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Optical Design for Nano

Lithography

Ehud Ben-Ari

Supervised By: Professor Shlomo Hava

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Table of Contents

Abstract ........................................................................................................................... 4

Optical Design for -Nano Lithography............................................................................ 4

1 .Theoretical Background Lithography and its challenges in IC process ............................. 5

1.1 The lithography process: ......................................................................................... 6

1.2 Lithography role in the IC (Integrated Circuit) fabrication......................................... 8

1.3 Optical lithography challenges ................................................................................ 9

1.3.1- Resolution....................................................................................................... 9

1.3.2 Diffraction:..................................................................................................... 12

1.4 Lithography methods to achieve high resolution ................................................... 14

1.4.1 Proximity Optical Lithography......................................................................... 15

1.4.2 Contact Optical Lithography............................................................................ 16

1.4.3 Projection Optical Lithography........................................................................ 16

1.4.4 Phase-Shifting Masks...................................................................................... 17

1.4.5 Increasing the NA (numerical aperture)- Immersion lithography ...................... 19

1.4.6 Lowering the wave length λ- Ultra-Violet Lithography ..................................... 20

2. EUVL- Extreme Ultra Violate Lithography .................................................................... 23

2.2 Multi Layers Optics: .............................................................................................. 27

2.2.1 Mo/Si ML Requirements: ................................................................................ 29

2.3 - ML Design for EUV systems ................................................................................. 30

2.3.1 Refractive index in the EUV spectral region: .................................................... 30

2.3.2 Reflectivity in EUV spectral region: ................................................................. 31

3. Lithography Photo masking ........................................................................................ 33

3.1 DUV Light Photo Masks and masking concept........................................................ 33

3.1.2 Mask substrate and absorber:......................................................................... 34

3.1.3 Pellicles .......................................................................................................... 35

3.1.4 Critical parameters for masks ......................................................................... 36

3.1.5 Mask transmission and thermal expansion...................................................... 37

3.1.6 Mask reflectivity............................................................................................. 37

3.1.7 Mask flatness ................................................................................................. 38

3.1.8 Defect level .................................................................................................... 38

3.2 EUV Mask and masking concept ............................................................................ 39

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3.2.1 Mask substrate and surface requirements:...................................................... 40

3.2.2 Mask fabrication and defects requirements .................................................... 41

3.2.3 Absorber stack and Backside conductivity coating ........................................... 45

3.2.4 Shadowing Affect ........................................................................................... 48

3.2.4 Bossung curve asymmetry and focus shift ....................................................... 49

4. Simulation.................................................................................................................. 51

4.1. System Design ..................................................................................................... 51

4.2. Reflectivity in EUV spectral region simulation ....................................................... 54

4.4. Paper Observations and conclusions .................................................................... 56

4.5 Simulation Code ................................................................................................... 60

5. Reference................................................................................................................... 65

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Abstract

Optical Design for -Nano Lithography

In today’s IC (integrated circuit) semiconductor, there are over a billion transistors.

The optical lithography process (photolithography) is one of the key processes in

reducing the limiting transistor dimensions (critical dimensions) onto silicon. The

dominant manufacturing technology today uses wavelengths of 193/248nm, with

which it is possible to achieve critical dimensions of up to 100nm (after additional

optical and process solutions). The radiation, which is transferred through a mask,

will pass through a series of lenses and will be focused on the light sensitive polymer

(photo sensitive polymer/photoresist), which covers the silicon wafer.

Decreasing critical dimensions further will require the use of wavelength in the EUV

spectral region, 10-14nm. Changing radiation from DUV to EUV poses challenges

and optical adaptations, for example: lenses, photoresist and masks.

This paper will include an overview of several lithography methods being used today

and a few that are under development stages ("NGL-" Next Generation

Lithographies). It will also describe and analyze the planning challenges of EUVL

Masks for mask technologies used today. Based on this paper, a simulation of a

system will be presented, which will show the changes in the EUVL (Extreme UV

Lithography) System output based on a user input.

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1 .Theoretical Background Lithography and its challenges in IC

process

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1.1 The lithography process:

Lithography creates a resist image on a pattern- usually a silicon wafer. The

subsequent etching, lift off, or ion implantation process is masked by the resist image

at the areas dictated by the lithography mask. Hence, the thin-film polymer material

on the wafer (called photo resist) is selectively removed, built up, or its characteristics

are selectively altered.

Replicating the mask pattern produces the resist image (except when mask making or

direct writing on a wafer which will not be discussed in this paper).

The condenser lens collects light from the source and illuminates the mask pattern.

Light then passes through the imaging lens to form an aerial image and to selectively

expose the resist. After the development process, in which the exposed parts (in a

positive type PR) are dissolved in a solution, the resist image is produced.

Figure 1.1- Basic optical lithography process

Schematic flow of the lithography process, through develop and etch.

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Schematic flow of the lithography process, through develop and ion implant.

A typical sequence of lithographic processing steps, illustrated for a positive resist

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Representation of the integration of the various lithographic process steps into a

photolithography cell.

1.2 Lithography role in the IC (Integrated Circuit) fabrication

Lithography is an important part of semiconductor manufacturing technology because

it is needed for every masking level. In a typical 0.13 µm CMOS integrated circuit

fabrication run with four metal layers, there are more than 30 masking levels using

474 processing steps, in which 212 steps are related to lithographic exposure, and 105

steps are related to pattern transfer using a resist image.

The lithography process is often the limiting factor of entering the next technology

node. For every node, the minimum feature sizes and their separations are reduced by

a factor of √2. Therefore, the succeeding generation to 1-µm lithography is 0.7 µm,

followed by 0.5 µm, 0.35 µm, 0.25 µm, 0.18 µm, 0.13 µm, 90 nm, 65 nm, 45 nm, 32

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nm, 22 nm, etc., necessitating improvements in resolution and overlay accuracy that

call for many of the following improvements: numerical aperture (NA) increase,

wavelength reduction, suppression of reflections, better resists, better masks, higher

stepping accuracy, higher-precision alignment, less lens distortion, better wafer

flatness, and many others.

Over the past three decades, the length-scales of the component devices have

decreased from around 15μm to around 30nm. However, the means by which the

components are manufactured, optical lithography remains principally the same.

Optical lithography comprises the formation of images with visible radiation in a

photo resist using proximity or projection printing. These methods rely upon a mask

to form the beam for the necessary image to be formed on the resist.

1.3 Optical lithography challenges

1.3.1- Resolution

VLSI devices consist of highly complicated and dense circuit patterns. Lithography,

supported by optical and process techniques, can offer resolutions of around 100nm.

However, as demand increases for smaller devices, the resolution offered by current

techniques will not be satisfactory.

Optical lithography, in its current form, is bound by some key parameters – numerical

aperture, depth of field, and resolution. The unexposed parts of the resist gradually

receive radiation because of diffraction in the system and scattering in the resist and

substrate layers, and hence, this affects the resolution of the system.

Because the mask essentially acts as a set of slits, we get diffraction within the optical

lithography system. Waves from the light source are emitted spherically. Therefore,

we also get spherical waves from the aperture. If the screen (or in this case, the resist)

is close to the aperture (or mask), then the curvature of the spherical wave is

important. This results in an image which will be similar to the aperture, and is known

as Fresnel diffraction. As the distance between the aperture and the screen is

increased, the image will look less like the aperture. Beyond a certain distance, known

as the Rayleigh distance (RD), there will be little change in the shape of the image,

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only its size will change. This is due to the curvature of the spherical wave becoming

negligible. This diffraction regime is known as Fraunhofer diffraction (see diffraction

in next section).

Rayleigh Distance is given by:

𝑅𝐷 = 𝑎2

𝜆⁄

Where ‘a’ represent the aperture and λ is the wavelength.

Two neighbored apertures will be distinguishable (resolution), when the maximum

intensity of one set of Airy's Rings coincides with the first minima of the second set

of Airy's Rings.

The intensity of Airy’s Rings from two neighboring apertures. The combined profile

is shown as a dotted line. This figure shows the Rayleigh resolution limit, equal to a

distance of 𝐷1

2 on the screen (a resist in the case of lithography).

After some optical manipulation and calculation we receive the below resolution

equation:

𝑅 =𝑘1𝜆

𝑛 sin 𝛼=

𝑘1𝜆

𝑁𝐴

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Here, R is the minimum resolvable separation (𝐷1

2), k1 is a constant dependent on the

absorbing properties of the resist, and the type of radiation used in the system, λ is the

wavelength of the exposing radiation and n is the refractive index of the resist. The

quantity nsinα is usually referred to the Numerical Aperture (NA).

The image formed in an optical system is only brought to focus in the appropriate

plane (or more accurately, a sphere).

The depth of field is the distance over which the image retains an acceptable focus,

The depth of field of an optical system, represented here as DOF, is the distance either

side of the plane of optimum focus over which the image retains an acceptable focus

𝐷𝑂𝐹 =𝑘2𝜆

𝑁𝐴2

Comparing the resolution equation to the DOF one, it’s clear that the Resolution and

depth of field are in conflict. Depth of field is improved (increased) by increasing the

wavelength of the radiation and by decreasing the numerical aperture. However,

decreasing the wavelength and increasing the numerical aperture improve resolution.

Therefore, a compromise is needed between resolution and depth of field. With

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today's equipment, the positioning of the resist within the lithographical system can be

accurately controlled, and depth of field becomes less of an issue. Obviously, the

industry cannot neglect the depth of field of the system, but resolution is the primary

factor.

1.3.2 Diffraction:

The first and most basic phenomenon occurring in projection imaging and affecting

resolution is the diffraction of light. Diffraction is usually thought of as the bending of

light as it passes through an aperture, which is certainly an appropriate description for

diffraction by a lithographic mask. More correctly, diffraction theory simply describes

how light propagates, including the effects of the surroundings (boundaries).

A simple interpretation of the physical principle behind diffraction is best captured by

Huygens principle: any wavefront can be thought of as a collection of radiating point

sources. The new wavefront at some later time can be constructed by summing up the

wavefronts from all of the radiated spherical waves.

Huygens’ principle: any wavefront can be

thought of as a collection of point sources radiating spherical waves

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For a simple chrome-glass mask, the mask electric-field transmittance for a normally

incident plane wave of illumination is binary: tm(x,y) is 1 under the glass and 0 under

the chrome. Let the x′–y′ plane be the diffraction plane, that is, the entrance to the

objective lens, and let z be the distance from the mask to this diffraction plane. We

will also assume monochromatic light of wavelength λ and that the entire system is in

a medium of refractive index n. Defining the spatial frequencies of the diffraction

pattern (which are simply scaled coordinates in the x′–y′ plane) as 𝑓𝑥 =𝑛𝑥′

𝜆𝑧 and 𝑓𝑦 =

𝑛𝑦′

𝜆𝑧, the electric field of our diffraction pattern, Tm(fx,fy), is given by the Fraunhofer

diffraction integral:

𝑇𝑚(𝑓𝑥, 𝑓𝑦) = ∬ 𝐸𝑖(𝑥, 𝑦)𝑡𝑚(𝑥, 𝑦)𝑒−2𝜋𝑖(𝑓𝑥𝑥,+𝑓𝑦𝑦)

∞

−∞

𝑑𝑥 𝑑𝑦

Where Ei is the electric field incident on the mask (and is just 1 for our unit

amplitude, normally incident plane wave). It can be seen that the diffraction pattern

(the electric field distribution as it enters the objective lens) is the Fourier transform of

the mask pattern transmittance.

The Fourier transforms for normally incident plane wave illumination (Ei = 1) of

isolated space gives rise to a sinc function (sin 𝑥

𝑥) diffraction pattern, and the equal

lines and spaces yield discrete diffraction orders:

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Two typical mask patterns, (a) an isolated space and (b) an array of equal lines and spaces, and the resulting Fraunhofer diffraction patterns assuming normally incident

plane wave illumination. Both tm and Tm represent electric fields

Where δ is the Dirac delta function, w is the spacewidth and p is the pitch (the

linewidth plus the spacewidth). The delta function is the mathematical representation

of a point of light.

1.4 Lithography methods to achieve high resolution

As mentioned above, there is a need to keep lowering the printed dimension of the

transistor to improve the IC device (according to Moors low). In order to do that, a

lithography method which allow as low as possible CDs (critical dimensions), with

good resolution should be chosen.

From Rayleigh’s resolution equation it can be concluded that the most important

variables to change in order to improve resolution are the wavelength and the

numerical aperture (λ and NA). However, we can see that a greater improvement in

resolution will be given by decreasing the wavelength of the exposing radiation (as

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we want to make R as small as possible). Therefore, in order to improve the critical

dimensions on the resist λ has to be beyond optical wavelengths with a view to using

ultra-violet and X-ray radiation in lithographical systems.

Phase-shifting masks are under development within the industry, and lasers are being

used within the industry to give more coherent light sources, which in turn results in a

more uniform resolution across the resist.

At present, most lithography systems for LSI circuits are using partially coherent light

from a KrF laser (λ=248nm) or ArF (λ=193nm) in combination with some resolution

enhancement techniques including phase-shifting masks and advanced resists.

The microelectronic industry is constantly striving for reductions in component sizes.

In order to achieve this, the lithographic industry either has to improve optical

lithography by using phase-shifting masks, or look to shorter wavelength radiation to

improve resolution.

Another element to keep in mind is that the lithographic method has to support high

volume manufacturing, meaning that even if the specific method bring good

resolution results it might not be usable in the industry, as it is very slow to apply on

the wafer.

1.4.1 Proximity Optical Lithography

Proximity optical lithography is relatively simple, as it requires no image formation

between the mask and the resist. The proximity system is essentially made up of a

light source, a condenser, a mirror, a shutter, a filter (the mask) and the stage on to

which the resist is positioned. In proximity lithography, the mask-resist separation is

usually around 20 to 50μm, and leads to an acceptable resolution for today's devices

of around 500nm. However, diffraction occurs between the mask and the resist, and

so we can increase resolution by narrowing the mask resist separation. Indeed, a much

better resolution would be achieved if the resist and the mask were in contact.

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1.4.2 Contact Optical Lithography

If we bring the mask into contact with the resist, we remove any diffraction that may

occur between the mask and the resist. By doing this, the resolution of the system is

increased without having to change the exposing wavelength or the numerical

aperture of the system.

In contact lithography, the mask is pressed against the resist with a pressure of

typically around 0.3atm. The system is then exposed using light with a wavelength of

around 400nm. This makes resolution of around 0.5μm possible, but the very nature

of contact between surfaces means that resolution will vary across the resist. The

contact also results in deformity of both the resist and the mask, and therefore the

mask can only be used for a short time (proximity lithography). However, provided

the masks are relatively inexpensive to produce, and the deformity to the resist is

acceptably small, contact lithography is a better method to use than proximity

lithography as it produces an improved resolution.

1.4.3 Projection Optical Lithography

Projection optical lithography offers higher resolution than proximity and contact

printing. Projection printing relies on an image formation system between the mask

and the resist.

Because the beam is focused between the mask and the resist, the resolution of the

system is good compared to the above techniques. The projection system consists of

several sub-systems, each of which can be manipulated to improve the overall

resolution of the system. The numerical apertures of the lenses can be increased up to

around 1.5, the practical limit (sinα term has a maximum of 1, n typically 1.5).

Substance Velocity of

Light kps

Refractive

Index

Space 299,792 1.00

Air 299,890 1.00

Water 225,442 1.33

Glass 197,349 1.52

Diamond 124,083 2.42

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Refractive index for few materials- Calculated based on ((𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑎𝑖𝑟) ⁄(𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑀𝑒𝑑𝑖𝑢𝑚))

1.4.4 Phase-Shifting Masks

For a conventional chrome-on-glass mask, the idealized mask transmittance is

considered to be binary: the light is 100 % transmitted through the glass areas and 100

% blocked by the chrome. The resulting the electric field transmittance function

tm(x,y) that is either 0 or 1 (and thus the term ‘binary’ mask to describe this type of

transmission). A phase-shifting mask (PSM) modifies not only the amplitude of the

transmitted electric field but the phase of the transmitted light as well.

The principle of phase-shifting masks: The intensity received by the resist in the

region between the two intensity peaks becomes negligible. Therefore, we can bring

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the peaks closer together, and therefore improve the resolution of the system

(Intensity is proportional to E2).

Two nearby regions of the mask transmit 100 % of the monochromatic light, but

experience different optical path lengths. In one region, the light passes through extra

glass (or fused silica) of thickness d and refractive index ng. In a nearby region, the

light travels through air of the same thickness (with refractive index of 1).

The phase difference between two plane waves traveling perpendicularly through the mask will be:

∆∅ = 2𝜋𝑑(𝑛𝑔 − 1)/𝜆

By adjusting the thickness of this extra layer of glass, 1800 phase difference between

the two waves can be obtained:

𝑑180 =𝜆

2(𝑛𝑔 − 1)

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1.4.5 Increasing the NA (numerical aperture)- Immersion lithography

Typically, the projection optics and the wafer stage occur in air or in a vacuum, in

order to increase resolution, which means the refractive index n is 1.0 and NA = sinθ.

The numerical aperture is, therefore, entirely decided by the size of the projection lens

and cannot be bigger than 1, and more practically is ≤ 0.93. Immersion technology

provides another way to increase the NA: by increasing n. The gap between the last

lens element and the resist can be filled with a liquid and all liquids have much higher

refractive indices n than air.

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n – Refractive index (g-glass, f- liquid medium, r-substrate, 0-air) This subject will be discussed in details in this paper.

1.4.6 Lowering the wave length λ- Ultra-Violet Lithography

In order to keep pace with the demand for the printing of ever smaller features,

lithography tool manufacturers have found it necessary to gradually reduce the

wavelength of the light used for imaging and to design imaging systems with ever

larger numerical apertures.

Moving forward according to Moors law, and examining the next generation

lithography (NGL) techniques by the largest companies, shows that there is high

likelihood, for EUV technology to be chosen as the successor of optical lithography.

Shortening the wavelength from optical to ultra-violet offers a viable alternative to

optical lithography as the requirement for smaller circuit patterns increases beyond

the present capabilities of optical lithography. Extreme Ultra-Violet (EUV)

lithography uses the same principle as the projection optical system. Using ultra-violet

wavelengths of 11-13nm gives a resolution which is significantly better than the

optical system.

Using EUV lithography compared to 193nm lithography in use today, present few

new challenges:

The absorption of radiation at this short wavelength is very strong.

Therefore, lens-based refractive optics cannot be used in this lithographic

system. Instead, a reflective optical system must be used. Multi-layer devices

which rely on interference for reflection must be used. In the U-V region,

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these devices usually have a reflectivity of only 60-70%, and hence the

number of "mirrors" in the system must be kept to a minimum or the intensity

level reaching the resist will be insufficient. The requirement for fewer optical

components means that asymmetric mirrors need to be used. Such mirrors

need to be extremely precise, with errors of the order of 0.1nm. The multi-

layer reflectors consist of a large number of alternating layers of materials

having dissimilar optical properties. They provide a constant reflectivity when

the thickness of each layer is λ/2.

Masks- EUVL masks are reflective. They consist of a patterned absorber of

EUV radiation placed on top of a multi layer reflector deposited on a robust

and solid substrate. The reflectance spectrum of the mask must be matched to

that of the multi layer-coated mirrors in the light path.

Taken from: http://www.nist.gov/pml/div685/extreme-uv-lithography.cfm

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The source of the U-V radiation- Radiation of this wavelength is more

energetic than visible light, and therefore we must have higher-powered

energy sources to produce the U-V radiation. Eventually a source will be

required that reliably provides sufficient power to yield adequate wafer

throughput in a manufacturing tool.

EUV Absorbent Resists- The main problem to be confronted in developing a

satisfactory photoresist for EUVL is the strong absorption of EUV radiation

by all materials. The absorption depth in standard organic resists used today is

less than 100nm. EUV resists will most likely be structured so that printing

occurs in a very thin imaging layer at the surface of the resist.

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2. EUVL- Extreme Ultra Violate Lithography

Continued improvements in optical projection lithography have enabled the printing

of ever finer features, the smallest feature size decreasing by about 30% every two

years. This has allowed the integrated circuit industry to produce ever more powerful

and cost-effective semiconductor devices. On average, the number of transistors in an

integrated circuit has doubled every 18 months. Currently, the most advanced

lithographic tools used in high-volume manufacture employ deep-ultraviolet (DUV)

radiation with a wavelength of 193 nm to print features that have line widths as small

as 100 nm.

Potential successors to optical projection lithography are being aggressively

developed. These are known as “Next-Generation Lithographies” (NGLs). EUV

lithography (EUVL) is one of the leading NGL technologies (others include X-Ray

lithography, ion beam projection lithography, and electron-beam projection

lithography).

In many respects, EUVL may be viewed as a natural extension of optical projection

lithography since it uses short wavelength radiation (light) to carry out projection

imaging. In spite of this similarity, there are major differences between the two

technologies. Most of these differences occur because the properties of materials in

the EUV portion of the electromagnetic spectrum are very different from those in the

visible and UV wavelength ranges.

EUVL provides photon based single exposure technique that resembles current optical

lithography techniques. With 14X reduction in wavelength compared to 193nm

technology, EUVL provide significant advantage in diffraction limited resolution.

But with such a dramatic drop in wavelength, the imaging system is substantially

different from existing systems. First, any substance heavily absorbs EUV light, even

gases- the optical path must be in a vacuum. Second, following its heavy absorption

characteristics, there is no transmitting material- EUV imaging depends on reflection.

Generating EUV photons from hot and dirty plasma sources requires new materials

(for long optic lifetime), and new optical design for efficient collection of the EUV

light.

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The need for reflective optics places a major challenge on the mask industry as for the

defect free and cost effective requirements. In addition low projection optics

aberration for EUV light requires polishing to a small fraction of the 13.5nm exposure

wavelength.

These challenges, along with few solutions will be discussed in this paper.

Schematic diagram of EUVL system

Taken from: http://spie.org/x51899.xml?pf=true&ArticleID=x51899

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A photo of a real EUVL system: ASMLs NXE:3100

Taken from: http://www.mysemicondaily.com/blog/2010/7/6/asmls-pre-production-euv-tool-achieves-first-light.html 2.1 EUVL Optical design configuration

Improving lithography system as mentioned previously is guided by the need to

receive lower resolution and higher depth of focus.

This is represented by the equations:

RES = k1 λ/ NA

And

DOF = k2 λ/ (NA)2

Where λ is the wavelength of the radiation used to carry out the imaging, and NA is

the numerical aperture of the imaging system. These equations show that better

resolution can be achieved by reducing λ and increasing NA. The penalty for doing

this, however, is that the DOF is decreased.

The case k1 = k2 = ½ corresponds to the usual definition of diffraction- limited

imaging. In practice, however, the acceptable values for k1 and k2 are determined

experimentally and are those values which yield the desired control of critical

dimensions (CD’s) within a tolerable process window.

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Lithography system performance has a major impact on determining these values.

Other impacting factors include the contrast of the resist being used and the

characteristics of any etching processes used. In the past, values for k1 and k2 greater

than 0.6 have been used comfortably in high-volume manufacture.

L.H.S Plot: The k1 and DOF values associated deferent lithography methods assuming k2 = k1 and NA =

0.6

R.H.S plot: The dashed black line shows the location of points corresponding to a resolution of 100

nm. The solid red line shows the location of points for which the DOF is 0.5 µm. Points in the region

between the two lines correspond to situations in which the resolution is 100 nm or better, and the DOF

is 0.5 mm or longer (faverable setuation).

Taken from: Intel Technology Journal Q3’98- “EUV Lithography—The Successor to Optical

Lithography?” Page 2

k1 Values for deferent NA in the EUV region

However, it has been necessary to extend imaging technologies to ever better

resolution by using smaller values for k1 and k2 and by accepting the need for tighter

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process control. EUVL is capable of printing features of 100 nm and smaller while

achieving a DOF of 0.5 µm and larger.

2.2 Multi Layers Optics:

If wavelengths of light in the range of 11–14 nm is used, it is possible to construct

reflecting optics of moderate efficiency (> 60%) using multilayer films. This opens up

the possibility of projection optics and reduction imaging. With a numerical

aperture of 0.25, a wavelength of ~13.5 nm, and a k1 value of 0.6, the resolution is

𝑅𝐸𝑆 =𝑘1𝜆

𝑁𝐴= 32𝑛𝑚

Multilayer film stack

Peak

wavelength of normal incidence

Reflectance

Mo/Si 13.4 67.50%

Mo2C/Si 13 61.80%

Mo/Be 11.3 70.20%

MoRu/Be 11.3 69.30%

Reflection occurs at interfaces between materials of different indices of refraction.

The larger the difference in refractive index the greater the reflectivity. At

wavelengths < 50 nm, all materials have indices of refraction ≈ 1. Thus, it is difficult

to create a highly reflective interface. At EUV wavelengths, it has proven possible to

make mirrors with moderate reflectivity, in the range of 60–70%, by the use of

multilayers. Multilayer reflectors are made by depositing alternating layers of high-Z

and low-Z materials, giving a small but effective difference between refractive indices

at each interface. By making the periodicity d of the multilayer stack satisfy the Bragg

condition, the net effect of small reflectivity at each interface is moderately

high reflectivity overall when the stack has a sufficient number of layers:

𝑑 =𝑚𝜆

2𝑐𝑜𝑠𝜃

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Taken from: http://spie.org/x33220.xml

The theoretical reflectance properties of a normal incident MO/Si (Molybdenum-

Silicon) ML are shown in the figure below. These coatings consist of a large number

of alternating layers of materials having dissimilar EUV optical constants, and they

provide a resonant reflectivity when the period of the layers is approximately λ/2.

If not designed properly, the ML can induce amplitude and phase error at the exit

pupil of the imaging system. These errors can bring the system to have poor critical

dimension uniformity across the field.

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The most common EUV multilayers are made of alternating layers of Mo and Si, and they function

best for wavelengths of about 13 nm. Curve showing the normal incidence reflectivity and phase upon

reflection of a Mo\Si ML as a function of wavelength. The coating is designed to have peak

reflectivity at 13.4 nm

The EUV reflectivity is only in the order of a few percent. Reflectivity is built up with

a multilayer stack consisting of 40- to 50-layer pairs of Mo and Si, to achieve 65~70%

reflectivity, enabling an all reflective optical system that includes the illumination

optics, the mask, and the imaging optics.

2.2.1 Mo/Si ML Requirements:

The primary materials-dependent requirements for Mo/Si interference coatings are

maximum reflectivity, sufficient stability, and minimum residual stress. Controlling

these characteristics is critical for the efficient operation of an EUVL system. A high

peak reflectivity of Mo/Si multilayer mirrors is extremely important. Considering an

all-reflective EUVL system with Mo/Si mirrors (illumination optics, projection optics,

and masks), the difference between two sets of multilayer mirrors with respectively,

70 and 68 percent reflectivity results in a 30 percent difference in integral light

intensity at the wafer plane (the peak reflectivity is not the only key factor). The

power on the wafer is given by the integral of the spectral power of the source and the

multiplied reflectivity from the N mirrors of the EUVL system:

𝑃𝑤 = ∫ 𝑃𝑠(𝜆) ∏ 𝑅𝑘(𝜆)𝑑𝜆

𝑛

𝑘 =1

Where Pw is the power delivered to the wafer, Ps is the spectral power of the source,

and Rk is the reflectivity of the k-mirror.

30

Table 2.1- Main Requirements for Mo/Si Multiayer Coatings in EUVL Applications

2.3 - ML Design for EUV systems

The interaction between electromagnetic radiation and media is described in terms of

the complex refractive index �̃� = n + iβ, which is a function of the wavelength λ. The

real (n) and imaginary (β) parts of ñ are termed the refractive index and the extinction

coefficient, respectively. The propagation of a monochromatic electromagnetic wave

with a wavelength λ through an isotropic and homogeneous medium in the x direction

is described by:

𝐸(𝑥) = 𝐸0 exp (−2𝜋𝛽𝑥

𝜆) exp [

2𝜋𝑖

𝜆(𝑛𝑥 − 𝑐𝑡)]

Where E0 is the field amplitude at x = 0, and c is the speed of light in vacuum.

2.3.1 Refractive index in the EUV spectral region:

In the EUV spectral region, the refractive index n of all materials is less than unity by

a small amount δ(n = 1 − δ) and characterizes the refractive properties of a medium or

the phase speed of a wave. n (δ) and β are referred to as the optical constants of a

medium. In the EUV region, the complex refractive index can be expressed by the

complex atomic scattering factor 𝑓 = ( 𝑓1 − 𝑖𝑓2) with:

31

�̃� = 𝑛 + 𝑖𝛽 = 1 − 𝛿 + 𝑖𝛽 = 1 −𝑁𝑎𝑟𝑒𝜆2

2𝜋(𝑓1 − 𝑖𝑓2)

Where Na is the number of atoms per unit volume, re = 2.82 × 10−15 m is the classic

radius of an electron, and λ is the wavelength.

Figure 2.3.1- Atomic scattering factors ( f1 and f2) and the optical constants (δ and β)

for silicon as a function of the wavelength in the EUV spectral region (5-20nm). In the EUV spectral region, all materials become more absorbing and more refracting

with increasing wavelength.

2.3.2 Reflectivity in EUV spectral region:

The amplitude reflection coefficients rs and rp for s- and p-polarization, at the

boundary of two materials with complex refractive indices ñ1 and ñ2 are obtained

from Fresnel equations and are given by:

𝑟𝑠 = 𝑛1̃𝑐𝑜𝑠𝛼1 − 𝑛2̃𝑐𝑜𝑠𝛼2

𝑛1̃𝑐𝑜𝑠𝛼1 + 𝑛2̃𝑐𝑜𝑠𝛼2

𝑟𝑝 = 𝑛1̃𝑐𝑜𝑠𝛼2 − 𝑛2̃𝑐𝑜𝑠𝛼1

𝑛1̃𝑐𝑜𝑠𝛼2 + 𝑛2̃𝑐𝑜𝑠𝛼1

α1 and α2 are the incidence and reflection angles.

32

From Snell law: 𝑛1̃𝑠𝑖𝑛𝛼1 = 𝑛2̃𝑠𝑖𝑛𝛼2

Normal incident reflection coefficient:

𝑟┴ =𝑛1̃ − 𝑛2̃

𝑛1̃ + 𝑛2̃

For EUVL Systems The reflectivity of the interface between vacuum (n = 1) and a

material with complex refractive index ñ = 1 − δ + iβ (where δ, β << 1) will be:

𝑅┴ = |𝑟┴ |2 =𝛿2 + 𝛽2

(2 − 𝛿)2 + 𝛽2≈

𝛿2 + 𝛽2

4

A higher reflectivity can be achieved by using a small grazing angle θ (θ =90° − α).

Polarization phenomenon.: Rs reflectivity increases monotonically from normal to

grazing incidence, whereas Rp shows a dip at α = 45 degrees. The Rp minimum

occurs at Brewster’s angle (αB) where the refracted and the reflected beams become

perpendicular. Because the refractive index of all materials in the EUV spectral range

is very close to unity, the minimum of Rp always appears close to 45-degree

incidence.

Total reflection: occurs if the radiation penetrates from high- to low-refractive index

material (n1 > n2). For grazing angles θ below the critical angle θC, the refracted

beam becomes parallel to the interface, and the reflectivity reaches 100 percent.

33

3. Lithography Photo masking

This paper will discuss the improvements and challenges when moving towards EUV

ML reflection masking, compared to the widely used Chrome on glass reticles.

In order to discuss EUV challenges, a short review of DUV Photo Masking concept is

needed (DUV Lithography is the controlling technology in IC manufacturing-

193/248nm).

3.1 DUV Light Photo Masks and masking concept

A photomask (mask) consists of patterned absorbers and/or phase shifters delineated

on a transparent substrate. According to the presence or absence of the absorbers and

phase shifters, as well as the number of levels of these patterning materials, the

photomask can be classified generically into six main types:

1. Binary intensity masks (BIM)—This is the most commonly used mask

type. Absorbers are placed in various areas of the mask, according to the

circuit pattern. The absorber completely blocks light as it hits the mask.

Alternately, light passes through the mask where no absorbers exist.

2. Binary phase mask (BPM)—There is no absorber on the mask. The only

pattern-dependent variation on the mask is a 180-deg phase shift. This is

typified by an unattenuated (chromeless) Phase Shift Mask- as explained

in page 10.

3. Binary complex mask (BCM)—The absorber passes or blocks light. The

phase shifter shifts light by 180 deg. There are phase-shifted and

nonphase-shifted areas on the mask.

34

4. Multilevel intensity mask (MIM)—An intensity mask may contain many

gray levels for specific applications, such as an exposure calibration mask

that contains many calibrated gray levels to facilitate rapid and economical

determination of the exposure dosage.

5. Multilevel phase mask (MPM)—The phase shifters produce many levels

of phase on the mask; presumably, 0 deg, 90 deg, and 180 deg, or 0 deg,

60 deg, 120 deg, and 180 deg.

6. Multilevel complex mask (MCM)—Either the absorber or the phase shifter

is multilevel. The latter is exemplified by the AltPSM in combination with

multilevel phase-shifting edges.

3.1.2 Mask substrate and absorber:

The most commonly used substrate material for mask in the UV region is fused silica.

35

1. Its thermal expansion coefficient at 0.5 ppm/º C is an order of magnitude

smaller than that of other candidates.

2. Fused silica is transparent from the visible region to below 200 nm. It is usable

for g-line (435.83 nm), i-line (365.02 nm), KrF (248.35 nm), and ArF (193.39

nm) wavelengths.

The mask absorber material is usually chromium because of its hardness and low

thickness needed for full absorption.

MoSi2 is primarily used as the phase-shifting absorber for the AttPSM. Its property

can be fine tuned to exhibit a 6% transmission and a 180-deg phase shift at the same

thickness.

3.1.3 Pellicles

A pellicle is a transparent membrane17 mounted on a frame that is attached to the

mask substrate. It is usually an organic polymer a few micrometers in thickness. The

6-mm frame thickness is carefully chosen so that if a particle not too large in size is

attached to the pellicle, the particle is completely out of focus and can, at most, induce

a tolerable exposure change in its locality.

The pellicle has a huge importance in case of particles. If the reticle is not protected,

there will be repeating defects on every wafer at every exposure field. If only one

foreign particle falls on the mask during transportation, loading/unloading to the

exposure tool, exposure, storage, or any other type of handling, the printed field will

be damaged across the entire wafer.

36

The pellicle material must withstand prolonged exposures without reducing its

transmission or smoothness. Tiny holes are drilled at the pellicle frame to prevent

trapping of harmful vapor generated during exposure.

3.1.4 Critical parameters for masks

Critical dimension (CD) control

The mean and standard deviation of the critical dimension (CD) designated by the

circuit designer are important parameters for the mask. The CD mean must be as close

to the desired value as possible. The desired value must be the target value on the

wafer multiplied by the reduction factor of the imaging system. A different value may

produce a larger error, depending on the feature shape, feature size, feature

environment, the optical train, the resist characteristics, and processing conditions.

This value is referred to as mask bias.

Placement accuracy

Each feature on the mask must be located at the desired position with respect to other

features on the same mask, as well as on other masks whose images must be overlaid

together. Hence, placement error contributes significantly to the overlay accuracy

budget. Placement errors are often induced by the mask-making machine, mostly due

to difficulties in controlling the position of the writing beam.

37

3.1.5 Mask transmission and thermal expansion

The transmission of the mask blank should be above 90%. From the point of view of

mask heating, a higher transmission is desirable. After reaching the material

transmission limit, the only way to increase transmission is to reduce the mask

thickness.

Mask heating causes thermal expansion. With a thermal expansion coefficient of 0.5

ppm/0C, raising the temperature of the mask substrate by 10C expands a 150-mm

square mask by 75 nm at each side. This can easily be corrected by fine tuning the

magnification of the exposure tool, especially in a projection tool. In lensless systems,

such as proximity printing, mask thermal expansion can be detrimental to overlay

because wafers at different stages of processing can exhibit subtle magnification

changes.

3.1.6 Mask reflectivity

One of the main concerns with chromium as a mask absorber is its high reflectivity at

the side facing the imaging lens. This reflection can reduce image contrast.

The figure below shows linewidth versus defocus plots at a range of exposure dosages

for mask absorber reflectivity of 66%, 33%, and 10%. The 10% result clearly

confirms better linewidth control and exposure tolerance. It is desirable to reduce

absorber reflection to 10% or lower.

38

Linewidth versus defocus at different exposures for three levels of mask reflectivity

R= Reflectivity, ∆E − Energy (Dose Delta), ∆I − Intensity Delta, ∆W −

line Width Delta

3.1.7 Mask flatness

The flatness of the mask must be a small part of the depth-of-focus (DOF) budget of

the entire imaging system. With a reduction system, the flatness requirement is very

relaxed because the DOF tolerance on the mask size is M2, with M being the

reduction ratio. For example, with a mask flatness of 500 nm, the focusing error at the

wafer side of a 4X reduction system is 31 nm. In addition to ensuring that the two

surfaces of the mask blank are well polished and parallel to each other, the mask

blank must have sufficient strength to support itself without sagging, which can

induce DOF error.

3.1.8 Defect level

The defect level is usually specified by the maximum allowable defect size as a

function of its vicinity to patterned features on the mask. A programmed defect mask

(PDM) consisting of artificial defects varying in size and distance to patterned

features is often used to empirically determine defect printability for specification.

Simulation is helpful to gain insight for designing the PDM. Because real defects are

usually irregular in shape, its printability must be further qualified with aerial image

measurement system (AIMS), which consists of a small-field imaging lens and

illuminator in an actinic wavelength to mimic the same λ/NA condition. Such an

optical system is much easier to build when compared to a scanner or stepper. The

NA needs only be 1/M (M being the reduction ratio) of the NA of the exposure

system. Therefore, 0.18 NA works for 0.72 NA of a 4X reduction system. Ultimate

qualification lies in exposing the mask in the production exposure system and

inspecting the printed wafer with wafer inspection tools.

39

3.2 EUV Mask and masking concept

EUVL (Extreme ultraviolet lithography) successful implementation as the IC future

fabrication technology is dependent mostly on the ability to create suitable mask

technology. Since EUV light is strongly absorbed by most materials, reflective optics

are applied (as discussed in the EUV Lithography chapter) to all components,

including the mask. As a result, EUV mask structure is radically different from that of

conventional optical lithography (193/248nm for example). All the mask components

must be prepared with great care to consider the 13.5nm reflection, which requires

nano-scale thin-film technologies. The reflection of a 13.5-nm wavelength requires a

multilayer (ML) structure consisting of many alternating layers of materials having

dissimilar EUV optical Constants. The Bragg reflection (constructive interference of

the partially reflected beam at several interfaces) is the principle to have EUV

reflection, and its efficiency is determined by the structural factor (the thickness of

each layer and their ratios) as well as optical properties (refractive index and

extinction coefficient).

An EUV mask consists of several layers that have unique mechanical, chemical and

optical functions. The mask substrate maintains the rigidity of the mask with

minimum distortion. It should have a flat, smooth surface with zero defects as well as

a low coefficient of thermal expansion (CTE). The ML is one of the key components

in terms of mask efficiency- if its reflectivity is below l00%, the mask will cause an

optical power loss. The ML capping layer protects masks from degradation and the

absorber layer in a mask has a similar purpose to the chrome layer of a deep

ultraviolet (DUV) in terms of pattern forming function.

40

Taken from article: Light-shield border impact on the printability of extreme-

ultraviolet mask- Takashi Kamo ; Kazuo Tawarayama ; Yuusuke Tanaka ; Yukiyasu Arisawa ;Hajime Aoyama ; Toshihiko Tanaka ; Osamu Suga

3.2.1 Mask substrate and surface requirements:

The ML is coated onto the substrate of an EUV mask to attain high reflectivity at the

13.5nm wavelength. The EUV reflectivity is degraded by the roughness of the

substrate surface, especially by the high spatial frequency roughness (HSFR), which

causes large angle scattering and loss of EUV light form the projection lens. Mask

MSFR (also referred to as slope error) leads to intensity variation in the image plane

and becomes a source of line edge roughness (LER) or image placement error. For a

0.25-NA optical system, the frequency range for MSFR is l0-6nm <f <0.004/nm and

for MSFR 0.004/nm<f <0.02nm. The mask flatness issue comes from the unique

EUVL imaging system design, which is a non telecentric illumination system. Any

height variation of the patterned mask surface (non flatness) causes an image

placement error (or overlay error) on the wafer.

HSFR- leads to loss of light throughput as the light scatters outside the exit pupil

41

MSFR-leads to small angle scattering, which causes wave front error and speckle

The image placement error on the wafer is defined using the below formula:

∆x =∆z ∗ tan θ

M

Where ∆z the non flatness of the mounted mask and θ is the illumination angle.

Assuming θ=5 degree illumination angle, the image placement error is about 1/40 of

the non flatness of the mounted mask ∆z.

∆Xwafer = (1

4) ∗ tan(50) ∗ ∆Zm ≅ 0.023∆Zm

3.2.2 Mask fabrication and defects requirements

Mask fabrication is being done while taking into consideration the importance of

defect clean surface. The biggest challenge for the EUV mask blank is defect

reduction. Defects on the substrate before ML deposition or defects generated inside

42

the ML during the deposition process have the potential to cause printable defects

during the lithography process.

Taken from: http://www.drlitho.com/cms/website.php?id=/en/research/emf.html

A substrate surface defect tends to propagate through the ML coating, which causes

disturbance of the reflected wave front. Depending on the deposition process and

defect location, it can be printable or nonprintable.

As shown in the figure below, if the defect is greater than a threshold value (diameter

and height), it can be printed on the surface of the wafer. This propagated mask

surface defect is called a phase detect.

43

Theoretical curve for the printability of a molybdenum-silicon (Mo/Si) ML detect as function of the detect height and full width at half maximum (FWHM).

At the EUV wavelength, every material has a refractive index close to 1 and

reflectivity of almost 0. As discussed previously, EUV Lithography optics are

required to be all reflective and a ML coated mirror consisting of a large number of

alternating material layers and having dissimilar EUV optical constants is being used

in order to achieve high reflectance by interfering EUV light.

According to Fresnel equation, the reflectivity of the boundary is proportional to the

difference in the indices of the refraction. The two different layers for the ML have

high and low atomic numbers, (Low layer lower number) to maximize the difference

in electron density. These materials also should have low EUV light absorption,

which is determined by the imaginary part of the refractive index (extinction

coefficient). Taken into account process capability as well as optical performance,

Mo/Si MLs are known to be among the best choices from the several material

combinations for high reflectivity at a wavelength around 13.5nm, and are essential

components for EUV exposure optics as well as for EUV masks.

The Mo layer- scatters the light, while the Si layer, which has low EUV absorption,

works as a spacer for periodic structure. The thickness of the Mo/Si pair (d spacing)

and the ratio of the Mo thickness to the two layer period are designed to exhibit

maximum reflection but minimum absorption. The period of the ML pairs should

satisfy the modified Bragg’s law to produce maximum reflectance at the EUV

wavelength:

nλ = 2d cos θ√1 − 2δ

1 − (cos θ)2

Where n is an integer, d is he period of the ML pairs (d spacing), λ is the EUV

wavelength, θ is the light incident angle to the mask normal (usually 5 deg), and b is

the bilayer-weighted n. δn is defined as 1-n, where n is the real part of the refractive

index. By increasing the number of bilayers over 40, reflectance can be improved up

to about 69%.

44

One reason for losing reflectance in the ML layers is imperfections that accrue during

the ML processing. The industry defect goal (High Volume Manufacturing goal), as

posted in 2009 was 0.003defects/cm2.

The most common imperfections are:

Formation of surface oxide- Typical Mo/Si MLs are terminated with Si, but their

reflectance tends to decrease in the presence of EUV light and water vapor due to

growth of the silicon oxide (SiO) layer. EUV irradiation creates low energy secondary

electrons that promote surface oxidation.

Silicide formation between Mo and Si layers- results in reflectance degradation as

well as ML period contraction. The Silicide layer thickness is interface-dependent.

The Silicide thickness of the Mo-on-Si layer is about two times thicker than that of

the Si-on Mo interface. A reduction of interdiffusion can be accomplished by

introducing thin diffusion barriers between the Mo and Si layers, which leads to a

transition from the traditional Mo/Si bilayer structure to an interface-engineered triple

or quadruple structure.

Measured reflectivity of Mo/Si, Mo/Si/C

and Mo/Si/SiC ML mirrors

Taken from Ref 23 EUV book

Roughness of interfaces- lowers ML

reflectance. There is a critical Mo

thickness where the roughness increases

dramatically due to amorphous-to crystalline translation. In an optimized ML for

EUV mask, the typical Mo thickness is well below that critical value. Using ML

smoothing techniques during the deposition process can effectively reduce roughness

problems caused by small substrate surface defects and substrate surface roughness.

The planarization process for smoothing substrate particles is using a secondary ion

45

source can smooth ~80nm diameter particles on the substrate to a height of 0.5nm,

which would render them non critical in the EUVL printing process.

3.2.3 Absorber stack and Backside conductivity coating

EUV mask requires two or three films, called the absorber stack, which is on top of

the ML. The absorber stack consists of a buffer layer, an absorber layer, and an ARC

(Low Reflective layer- ARC=Anti Reflective Coating). The buffer layer protects the

ML during absorber etch and repair, and the ARC secures the efficiency of optical

inspection. The backside metal coating enhances the chucking force when reticle is

mounted.

Absorber Layer

The absorber layer must exhibit several characteristics, including high EUV

absorption, stability under EUV radiation, high image contrast during inspection,

conductivity high etch selectivity to buffer, and low DUV reflectivity to afford optical

surface defect inspection.

Cr and TaN are used the most for the absorber layer. Cr, currently used in

conventional optical masks, can be deposited with low defect density and low stress.

The Cr etch process, however, generally induces a large negative etch bias on the

order of 50 to 80 nm. Ta-based materials can be easily etched with Cl2-based

chemistry and yield very little etch bias. Aerial image contrast depends on the

absorber material (higher with TaN and Cr) as well as the absorber thickness (higher

with a thicker absorber). However, a low-refractive- index (n) material like TaN can

46

act as an attenuated phase shift mask (PSM), resulting in an even higher contrast at

low thickness (~45 nm in the case of TaN).

Wafer plane aerial image contrast as a function of absorber height for various

absorbers with no buffer.

Buffer Layer:

Because the buffer layer must be able to protect the ML during absorber etch and

absorber pattern repair, it needs to have the following characteristics:

Low pinhole defectivity

High etch selectivity to the absorber layer during absorber etch and repair

High etch selectivity to ML capping during the buffer layer removal

Low EUV absorption such that a buffer defect can be tolerated without repair

Stability during chemical cleaning.

The buffer layer can be made from few deferent materials depending on the process:

SiO2, SiON,Ru,C,Cr and CrN.

Anti-Reflecting Coating (Low Reflectivity Layer):

The EUV mask can inspected using reflection mode only (compared to traditional Cr

on glass mask that can be inspected using reflection and transmission). The image

contrast depends on the reflectivity difference between the reflector region (ML or

repair buffer) and absorber region.

47

The image contrast is than defined as:

Image Contrast= RML−Rabs

RML+Rabs × 100%

When R is the reflectivity of the ML and the Absorber.

Since any metal layer would reflect too much of the DUV light (being used for

inspection of the mask during production), an ARC is needed for DUV to reduce this

reflection as much as possible. The EUV light reflection at the absorber can be

decreased easily by adjusting the thickness. Coupled with the typical ML reflectivity

of 55 to 60% at the DUV wavelengths the considerable reflection on top of the

absorber layer requires the antireflection of the ARC layer to reduce the light

reflection from the top of the absorber. Image contrasts of 75% to 88% can be

achieved using 33nm SiON-ARC. In addition to the low reflectivity at the inspection

wavelength, the ARC needs to have these properties:

Easy to etch with zero etch bias

High etch resistance during buffer etch

Common etch chemistry with absorber etch

Good chemical cleaning durability

Backside Conductive Coating:

Both in-plane distortion (IPD) and out-of-plane distortion (OPD) will occur due to the

residual stress of the ML, buffer layer, absorber layer, and ARC. Since the EUV mask

is a reflective mask, it is possible to chuck the mask from its backside to flatten the

mask (See section 3.2.1- surface requirements), and reduce the distortion affect. The

traditional vacuum chuck will not work in EUV exposure tool, since the wafer

exposure is performed in high vacuum. One possible way is to use an e-chuck

(electrostatic chuck), and this is why a conductive mask backside coating is required.

e-chuck (electrostatic chuck):

48

Taken from: “Determination of local electrostatic forces for EUVL mask chucks”, Gerhard Kalkowskia, Thomas Peschela, Stefan Rissea, Sandra Mullera, Roxann L. Engelstadb,

3.2.4 Shadowing Affect

The mask shadowing effect is a unique problem caused by the combination of oblique

illumination and mask topography. Due to this effect a printed CD bias and position

shift will occur.

Optics illustration of EUV mask shadowing effect.

Taken from: http://palc.postech.ac.kr/research/euv/euv.htm

Compared to the designed mask CD, the mask space features will print smaller and

the line features will print larger. This effect is stronger with increasing thickness of

the absorber stack:

Space CD (Printed) = CD (Designed) - (2d × tan θ) × M

Line CD (Printed) = CD (Designed) + (2d × tan θ) × M

Where the printed CDs are measured at the wafer plane, M is the EUV scanner

reduction factor and θ is the light incident angle to the mask.

49

The shadowing effect can be essentially decreased by reducing absorber height.

However, reduction of absorber height has a side effect that is an increased

reflectivity of a mask black border resulting in field-to-field stray light due to parasitic

reflections. One of the solutions to this problem is optical process correction on field

edges.

3.2.4 Bossung curve asymmetry and focus shift

The analysis maps a control surface for critical dimensions (CD’s) as a function of the

variables of focus and exposure (dose). Most commonly the technique is used to

calculate the optimum focus and dose process point that yields the greatest depth-of-

focus (DoF) over a tolerable range of exposure latitude.

When EUV mask with a given topography is considered, the Bossung curve of a line

at a large pitch is tilted and the best focus is shifted. This focus shift is pitch-

dependent. From the periodic lines to the isolated lines, the focus shift increases as the

pitch increases

L.H.S plot- Bussong curve of 30nm dense lines R.H.S plot- Bussong curve of 30nm dense lines at 200nm pitch

Both plots are for 100nm TaN absorber mask with no buffer Taken from Ref.87 EUV

The maximum focus- shift difference between dense and isolated lines for the TaN

case is as large as 40 nm. When the focus shifts are different between different

50

pitches, the scanner focus adjustment cannot compensate for the focus shift of all the

lines with different pitches. Since the total depth of focus (DoF) is only about 100 nm

in EUVL, a 40-nm focus mismatch between the dense and isolated lines has a big

impact on the total lithographic process window. This focus shift depends on the

buffer and absorber materials.

51

4. Simulation

4.1. System Design

In order to show the difference and system requirements, a simulation using Matlab

software was designed. The system code, build based on the previous chapters in this

document, intends to enable the user to input few EUV variables and receive few of

the system parameters.

System constants:

Illumination angle of 1.5 degree for all ML optical components- including

reticles

ML Mirror reflection constant at 67.5, according to plot in 3.2.2 for incident

illumination angle of 1.5 degree.

ML Mirror reflection is stable on the above value for illumination angle of 0-

13 degrees (according to plot below). This enables more freedom when

designing the system and placing the mirrors.

40 layer for all ML optics with 7 nm period

System Input by user:

K1 and K2- Process dependent constants

System Wave Length in nm

System Numerical Aperture

Number of mirrors in the system

Input LASER energy (W/cm2)

Mounted Mask non flatness in nm

Mask Space and Line designed CDs

Reticle absorber thickness

52

System output:

1. Resolution (nm)- based on calculation demonstrated in 2.1. This size refers to

the best possible half pitch (half the distance between identical features) of a

memory cell.

2. Depth of field- Based on calculations demonstrated in 2.1

3. Power delivered to wafer- Based on calculation in 2.2.1 and reflection table

2.1. Power delivered to the wafer is demonstrated here in (W/cm2) units. In

real systems, the power is represented in Joule (W*Sec), since the system is

scanning the reticle on the wafer and scan time (sec) has a major effect on the

amount of energy on the surface of the wafer.

4. Image placement error (nm) on the wafer- Based on calculations demonstrated

in 3.2.1

5. Printed space CDs (nm)- Based on calculations demonstrated in 3.2.4

6. Printed Line CDs (nm)- Based on calculations demonstrated in 3.2.4

53

System input interface: System Output:

ML Mirror reflection is stable on the above value for illumination angle of 0-13

degrees:

54

Taken from:

http://en.wikipedia.org/wiki/File:EUV_multilayer_reflectivity_vs_angle_and_polarization.pn

g

4.2. Reflectivity in EUV spectral region simulation

The EUV optical components are placed under vacuum in order to reduce the

absorption of energy.

The most commonly used building material for the multilayer optics, are Silicon and

Molybdenum. As presented in 2.3.2, the incident angle of reflection has huge affect

on the system properties, especially since the system must include multiple ML

mirrors to navigate the light to the wafer. Finding the correct angle and the impact on

the component reflection is an important part of the system design.

Using calculation presented at 2.3.2, the reflection of the interface between vacuum

and Si/Mo was simulated.

�̃� = 1 −𝑁𝑎𝑟𝑒𝜆2

2𝜋(𝑓1 − 𝑖𝑓2 )

55

𝑟𝑠 = 𝑛1̃𝑐𝑜𝑠𝛼1 − 𝑛2̃𝑐𝑜𝑠𝛼2

𝑛1̃𝑐𝑜𝑠𝛼1 + 𝑛2̃𝑐𝑜𝑠𝛼2

𝑟𝑝 = 𝑛1̃𝑐𝑜𝑠𝛼2 − 𝑛2̃𝑐𝑜𝑠𝛼1

𝑛1̃𝑐𝑜𝑠𝛼2 + 𝑛2̃𝑐𝑜𝑠𝛼1

𝑅┴ = |𝑟┴ |2 =𝛿2 + 𝛽2

(2 − 𝛿)2 + 𝛽2≈

𝛿2 + 𝛽2

4

In order to calculate the refractive index of the interface, the elements properties

below have been used:

Element Atomic Wight

(amu) Density (g/cm3)

Atomic scattering

factors

Si 28 2.33 0.3069

Mo 95.94 10.28 14.4185

W 183.84 19.25 13.0514

Vacuum-Si reflection for 13.5nm wavelength as a function of the incident angle (log

scale)

56

Vacuum-Mo reflection for 13.5nm wavelength as a function of the incident angle (log

scale)

4.4. Paper Observations and conclusions

1. Resolution and DOF:

As seen in the plot above (resolution and DOF change through wavelength), under

given conditions, resolution and DOF will yield values of around R=40nm and

DOF=140nm.

Like in the DUV based technology, it is possible to achieve up to 1.3 times the

wavelength using some optical improvements (phase shift masks for example)- EUV

systems can print up to 18nm features on the wafers (half pitch). The DOF is

improved compared to DUV systems. This can be seen from the DOF equation- The

NA is now in values of around 0.3 (compared to values of around 1.3 in DUV

immersion based lithography systems).

𝐷𝑂𝐹 =𝑘2𝜆

𝑁𝐴2

57

Medium Wavelength(nm) NA Resolution

(nm) DOF k1,k2

Air 248 0.9 170 200 0.65

Water 193 1.3 70 95 0.65

Vacuum 13.5 0.3 40 140 0.65

2. Number of optical components in the system:

As presented above, the reflectance of a ML optical component in the EUV system

will never be 100%. If the Mo/Si mirror is placed in an angle between 0-13 degrees,

the reflection should be close to 67%. For this reason, using minimum amount of

absorbing optical components to direct the light from the laser source to the wafer is

obvious.

Source Energy (W/cm2)

ML Components

Energy on the wafer (W/cm2)

% decrees

200 1 134.0 33.0

200 2 89.8 55.1

200 3 60.2 69.9

200 4 40.3 79.8

200 5 27.0 86.5

200 6 18.1 91.0

200 7 12.1 93.9

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0 2 4 6 8

ML Vs. Energy on the wafer (W/cm2)

Energy on the wafer

(W/cm2)

58

3. Impact of mounted reticle non flatness on image misplacement:

Transferring the image from the mask to the silicon wafer has to be done in very high

accuracy for obvious reasons. Any deformation or non flatness of the reticle will

reflect as misplacement error on the wafer.

The misplacement on the wafer will grow linearly with the non flatness of the reticle.

For scanner reduction factor of 1:4 and illumination angle of 1.50:

Reticle Non flatness (nm) Wafer Misplacement Error (nm)

0 0

10 0.06

20 0.13

30 0.2

40 0.26

50 0.32

60 0.4

Using the e chuck shown in 3.2.3, which mounts the reticle in large numbers of

vacuum spots, should reduce the reticle non flatness.

4. Impact of shadowing effect on critical dimensions :

Even though, as shown above, the reflectivity of the Mo/Si ML is stable between 0-13

degrees, the printed CDs will be affected.

For scanner reduction factor of 1:4 and absorber thickness of 20nm and mask

designed CDs of 35nm:

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50 60

Wafer MissPlacment Error (nm)

Wafer

MissPlacment

Error (nm)

59

Incident angle (Degrees) Space CDs Space CD % reduction Line CDs Line CD % increase

0 35 0 35 0

1.5 31 -12 39 11

3 27 -24 43 19

5 21 -40 49 29

7 15 -56 55 36

9 10 -72 60 42

11 4 -89 66 47

13 -2 -106 72 51

15 -8 -122 78 55

-140

-120

-100

-80

-60

-40

-20

0

20

40

60

80

1 2 3 4 5 6 7 8 9 10

% C

han

ge

CD % Change Vs. Illum Angle

Line CD % increase

Space CD % reduction

60

4.5 Simulation Code

%EUV ML Reticle Design

close all;

clear all;

%%%%%%%%%%%%%%%%%%%%%%%%System Constants%%%%%%%%%%%%%%%%%%

%Reduction from reticle to wafer=4

% reticle tetha=1.5 degree

%%%%%%%%%%%%%%General Parameters- all in nm

n_air=1;

prompt = {'Enter k1:','Enter k2:','Enter WaveLength (nm):','Enter

NA:','Enter System Mirrors Num','Enter Starting Energy

(W/cm2):','Enter Reticle non flatness (nm):','Enter Designed Space

CDs (nm):','Enter Designed Line CDs (nm):','Enter Reticel Absorber

Thickness(nm):'};

dlg_title = 'System input';

num_lines = 1;

def = {'0.65','0.65','13.5','0.25','5','200','30','40','40','45'};

answer = inputdlg(prompt,dlg_title,num_lines,def);

re=2.82*10^-15*10^9;%radius of electron in nm

k1= str2num(answer{1});

k2= str2num(answer{2});

lambda=str2num(answer{3});

NA=str2num(answer{4});

Mirr=str2num(answer{5});

m=1;

61

tetha=1.5;

%%%%%%%%EUV System

Res=k1*lambda/NA;

DOF=k2*lambda/(NA)^2;

d=m*lambda/(2*cos(tetha));

Ps=str2num(answer{6});

Pw=Ps*0.61^(Mirr);

Zret=str2num(answer{7});

Sysreduct=4;

Plcerr=(1/Sysreduct*tand(tetha)*Zret);

SCDd=str2num(answer{8});

LCDd=str2num(answer{9});

thx=str2num(answer{10});

SCDp=SCDd-(2*thx*tand(tetha)*Sysreduct);

LCDp=SCDd+(2*thx*tand(tetha)*Sysreduct);

h = msgbox({'Resolution ' num2str(Res),'Depth of Field '

num2str(DOF),'Power Deliverd to Wafer (W/cm2) ' num2str(Pw),'Image

Placement Err (nm)' num2str(Plcerr),'Printed Space CDs '

num2str(SCDp),'Printed line CDs ' num2str(LCDp)}, 'Results Based on

input');

%%%%DOF and resolution vs wavelength

lambda=20;

for lambda=20:-0.5:0

Res=k1*lambda/NA;

62

DOF=k2*lambda/(NA)^2;

figure (2);

hold on;grid on;

plot(lambda,Res,'--

sb','linewidth',1,'markersize',4,'markerfacecolor','g');

plot(lambda,DOF,'--

sb','linewidth',1,'markersize',4,'markerfacecolor','r');

xlabel('Wavelength (nm)')

ylabel('resolution and depth of focus (nm)')

legend('Res','DOF')

title('R and DOF for per system requerments through wavelength in

EUV region');

hold off;

end

%EUV Reflection for MoSi ML

close all;

clear all;

%%%%%%%%%%%%%%General Parameters- all in nm

n_air=1;

f1_euv=13.015;%Atomic scatering factores calculated from plots

f2_euv=0.1;%%f1_euv;%at 13.5nm wavlegth

betha_si_euv=0.0025;

Na=63;%mo

re=2.82*10^-15*10^9;%radius of electron in nm

k1=0.75;

63

k2=0.75;

lambda=13.5;

NA=0.25;

m=1;

n=1-(Na*re*lambda^2)*(f1_euv)/(2*pi);%-

i*f2_euv);%0.99;%2.55;%n_air+i*betha_si_euv

tetha=0;

%%%%%%%%EUV System

Res=k1*lambda/NA;

DOF=k2*lambda/(NA)^2;

d=m*lambda/(2*cos(tetha));

alfa1=tetha;

alfa2=asind(n*sind(alfa1)/n_air);

rs=(n*cosd(alfa1)-n_air*cosd(alfa2))/(n*cosd(alfa1)+

n_air*cosd(alfa2));

rp=(n*cosd(alfa2)-n_air*cosd(alfa1))/(n*cosd(alfa2)+

n_air*cosd(alfa1));

r_norm=(n-n_air)/(n+n_air);

R_norm=abs(r_norm)^2;

Rp=(rp)^2;

Rs=(rs)^2;

%%%Reflectivity vs angle

tetha=0;

for tetha=0:1:90

alfa1=tetha;

alfa2=asind(n*sind(alfa1)/n_air);

64

rs=(n*cosd(alfa1)-n_air*cosd(alfa2))/(n*cosd(alfa1)+

n_air*cosd(alfa2));

rp=(n*cosd(alfa2)-n_air*cosd(alfa1))/(n*cosd(alfa2)+

n_air*cosd(alfa1));

r_norm=(n-n_air)/(n+n_air);

R_norm=abs(r_norm)^2;

Rp=(abs(rp))^2*100;

Rs=(abs(rs))^2*100;

hold on;grid on;

plot(tetha,log10(Rp),'--

sb','linewidth',2,'markersize',8,'markerfacecolor','g');

plot(tetha,log10(Rs),'--

sb','linewidth',2,'markersize',8,'markerfacecolor','r');

xlabel('incidence angle')

ylabel('Log scale of Rs,Rp (%)')

legend('Rp','Rs');

%axis([0 90 0:0.001:0.1]);

hold off;

end

65

5. Reference

1. Larry F. Thompson, C Grant Wilson and Murrae J. Bowden “Introduction to Microlithography” .Second Edition. ASC (1994). PP 20-100

2. Vivek Bakshi “EUV Lithography”. SPIE, (2009) PP 1-46, 326,346

3. Jos Benschop “EUV:Status and Challenges Ahead. Inetrnational Workshop on EUVL,

Maui 2010”. ASML (2010)

4. 4.John E.Bjorkhlm “EUV Lithography-The Successor to Optical Lithography?”.

Advanced Lithography Depatment, Thchnology and Manufacturing Group, Santa

Clara, CA. Intel Technology Journal Q3’98.

5. Atsuhiko Kato “Chronology of lithography Milstones” Version 0.9 (2007) 6. Stefan Wurm “EUV Lithography Development and Research Challangr\es of the 22

nm Half Pitch” Journal of Photopolymer Science and Technology Vol.22 (2009).

7. K. L. Blaedel. J. S. Taylor. S. D. Hector, at al., “Vendor capability for thermal expansion mask substrates for EUV lithography,” Proc . SPIE 46X8 767—778 (2002).

8. F. Ruggeberg. T. Leutbecher, S. Kirchner, at al., “Flatness Correction of pol-shed

quartz glass substrates.” in 2nd International Symposium on extreme UV Lithography.

Antwerp, Belgium, Oct. 2003, SEMATECH Inc

9. Bossung Curves; an old technique with a new twist for sub-90 nm nodes-Terrence E. Zavecz – TEA Systems

10. MultiLayer Interface Coating for EUVL Sergiy Yulin

11. Closing the gap for EUV mask repair- T. Breta, R. Jonckheereb, D. Van den Heuvel b, C. Baura, M. Waiblingera, G. Baraliaa bIMEC, Kapeldreef 75, B-3001 Leuven,

Belgium

12. P. B. Mirkarimi, E. Spiller. S. L. Baker, et a), “Developing a viable multilayer coating process for extreme ultraviolet lithography reticles,” j Micrrlith., Microfab., Microsys.

3(l), 139—145 (2004).

13. T. W Barbee, Jr., S. Mrowka. and M. C. Hcttrick, “Molybdenum-silicon multilayer

mirrors for the extreme ultraviolet" App. Opt. 24(6), 883—883 (1985).

14. J. M. Slaughter. D. W. Schulze, C. R. Hills. et at. “Structure and performance ot Si/Mo multilayer mirrors for the extreme ultraviolet.” J. .Appl. Phys. 76(4). 2134—2156

(1994).

15. P - Y. Yan. in handbook of Photomask Manufacturing S. Ri,i. CRC Press/Taylor &

Francis Informa Group, Boca Raton. FL. p. 239 2005).

66

16. Imaging performance improvements by EUV mask stack optimization Natalia Davydovaa, Eelco van Settena, Robert de Kruifa, Dorothe Oorschota, Mircea Dusab,