W/cm-°K), surface temperature rise (°K), and thermal load on the optic (W/cm2).

By substitution, we determine that the distortion scales as the square of the optic thickness and linearly with the thermal load and material properties: ~

= ~2~'O(O//O').

[4]

In the fabrication of high-precision mirror substrates, there is generally a m a x i m u m value of the aspect ratio (c = d/g, where d = mirror diameter and g = optic substrate thickness) for which fabrication tolerances (such as surface figure accuracy) can be met. We treat c, the aspect ratio, as a parameter of this analysis,

174

HAWRYLUK AND CEGLIO

c2 -

4A ,/i.~ 2

[5]

where A is the mirror area. Thus, the distortion for a circular mirror scales as

be -

4&OA(a/~r) ./rC2

[6]

where ~°A is the total power loading on the mirror (watts). For a constant aspect ratio, c, the total linear distortion of a mirror is independent of mirror size and only dependent upon the total power loading (~qA) and material properties (a/a). These conclusions have been verified by our two-dimensional heat transfer code for four separate materials and by scaling the mirror geometry and the thermal load by nearly two orders of magnitude. Thus, we can calculate the distortion for a particular mirror geometry using the rigorous two-dimensional code analysis and, using these simple scaling rules, accurately estimate the distortion for a similarly shaped mirror with different materials (i.e., " a / a " ) , different aspect ratios (i.e., "c") or different power loading (i.e., "£°A"). For example, the thermal distortion for a fused silica (SIO2) mirror is 51 times greater than in a similar mirror made from ULE; the distortion for a similarly shaped ULE mirror but twice as thick (i.e., a 2:1 aspect ratio) will be 4 times greater; and the distortion for a similarly shaped ULE mirror with twice the thermal load will be 2 times greater. The thermal distortion for an f/1 mirror is greater than the distortion for an f/5 mirror. However, as shown in Figs. 6 and 7, the distortion for the f/5 mirror is virtually indistinguishable from the distortion for a flat mirror. Thus, the data from Figs. 6 and 7 may be used for optical elements with f/#'s > 5. From Figs. 6 and 7, we conclude that the thermal distortion for a f/5 mirror (or a mirror with a larger f/#) made from silicon, silicon dioxide, Zerodur-M, and ULE is 3.5 × 10 -3 n m / m W , 8 × 10 -2 n m / m W , 2.5 X 10 .3 n m / m W , and 1.6 × 10 .3 n m / m W , respectively. We also investigated the thermally induced surface distortion on mirrors with spatially or temporally varying thermal loads. In the SXPL system, the radiation incident on the mirrors will be reflected offa mask and imaged onto the wafer. Since the mask pattern is not imaged onto the optics, no large spatial variations in intensity on the optics are expected. For the purpose of this analysis, we investigated a +20% power loading modulation with a 1-mm spatial period on a constant background, Fig. 8 (left). Under these conditions, the thermally induced distortions for a mirror with a spatially varying thermal load were identical to the distortions induced by a uniform thermal load. We analysed the effects of temporally varying thermal loading on the optic for two different temporal conditions: a thermal "step function" and a pulsed thermal source consisting of a series of 1-ns pulses at a 1-kHz repetition rate, Fig. 8 (right). We assumed a 5 cm diameter, 1 cm thick, silicon optic, with a time-averaged power loading of 10 m W / c m 2. The temperature rise for a thermal loading described by the step function on a silicon optic is plotted as a function of the diffusion time constant, Fig. 9a. The peak surface temperature for an optic fabricated from different materials, for a different

SXPL POWER LOADING LIMITATIONS

o

F-L_ +20%

U__ 1 mm

175

f ) O

O..

IX.

Spatial variation

Temporal variation

FIG. 8. The spatial and temporal variationsof the power loading used in these analysesis illustrated.

geometry, or under different power loading, can be computed using scaling relations derived earlier. Note that the temperature of the mirror increases during an initial transient phase, then asymptotically approaches its steady state value. After several diffusion time constants (ra = g 2 / ~ where a, is the thermal diffusivity in cm2/sec), the average surface temperature of the optic, and therefore the thermally induced distortion, is identical to that from a steady state source. The surface temperature rise resulting from a pulsed thermal load was calculated and compared to the temperature rise resulting from the step-function thermal load. Initially, the peak surface temperature rise from the pulsed load is considerably larger than the temperature rise from the step function, Fig. 9b, but decreases quickly. Since the steady-state average loading from the two sources is identical, the two loading conditions approach identical average values. In Fig. 9c, we plot the surface temperature for a silicon optic after six diffusion time constants, for both the step function and the pulsed thermal loading conditions.

IV. THE EFFECTS OF GRAVITY AND SUBSTRATE COOLING ON IMAGING OPTICS We have also analyzed the distortions on the imaging mirrors that are induced by gravity or by temperature variations in the backing plate. We assumed that the force of gravity was normal to the mirror surface. The magnitude of the distortion with the optic in either an "up" or "down" configuration was identical but opposite in direction. For a 25 cm diameter, f/5 mirror with a 4:1 aspect ratio and a fixed backing plate, gravity can distort a ULE mirror by 0.3 nm, Fig. 10. Such a large figure error will severely impact the mirror figure error budget. However, unlike thermally induced distortions, gravitationally induced distortions are static and can be compensated for by appropriate substrate fabrication. Gradients in the backing plate temperature can also distort the mirror. A _0.5°C temperature gradient across the backing plate (i.e., a plate whose temperature is 24.5°C at one edge, 25 °C in the center, and 25.5 °C at the other edge) can induce approximately 0.4 nm distortion to the mirror, Fig. 11. In order to minimize the thermal distortion, the cooling structure for the imaging mirrors must be designed to minimize lateral temperature gradients (required AT g 0.1 °C).

176

H A W R Y L U K AND CEGLIO

A 0.01 0

0.008

n"

Y

0.006

0.004

0.002

0 0

I

I

I

I

2

3

4

5

time ( t/-rd)

B

2E-3

1.5E-3

¢2" •,i o

2

1E-3

E~ X t

I

2

I

I

4

I

I

6

I

I

8

10

8

10

Time (msec)

C 1E-2 [

Pulsed

T

~=~.~di,~

~

OE~

E~

/ E ~

4E-3

o

~ 0

2

4

6

Time (msec) (after 6 diffusion times)

FIG. 9. (A) The calculated temperature rise for a silicon optic subjected to a thermal loading "step function," i.e., the thermal load is initiated at time t = 0. (B) The calculated temperature rise for a silicon optic subjected to a thermal "step function" is compared to the calculated temperature rise for the same silicon optic subjected to a temporal loading illustrated in Fig. 8 on the right. (C) The calculated temperature rise for a silicon optic subjected to a thermal "step-function" is compared to the calculated temperature rise for the same silicon optic subjected to a temporal loading illustrated in Fig. 8 (right side) and after the source has been running continuously for six diffusion time constants.

177

SXPL POWER LOADING LIMITATIONS O,O4

,-,

0.4

0.03

v

0.3

E

0.02

i

~. ._~ E~

0,Ol

~-~

E

E r" C

.m r't

0

2.5

5

7.5

10

0.2

0.1 I

I

,

12.5

10

Radius

Radius

FIG. 10. The gravity-induced distortion on a 25 cm diameter, f/5 concave mirror with an aspect ratio of 4:1. The back of the mirror is in the fixed backing plate configuration.

V. DISTORTIONS ON CONDENSER OPTICS

As mentioned earlier, system resolution is more tolerant of distortion in the condenser optics than in the imaging optics. Analysis (7) indicates that the condenser optics for a conventional condenser system can tolerate approximately 1 ~zm of thermal distortion without sacrificing system resolution or depth of focus. For the system design shown in Fig. 1, a broadband, Lambertian x-ray emitter (characteristic of a laser produced plasma source driven by a 400 W optical laser) is assumed. For a collection solid angle of 0.2 sr (8), the first condenser mirror collects approximately 6% of the radiation emitted by the source. If we assume that all the laser energy is converted into broadband radiation, and that all the radiation incident upon the first condenser mirror is absorbed, then the thermal load on the first condenser mirror is 25 W. The distortion for a condenser mirror absorbing 25 Watts of radiation (and with a constant temperature backing plate) is approximately 90 nm, 66 nm, and 40 nm for silicon, Zerodur-M, and ULE, respectively (using the scaling relations derived earlier), and we therefore conclude that these three materials are suitable substrates. A condenser mirror with a fused silica substrate would undergo approximately 2 ~m of thermally induced distortion under similar conditions and may not be suitable. VI. IMPLICATIONS FOR SXPL IMAGING SYSTEMS

To achieve diffraction limited performance from an imaging system, the wavefront error between the object and its image cannot be greater than +X/4. For an imaging

E

0.5

0.4

edge supported

0.4

"-" 0.3

edge s u p ~

03

n" o 0 2 .~Q. 0.1 a

o o

2.5

5

,:

7.5

Radius

10

12.5

~ 0.1 .~_ a 0

l

0

5

E

,15

10

12.5

Radius

FIG. l 1. The distortion on an f/5 concave mirror, 25 cm in diameter (with an aspect ratio of 4:1) produced by a nonuniform temperature distribution (_+0.5°C) on the backing plate.

178

HAWRYLUK AND CEGLIO 80

o

so

ta~

40

~o~

D-

E

N~

20

E 0.4

I

J

I

J

I

0.45

0.5

0.55

0.6

0.65

017

0.75

Mirror Reflectivity

FIG. 12. The maximum x-raypower that can be deliveredto the waferis limited by the thermal distortion in the imaging optics and is a function of both the mirror reflectivityand the number of imaging optics. For present x-ray mirrors (R = 66%) and SXPL imaging system designs (N = 4), the maximum average power that can be delivered to the wafer is approximately20 mW.

system consisting of a single reflective imaging mirror, this requirement implies that the surface figure of the mirror must be accurate to +X/8. For a multielement reflective imaging system, the required surface figure accuracy for each optic will be dependent upon the optical design. However, presuming a statistical distribution of figure errors in a multielement mirror system, the required surface figure accuracy per mirror will be _+?,/8fN, where N is the n u m b e r of reflections in the imaging system. For the imaging system shown in Fig. 1 (N = 4) and for X = 13 rim, the required surface figure accuracy for each mirror is +0.8 nm. There are several potential sources of surface figure error in high precision optical components (i.e., optic manufacturing, metrology, mounting distortions, etc.), a n d the total figure error must be appropriately budgeted a m o n g the various contributors. A reasonable thermal distortion budget for an imaging mirror is on the order of 0.1 n m (12). F r o m the thermal distortions calculated in Section IV, we conclude that the m a x i m u m allowable thermal loading, qmax, for silicon, silicon dioxide, Zerodur-M, and ULE mirror substrates is approximately 29, 1, 40, and 63 mW, respectively. Practical throughput requirements (i.e., Pw > 5 m W ) for a four-mirror imaging system suggest that silicon dioxide m a y require unrealistically high mirror reflectivities (R > 70%, see Fig. 2 or Eq. [1]). Crystalline silicon m a y have suitable thermal properties but it is difficult to polish to an appropriate (possibly aspheric) shape. It appears that, a m o n g the materials considered, ULE is the best choice for the precision imaging optics substrate material. From Eq. [1], the m a x i m u m allowable thermal loading on the imaging optics uniquely defines the m i n i m u m acceptable mirror reflectivity and the m a x i m u m allowable power delivered to the wafer. For the SXPL stepper design illustrated in Fig. 1 (i.e., N = 4) and with our system goals (i.e., qma~ = 63 m W and Pw = 5 mW), we determine that Rmin is 50%. Note that a larger n u m b e r of imaging mirrors (i.e., N >

179

SXPL POWER LOADING LIMITATIONS

4) or a greater required throughput (i.e., Pw > 5 mW) will require a higher minimum mirror reflectivity. The maximum average power delivered to the wafer as a function of both mirror reflectivity and the number of imaging mirrors, N, is illustrated in Fig. 12. Using a model proposed by Early (13), we have calculated the maximum wafer throughput for a SXPL stepper. In this model, it is assumed that N = 3. It is further assumed in this model that exposures are on 8-in. wafers; will require 30 s per wafer for overhead; 46 fields per wafer, each requiring 0.5 s/field step time and 20% overscan. We assumed a utilization fraction of 100% in our calculations. From this model, we calculate the maximum wafer throughput as a function of mirror reflectivity and xray power delivered to the wafer, Figs. 13 and 14, for several resist sensitivities. In Fig. 14, we identify the maximum power delivered to the wafer (as determined by the thermal loading limit) for a number of mirror reflectivities. This thermal limit restricts the maximum SXPL wafer throughput for a given mirror reflectivity. For example, a maximum mirror refiectivity of 65% limits the maximum power deliveredto the wafer to 35 mW. For a resist sensitivity of 10 mJ/cm 2, the maximum wafer throughput is approximately 24 eight-inch wafers per hour. Increasing the amount of source power delivered to the SXPL stepper in an attempt to increase the throughput will only violate the thermal loading limit on the mirror M1. This strategy will distort the imaging optics and degrade system resolution. The penalty for inefficient mirror reflectivity or insensitive resists is a decrease in system throughput which cannot be compensated for by increased source power. VIII. CONCLUSIONS

We have analyzed the effect of thermal loading on precision imaging mirrors and have presented normalized plots for the axial and radial distortion on these mirrors. Scaling laws for the thermally induced distortion were developed. From these results, it is possible to determine the distortion for similarly shaped mirrors made from different materials, with different aspect ratios, and with different thermal loads. 50-

40-

e,..

a0

0

0.5

I

,

0.55

.

.

0.6

Mirror

,

,

0.65

,

.

0.7

,

0.75

Reflectivity

FIG. 13. Using the model in Ref. (13), the maximum wafer throughput as a function of mirror reflectivity and resist sensitivity can be calculated. In this model, three imaging optics were assumed.

180

HAWRYLUK AND CEGLIO

Maximum x-ray power

Maximum x-ray power

Maximum x-ray power

Maximum x-ray power for mlrrorswith for mirrorswith for mirrorswith for mlrrorswith R=55%~. IR=60% ~'--R--65% --R=70% 6O

!

, 6=2m j / c m e ~

~ 20.

o , ~ ~ 10

20

30

40

50

X-ray Power at Wafer (mwl FIG. 14. The maximum wafer throughput as a function of average x-ray power at the wafer for a number of resist sensitivities (S) is calculated using the model in Ref. (13) and assuming a 100% utilization factor. The dotted vertical lines indicate the maximum average power that can be delivered to the wafer (as determined by the thermal loading limit on the imaging optics) for the indicated mirror reflectivity. For example, with a mirror reflectivity of 65%, the maximum average x-ray power delivered to the wafer is 34.6 mW and the maximum throughput for a 10 mJ/cm 2 resist is approximately 24 eight-inch wafers per hour.

In addition, the distortion produced by gravity and by nonuniform cooling of the mirrors was analyzed. In general, many of these distortions can be reduced with the use of thinner optics. Larger aspect ratio mirrors have reduced thermal and gravity induced distortions, but fabrication difficulties generally limit the mirror aspect ratios. The anticipated temporal and spatial variations for x rays incident upon the precision imaging mirrors in a SXPL system do not significantly alter the results from a steady state, uniform illumination model of thermal distortion effects. From our analysis of the thermal loading and distortion of imaging mirrors in a SXPL stepper, it is our conclusion that imaging mirrors using a ULE substrate cannot tolerate an average thermal loadgreater thafi approximately 63 mW and that a SXPL stepper with a four-mirror imaging system will require multilayer mirrors with a reflectivity greater than 50% for Pw = 5 mW. Greater power requirements at the wafer will require greater mirror reflectivities. The direct penalty for an inefficient system due to either inefficient mirrors or insensitive resists is a decrease in system throughput. While the thermal loading on condenser mirrors in a practical SXPL system may be large (up to 500 mW/cm 2 for the first condenser mirror), a properly designed condenser system is tolerant of approximately 1 #m of distortion on the condenser mirrors without compromising system resolution. This requirement can be achieved with moderate cooling of the condenser mirrors and appropriate selection of substrate materials. IX. ACKNOWLEDGMENTS The authors acknowledge the work of Gary L. Johnson and R. Martin from the LLNL Thermo-Fluid Mechanics Group for thermal analysis and computer simulations. The authors also acknowledge the active

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support of J. I. Davis, E. Storm, and E. M. Campbell of LLNL. This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract W7405-ENG-48. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

A. M. HAWRYLUKAND L. SEPPALA,J~ Wac. Sci. Technol. B 6(6), 2162 (Nov/Dec 1988). H. KJNOSHITA,J. Vac. Sci. Technol., B 7(6), 1648 (Nov/Dec 1989). O. WOODAND W. SILVFAST,J. Va¢. Sci. Technol. B 7(6), 1613 (Nov/Dec 1989). D. STEARNSet aL, "Multilayer Mirror Technology for Soft X-ray Projection Lithography, Proceedings of the Topical Meeting on Soft X-Ray Projection Lithography, April 1992." T. JEWEL, K. THOMPSON,AND J. RODGERS, SPIE, 1527 (1991). VISWANATHANel al., "Proceedings of the Topical Meeting on Soft X-ray Projection Lithography, April 1992." G. SOMMERGREN,"Work in Progress Seminar," Dec. 11, 199 l; private discussion. N.M. CEGLIOAND A. M. HAWRYLUK,"Proceedings of the Topical Meeting on Soft X-Ray Projection Lithography, April 1992." Zerodur-M is a low expansion material from Schott Glass. ULE is a low expansion material from DuPont. American Institute of Physics, "Handbook," 1972. K. EARLYAND W. ARNOLD,"Proceedings of the 1993 OSA Topical Meeting on Soft X-ray Projection Lithography, Monterey, CA.," (A. Hawryluk and R. Stulen, Eds.).