Photolithography: The Basics of Projection Printingnanocad.ee.ucla.edu/pub/Main/SnippetTutorial/AerialImage...Photolithography Photolithography is at the Center of the Wafer Fabrication

Photolithography:The Basics of Projection Printing

Photolithography

Photolithography is at the Center of the Wafer Fabrication Process

*

Thin Films

Implant

Diffusion Etch

Test/Sort

Polish

PhotoPatterned

wafer

Photolithography Types

Projection System

Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007

4

Light Source

Condenser Lens

Mask

Objective Lens Wafer

Block diagram of a generic projection imaging system

Projection System


5

Light Source

Condenser Lens

Mask


Illumination System Illumination system delivers light to the maskSufficient intensityProper directionalityProper spectral characteristicsAdequate uniformity across the field

Projection System


6

Light Source

Condenser Lens

Mask


Illumination System

Maskchanges the transmittance of the lightCauses diffraction

Diffraction

Projection System


7

Light Source

Condenser Lens

Mask


Illumination System

Objective lensPicks up a portion of the diffraction patternProjects the image onto the photoresist

Image Formation

Diffraction Analysis


8

Light Source

Condenser Lens

Mask


Illumination System

Maskchanges the transmittance of the lightCauses diffraction

Diffraction

Diffraction

• Theory of propagation of light

– Solution to Maxwell’s Equations: complicated

• Diffraction Integrals for far field: simpler

– Light propagation in homogenous medium

Fresnel Diffraction

Region

(z » w)

Kirchhoff Diffraction Region

(z > /2)

Fraunhofer Diffraction

Region

(z » w2/)

Fraunhofer Diffraction Integrals

Fraunhofer Diffraction Integral

Mask Transmittance Function:

• How does the mask transmit light?

• Requires the solution of Maxwell’s equations for that material: complicated!

Kirchhoff boundary condition

• Feature size > 2λ && chrome thickness < λ/2

• Ignore diffraction caused by mask topography

),( yxtm

chrome 0

regionnt transpare 1),(

yxtm

Fraunhofer Diffraction Integral

mask at theincident field Electric : ),(

function mittancemask trans : ),(

medium theofindex refractive :

planen diffractio mask to from distance :

light ofh wavelengt:

planen diffractio :plane ''

planemask : plane

yxE

yxt

n

z

yx

yx

Given

m

dxdyeyxtyxEffTyfxfi

myxmyx )(2

),(),(),(

z

nyf

z

nxf

ff

ffT

where

yx

yx

yxm

',

'

patternn diffractio of sfrequencie Spatial : ,

patternn diffractio theof field Electric : ),(

Fourier OpticsThe diffraction pattern is just the fourier transform of the mask pattern transmittance!

)),(),((),( yxtyxEFffT myxm

Diffraction Examples


12

fx 0 0

mask

0 1

Tm(fx)

tm(x)

Two typical mask patterns, an isolated space and 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.

x

xxm

f

wffT

)sin()(

j

x

x

xxm

p

jf

f

wf

pfT )(

)sin(1)(


13

0.0

0.2

0.4

0.6

0.8

1.0

-3 -2 -1 0 1 2 3

w fx

Inte

nsi

ty

Magnitude of the diffraction pattern squared (intensity) for a single space (thick solid line), two spaces (thin solid line), and three spaces (dashed lines) of width w. For the multiple-feature cases, the linewidth is also equal to w.

Image Formation: Imaging Lens


14

Light Source

Condenser Lens

Mask


Illumination System

Objective lensPicks up a portion of the diffraction patternProjects the image onto the photoresist

Image Formation

Imaging Lens

• The diffraction pattern extends throughout the x’-y’ plane

• The objective lens (finite size) can only capture a part of this pattern

– Higher spatial frequencies lost

16

Aperture

(x’, y’)-plane

Object Plane

max

Objective Lens

Entrance Pupil

maxsinnNA

NA

p

n

z

nyf

n

z

nxf

y

y

xx

min

1

sin'

sin'

NA/λ : The maximum spatial frequency that can enter the lensLarge NA => larger portion of diffraction pattern is captured => better image

NAKR

1

Formation of the Image

• Lens Pupil Function

– Mathematical description of the amount of the light entering the lens

• Lens performs the inverse fourier transform of the transmitted diffracted pattern

NAff

NAffffP

yx

yxyx

22

22

,0

,1),(

),(),(),(

),(),(

1

yxyxM ffPffTFyxE

yxgyxgFF

18

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

-w -w/2 0 w/2 w

Horizontal Position

Re

lative

In

ten

sity

N = 1

N = 3

N = 9

Aerial images for a pattern of equal lines and spaces of width w as a function of the number of diffraction orders captured by the objective lens (coherent illumination). N is the maximum diffraction order number captured by the lens.

PSF: Point Spread Function

• Means of characterizing the resolving capability of an imaging system

• Normalized image of an infinitely small contact hole

NANAR

JPSF

rNA

JffPFyxE

ffTyxt

ideal

yx

yxmm

7.0 to66.0

)2(

)2(),(),(

1),()0,0(),(

2

1

11

0.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Normalized Radius = rNA/

0.2

0.4

0.6

0.8

1.0

No

rma

lize

d I

nte

nsity

Oblique Illumination

• Plane wave strikes at an angle ϴ’

– Phase differs for different points on mask

• Shift in the position of the diffraction pattern

NA

kR

ffPffffTFffyxE

f

eyxE

yxyyxxmyx

x

xi

2

)},()','({)',',,(

'sin'

),(

1

1

'sin2

Diffraction Pattern

Lens Aperture

Mask Pattern (equal lines and spaces)

Photolithography: The Basics of Projection Printingnanocad.ee.ucla.edu/pub/Main/SnippetTutorial/AerialImage...Photolithography Photolithography is at the Center of the Wafer Fabrication

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