Optimized Overlay Metrology Marks Theory and Experiment

166IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING,VOL.17,NO.2,MAY2004 Optimized Overlay Metrology Marks:

Theory and Experiment

Mike Adel,Mark Ghinovker,Boris Golovanevsky,Pavel Izikson,Elyakim Kassel,Dan Yaffe,Alfred M.Bruckstein,

Roman Goldenberg,Yossi Rubner,and Michael Rudzsky

Abstract—In this paper,we provide a detailed analysis of overlay metrology mark and find the mapping between various properties of mark patterns and the expected dynamic precision and fidelity of measurements.We formulate the optimality criteria and sug-gest an optimal overlay mark design in the sense of minimizing the Cramer–Rao lower bound on the estimation error.Based on the developed theoretical results,a new overlay mark family is pro-posed—the grating marks.A thorough testing performed on the new grating marks shows a strong correlation with the underlying theory and demonstrate the superior quality of the new design over the overlay patterns used today.

Index Terms—Box-in-box marks,Cramer–Rao lower bound, dynamic precision,Fisher information matrix,grating marks, overlay mark,overlay mark fidelity,overlay metrology.

I.I NTRODUCTION

A CCURATE and precise overlay metrology is a critical re-

quirement in order to achieve high product yield in micro-electronic manufacturing.New challenges become evident as microlithography processes are developed for each new design rule node.A critical link in the overlay metrology chain is the metrology mark which is chosen to be included on the reticle, printed on the wafer,subsequently processed and which is ulti-mately imaged in the metrology tool in the metrology process. In this publication a theoretical and experimental study is de-scribed that shines new light on the limitations of existing mark designs while proposing and validating new designs of superior performance.

In Fig.1a standard overlay(BiB)1mark is shown schemat-ically.It consists of two“boxes”printed on two subsequent layers—top(grey)and bottom(black)—between which the overlay is measured.By design the centers of symmetry of the inner(grey)and outer(black)boxes coincide.The actual

Manuscript received December22,2003;revised January20,2004.This work was supported by the Israel Ministry of Industry and Trade in the framework of the“Magneton”program.

M.Adel,M.Ghinovker,B.Golovanevsky,P.Izikson,E.Kassel,and D.Yaffe are with KLA-Tencor,Optical Metrology Division,Migdal HaEmek23100, Israel(e-mail:mike.adel@https://www.wendangku.net/doc/ea7529873.html,;mark.ghinovker@https://www.wendangku.net/doc/ea7529873.html,; boris.golovanevsky@https://www.wendangku.net/doc/ea7529873.html,;pavel.izikson@https://www.wendangku.net/doc/ea7529873.html,; Elyakim.Kassel@https://www.wendangku.net/doc/ea7529873.html,;Dan.Yaffe@https://www.wendangku.net/doc/ea7529873.html,).

A.M.Bruckstein,R.Goldenberg,Y.Rubner,and M.Rudzsky are with the Computer Science Department,Technion,Haifa32000,Israel(e-mail: freddy@cs.technion.ac.il;romang@cs.technion.ac.il;yossi@rubner.co.il; rudzsky@cs.technion.ac.il).

Digital Object Identifier10.1109/TSM.2004.826955

1In the present paper we unify all conventional overlay mark types—box-in-box,bar-in-bar,frame-in-frame,etc.—under the generic abbreviation

“BiB.”

Fig.1.Standard BiB mark(schematically).

overlay appears as misregistration between the centers of

symmetry of the“black”and“grey”layers.

There are two major use cases in overlay metrology for

microlithography.The first and the most obvious is termed lot

dispositioning.If measured overlay exceeds some allowable

threshold,the lot cannot proceed to the next process step.This

generally results in rework,that is the lot is returned to the

previous lithography step after the resist is stripped.This is

provided the overlay measurements were done immediately

after development.Under some circumstances the overlay

measurements after development are not viable,and are done

after etch.In this case,there is no option for rework,and lots

outside of allowable thresholds are scrapped.

The second use case of overlay metrology is for correction of

the exposure https://www.wendangku.net/doc/ea7529873.html,ually,the overlay is measured at four cor-

ners of the field and over several fields on the wafer,which pro-

vides the necessary statistical sampling to enable stepper cor-

rections model to be calculated.This model includes intra-field

and inter-field correctibles,such as offset,rotation and scale.

These correctibles are fed back to the exposure tool to improve

performance on subsequent lots.

Conventional BiB based metrology has been the standard

overlay metrology for almost two decades.However,as the

overlay budget shrinks together with the lithographic design

rules,a number of performance limitations are becoming evi-

dent.These shortcomings are addressed in the section below.

Application of grating structures to lithography and metrology

fields is being extensively studied.One of such applications 0894-6507/04$20.00?2004IEEE

ADEL et al.:OPTIMIZED OVERLAY METROLOGY MARKS:THEORY AND EXPERIMENT167 is for scatterometry based critical dimension(CD)metrology

([9],[16],[15],[11]).Gratings are also used for phase shift

monitoring([7]).ASML is using grating patterns as alignment

marks([14]).In the current paper,we introduce grating marks

for overlay metrology.

A.Device Correlation

As design rules shrink to100nm and below,difference in BiB

feature size and device feature size have become significant.

Both lithographic pattern placement errors(PPE)[4],[10]and

influences of other processes(like chemical-mechanical pla-

narization—CMP)are known to be feature size and density de-

pendent[12].Therefore,overlay metrology results based on BiB

marks may suffer from discrepancies compared with device fea-

ture overlay.

B.In-Chip to Scribe-Line Discrepancy

Another source of BiB-to-device overlay discrepancy orig-

inates from their different spatial location in the exposure tool

field.Typically,BiB marks are printed in the scribe lines near the

field corners.Optical conditions(aberrations,focus deviations,

etc.)near the field edges may differ from those in the field in-

terior,where the device features are printed.Since both overlay

budget and process window(as defined by allowed exposure

tool focus and exposure)shrink together with the design rules,

in-chip to scribe-line discrepancies are becoming critical.

C.Process Robust Marks

Conventional BiB marks are frequently considered design

rule violations in modern IC manufacturing processes.BiB

marks are generically built of wide lines and require empty

surrounding spaces(exclusion zones;see Fig.1)for successful

measurement.Both these facts usually contradict pattern

density and feature size design rule requirements commonly in

practice today.Such violations make handling of BiB marks by

the layout engineer problematic and more importantly have a

negative impact on process robustness of the metrology mark

since the process is optimized for features and patterns of

significantly different dimensions[6].

D.Tool Induced Shifts

Currently overlay measurements are performed on optical

imaging based tools.Optical aberrations and illumination

imperfections are an unavoidable reality of optical metrology

system design and manufacture.A simple and quantitative

metric of the quality of the optical metrology tool is Tool

Induced Shift(TIS).TIS is defined as the average of the overlay

measurements performed on a given overlay mark before and

after rotation by180

:

(1)

Nonzero TIS is an indication that the metrology tool has in-

duced a systematic discrepancy in the overlay result due to the

above system imperfections.TIS is however,by definition,a

calibratable error,if measurements are performed at both orien-

tations on a subset of representative marks.A more

important

Fig.2.Schematic arrays of densely printed overlay marks used for OMF

calculation.

metrology uncertainty contributor is TIS variability,defined as

three times the standard deviation of the TIS measured

over

sites across the wafer.

https://www.wendangku.net/doc/ea7529873.html,rmation Content

In spite of the large space occupied by the conventional BiB

mark,it contains a relatively sparse amount of information for

overlay measurement.Generically,each BiB mark consists of

four inner and four outer bars only,usually utilizing less than

20%of the occupied real estate.By increasing the informa-

tional content of the overlay mark one can minimize the effect

of random(both spatial and temporal)noise on overlay mea-

surement.There are two measurable parameters representing

overlay measurement uncertainty due to temporal and spatial

noise:dynamic precision and overlay mark fidelity(OMF)re-

spectively.

F.Dynamic Precision

Dynamic Precision is defined as three times the standard de-

viation of the results of a series of measurements of the same

overlay mark,when these measurements are done in a dynamic

loop(including wafer alignment,mark acquisition and measure-

ment itself).This parameter quantifies temporal noise in the

measurement of a given overlay mark.

G.Overlay Mark Fidelity(OMF)

Suppose,one can eliminate the temporal noise in the overlay

measurement(by means of averaging over many dynamic loops

of measurements on the same mark).This still does not ensure

that by measuring two nominally identical marks one will ob-

tain identical results.OMF is defined as three times the standard

deviation of the measurement results of

the densely printed

identical overlay marks after compensating for dynamic preci-

sion[1](see Fig.2).

In the present paper,we dwell on the last three shortcomings,

that is information content,precision and mark fidelity.We first

compare different mark design options from a theoretical per-

spective,focusing on the sampling,temporal noise,and spatial

noise aspects.We then introduce an optimized grating overlay

168IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING,VOL.17,NO.2,MAY

2004

Fig.3.BiB overlay mark with right-outer and top-inner regions of interest.

mark,which demonstrates superior performance over the con-ventional BiB marks.We present experimental data on dynamic precision(as a measure of temporal noise)and OMF(as a mea-sure of spatial noise)for the new grating overlay marks as com-pared with conventional BiB marks.

II.T HEORY:D ESIGNING P ATTERNS FOR O PTIMAL O VERLAY R EGISTRATION AND P OSITION E STIMATION

In this section,we analyze the dependence of the dynamic precision and fidelity of the overlay measurement on various pattern parameters.The overlay measurement is based on mea-surements of horizontal and vertical positions of known pat-terns.

Fig.3shows an example of the BiB overlay mark with right-outer and top-inner regions of interest.

The frame’s edges are corrupted by noise whose character de-pends on various factors.We shall deal with two types of noise: additive Gaussian noise at the wafer level and additive Gaussian noise at the camera level.The first type of noise is spatial noise whose source is the manufacturing process,and the second type is a dominant source of the temporal noise in the measurement process.

In this paper,we explore how the position estimation error is affected by various pattern characteristics and by the parameters of the measurement process,by deriving the Cramer–Rao lower bound on the estimation error for arbitrary patterns and,then address the question of designing patterns that are optimal in the sense of minimizing the location error.

A.Problem Definition

We shall first deal with the measurement of horizontal po-

sition of a known one-dimensional(1-D)

pattern in a

two-dimensional(1-D)image.Vertical position estimation can be done in a similar way.We assume in this case that the mea-surement is performed for every image row independently,and then an average pattern location estimate is returned as a result.

A periodic pattern of lines may be represented

by

(2)

where is a1-D pattern repeated on every line

and

is the“spatial noise”on the wafer.

Then the pattern at each row of the image acquired by the

camera can be described

by

(3)

where is an overall point spread function,composed of the op-

tical and camera point spread

functions,is the convolution op-

erator,

and is the temporal noise at the camera output.All sig-

nals are assumed band limited and the noise terms are assumed

to be filtered and hence,band-limited,white,and Gaussian.

The task is to find best match locations of the designed

pattern

given the

signals measured over all image rows.In

the analysis below,we derive the distribution of the pattern loca-

tion estimates over all measurements.The statistical analysis is

based on the Cramer–Rao bound,a well-known statistical tool

[8],[5].

We can now define the following three problems

1)Find the dependence of the dynamic precision and overlay

mark fidelity(OMF)metrics on the general parameters

characterizing an one dimensional pattern and the mea-

surement method without going into the detailed structure

of the

pattern.

2)Given the

pattern,what is a lower bound on the

unbiased estimation of the pattern location?

3)What is the optimal

pattern in the sense of mini-

mizing the Cramer–Rao lower bound on the estimation

error?

B.Dynamic Precision and Fidelity Estimations

In this section,we evaluate the precision and fidelity of the

measurement process based on some general physical parame-

ters of the measured signal and the measurement process,such

as optical system aperture,wave length,pattern size,signal-to-

noise ratio(SNR),and others,without considering the detailed

structure of the

pattern.

1)Single Line Measurement:On every image row we esti-

mate the pattern location by using the optimal Matched Filter or

correlation method.

Let be the estimator of the pattern loca-

tion of1–D

signal immersed in white Gaussian noise.It

is known on the basis of very general statistical principles that

the variance

of is bounded below by the Cramer–Rao bound,

which is given by(see,e.g.,[8],

[5]).

(4)

where is the signal’s

energy,is the unilateral

spectral density of the noise,

and

is the square of the effective bandwidth of the signal,

where

is a Fourier transform

https://www.wendangku.net/doc/ea7529873.html,ing the

definitions

and

where is the average

signal

power,is the signal

length,is the noise power

and

is the noise bandwidth,we

get

This formula shows that the precision is a function of the signal

and noise bandwidths,signal to noise ratio,and the overall

length of the signal.

研究生《高等半导体器件物理》试题

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参考文献： 1.沃纳，半导体器件电子学，电子工业出版社，2005 2.施敏，现代半导体器件物理，科学出版社，2002 3.王良臣等，半导体量子器件物理讲座（第一讲~第七讲），物理（期刊），2001~2002

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