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Publications

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NBSIR 82-2548

Design Considerations for the

Cross-Bridge Sheet Resistor

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Washington, DC 20234

July 1982

QC

*

100

,lbb

62-2W6

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 82-2548

DESIGN CONSIDERATIONS FOR THE

CROSS-BRIDGE SHEET RESISTOR

3S> «;VAwxiAJtDo

JUL 2 9 1982

G. P. Carver, R. L. Mattis, and M. G. Buehler

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Washington, DC 20234

July 1982

U.S. DEPARTMENT OP COMMERCE, Malcolm Baldrlge, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director

Table of Contents

Page

1.. Introduction 1

2. Test Structure Design, Fabrication, and Measurement ........ 2

3. Symmetry Tabs .............. ...... 6

4. Shunting Effect Caused by the Voltage Taps 8

5. Tap-to -Corner Distance Study ........ , . 12

6. Summary and Design Considerations ................. 13

Acknowledgments .................. 16

References .................... ...... 18

List of Figures

1 . Line drawings of the cross-bridge sheet resistor without symmetry

tabs and the cross bridge with symmetry tabs on test pattern

NBS-12 ... ...... 3

2. Bridge sheet resistor test structures with multiple voltage taps of

different widths 3

3. The bridge tap-to-corner distance study sheet resistors . 4

4. Schematic diagram of the bridge ...... 9

5. Outline drawing of a cross-bridge sheet resistor test structure . . 17

List of Tables

1. Average Measured Values (and Standard Deviations) for Metal and

Base Layer Devices on Each Wafer for the Sheet Resistance, Asymmetry

Factor Fa

, Zero-Offset Factor FQ/ Linearity Factor F^, and Linewidth

for the Nominally 12-ym Linewidth Cross Bridge with Symmetry Tabs . 5

2. Comparison of Sheet Resistances (and Standard Deviations Expressed

as a Percent) Determined Measuring Cross -Bridge Sheet Resistors With

and Without Symmetry Tabs

3. Average Channel Widths Measured Using the Tap-to-Corner Distance Test

Structures . . 14

iii

Design Considerations for the Cross-Bridge Sheet Resistor

by

G. P. Carver, R. L. Mattis, and M. G. Buehler*

Center for Electronics and Electrical Engineering

National Bureau of Standards

Washington, DC 20234

The cross-bridge sheet resistor test structure is used to obtain

the sheet resistance and electrical linewidth of a conducting layer. It has been used to characterize various conducting layers

found in an integrated circuit fabrication process and to evaluate

lithographic equipment used for processing photomasks and wafers.

Three geometrical design factors for the cross bridge have been

investigated and are shown to cause systematic inaccuracies of less

than 1 percent in the sheet resistance and linewidth measurements.

Based upon experimental results from sequences of devices with incrementally different geometrical parameters, several design criteria for the cross-bridge sheet resistor have been established.

Key words: cross-bridge structure; linewidth; microelectronic test

structure; process control; sheet resistance; test structure.

1 . INTRODUCTION

The cross-bridge sheet resistor is a microelectronic test structure useful

for the automated electrical measurement of the sheet resistance and of the

linewidth of conducting layers [1]. Data obtained using this test structure

have been used to evaluate integrated circuit process-related sheet resistance spatial nonuniformities [2] and lithography-related linewidth variations [3]. Such specialized applications require a sensitive, precise measurement vehicle which is able to resolve reliably small differences in sheet

resistance and linewidth. The design of the cross-bridge sheet resistor and

the four-point Kelvin measurement technique associated with it provide a precise measurement tool which can be used, for example, to investigate optical systems using electrical test methods [3]. Automated electrical measurements are important in these types of measurements because statistically

significant results are obtained easily and inexpensively [4].

In a previous study, the effect of the geometrical design of a cross -shaped

van der Pauw sheet resistor on the accuracy of the measured sheet resistance

was determined analytically [5]. The theoretical results of that study were

verified experimentally in a succeeding study [6]

,

which also included an investigation of the effects of interferences, such as surface leakage current and joule heating, which affect the accuracy of the results. Several

design suggestions which can help minimize interfering effects were given

[6]

The advantages of the combined van der Pauw and bridge sheet resistor

test structure, called the cross-bridge sheet resistor, are described in a

* Present address: Jet Propulsion Laboratory, Pasadena, CA 91103

1
report [1] which also includes experimental results that illustrate the utility of electrical linewidth measurements for process control.

Additional design considerations for the cross-bridge sheet resistor are

addressed in the present work. The analysis is impeded by the difficulty of

separating random errors which result from process variations from the systematic errors being investigated. Nevertheless, it appears possible to

deduce certain information from the measurement results obtained in this

study. This information leads to design criteria for cross-bridge test

structures which have geometry-imposed systematic errors of 1 percent or less

and provides insight into factors which may limit the usable precision of the

measurements

The geometrical design factors discussed in this report are the "symmetry

tabs" [1], the voltage tap width, and the bridge voltage tap-to-corner distance.

2. TEST STRUCTURE DESIGN, FABRICATION, AND MEASUREMENT

The test structures used in this study were contained in the developmental

test pattern NBS-T2. This test pattern [7] was assembled to evaluate certain

geometrical aspects of the design of the cross-bridge sheet resistor. The

test structures primarily intended . for the cross-bridge sheet resistor study

include van der Pauw cross sheet resistors, cross-bridge sheet resistors with

and without symmetry tabs, bridge sheet resistors with different voltage tab

widths, and bridge sheet resistors with different tap positions relative to

the end of the conducting channel which forms the bridge. The cross bridge

sheet resistors in NBS-12 occur in a sequence of channel widths, 6, 12, 18,

and 24 ym. In each of four such sequences the conducting channel of the

structures is formed of either the metal, the base (source/drain), the emitter (channel stop) within a base region, or the base-under-emitter layers.

One entire series, the base layer, is shown in outline in figures 1 to 3. In

this paper, results are reported on the metal and base layers.

The test pattern was fabricated using a bipolar process [3] . The substrates

were 50-mm diameter <11 1> oriented silicon wafers. Both p- and n-type wafers

with room temperature resistivity of approximately 5 £2«cm were used. In both

cases, the junction depth for the base diffusions was approximately 1.7 ym.

From the cross bridge sheet resistor, values for the sheet resistance Rs and

its asymmetry factor FA

, offset factor FQ

, and linearity factor FL

, and the

effective linewidth W____ were determined using previously described procedures and expressions defined in reference 6. To illustrate the range of

values obtained for the above parameters, the results from the cross-bridge

structure with symmetry tabs and a nominally 12-ym wide channel are given in

table 1 for each of the metal and base layers on two wafers. The value of

the current used for each measurement was automatically adjusted to provide a measured voltage of approximately 10 mV. For the determination of the linearity factor Fl

, the current was increased to a value twice as large as was used initially for the base layer sheet resistors. (However, the current

was halved in the case of the metal layer sheet resistors to avoid attempting

to exceed the maximum current available from the constant current supply.

)

2
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Figure 1. Line drawings of the cross-bridge sheet resistor without symmetry

tabs and the cross bridge with symmetry tabs on test pattern NBS-12. These

__ * devices are repeated for the other conducting layers in the process. From

left to right, the conducting channel linewidths were designed to be 5, 12,

18, and 24 ym.

Figure 2. Bridge sheet resistor test structures with multiple voltage taps

of different widths. There are four pairs of voltage taps with widths of 6,

12, 18, and 24 ym and centerline-to-center line spacing of 80 ym. The bridge

channel is nominally 24 ym wide in one structure and 36 ym wide in the other.

These structures were fabricated in the metal and base diffusion layers.

3
Figure 3. The bridge tap-to-corner distance study sheet resistors. Each

structure is a bridge sheet resistor 20 urn wide with 6- pm wide voltage taps

The currant and upper voltage taps are fixed, but the lower voltage tap

varies from 80 to 0 pm, in 20- pm increments, from structure to structure.

These structures were fabricated in the metal and base diffusion layers.

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The sheet resistance asymmetry, offset, and linearity factors were used as screening parameters to eliminate outliers. In this study, data outside

three sample standard deviations from the mean value of the sample population

were eliminated from the data set which included all the cross bridges of a single geometry.

All measurements were made at room temperature. Temperature variations during collection of a set of data were controlled to within about 1°C. The

data were obtained using a computer-controlled data acquisition system composed of an automated wafer prober and programmable scanners, constant current supply, and digital voltmeter. On their most sensitive scales, the

current source and the five-digit voltmeter have microampere and microvolt

resolution, respectively. Based on the manufacturer's published specified

maximum inaccuracy of the instruments, including the basic instrument uncertainty, the inaccuracy caused by temperature and line voltage variations, and

the inaccuracy caused by ''drift," the expected uncertainties were ±6 yA +

0.01 percent of the programmed value for the constant current source and ±5

yV + 0.005 percent of the reading for the voltmeter. (These values are estimated for the operating conditions of the instruments during the measurements. ) As listed in table 1 , the maximum instrument errors in measuring the

sheet resistance derived from these considerations are much smaller than the

sample standard deviations observed for the measured average sheet resistance

values.

3. SYMMETRY TABS

Symmetry tabs on the cross-bridge sheet resistor are extensions past the taps

of three arms of the cross to compensate for any effect the bridge, which is an extension to the fourth arm, may have on the measurement of the sheet resistance R

s

[ 1 ]

The symmetry tabs are included on the structures shown in

the bottom row of figure 1. The cross-bridge dimensions are: bridge length

L, 180 urn; conducting channel width W, 6 to 24 ym in 6-ym increments; voltage

tap width M, 6 ym; minimum " tap-to-corner" distance, 39 ym; and tap length N,

18 to 24 ym (see fig. 4). The length of the symmetry tabs is 34 ym.

Within the uncertainties of this experiment, no significant difference was observed between measurements on the structures 'without symmetry tabs and the

structures with the extensions. This conclusion is based upon data summarized in table 2. The column at the far right shows the mean values of the

relative difference between the sheet resistance measured, first using the

cross-bridge resistor with tabs and the sheet resistance measured, then using

the structure without symmetry tabs in each chip for each linewidth. The

differences appeared to be randomly distributed in amplitude and in spatial

position on the wafer.

As seen in the right-hand column, the relative differences are smaller than

1 percent, except in one case. In every case, however, these differences are smaller than the uncertainties (standard deviations) in the mean values of

the measured resistivities. This latter relationship is not sufficient to

guarantee that the differences are statistically insignificant because there

are systematic variations in sheet resistance across the wafers. Systematic

variations in R

s cause the standard deviation of the mean sheet resistance

values to be larger than they would be solely in the presence of randomly

6
Table

2.

Comparison

of

Sheet

Resistances

(and

Standard

Deviations

Expressed

asa

Percent)

Determined

Measuring

Cross-bridge

Sheet

Resistors

With

and

Without

Symmetry

Tabs.

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occurring^ variations. Furthermore, systematic variations in R

s could also

cause an average difference in R

s between the cross bridges with and without tabs to be measured because the devices are spatially separated. The

values of the expected systematic differences in R

s

, obtained by estimating

the average incremental systematic resistivity between structures with and

without symmetry tabs from inspection of wafer maps of the sheet resistance,

are much less than the measured difference values. Based on these considerations and the relative magnitudes of the uncertainties, it can be concluded

that within the measurement accuracy of the present data, the differences

between cross bridges with and without symmetry tabs are found to be statistically insignificant.

The data in table 2 show that the measured sheet resistance is found to increase with decreasing linewidth. This behavior may be due to nonuniform

resistivity profiles and to cross-sectional effects in layers of finite

thickness. Edge effects (edge slope in metal, corner rounding in doped layers) become a larger fraction of the nominal width of the structure in narrower structures.

4. SHUNTING EFFECT CAUSED BY THE VOLTAGE TAPS

The voltage taps on the conducting channel that forms the bridge partially - shunt the current; the channel current penetrates into the taps. At the

voltage taps, the width of the conducting channel increases and the resistance per unit length of channel decreases [9]. Therefore, the finite width

of the taps reduces the measured voltage and the computed value of the resistance between the taps compared to the voltage and resistance which would be

measured if the taps were infinitesimally narrow.

The voltage difference AV measured between the bridge taps is given by

AV = I(R

1 + R ) ,

( 1

)

where I is the current in the conducting channel and the sum (R^ + R

2

) is

the total resistance between the midlines of the two voltage taps, as shown

in figure 4. In terms of the sheet resistance R , the resistance R-j is

gi ven by

( 2 )

where L is the distance between the midlines of the two voltage taps, M is

the width of the taps, and W is the width of the conducting channel of the

bridge. By assuming that the taps are composed of material with the same sheet resistance as the conducting channel, the resistance R

2 may be written

R

2

R M_

s W + N

/ eff

(3)

where N

0 £^ is an effective tap length which corresponds to the additional

width that the conducting channel would have if the current were uniform in

8
*T 1 1 R2/2 Ri R2/2

Figure 4- Schematic diagram of the bridge. The resistance of the conducting

channel between the voltage taps is R^ . The resistance of each of the . shaded portions of the structure is R

2

« The midlines of the voltage taps are the dash and dotted lines. The geometrical bridge length L, tap width M,

and channel width W- are shown* The effective length of the taps is the

distance The voltage difference between the taps is considered to be

the potential difference between the midlines of the taps.

9
the region between the edges of each of the voltage taps, the region between

c'c and d'd in figure 4.

The actual current density in this region is not uniform. Referring to the

figure, progressing upward from point e along the midline of the tap, the

current density decreases, starting from the value it has in the conducting

channel far away from the taps. The distance the current actually penetrates

into each tap is limited only by the end of the tap, although it is affected

by the details of the contact window. Nevertheless, the distance (W + N

e ^^) can be thought of as the electrically equivalent width of the conducting

channel caused by the shunting effect of the voltage taps.

In terms of the geometrical dimensions of the bridge, the measured voltage

difference between the taps, given in eq (1), can be written

AV = IR

L - M

W

M

N -- + W

ef f

(4)

or

AV IR

s M / ^eff \

t V

,.ff+ V

‘ (5)

From eq (5), the shunting caused by the taps can be considered to be a decrease in the electrical length of the bridge. The effective electrical

length of the bridge is then given by

L

eff

L

Defining the quantity e by:

M_ /

N

ef f

L

\ eff

+ W

( 6 )

£

eff

N

eff

+ W ' (7)

the effective bridge length is

L = L - Me . eff

( 8 )

The effective bridge length is reduced by the amount Me.

If Neff is zero, z is zero and L

e ff equals L; there are no shunting effects

and there is no difference between the electrical and geometrical lengths of

the bridge. If is large compared to W, e is greater than zero but always

less than unity. This situation corresponds to each tap acting as a short

along one side of the conducting channel. The electrical length of the bridge

L

e ££ is smaller than the geometrical length L by some fraction z of the tap

width M.

10
The shunting effect of the voltage taps introduces an error into the width

measurement by causing the electrical length of the bridge to be shorter than

the physical length. The equation for the measured channel width w

meas

is

W = R L ~ meas s A

(9)

Substituting for AV from eq (5) and inserting the parameter e, w

meas is

given by

w = w

meas

Using the relation between L and Leff / eq (7), this may be written

1 - Me ( 10 )

W

meas

W

(11 )

The shunting effect of the voltage taps acts to increase the measured width

compared to the actual electrical channel width. [The inverse relationship

in eq (10) occurs because of the inverse relationship between W and L in eq

( 2 ). )

An actual calculation of Ne££ would provide a value for Mg which could be

used as a correction factor for L, according to eq (8). The maximum allowable physical value for z occurs when the voltage taps produce the largest

possible shunting effect which is a short circuit along one edge of the conducting channel, between points a and b. The average electrical decrease in

the conducting channel length would be M/2 in this situation. That is,

L > L __ > L eff

_M2

’

It is believed that this simple model substantially overestimates the maximum

possible systematic inaccuracy in the measured linewidth. It also ignores

the expected dependence of e on W, which is suggested by the definition of z.

Using methods similar to those used in the analysis of the cross sheet resistor [5], the ratio M/N

e££ was estimated. The technique, which is a numerical

iterative approach to the chain rule, involves calculating values for M/N

e ££

as a function of the ratios N/M, L/M, and W/M. Considering M/Ne ££ to be a function of only one of the ratios while the other two are held constant, it

can be established through the iterative process that M/N

e ££ asymptotically

approaches a maximum for small values of M compared with L. Specifically,

for M << L and M < 2 W, it was found that M/N^^ approached a value of approximately 6.

Since from eq (7)

11
the value of e can be estimated to be always less than approximately 0.15 for

all cross bridges used in this study.* This estimate agrees with a previous

analysis based on conformal transformations [10]. It implies that (L - L

e ff)

is less than 0.9 ym and the ratio wmeas /w is no greater than 1.005. Experimental confirmation of this result is unavailable because the linewidth calculated from the structures presented in figure 2 showed no statistically

significant variation. The uncertainties and scatter in the data were larger

than the expected differences caused by tap shunting. The primary reason for

this was filleting at the corners where the taps meet the conducting channels. This commonly occurs with wet chemistry etching and thermal diffusions. Visual observation indicates that some of the narrower taps are more

than twice their design width at the point where they meet the conducting

channel of the bridge. The filleting is not uniform and some of the taps are not symmetrical. The result is that the parameter M is not well defined and

the variability contributes to the uncertainty in w

meas

*

It is important that the tap shunting effect causes a systematic overmeasurement of the linewidth. The shunting does not affect the resolution of

the measurement or the utility of cross bridges provided that process-induced

variations in structure geometry or sheet resistance do not cause large measurement variations. Such effects do not appear to influence cross bridges

with the dimensions used in this study for lineVidth uniformity measurements,

but may become important when the linewidth of the structures is in the range

of a micrometer or less.

5. TAP-TO-CORNER DISTANCE STUDY

The tap-to-corner distance study test structures are a series of bridge sheet

resistors that have one of the two voltage taps placed at different distances

from one end of the conducting channel which forms the bridge, as shown in

figure 3. Each structure is a bridge sheet resistor, formed in the metal or base layers, with a 20-ym wide conducting channel and 6-ym wide voltage taps.

The tap-to-corner distance structures were intended to study the effect of

the proximity of a bridge tap to the current contact corner. The corner

represents the end of the linear portion of the bridge. It is expected that

the current density is nonuniform in the region of the current contacts and

that this nonuniformity affects the measured value of the potential between

the voltage taps. In all po tentiome trie measurements of this type, uniform

current density in the vicinity of the taps is a necessity.

The voltage tap-to-corner distance between the bottom of the bridge and the

lower voltage tap varies from structure to structure in the sequence 0, 20,

40, 60, and 80 ym. As can be seen in the diagrams, the distance is measured

* For the cross bridges used in this study, M was always less than or equal

to W. For the case M equals W, M/Ne ff was estimated to be 5.6.

12
from the midline of the tap to the upper edge of the conducting path connecting the bridge to the probe pad at the lower left.

Because the structures were designed with constant length of the linear portion and fixed upper tap position, the distance between the two voltage taps

also changes as the lower tap-to-corner distance changes. The length of the

bridge changes in the sequence 160, 140, 120, 100, and 80 ym. The shunting

effect caused by the width of the voltage taps is an interference to the

measurement, and compensation must be made for this effect.

The data obtained using the tap-to-corner distance test structures are presented in table 3. The calculated channel widths, averaged over about 60

devices of each type on each wafer, are approximately 23 ym for the base

structures and 17 ym for the metal structures. The difference between these

values and the design value of 20 ym is due to lateral diffusion of the base

layer, overetching of the oxide cut for the base layer diffusion, and overetching of the metal layer.

To evaluate these linewidth results, account has to be taken of the shunting

effect due to the voltage taps; a value for e must be assumed. The best

value for z is taken as 0.15, as described in the previous section. Using

this value, Le ff is calculated from eq (8). Then, in the rightmost column,

values for W were determined using eq (10). The measurements on devices with

the tap-to-corner distances equal to zero yield a significantly larger value

of linewidth than the other devices in each case. Typically, the bridges

with the tap-to-corner distance greater than zero agree to within a few

tenths of a percent, whereas the bridge with zero tap-to-corner distance

yields a corrected linewidth which is about 1 percent higher than the mean of

the other values

Generally, the results suggest that when the tapwidth is much smaller than

the channel width, the voltage tap near the end of the conducting channel

should be placed at least one channel width (nominally 20 yn in this case)

away from the end of the straight portion of the conducting channel which

forms the bridge. Because the cross bridge can easily be designed so that

the tap-to-corner distance is at least as large as the channel width, a detailed statistical analysis in support of this empirical study is not felt to

be necessary.

6. SUMMARY AND DESIGN CONSIDERATIONS

For cross-bridge sheet resistor test structures with nominally 6-, 12-, 18-,

and 24- ym wide conducting channels, three geometrical factors affecting the

accuracy of the measurement of linewidth have been addressed. The three

factors are the presence or absence of symmetry tabs on three arms of the cross portion of the structure, the finite width of the bridge voltage taps,

and the distance between a voltage tap and the end of the linear portion of

the bridge conducting channel ( " tap-to-corner” distance). In each case the

effects were found to be less than about 1 percent on the measurement of

linewidth for cross-bridge structures with the dimensions used in this study.

A characteristic of these results was that in every case the standard deviation of the mean of the measurements was always larger than the expected

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16.43
uncertainty due to the instruments. This outcome is not surprising because

the results were averaged across the wafers and therefore include the systematic process -induced intrawafer variations in sheet resistance and linewidth.

(This situation was discussed in sec. 3.) Furthermore, there are random

variations caused by the fabrication process which contribute to the measurement variations. Random variations occurring on the scale of the dimensions

of the structures include edge roughness, corner rounding, pinholes, and

other imperfections, including those present on the mask set. Averaging over

a wafer reduces the random variations (if they are distributed in a truly

random fashion), but usually increases the statistical uncertainty due to

process variations which vary slowly across a wafer, the systematic variations.

With the process-related systematic variations of the wafers used in this

study, it was not possible to measure reliably differences due to the geometrical factors addressed here of less than 1 percent. Each of the geometrical

factors included in this study was found to have an effect of less than 1 percent on the measurement of sheet resistance and linewidth, with the exception of the case where the tap-to-corner distance was 0.

It is important to differentiate between factors which affect the accuracy of

a measurement and those which affect the resolution of the measurement. The

absolute accuracy of the results is governed by the experimental apparatus,

the geometrical design of the cross bridge, process uniformity, and the measurement strategy. The geometrical factors addressed in this study introduce

systematic errors in the sheet resistance and linewidth measurements.

Process -induced random variations and systematic process-related variations

contribute to the imprecision of the measurement. If the fabrication process

is under control and if the random variations are small (or if enough measured values are averaged), the cross-bridge sheet resistor can be used to

obtain extremely precise results.

Based upon the results reported in this paper, geometrical factors which lead

to inaccuracy in the measurements on cross-bridge sheet resistors are: (1)

systematic in that they affect all structures equally; (2) quantifiable,

because the magnitude of the effect, or at least the maximum effect, on the

measurement can be determined; and (3) minimizable, through proper design and

use of the test structure.

A test structure that is well designed and well characterized is one that can

be used to obtain unambiguous results that are not affected by other materials or process characteristics. The information needed to develop a welldesigned test structure is obtained by careful modeling of the structure and

through comparison with measurements on actual structures. This study is

part of the process toward completing the development of the cross-bridge

sheet resistor test structure. With the information obtained from these

results, details of the suggested design for the cross-bridge sheet resistor

are further resolved. The suggested design conforms with the objectives of

the modular probe-pad array [4,11]. An outline drawing of the structure is

shown in figure 5, which also identifies the various geometrical parameters.

15
If the intent is to avoid having to make corrections to the data and if systematic inaccuracy caused by geometry is acceptable providing it is less than

about 1 percent, then the following inequalities should be met:

N > M

L > 15 M

w 2. M

A1 > W

A

q

> W

Based on the present data, the proposed design results in geometry-related

inaccuracies significantly below the 1 -percent level. Nevertheless, it is

possible that, in some processes, variations in edge and sidewall quality,

materials irregularities, variations in etching, and other process-related,

randomly occurring imperfections will contribute to inaccuracy levels greater

than 1 percent. Even in that case, however, experimental data from the cross bridge and from other test structures, along with appropriate models, can be

used to evaluate and possibly compensate for effects of nonideal processing.

Acknowledgments

The authors are indebted to Schuyler D. Grant for the calculations of the

ratio M/Neff , to W. Murray Bullis for a thorough review of the manuscript,

and to E. Jane Walters for editorial preparation of the manuscript.

16
Figure 5. Outline drawing of a cross-bridge sheet resistor test structure.

The sheet resistance R

s and the effective linewidth W are determined by a van der Pauw and a bridge measurement. Reference [1] describes the

measurement technique. The geometrical parameters identified in the figure

are described in the text.

17
REFERENCES

1. Buehler, M. G. , Grant, S.- D. , and Thurber, W. R. , Bridge and van der

Pauw Sheet Resistors for Characterizing the Linewidth of Conducting

Layers, J. Electrochem . Soc . 1 25 , 650-654 (1978).

2. Russell, T. J. , Maxwell, D. B. , Reimann, C. T. , and Buehler, M. G. , A

Microelectronic Test Pattern for Measuring Uniformity of an Integrated

Circuit Fabrication Technology, Solid State Technology 22 (2), 71-74

(February 1979).

3. Linholm, L. W. , and Buehler, M. G. , A Cross-Bridge Structure Array for

Characterizing Intrachip Linewidth Variations, Electrochemical Society

Extended Abstracts3 Abstract No. 191, May 1979.

4. Carver, G. P. , Linholm, L. W. , and Russell, T. J. , The Use of Microelectronic Test Structures to Characterize IC Materials, Processes, and Processing Equipment, Solid State Technology _23_ (9 ), 85-92 (September

1980).

5. David, J. M. , and Buehler, M. G. , A Numerical Analysis of Various Cross

Sheet Resistor Test Structures, Solid-State Electron . _2£, 539-543 (1977).

6. Buehler, M. G. , and Thurber, W. R. , An Experimental Study of Various

Cross Sheet Resistor Test Structures, J, Electrochem. Soc . 1 25 , 645-650

(1978).

7. Carver, G. ?. , Mattis, R. L. , and Buehler, M. G. , Microelectronic Test

Patterns NBS-12 and NBS-24, NBSIR 81-2234 (May 1981).

8. Leedy, T. F. , and Liu, Y. M. , Semiconductor Measurement Technology:

Microelectronic Processing Laboratory at NBS , NBS Special Publication

400-53 (December 1978).

9. Buehler, M. G. , Cross-Bridge Sheet Resistor, in Semiconductor Measurement Technology Progress Report, July 1 to September 30, 1976, W. M.

Bullis and J. F. Mayo-Wells, eds., NBS Special Publication 400-36, pp.

45-46 (July 1978).

10. Hall, P. M. , Resistance Calculations for Thin Film Patterns, Thin Solid

Films _1_, 277-295 ( 1968).

11. Buehler, M. G. , Comprehensive Test Patterns with Modular Test Structures: The 2 by N Probe-Pad Array Approach, Solid State Technology

22 (10), 89-94 (October 1979).

18
NBS-1I4A (REV. »-78i

U.S. OEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 82-2548

Z.Gev't. Accession No. 3. Recipient* i Accession No.

fjjjl July 1932

4. TITLE AND SUBTITLE

Design Considerations for the Cross-Bridge Sheet Resistor

5. Publication Date July 1982

Performing Organization Code

::|J|v " ... .

7. AUTHOR( S) G. P. Carver, R. L. Mattis, and M. G. Buehler3. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADORESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

Pfoject/Tasfc/Worfc Unit No.

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12. SPONSORING ORGANIZATION NAME AND COMPLETE ADORESS (Street, city, state, ZIP) 13. Type of Report & Period Covered

15. SUPPLEMENTARY NOTES

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I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 2 OO^word or teas (actual summary of most significant information. If document includes a significant bibliography or

literature survey, mention it here.)' The cross-bridge sheet resistor test structure is used to obtain the sheet resistance and electrical linewidth of a conducting layer. It has been used to characterize various conducting layers found in an integrated circuit fabrication process

and to evaluate lithographic equipment used for processing photomasks and wafers.

Three geometrical design factors for the cross bridge have been investigated and are shown to cause systematic inaccuracies of less than one percent in the sheet resistance and linewidth measurements. Based upon experimental results from sequences of

devices with incrementally different geometrical parameters, several design criteria

for the cross-bridge sheet resistor have been established.

17. KEY WORDS ( six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Cross-bridge structure; linewidth; microelectronic test structure; process control;

sheet resistance; test structure.

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