- Email: [email protected]
Elimination of effects due to patterning imperfections in electrical test structures for submicrometer feature metrology
Solid-State Electronics Vol. 35, No. 3, pp. 435-442, 1992 Printed in Great Britain
0038-1101/92 $5.00 + 0.00 Pergamon Press plc
ELIMINATION OF EFFECTS DUE TO PATTERNING IMPERFECTIONS IN ELECTRICAL TEST STRUCTURES FOR SUBMICROMETER FEATURE METROLOGYI" R. A. ALLEN and M. W. CRESSWELL National Institute of Standards and Technology, Semiconductor Electronics Division, Gaithersburg, MD 20899, U.S.A. (Received 16 August 1991; in revised form 27 September 1991) Abstract--This paper describes the elimination of a substrate-dependent systematic error that was experienced in prior work on measuring the separation of parallel features with an electrical test structure with total errors less than 10 nm. The test structure was an enhancement of a sliding-wire voltage-dividing potentiometer which scaled the overall test structure geometry to obtain greater sensitivity. It also incorporated features to eliminate adverse effects of voltage tap- and bridge-linewidth sealing. The measurement algorithm that was developed provided the relative separations of sets of features of the 10 nm level. However, absolute measurements were offset by a quantity characteristic of the substrate for which they were extracted. The evidence suggested that these systematic errors were not caused by the primary pattern generation tool. As a result of observations, measurements and simulations, this paper attributes the substrate-characteristic systematic error to an orientation dependence of the quality of replication of certain features of the test structure. An alternative design and measurement algorithm is shown to be able to practically eliminate these errors.
INTRODUCTION
Evaluation of the function of high-precision lithographic and etching tools for VLSI fabrication requires methods capable of measuring the distance between conducting features with precision of better than 50 nm. In Ref.[l], an electrical test structure was described that, according to simulation, should provide measurements with precision better than 10 nm using m o d e m test equipment. The experimental results in Ref.[1] showed this structure to provide measurements to better than 50 nm. However, a systematic error characteristic of the substrate upon which the test structures were replicated was observed. In this paper, this systematic error is attributed, by observations, measurements and simulations, to certain imperfections in the replication of the test structure. An alternative test structure design and measurement-extraction algorithm is described that should virtually eliminate these errors.
tiometer[6], shown in Fig. 1, has continued to be widely applied to determine the relative positions of parallel conducting features in IC wafer-fabrication, process-compatible test structures. It determines the distance the pointer P1 "slides" horizontally along the "wire" AB relative to the positions of pointers P2 and P3. The wire is referred to as the "bridge" of the device when it is implemented on VLSI wafers and pointer P1 is referred to as the "center" tap. Pointers P2 and P3, which serve as kelvin contacts for extracting the voltage drop along the bridge, are referred to as " e n d " taps whose center-to-center spacing L serves as the "ruler" for the measurement of x. To determine the offset distance x of the pointer from the midpoint of the bridge when it is construtted of material with a uniform resistance per unit length, the ratios RIL/2+~ : RIL and (L /2 + x ) : L are
P2
P1 -4
P3
.-
BACKGROUND
Recent work achieving resolutions better than 100nm, such as that by Fay and Hasan[2] and Kuroki et al.[3] used test structures such as the Stiekman-type[4] and the van der Pauw-typ¢[5], each of which introduces special fabrication requirements. Therefore, the sliding-wire, voltage-dividing potenLI2 L
Fig. 1. The active region of a sliding-wire, voltage-dividing potentiometer test structure.
tContribution of the National Institute of Standards and Technology, not subject to copyright. 435
436
R . A . ALLEN and M. W. CRESSWELL
equated, giving the following equation for x as a function of L (as-drawn value), RIL/2+ x (measured) and RIL (measured):
x = L(RIL/2+-xRIL \
~)"
(1)
However, there are limits to the method embodied in eqn (1) that have so far constrained the usefulness of the concept to the evaluation of high-precision tools and processes in wafer fabrication. The first of these limits is the requirement for effective point contacts at taps P1, P2 and P3. To avoid introducing a systematic error due to shortening of the electrical length of the bridge by the finite-width taps, the bridge length is typically made at least 20 times the width of the widest of P1, P2 and P3. However, when the device is scaled to a size to maintain such a ratio, the second limit is encountered: the sensitivity of the structure is reduced and the extracted measurement is the small difference between two numbers extremely close to 0.5, giving rise to a random error. Both sources of uncertainty must be considered in order to enable the reliable measurement of the offset x. As a consequence, even with modern test equipment, the measurement of x with acceptably low error with this technique is generally limited to cases where x is greater than several tenths of 1 pm. The so-called nanometer alignment test structure[l] shown in Fig. 2 is an enhancement of the voltagedividing potentiometer which allows scaling the structure geometry to achieve 10 nm resolution. It accomplishes this by allowing for the measurement of and correction for the effect of the finite width of a voltage tap on the electrical length of the line. Consequently, the bridge can be made arbitrarily short allowing enhanced sensitivity without introducing systematic error due to tap width per se. There are two features which represent the fundamental difference between the nanometer test structure shown in Fig. 2 and the original test structure based on the architecture in Fig. 1. The first feature is the pair of segments defined by the voltage taps connected to pads 6 and 3 and pads 3 and 2. The bridge-length shortening effect of a single tap is extracted from these equal-length segments through use of "dummy taps" appearing as short, open-ended
;
,,
i
i•/i l L/2÷x
\ L/2-x
Fig. 2. One possible implementation of the nanometer alignment structure. This particular geometry is the one used in the experimental portion of this work.
stubs on the segment between the taps connected to pads 3 and 2. These dummy taps serve to emulate the effects of a voltage tap on current traveling along the segment. Since each segment is of length L 1 and W, the difference in the "electrical" lengths of the segments is due to the effects of current shunting through the voltage taps in the region of their attachment. From this difference in electrical lengths, the effective electrical line shortening due to a single tap can be calculated. The second feature is the length L of the bridge defined by the voltage taps connected to pads 1 and 2. Because the line-shortening effect due to a single tap is now measurable, the length L can be scaled without the introduction of tap-related systematic errors in x. The basic test methodology for the structure shown in Fig. 2 is to first measure the effective shortening of the bridge due to a single tap 6L. Then the measured offset, x ....... a, is calculated by using eqn (1) with length L replaced by electrical length L - 26L. Specifically, a current is forced between pads 5 and 8 and voltages Vr~, V~, Vf7 and V~ are measured where the " + " sign refers to a positive current polarity. The current is reversed and voltages V~, Vfi, V~ and Vfi are measured where the " - " sign refers to a negative current polarity. Therefore, all these voltages are algebraically positive quantities. The average of the magnitudes of each pair of voltages is calculated. For example, V63= (V~3 + V~3)/2. The effective shortening of the bridge due to a single tap 6L is given by:
=, l({1"63-
V32\
)'
(2)
where n is the number of dummy taps between the taps connected to pads 3 and 2. From this, the measured offset, x . . . . . ~, is calculated by:
{V27
1\
x ...... .=~-V~21-~)(L-26L) •
(3)
In Ref.[1], it was shown that the value of xm..,u~.d extracted by using eqns (2) and (3) from several sites on a single mask was equal to the design values increased by a constant amount. Parenthetically, this still provides a major improvement over the sliding wire potentiometer because 6L cannot be predicted and eliminated from measurements due to its strong dependence on the actual, as-fabricated geometries of the intersection of the bridge and tap. However, with the 6L correction and subtracting this constant difference from each value of xm..,u~, the average residual difference of the measured value from the design value was 0 + 15 nm. In the original paper[l], the hypothesis was presented that this constant difference in x m . ~ from x d ~ was a characteristic of the substrate on which the test structures were fabricated. The data that are presented in this paper, taken from two new substrates, confirm these results. In addition, a quantitative expression for xm,~,~, incorporating features that could cause this increase, is presented
Elimination of effects due to patterning imperfections Table 1. Dimensionsof the test structuresmeasured in this study. For all structures the length of the bridge L was 24 #rn and the lengths of the segmentsused to extract the line-shorteningfrom a singletap LI were 165~m Bridge Tap Structure linewidth,W linewidth,T x~ita group ~ m) (~m) (nm) 1 1 1 0, 10, 50, 500 2 2 2 0, 10, 50, 500 3 1 4 0, 10, 50, 500 4 4 4 0, 10, 50, 500 and supported with measurements and simulations. Finally, a test structure architecture that obviates the entire problem is discussed.
EXPERIMENTAL PROCEDURE
A test chip containing a number of the test structures shown in Fig. 2 was designed and printed on a master chrome plate at 10 x by a MEBES-76f electron beam system with 0.1 x 0.1/~m pixel size. The master was then stepped across working masks at 10 x reduction and 10-mm stepping distances with an optical tool, providing drawn offsets, xd~i~, of 0, 10, 50 and 500 nm in a selection of test structures in each of a 10 x 10 array of chips. Two different working masks were fabricated and installed on a d.c. parametric tester for measurement extraction. The first mask was anti-reflective (AR) chrome (Mask 16). The second was bright chrome (Mask 11). Drawn dimensions of the tap and bridge linewidths of four groups of test structures that were measured are listed in Table 1. Tables 2 and 3 list extracted values of #L and x ~ , ~ for the structures measured on the two working masks. The values of fiL in Tables 2 and 3 are the averages of the four structures in each group. A single, complete set of values of x . . . . . ~d, calculated using eqn (3), is also shown. Figures 3 and 4 are plots of Xmcas,r,~,calculated by using eqn (3), and averaged over all four mask sites, vs Xd~i~ for the respective masks. Partial validation of the electrical length shortening effect of attached voltage taps represented by eqn (3) is provided. The slope of each of the lines is very close to unity, indicating that the measured offsets differ from all the design offsets by a constant amount. Significant nonzero y-axis intercept values in Figs 3 and 4 remain to be explained. For Mask 16, as shown in Fig. 3, the intercepts are in the range of 0.1-0.2#m; for Mask 11, as shown in Fig. 4, the intercepts are clustered around the origin. However, since both working masks were fabricated with 10 x
tCertain commercial equipment, instruments or materials are identified in this paper to specify the experimental procedure adequately. Such identificationdoes not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment are necessarily the best available for the purpose.
437
reduction of the same master and by using techniques that were reasonably expected to provide precise location of the geometric centerlines of the taps to within 10 nm, the intercepts observed for Mask 16 are so far unexplainably large. Further, since the intercepts for Mask 11 are different from those for Mask 16, it was confirmed that their source was not the master mask, but complications introduced in the replication of the working masks. We now show that the observed intercepts are in fact systematic errors in the apparent location of the offset of the center tap relative to the end taps caused by a subtle flaw of the working mask replication process. It was hypothesized[l] that the intercepts were due to the effects of inside comer rounding of the tap-tobridge intersections introduced in the working mask replication process. There are two effects that inside corner rounding could have on the extracted measurement of x which would cause apparent misplacement of the center tap. The first occurs if the taps attached to opposite sides of the bridge are of different electrical widths at the intersections of the taps to the bridge. In this case a single value of 6L, extracted from taps on one side of the bridge only, does not adequately describe the bridge length shortening effect. The second occurs if the tap-to-bridge inside corners are rounded in such a way as to displace the electrical centers of the taps on different sides of the bridge in different directions (or differently in the same direction). The net effect would have to move the electrical center of the center tap relative to the electrical centers of the end taps. At this point, it should be emphasized that inside corner rounding p e r se does not render the technique unworkable; once these effects are understood, they can be compensated for in the initial design, A high-powered optical microscope was used to examine the extent of visible comer rounding. On Mask 16 there was substantial corner rounding which varied with the corner's orientation. However, the corner rounding at particular tap-to-bridge intersections on the same side of the bridge and the same side of the tap appeared to be the same. That is, translationally equivalent corners had the same magnitude of corner rounding, but the corner rounding at each orientation was different from that at any other orientation. On Mask 11, although there was prominent corner rounding, there were not the marked differences apparent on Mask 16. Due to the diffraction limits of optical microscopy in accurately resolving submicrometer features, the description of the comer rounding given here is qualitative but is important because it serves as a starting point for analyzing the origin of the intercepts observed in Figs 3 and 4. Figure 5 shows the very small geometrical features responsible for the nonzero intercepts. In Fig. 5, if the magnitude of corner rounding is different on opposite inside corners of the same tap-to-bridge intersection, for example on side A of the bridge, the electrical
R. A. ALLEN and M. W. CRESSWELL
438
Table 2. Measured values of the electrical line shortening parameter 6L for a single tap and the measured displacement Xm~,~ of the center tap for a n AR chrome Mask 16 t~L (~m)
Site W=I,T=I 3, 3 0.966 4, 5 0.828 5, 4 0.815 6, 6 0.717 Specific data, Mask site (4, 5):
W=2, T = 2 0.862 0.809 0.843 0.778
W=I,T=4 2.229 2.170 2.396 1.913
W=4, T=4 0.923 0.885 0.914 0.844
xm..... d ~um) Xd©siSn
(Itm) 0.00 0.01 0.05 0.50 Intercept, xo(#m) Intercept, xo (Fig. 3) (p.m) ( D a t a from four sites)
W=I,T=I 0.094 0.158 0.191 0.614 0.127
W=2, T=2
0.119 _+0.034
0.148 + 0.021
0.135 0.148 0.188 0.652 0.137
c e n t e r o f t h e i n t e r s e c t i o n is d i s p l a c e d laterally f r o m t h e g e o m e t r i c a l c e n t e r o f the d r a w n i n t e r s e c t i o n by 6tA. A s l o n g as b o t h o f a p a i r o f t a p s have e q u a l 6 t - v a l u e s , s u c h as t h o s e o n t h e B-side o f the bridge, t h e lateral s e p a r a t i o n o f the electrical c e n t e r s o f their i n t e r s e c t i o n s is e q u a l to their geometrical c e n t e r - t o c e n t e r s e p a r a t i o n . O n the o t h e r h a n d , if each o f a p a i r o f t a p s h a s different d i s p l a c e m e n t values, s u c h as w h e n o n e t a p is f r o m the A - s i d e o f t h e bridge a n d the o t h e r is f r o m the B-side o f the bridge, t h e n the electrical s e p a r a t i o n o f the i n t e r s e c t i o n s will be different f r o m t h e g e o m e t r i c a l o n e by, in this case, t h e a m o u n t 6tA -- 6tB. T h e r e f o r e , e q n (3) d o e s n o t give a c o r r e c t value f o r Xmeasurcd unless 6tA=&t B and 6LA = &LB. Visual i n s p e c t i o n o f t h e t w o w o r k i n g m a s k s t h a t were used here revealed t h a t this c o n d i t i o n was p r o b a b l y n o t satisfied, p a r t i c u l a r l y in t h e case o f M a s k 16. I n k e e p i n g w i t h these o b s e r v a t i o n s , we n o w s h o w t h a t a n y d e v i a t i o n o f t h e q u a n t i t i e s fit^ - tSte a n d ~L^ - 6L~ f r o m zero is entirely consiste n t with the o b s e r v a t i o n s r e p o r t e d here.
W=I,T=4 0.217 0.210 0.243 0.772 0.201
W=4, T = 4 0.099 0.100 0.120 0.592 0.086
0.197 + 0.018
0.110 _+0.025
Specifically, we n o w s h o w t h a t i f either 6t A :/: 6ta o r ~L A ~ &Ls ( w h e n either 6tA ~ c~te o r 6L A =~ 6Ls there is said to exist differential d i s p l a c e m e n t a n d differential b r i d g e - l e n g t h s h o r t e n i n g , respectively), t h e n the i n t e r c e p t o f the curve o f Xm~ur~ VS Xdesi~, w h e r e x . . . . . . ~d is given by e q n (3), will be n o n z e r o . H o w e v e r , the slope o f the curve will be u n a f f e c t e d just as o b s e r v e d in Figs 3 a n d 4. F o r the g e o m e t r y s h o w n in Fig. 5 (and using the v o l t a g e t a p n o t a t i o n o f Fig. 2; i.e. the c e n t e r t a p is c o n n e c t e d to p a d 7 a n d t h e e n d t a p s are c o n n e c t e d to p a d s l a n d 2), e x a m i n a t i o n s h o w s t h a t t h e general e x p r e s s i o n for v o l t a g e division for a test s t r u c t u r e t h a t h a s u n e q u a l values f r o m o n e side o f the bridge to the o t h e r o f both the d i s p l a c e m e n t s 6t^ a n d ~ts and t h e electrical length s h o r t e n i n g p a r a m e t e r s $LA a n d c~La, is: -
+ x - (&A -- 6is) --
V2_._.2~ = 2
(4)
V21
L -- tSLA - ~LB
Table 3. Measured values of the electrical line shortening parameter 6L for a single tap and the measured displacement x~,,u=d of the center tap for bright chrome Mask 11 6L (/~m) Site 3, 3 4, 5 5, 4 6, 6 Specific data, Mask site (4,
W=I,T=I 0.694 0.692 0.667 0.595
W=2, T=2
W=I,T=4
0.653 0.683 0.712 0.672
2.407 2.377 2.341 2.263
W=4, T=4 0.802 0.779 0.834 0.840
5):
xm~,~,~ (t~m) Xdesilpl ~m) 0.00 0.01 0.05 0.50
Intercept, x0(#m ) Intercept, x0 (Fig. 4) ~ m ) (Data from four sites)
W=I,T=I
W=2,
T=2
W=I,T=4
W=4,
T=4
- 0.017 - 0.027 0.011 0.477
- 0.015 - 0.001 0.033 0.498
0.037 0.048 0.078 0.527
- 0.001 - 0.019 0.021 0.479
- 0.031 - 0.035 + 0.011
- 0.015 - 0.019 + 0.005
0.035 0.038_+0.008
- 0.019 - 0.022 _+0.005
Elimination of effects due to patterning imperfections 0,8
I
I
I
I
I
439
End Tape
I
0.7
0.6 0.5
]
!
0.4
L? 0.,3
•
M~
-0,1
0.0
'
'
I
1
0.1
0.2
0.3
0.4
Fig. 5. The basic three-tap bridge with asymmetric corner rounding introduced. The dashed lines indicate how "ideal" corners would be placed. 0.5
Xd.,L,, O~m) Fig. 3. Graph of data from AR chrome Mask 16. Each data point is the average for the four sites measured on the mask.
are not true, then a plot of x . . . . ~d vs xa,i~ will have a slope of unity, but an intercept, x0 of:
(1 V 2 7 ~ x0 = A t - A L
Now, if we define corresponding differential quantities At = ~ t A - 6tB and A L = ~iLA --6LB, and for convenience writing 6L = t$LA, we have:
x--At--AL
V27~-(V27--~
(L - 26L). (5)
-- [721,] -- •V21
The comparison of eqn (5) with eqn (3) shows that eqn (3) is a special case of eqn (5) and applicable only to those situations where both the differential displacement At and the differential line shortening per tap AL are zero. It also shows that if eqn (3) is used in those situations where the two conditions above
0.8
I
I
I
I
0,7 0.6 0.5 0.40.3
M~rkll
0.2 0.1
0.0
ir.2,r=~~ io --
lw//
Iv I•
- -
,-t.r-+ W=4,T=4
1
-0.1 0.0
i ,e r--'i
aestgn :.' Ldeslgn----i Center Tap i Geometrical [ Center of Tap I Electrical Center of Tap
I O. I
I 0.2
I 0.3
I 0.4
0.5
Fig, 4. Graph of data from bright chrome Mask 11. Each d a t a point is the average for the four sites measured on the
mask.
~
VEtf
(6)
A conclusion of this paper is, therefore, that the intercepts shown in Figs 3 and 4 do indeed exactly represent the quantity x0 in eqn (6). Unfortunately, the existing test structure does not permit the separate extractions of the displacements and differential lineshortening parameters. However, in the next section we show by modeling that the preceding conclusion is very plausible. We further show how future design modifications resolve the problems caused by the differential displacements and differential line-shortening. MODELING OF THE TEST STRUCTURE WITH VARYING AMOUNTS OF CORNER ROUNDING To determine whether the extent of corner rounding consistent with the qualitative observations that are reported here and the linewidths of the subject test structures could generate values of At and AL large enough to account for the observed intercepts on the xm.s,~ vs xd,sig,curves, the active region of the test structure (Fig. 5) was modeled by using resistor networks in SPICE, The structure modeled is a bridge with three voltage taps and corner-rounding parameters A1, A2, B1 and B2 of Fig. 5. These parameters represent the respective distances that the rounding of the inside corners encroaches along the length of the bridge, as shown in Fig. 5, where the geometrical center line of the lower central tap is parallel to and half-way between the geometrical center lines of the two upper end taps. Left,~ and Lefr.~ are the effective lengths of the bridge segments for the purposes of voltage division. They may be expected to differ from the as-designed center-to-center separation Ld,i~ to an extent depending on parameters A I , A2, B1 and B2. In each of the following cases, it was assumed that all translationally equivalent corners (that is, those with the same angular orientation)
440
R. A. ALLENand M. W. CRBgSWELL
would have the same magnitude of corner rounding, in conformance with visual observations. In addition, for convenience, in all cases AI = B2 and A2 = B1, this leads to no loss of generality; it simply means that 6 t A = --tSl B.
Three different test-structure architectures were simulated. The first case was a bridge with a single tap with no inside corner rounding for the purpose of inspecting the dependence of 6L on the ratio of the tap and bridge linewidths. The second case was the three-tap configuration shown in Fig. 5 that implements the offset measurement features of the test structure shown in Fig. 2. For each set of cornerrounding parameters, the simulation provided the extracted value of Xm,s,~ for Xdes~ = 0. That is, the geometrical center line of the center tap on side A of the bridge was drawn exactly half-way between the geometrical center lines of the two taps on side B of the bridge. The objective was to simulate the dependence Of Xm..... d [calculated by using eqn (3) since eqn (5) would, of course, provide the correct value, x = 0] on the differential electrical displacement of the effective tap positions. The third case, shown in Fig. 6, used a similar geometry to the second case with the exception that the voltage taps extended from both sides of the bridge. For convenience, voltage taps which extend from one side of the bridge only (such as those shown in Fig. 5) are referred to as "noncrossing taps" and ones that extend from both sides of the bridge (such as those shown in Fig. 6) are referred to as "crossing taps." The SPICE simulations were performed as follows: first, a 0.1/~m grid was set up over an area large enough to cover all possible cases. Second, the bridge/tap combinations were set up, with all grid points included in the bridge or tap connected to each nearest neighbor by equal-value resistors. Next, corner rounding was included by connecting the grid points that represent the corner rounding to each nearest neighbor. To perform the actual simulation, a potential difference was applied across the bridge. Preliminary simulations showed that, in all three cases, the voltage taps were sufficiently separated that
B1
B2 --d B1
:;
i
^2
:, L d a a l g n ~ ! Gaomatrl cal 1 Canter of Tap I Electrical Canter of Tap
Ldaalgn
Fig. 6. The modified three-tap structure, showing crossing taps and including corner rounding. The dashed lines indicate how "ideal" corners would be placed.
Table 4. SPICE simulation results for various geometries with noncrossing taps. The devices were simulated as resistor networks on a 0.1/~m grid. Each node included in the geometry was connected to all nearest neighbor nodes Change in effective line length, 6L of a 15-/~m-long bridge due to a single tap with no corner rounding Dimensions of test structures Bridge linewidth, W
(/~m)
Tap linewidth, T (t,m)
6L (~m)
1.0 1.0
1.0 4.0
0.157 1.778
Results from the simulations of a 15-tzm-long, l-,am-wide, bridge with three 1-/~m wide, 3-#m-long, voltage taps (see Fig. 5). Since AI = B2 and A2 = B1, 6t^ = -¢$t n and Xmeasu~d = 6 t ^ - - f i t a = 2 6 t A Curvature parameters (/~m)
Xmeasur~ Calculated using
AI, B2
A2, BI
6L (urn)
eqn (3) (/tin)
0.0 0.2 0.4 0.6 0.6
0.0 0.0 0.2 0.2 0.4
0.157 0.194 0.291 0.361 0.425
0.000 0.084 0.121 0.262 0.140
the taps did not interfere with each other electrically and that the open ends of the voltage taps were equipotentials. Table 4 shows the results of the first two cases. The top section of Table 4 shows a very strong relationship between tap and 6L. Increasing the tap linewidth from 1 to 4 #m for a 1/~m bridge linewidth increased 6L by more than a factor of 10 to almost 2 #m. This result emphasizes that the classical voltage division formula eqn (1), without provisions for electrical length-shortening of the bridge, applied to extracted voltages would typically give an error of over 30% in the measurement of x even with perfect corners, whereas simply providing for a single value of 6L without side-to-side differentiation reduces this by an order of magnitude. The second part of Table 4 shows the effects of introducing asymmetric corner rounding on 6L and Xme..... d" The value of tSL is markedly increased by nominal amounts of corner rounding. This result supports the hypothesis offered in Ref.[1] that 6L measurements tend to be substantially elevated above those for clean corners by the presence of nominal inside corner rounding. It also suggests that the bulk of current-shunting occurs in the very small region of the taps adjoining the bridge. In addition, Table 4 shows that only small differences in the amount of inside corner rounding from one side on the tap to the other have a significant effect on x . . . . . . d" In particular, a difference of only 0.2 to 0.4/tm per tap (e.g. B 2 = B I + 0 . 2 / ~ m and A1 = A 2 + 0 . 2 t t m ) was enough to produce the offsets measured on Mask 16 reported here. Results frem the third case, that of the crossing voltage taps in Fig. 6, are shown in Table 5. Alongside these are comparable results from Table 4 for noncrossing taps. The first result from the data is the increase in 6L for a crossing tap over that for a noncrossing tap by slightly less than a factor of two, which is about what might be anticipated since the
441
Elimination of effects due to patterning imperfections Table 5. Comparison of simulation results for noncrossing (from Table 4) and crossing taps. "Opposite side" refers to voltages measured through a set of taps where the center tap is on the opposite side of the bridge from the end taps; "same side" refers to voltagesmeasured through a set of taps all extending from the same side of the bridge Xmcasutcd
Calculated using eqn (3) Voltage tap/measurement Configuration Curvature parameters A1, B2 0.0 0.2 0.4 0.6 0.6
A2, BI 0.0 0.0 0.2 0.2 0.4
~L (~m) Taps Nonerossing Crossing o. 157 0.287 0.194 0.350 0.291 0.511 0.361 0.626 0.425 0.718
bridge-current shunting effect is doubled at each tap-to-bridge intersection. The second and most important result is the effectiveness of crossing taps to eliminate the effects due to corner rounding. The results clearly show that, with crossing taps in conjunction with all voltages being measured from taps extending from that same side of the bridge, one can effectively eliminate the systematic error illustrated by the intercepts in Figs 3 and 4 and expressed in eqn (6). N o t e that eqn (3), for which the parametric inputs are straightforward to extract, gives exactly the target results for the offset when all voltages are extracted from the same side of the bridge, regardless of the extent of both the differential corner rounding and the asymmetry of corner rounding on individual taps. The simulation shows that, by constructing the test structure as shown in Fig. 6 and working with voltages extracted from one side at a time, a very robust method for extracting the separation for parallel features at 10 nm level is provided. This result assumes, of course, that the rounding symmetries shown in Fig. 6 are achieved in practice. Although visual inspection of these masks revealed the taps to be translationally similar, the effect of introducing small random perturbations to the curvature parameters in the future should be modeled. The results of this modeling will give a value to the limits of the precision of the improved test structure. While this result suggests that a structure with noncrossing taps that all extend from the same side of the bridge would be as effective, there are two additional, secondary benefits of using crossing taps. The first is that the increase in the magnitude of 6L allows reduction in the number of d u m m y taps, in turn allowing a reduction in L 1, minimizing potential random errors due to nonuniformity in the test structure over distance. The second advantage concerns the utilization of this test structure for multilevel registration applications, such as via to first-layer metal. These issues are the themes of future papers which will address such applications, as well as the presentation of measurements extracted from single-level structures with crossing voltage taps.
Crossing Noncrossing Opposite side 0.000 0.084 0.121 0.262 0.140
Opposite side 0.000 0.062 0.085 o. 174 0.090
Same side 0.000 0.001 0.001 0.000 0.000
CONCLUSIONS In earlier work, a modified sliding-wire potentiometer capable of providing the relative separations of features in a local region with errors less than 20 nm was described. In that prior work, a systematic error of unknown origin was encountered which had the same effect as a misalignment of taps extending from one side of the current-carrying bridge relative to taps extending from the opposite side of the bridge. The present work shows that the magnitude of the error for a particular set of test structure linewidths tends to be characteristic of the substrate on which the test structures are replicated. Specifically, these errors are attributed to imperfections at the inside corners of the intersection of the voltage taps with the bridge. This result is from SPICE modeling of the as-drawn test structure with small geometric modifications to simulate the effects of corner rounding as observed in a high-powered microscope. It is shown that two specific design changes to the original test structure will eliminate the subject systematic error. These changes are: (a) all voltage taps must extend from both sides of the bridge; and (b) all voltages must be measured through taps extending from the same side of the bridge. The result is a feature placement metrology tool that provides measurement of feature placement to within I0 nm yet requires nothing beyond conventional fabrication techniques and test equipment.
Acknowledgements--The authors wish to acknowledge the valued contributions of Colleen Ellenwood for digitization of the design of the test structure, of Larry Buck for his careful measurements of the test structures, of Dr Michael Gaitan, Loren Linholm, Dr Jeremiah Lowney and Dr Robert Larrabee for their technical discussions, and of Jane Waiters and Jo Gonzalez for their invaluable editorial support in preparing the manuscript. The staff of Photronix Corporation are acknowledged for their recommendations and technical inputs in the preparation of the patterned chrome plates. The assistance of Keithley Corporation, in particular Michael Peters and Bert Blaha, is acknowledged in providing corroborating measurements of the plates. This work was supported in part by the X-Ray Lithography Program of the Defense Advanced Research Projects Agency.
R. A. ALLEN and M. W. CRESSWELL
442 REFERENCES
1. M. W. Crcsswell, M. Gaitan, R. A. Allen and L. W. Linholm, Proc. 1991 ICMTS, p. 129 (1991). 2. B. Fay and T. Hasan, Solid-St. Technol. May, 239 (1986).
3. Y. Kuroki, S. Hasegawa, T. Honda and Y. Iida, Proc. 1991 ICMTS, p. 123 (1991). 4. K. H. Nicholas, I. J. Stemp and H. E. Brockman, J. Electrochem. Soc. 128, 609 (1981). 5. D. S. Perloff, Solid-St. Electron. 21, 1013 (1978). 6. T. J. Russell, T. F. I~cdy and R. L. Mattis, Technical Digest--1977 Int. Electron Devices Mtg (1977).
0038-1101/92 $5.00 + 0.00 Pergamon Press plc
ELIMINATION OF EFFECTS DUE TO PATTERNING IMPERFECTIONS IN ELECTRICAL TEST STRUCTURES FOR SUBMICROMETER FEATURE METROLOGYI" R. A. ALLEN and M. W. CRESSWELL National Institute of Standards and Technology, Semiconductor Electronics Division, Gaithersburg, MD 20899, U.S.A. (Received 16 August 1991; in revised form 27 September 1991) Abstract--This paper describes the elimination of a substrate-dependent systematic error that was experienced in prior work on measuring the separation of parallel features with an electrical test structure with total errors less than 10 nm. The test structure was an enhancement of a sliding-wire voltage-dividing potentiometer which scaled the overall test structure geometry to obtain greater sensitivity. It also incorporated features to eliminate adverse effects of voltage tap- and bridge-linewidth sealing. The measurement algorithm that was developed provided the relative separations of sets of features of the 10 nm level. However, absolute measurements were offset by a quantity characteristic of the substrate for which they were extracted. The evidence suggested that these systematic errors were not caused by the primary pattern generation tool. As a result of observations, measurements and simulations, this paper attributes the substrate-characteristic systematic error to an orientation dependence of the quality of replication of certain features of the test structure. An alternative design and measurement algorithm is shown to be able to practically eliminate these errors.
INTRODUCTION
Evaluation of the function of high-precision lithographic and etching tools for VLSI fabrication requires methods capable of measuring the distance between conducting features with precision of better than 50 nm. In Ref.[l], an electrical test structure was described that, according to simulation, should provide measurements with precision better than 10 nm using m o d e m test equipment. The experimental results in Ref.[1] showed this structure to provide measurements to better than 50 nm. However, a systematic error characteristic of the substrate upon which the test structures were replicated was observed. In this paper, this systematic error is attributed, by observations, measurements and simulations, to certain imperfections in the replication of the test structure. An alternative test structure design and measurement-extraction algorithm is described that should virtually eliminate these errors.
tiometer[6], shown in Fig. 1, has continued to be widely applied to determine the relative positions of parallel conducting features in IC wafer-fabrication, process-compatible test structures. It determines the distance the pointer P1 "slides" horizontally along the "wire" AB relative to the positions of pointers P2 and P3. The wire is referred to as the "bridge" of the device when it is implemented on VLSI wafers and pointer P1 is referred to as the "center" tap. Pointers P2 and P3, which serve as kelvin contacts for extracting the voltage drop along the bridge, are referred to as " e n d " taps whose center-to-center spacing L serves as the "ruler" for the measurement of x. To determine the offset distance x of the pointer from the midpoint of the bridge when it is construtted of material with a uniform resistance per unit length, the ratios RIL/2+~ : RIL and (L /2 + x ) : L are
P2
P1 -4
P3
.-
BACKGROUND
Recent work achieving resolutions better than 100nm, such as that by Fay and Hasan[2] and Kuroki et al.[3] used test structures such as the Stiekman-type[4] and the van der Pauw-typ¢[5], each of which introduces special fabrication requirements. Therefore, the sliding-wire, voltage-dividing potenLI2 L
Fig. 1. The active region of a sliding-wire, voltage-dividing potentiometer test structure.
tContribution of the National Institute of Standards and Technology, not subject to copyright. 435
436
R . A . ALLEN and M. W. CRESSWELL
equated, giving the following equation for x as a function of L (as-drawn value), RIL/2+ x (measured) and RIL (measured):
x = L(RIL/2+-xRIL \
~)"
(1)
However, there are limits to the method embodied in eqn (1) that have so far constrained the usefulness of the concept to the evaluation of high-precision tools and processes in wafer fabrication. The first of these limits is the requirement for effective point contacts at taps P1, P2 and P3. To avoid introducing a systematic error due to shortening of the electrical length of the bridge by the finite-width taps, the bridge length is typically made at least 20 times the width of the widest of P1, P2 and P3. However, when the device is scaled to a size to maintain such a ratio, the second limit is encountered: the sensitivity of the structure is reduced and the extracted measurement is the small difference between two numbers extremely close to 0.5, giving rise to a random error. Both sources of uncertainty must be considered in order to enable the reliable measurement of the offset x. As a consequence, even with modern test equipment, the measurement of x with acceptably low error with this technique is generally limited to cases where x is greater than several tenths of 1 pm. The so-called nanometer alignment test structure[l] shown in Fig. 2 is an enhancement of the voltagedividing potentiometer which allows scaling the structure geometry to achieve 10 nm resolution. It accomplishes this by allowing for the measurement of and correction for the effect of the finite width of a voltage tap on the electrical length of the line. Consequently, the bridge can be made arbitrarily short allowing enhanced sensitivity without introducing systematic error due to tap width per se. There are two features which represent the fundamental difference between the nanometer test structure shown in Fig. 2 and the original test structure based on the architecture in Fig. 1. The first feature is the pair of segments defined by the voltage taps connected to pads 6 and 3 and pads 3 and 2. The bridge-length shortening effect of a single tap is extracted from these equal-length segments through use of "dummy taps" appearing as short, open-ended
;
,,
i
i•/i l L/2÷x
\ L/2-x
Fig. 2. One possible implementation of the nanometer alignment structure. This particular geometry is the one used in the experimental portion of this work.
stubs on the segment between the taps connected to pads 3 and 2. These dummy taps serve to emulate the effects of a voltage tap on current traveling along the segment. Since each segment is of length L 1 and W, the difference in the "electrical" lengths of the segments is due to the effects of current shunting through the voltage taps in the region of their attachment. From this difference in electrical lengths, the effective electrical line shortening due to a single tap can be calculated. The second feature is the length L of the bridge defined by the voltage taps connected to pads 1 and 2. Because the line-shortening effect due to a single tap is now measurable, the length L can be scaled without the introduction of tap-related systematic errors in x. The basic test methodology for the structure shown in Fig. 2 is to first measure the effective shortening of the bridge due to a single tap 6L. Then the measured offset, x ....... a, is calculated by using eqn (1) with length L replaced by electrical length L - 26L. Specifically, a current is forced between pads 5 and 8 and voltages Vr~, V~, Vf7 and V~ are measured where the " + " sign refers to a positive current polarity. The current is reversed and voltages V~, Vfi, V~ and Vfi are measured where the " - " sign refers to a negative current polarity. Therefore, all these voltages are algebraically positive quantities. The average of the magnitudes of each pair of voltages is calculated. For example, V63= (V~3 + V~3)/2. The effective shortening of the bridge due to a single tap 6L is given by:
=, l({1"63-
V32\
)'
(2)
where n is the number of dummy taps between the taps connected to pads 3 and 2. From this, the measured offset, x . . . . . ~, is calculated by:
{V27
1\
x ...... .=~-V~21-~)(L-26L) •
(3)
In Ref.[1], it was shown that the value of xm..,u~.d extracted by using eqns (2) and (3) from several sites on a single mask was equal to the design values increased by a constant amount. Parenthetically, this still provides a major improvement over the sliding wire potentiometer because 6L cannot be predicted and eliminated from measurements due to its strong dependence on the actual, as-fabricated geometries of the intersection of the bridge and tap. However, with the 6L correction and subtracting this constant difference from each value of xm..,u~, the average residual difference of the measured value from the design value was 0 + 15 nm. In the original paper[l], the hypothesis was presented that this constant difference in x m . ~ from x d ~ was a characteristic of the substrate on which the test structures were fabricated. The data that are presented in this paper, taken from two new substrates, confirm these results. In addition, a quantitative expression for xm,~,~, incorporating features that could cause this increase, is presented
Elimination of effects due to patterning imperfections Table 1. Dimensionsof the test structuresmeasured in this study. For all structures the length of the bridge L was 24 #rn and the lengths of the segmentsused to extract the line-shorteningfrom a singletap LI were 165~m Bridge Tap Structure linewidth,W linewidth,T x~ita group ~ m) (~m) (nm) 1 1 1 0, 10, 50, 500 2 2 2 0, 10, 50, 500 3 1 4 0, 10, 50, 500 4 4 4 0, 10, 50, 500 and supported with measurements and simulations. Finally, a test structure architecture that obviates the entire problem is discussed.
EXPERIMENTAL PROCEDURE
A test chip containing a number of the test structures shown in Fig. 2 was designed and printed on a master chrome plate at 10 x by a MEBES-76f electron beam system with 0.1 x 0.1/~m pixel size. The master was then stepped across working masks at 10 x reduction and 10-mm stepping distances with an optical tool, providing drawn offsets, xd~i~, of 0, 10, 50 and 500 nm in a selection of test structures in each of a 10 x 10 array of chips. Two different working masks were fabricated and installed on a d.c. parametric tester for measurement extraction. The first mask was anti-reflective (AR) chrome (Mask 16). The second was bright chrome (Mask 11). Drawn dimensions of the tap and bridge linewidths of four groups of test structures that were measured are listed in Table 1. Tables 2 and 3 list extracted values of #L and x ~ , ~ for the structures measured on the two working masks. The values of fiL in Tables 2 and 3 are the averages of the four structures in each group. A single, complete set of values of x . . . . . ~d, calculated using eqn (3), is also shown. Figures 3 and 4 are plots of Xmcas,r,~,calculated by using eqn (3), and averaged over all four mask sites, vs Xd~i~ for the respective masks. Partial validation of the electrical length shortening effect of attached voltage taps represented by eqn (3) is provided. The slope of each of the lines is very close to unity, indicating that the measured offsets differ from all the design offsets by a constant amount. Significant nonzero y-axis intercept values in Figs 3 and 4 remain to be explained. For Mask 16, as shown in Fig. 3, the intercepts are in the range of 0.1-0.2#m; for Mask 11, as shown in Fig. 4, the intercepts are clustered around the origin. However, since both working masks were fabricated with 10 x
tCertain commercial equipment, instruments or materials are identified in this paper to specify the experimental procedure adequately. Such identificationdoes not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment are necessarily the best available for the purpose.
437
reduction of the same master and by using techniques that were reasonably expected to provide precise location of the geometric centerlines of the taps to within 10 nm, the intercepts observed for Mask 16 are so far unexplainably large. Further, since the intercepts for Mask 11 are different from those for Mask 16, it was confirmed that their source was not the master mask, but complications introduced in the replication of the working masks. We now show that the observed intercepts are in fact systematic errors in the apparent location of the offset of the center tap relative to the end taps caused by a subtle flaw of the working mask replication process. It was hypothesized[l] that the intercepts were due to the effects of inside comer rounding of the tap-tobridge intersections introduced in the working mask replication process. There are two effects that inside corner rounding could have on the extracted measurement of x which would cause apparent misplacement of the center tap. The first occurs if the taps attached to opposite sides of the bridge are of different electrical widths at the intersections of the taps to the bridge. In this case a single value of 6L, extracted from taps on one side of the bridge only, does not adequately describe the bridge length shortening effect. The second occurs if the tap-to-bridge inside corners are rounded in such a way as to displace the electrical centers of the taps on different sides of the bridge in different directions (or differently in the same direction). The net effect would have to move the electrical center of the center tap relative to the electrical centers of the end taps. At this point, it should be emphasized that inside corner rounding p e r se does not render the technique unworkable; once these effects are understood, they can be compensated for in the initial design, A high-powered optical microscope was used to examine the extent of visible comer rounding. On Mask 16 there was substantial corner rounding which varied with the corner's orientation. However, the corner rounding at particular tap-to-bridge intersections on the same side of the bridge and the same side of the tap appeared to be the same. That is, translationally equivalent corners had the same magnitude of corner rounding, but the corner rounding at each orientation was different from that at any other orientation. On Mask 11, although there was prominent corner rounding, there were not the marked differences apparent on Mask 16. Due to the diffraction limits of optical microscopy in accurately resolving submicrometer features, the description of the comer rounding given here is qualitative but is important because it serves as a starting point for analyzing the origin of the intercepts observed in Figs 3 and 4. Figure 5 shows the very small geometrical features responsible for the nonzero intercepts. In Fig. 5, if the magnitude of corner rounding is different on opposite inside corners of the same tap-to-bridge intersection, for example on side A of the bridge, the electrical
R. A. ALLEN and M. W. CRESSWELL
438
Table 2. Measured values of the electrical line shortening parameter 6L for a single tap and the measured displacement Xm~,~ of the center tap for a n AR chrome Mask 16 t~L (~m)
Site W=I,T=I 3, 3 0.966 4, 5 0.828 5, 4 0.815 6, 6 0.717 Specific data, Mask site (4, 5):
W=2, T = 2 0.862 0.809 0.843 0.778
W=I,T=4 2.229 2.170 2.396 1.913
W=4, T=4 0.923 0.885 0.914 0.844
xm..... d ~um) Xd©siSn
(Itm) 0.00 0.01 0.05 0.50 Intercept, xo(#m) Intercept, xo (Fig. 3) (p.m) ( D a t a from four sites)
W=I,T=I 0.094 0.158 0.191 0.614 0.127
W=2, T=2
0.119 _+0.034
0.148 + 0.021
0.135 0.148 0.188 0.652 0.137
c e n t e r o f t h e i n t e r s e c t i o n is d i s p l a c e d laterally f r o m t h e g e o m e t r i c a l c e n t e r o f the d r a w n i n t e r s e c t i o n by 6tA. A s l o n g as b o t h o f a p a i r o f t a p s have e q u a l 6 t - v a l u e s , s u c h as t h o s e o n t h e B-side o f the bridge, t h e lateral s e p a r a t i o n o f the electrical c e n t e r s o f their i n t e r s e c t i o n s is e q u a l to their geometrical c e n t e r - t o c e n t e r s e p a r a t i o n . O n the o t h e r h a n d , if each o f a p a i r o f t a p s h a s different d i s p l a c e m e n t values, s u c h as w h e n o n e t a p is f r o m the A - s i d e o f t h e bridge a n d the o t h e r is f r o m the B-side o f the bridge, t h e n the electrical s e p a r a t i o n o f the i n t e r s e c t i o n s will be different f r o m t h e g e o m e t r i c a l o n e by, in this case, t h e a m o u n t 6tA -- 6tB. T h e r e f o r e , e q n (3) d o e s n o t give a c o r r e c t value f o r Xmeasurcd unless 6tA=&t B and 6LA = &LB. Visual i n s p e c t i o n o f t h e t w o w o r k i n g m a s k s t h a t were used here revealed t h a t this c o n d i t i o n was p r o b a b l y n o t satisfied, p a r t i c u l a r l y in t h e case o f M a s k 16. I n k e e p i n g w i t h these o b s e r v a t i o n s , we n o w s h o w t h a t a n y d e v i a t i o n o f t h e q u a n t i t i e s fit^ - tSte a n d ~L^ - 6L~ f r o m zero is entirely consiste n t with the o b s e r v a t i o n s r e p o r t e d here.
W=I,T=4 0.217 0.210 0.243 0.772 0.201
W=4, T = 4 0.099 0.100 0.120 0.592 0.086
0.197 + 0.018
0.110 _+0.025
Specifically, we n o w s h o w t h a t i f either 6t A :/: 6ta o r ~L A ~ &Ls ( w h e n either 6tA ~ c~te o r 6L A =~ 6Ls there is said to exist differential d i s p l a c e m e n t a n d differential b r i d g e - l e n g t h s h o r t e n i n g , respectively), t h e n the i n t e r c e p t o f the curve o f Xm~ur~ VS Xdesi~, w h e r e x . . . . . . ~d is given by e q n (3), will be n o n z e r o . H o w e v e r , the slope o f the curve will be u n a f f e c t e d just as o b s e r v e d in Figs 3 a n d 4. F o r the g e o m e t r y s h o w n in Fig. 5 (and using the v o l t a g e t a p n o t a t i o n o f Fig. 2; i.e. the c e n t e r t a p is c o n n e c t e d to p a d 7 a n d t h e e n d t a p s are c o n n e c t e d to p a d s l a n d 2), e x a m i n a t i o n s h o w s t h a t t h e general e x p r e s s i o n for v o l t a g e division for a test s t r u c t u r e t h a t h a s u n e q u a l values f r o m o n e side o f the bridge to the o t h e r o f both the d i s p l a c e m e n t s 6t^ a n d ~ts and t h e electrical length s h o r t e n i n g p a r a m e t e r s $LA a n d c~La, is: -
+ x - (&A -- 6is) --
V2_._.2~ = 2
(4)
V21
L -- tSLA - ~LB
Table 3. Measured values of the electrical line shortening parameter 6L for a single tap and the measured displacement x~,,u=d of the center tap for bright chrome Mask 11 6L (/~m) Site 3, 3 4, 5 5, 4 6, 6 Specific data, Mask site (4,
W=I,T=I 0.694 0.692 0.667 0.595
W=2, T=2
W=I,T=4
0.653 0.683 0.712 0.672
2.407 2.377 2.341 2.263
W=4, T=4 0.802 0.779 0.834 0.840
5):
xm~,~,~ (t~m) Xdesilpl ~m) 0.00 0.01 0.05 0.50
Intercept, x0(#m ) Intercept, x0 (Fig. 4) ~ m ) (Data from four sites)
W=I,T=I
W=2,
T=2
W=I,T=4
W=4,
T=4
- 0.017 - 0.027 0.011 0.477
- 0.015 - 0.001 0.033 0.498
0.037 0.048 0.078 0.527
- 0.001 - 0.019 0.021 0.479
- 0.031 - 0.035 + 0.011
- 0.015 - 0.019 + 0.005
0.035 0.038_+0.008
- 0.019 - 0.022 _+0.005
Elimination of effects due to patterning imperfections 0,8
I
I
I
I
I
439
End Tape
I
0.7
0.6 0.5
]
!
0.4
L? 0.,3
•
M~
-0,1
0.0
'
'
I
1
0.1
0.2
0.3
0.4
Fig. 5. The basic three-tap bridge with asymmetric corner rounding introduced. The dashed lines indicate how "ideal" corners would be placed. 0.5
Xd.,L,, O~m) Fig. 3. Graph of data from AR chrome Mask 16. Each data point is the average for the four sites measured on the mask.
are not true, then a plot of x . . . . ~d vs xa,i~ will have a slope of unity, but an intercept, x0 of:
(1 V 2 7 ~ x0 = A t - A L
Now, if we define corresponding differential quantities At = ~ t A - 6tB and A L = ~iLA --6LB, and for convenience writing 6L = t$LA, we have:
x--At--AL
V27~-(V27--~
(L - 26L). (5)
-- [721,] -- •V21
The comparison of eqn (5) with eqn (3) shows that eqn (3) is a special case of eqn (5) and applicable only to those situations where both the differential displacement At and the differential line shortening per tap AL are zero. It also shows that if eqn (3) is used in those situations where the two conditions above
0.8
I
I
I
I
0,7 0.6 0.5 0.40.3
M~rkll
0.2 0.1
0.0
ir.2,r=~~ io --
lw//
Iv I•
- -
,-t.r-+ W=4,T=4
1
-0.1 0.0
i ,e r--'i
aestgn :.' Ldeslgn----i Center Tap i Geometrical [ Center of Tap I Electrical Center of Tap
I O. I
I 0.2
I 0.3
I 0.4
0.5
Fig, 4. Graph of data from bright chrome Mask 11. Each d a t a point is the average for the four sites measured on the
mask.
~
VEtf
(6)
A conclusion of this paper is, therefore, that the intercepts shown in Figs 3 and 4 do indeed exactly represent the quantity x0 in eqn (6). Unfortunately, the existing test structure does not permit the separate extractions of the displacements and differential lineshortening parameters. However, in the next section we show by modeling that the preceding conclusion is very plausible. We further show how future design modifications resolve the problems caused by the differential displacements and differential line-shortening. MODELING OF THE TEST STRUCTURE WITH VARYING AMOUNTS OF CORNER ROUNDING To determine whether the extent of corner rounding consistent with the qualitative observations that are reported here and the linewidths of the subject test structures could generate values of At and AL large enough to account for the observed intercepts on the xm.s,~ vs xd,sig,curves, the active region of the test structure (Fig. 5) was modeled by using resistor networks in SPICE, The structure modeled is a bridge with three voltage taps and corner-rounding parameters A1, A2, B1 and B2 of Fig. 5. These parameters represent the respective distances that the rounding of the inside corners encroaches along the length of the bridge, as shown in Fig. 5, where the geometrical center line of the lower central tap is parallel to and half-way between the geometrical center lines of the two upper end taps. Left,~ and Lefr.~ are the effective lengths of the bridge segments for the purposes of voltage division. They may be expected to differ from the as-designed center-to-center separation Ld,i~ to an extent depending on parameters A I , A2, B1 and B2. In each of the following cases, it was assumed that all translationally equivalent corners (that is, those with the same angular orientation)
440
R. A. ALLENand M. W. CRBgSWELL
would have the same magnitude of corner rounding, in conformance with visual observations. In addition, for convenience, in all cases AI = B2 and A2 = B1, this leads to no loss of generality; it simply means that 6 t A = --tSl B.
Three different test-structure architectures were simulated. The first case was a bridge with a single tap with no inside corner rounding for the purpose of inspecting the dependence of 6L on the ratio of the tap and bridge linewidths. The second case was the three-tap configuration shown in Fig. 5 that implements the offset measurement features of the test structure shown in Fig. 2. For each set of cornerrounding parameters, the simulation provided the extracted value of Xm,s,~ for Xdes~ = 0. That is, the geometrical center line of the center tap on side A of the bridge was drawn exactly half-way between the geometrical center lines of the two taps on side B of the bridge. The objective was to simulate the dependence Of Xm..... d [calculated by using eqn (3) since eqn (5) would, of course, provide the correct value, x = 0] on the differential electrical displacement of the effective tap positions. The third case, shown in Fig. 6, used a similar geometry to the second case with the exception that the voltage taps extended from both sides of the bridge. For convenience, voltage taps which extend from one side of the bridge only (such as those shown in Fig. 5) are referred to as "noncrossing taps" and ones that extend from both sides of the bridge (such as those shown in Fig. 6) are referred to as "crossing taps." The SPICE simulations were performed as follows: first, a 0.1/~m grid was set up over an area large enough to cover all possible cases. Second, the bridge/tap combinations were set up, with all grid points included in the bridge or tap connected to each nearest neighbor by equal-value resistors. Next, corner rounding was included by connecting the grid points that represent the corner rounding to each nearest neighbor. To perform the actual simulation, a potential difference was applied across the bridge. Preliminary simulations showed that, in all three cases, the voltage taps were sufficiently separated that
B1
B2 --d B1
:;
i
^2
:, L d a a l g n ~ ! Gaomatrl cal 1 Canter of Tap I Electrical Canter of Tap
Ldaalgn
Fig. 6. The modified three-tap structure, showing crossing taps and including corner rounding. The dashed lines indicate how "ideal" corners would be placed.
Table 4. SPICE simulation results for various geometries with noncrossing taps. The devices were simulated as resistor networks on a 0.1/~m grid. Each node included in the geometry was connected to all nearest neighbor nodes Change in effective line length, 6L of a 15-/~m-long bridge due to a single tap with no corner rounding Dimensions of test structures Bridge linewidth, W
(/~m)
Tap linewidth, T (t,m)
6L (~m)
1.0 1.0
1.0 4.0
0.157 1.778
Results from the simulations of a 15-tzm-long, l-,am-wide, bridge with three 1-/~m wide, 3-#m-long, voltage taps (see Fig. 5). Since AI = B2 and A2 = B1, 6t^ = -¢$t n and Xmeasu~d = 6 t ^ - - f i t a = 2 6 t A Curvature parameters (/~m)
Xmeasur~ Calculated using
AI, B2
A2, BI
6L (urn)
eqn (3) (/tin)
0.0 0.2 0.4 0.6 0.6
0.0 0.0 0.2 0.2 0.4
0.157 0.194 0.291 0.361 0.425
0.000 0.084 0.121 0.262 0.140
the taps did not interfere with each other electrically and that the open ends of the voltage taps were equipotentials. Table 4 shows the results of the first two cases. The top section of Table 4 shows a very strong relationship between tap and 6L. Increasing the tap linewidth from 1 to 4 #m for a 1/~m bridge linewidth increased 6L by more than a factor of 10 to almost 2 #m. This result emphasizes that the classical voltage division formula eqn (1), without provisions for electrical length-shortening of the bridge, applied to extracted voltages would typically give an error of over 30% in the measurement of x even with perfect corners, whereas simply providing for a single value of 6L without side-to-side differentiation reduces this by an order of magnitude. The second part of Table 4 shows the effects of introducing asymmetric corner rounding on 6L and Xme..... d" The value of tSL is markedly increased by nominal amounts of corner rounding. This result supports the hypothesis offered in Ref.[1] that 6L measurements tend to be substantially elevated above those for clean corners by the presence of nominal inside corner rounding. It also suggests that the bulk of current-shunting occurs in the very small region of the taps adjoining the bridge. In addition, Table 4 shows that only small differences in the amount of inside corner rounding from one side on the tap to the other have a significant effect on x . . . . . . d" In particular, a difference of only 0.2 to 0.4/tm per tap (e.g. B 2 = B I + 0 . 2 / ~ m and A1 = A 2 + 0 . 2 t t m ) was enough to produce the offsets measured on Mask 16 reported here. Results frem the third case, that of the crossing voltage taps in Fig. 6, are shown in Table 5. Alongside these are comparable results from Table 4 for noncrossing taps. The first result from the data is the increase in 6L for a crossing tap over that for a noncrossing tap by slightly less than a factor of two, which is about what might be anticipated since the
441
Elimination of effects due to patterning imperfections Table 5. Comparison of simulation results for noncrossing (from Table 4) and crossing taps. "Opposite side" refers to voltages measured through a set of taps where the center tap is on the opposite side of the bridge from the end taps; "same side" refers to voltagesmeasured through a set of taps all extending from the same side of the bridge Xmcasutcd
Calculated using eqn (3) Voltage tap/measurement Configuration Curvature parameters A1, B2 0.0 0.2 0.4 0.6 0.6
A2, BI 0.0 0.0 0.2 0.2 0.4
~L (~m) Taps Nonerossing Crossing o. 157 0.287 0.194 0.350 0.291 0.511 0.361 0.626 0.425 0.718
bridge-current shunting effect is doubled at each tap-to-bridge intersection. The second and most important result is the effectiveness of crossing taps to eliminate the effects due to corner rounding. The results clearly show that, with crossing taps in conjunction with all voltages being measured from taps extending from that same side of the bridge, one can effectively eliminate the systematic error illustrated by the intercepts in Figs 3 and 4 and expressed in eqn (6). N o t e that eqn (3), for which the parametric inputs are straightforward to extract, gives exactly the target results for the offset when all voltages are extracted from the same side of the bridge, regardless of the extent of both the differential corner rounding and the asymmetry of corner rounding on individual taps. The simulation shows that, by constructing the test structure as shown in Fig. 6 and working with voltages extracted from one side at a time, a very robust method for extracting the separation for parallel features at 10 nm level is provided. This result assumes, of course, that the rounding symmetries shown in Fig. 6 are achieved in practice. Although visual inspection of these masks revealed the taps to be translationally similar, the effect of introducing small random perturbations to the curvature parameters in the future should be modeled. The results of this modeling will give a value to the limits of the precision of the improved test structure. While this result suggests that a structure with noncrossing taps that all extend from the same side of the bridge would be as effective, there are two additional, secondary benefits of using crossing taps. The first is that the increase in the magnitude of 6L allows reduction in the number of d u m m y taps, in turn allowing a reduction in L 1, minimizing potential random errors due to nonuniformity in the test structure over distance. The second advantage concerns the utilization of this test structure for multilevel registration applications, such as via to first-layer metal. These issues are the themes of future papers which will address such applications, as well as the presentation of measurements extracted from single-level structures with crossing voltage taps.
Crossing Noncrossing Opposite side 0.000 0.084 0.121 0.262 0.140
Opposite side 0.000 0.062 0.085 o. 174 0.090
Same side 0.000 0.001 0.001 0.000 0.000
CONCLUSIONS In earlier work, a modified sliding-wire potentiometer capable of providing the relative separations of features in a local region with errors less than 20 nm was described. In that prior work, a systematic error of unknown origin was encountered which had the same effect as a misalignment of taps extending from one side of the current-carrying bridge relative to taps extending from the opposite side of the bridge. The present work shows that the magnitude of the error for a particular set of test structure linewidths tends to be characteristic of the substrate on which the test structures are replicated. Specifically, these errors are attributed to imperfections at the inside corners of the intersection of the voltage taps with the bridge. This result is from SPICE modeling of the as-drawn test structure with small geometric modifications to simulate the effects of corner rounding as observed in a high-powered microscope. It is shown that two specific design changes to the original test structure will eliminate the subject systematic error. These changes are: (a) all voltage taps must extend from both sides of the bridge; and (b) all voltages must be measured through taps extending from the same side of the bridge. The result is a feature placement metrology tool that provides measurement of feature placement to within I0 nm yet requires nothing beyond conventional fabrication techniques and test equipment.
Acknowledgements--The authors wish to acknowledge the valued contributions of Colleen Ellenwood for digitization of the design of the test structure, of Larry Buck for his careful measurements of the test structures, of Dr Michael Gaitan, Loren Linholm, Dr Jeremiah Lowney and Dr Robert Larrabee for their technical discussions, and of Jane Waiters and Jo Gonzalez for their invaluable editorial support in preparing the manuscript. The staff of Photronix Corporation are acknowledged for their recommendations and technical inputs in the preparation of the patterned chrome plates. The assistance of Keithley Corporation, in particular Michael Peters and Bert Blaha, is acknowledged in providing corroborating measurements of the plates. This work was supported in part by the X-Ray Lithography Program of the Defense Advanced Research Projects Agency.
R. A. ALLEN and M. W. CRESSWELL
442 REFERENCES
1. M. W. Crcsswell, M. Gaitan, R. A. Allen and L. W. Linholm, Proc. 1991 ICMTS, p. 129 (1991). 2. B. Fay and T. Hasan, Solid-St. Technol. May, 239 (1986).
3. Y. Kuroki, S. Hasegawa, T. Honda and Y. Iida, Proc. 1991 ICMTS, p. 123 (1991). 4. K. H. Nicholas, I. J. Stemp and H. E. Brockman, J. Electrochem. Soc. 128, 609 (1981). 5. D. S. Perloff, Solid-St. Electron. 21, 1013 (1978). 6. T. J. Russell, T. F. I~cdy and R. L. Mattis, Technical Digest--1977 Int. Electron Devices Mtg (1977).