Figure 2.1 Block diagram of a generic projection imaging system

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

1

Light Source

Condenser Lens

Mask

Objective Lens Wafer

Figure 2.1 Block diagram of a generic projection imaging system.


2

Diffraction by a Slit Plane Wave Propagation

Figure 2.2 Pictorial representation of Huygens’ principle, where any wavefront can be thought of as a collection of point sources radiating spherical waves.


3

Fresnel Diffraction

Region (z » w)

Kirchhoff Diffraction Region

(z > /2)

Fraunhofer Diffraction

Region

(z » w2/)

Figure 2.3 Comparison of the diffraction ‘regions’ where various approximations become accurate. Diffraction is for a slit of width w illuminated by light of wavelength , and z is the distance away from the mask.


4

fx 0 0

mask

0 1

Tm(fx)

tm(x)

Figure 2.4 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.


5

0.0

0.2

0.4

0.6

0.8

1.0

-3 -2 -1 0 1 2 3

w fx

Inte

nsi

ty

Figure 2.5 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.


6

Aperture

(x’, y’)-plane

Object Plane

max

Objective Lens

Entrance Pupil

Figure 2.6 The numerical aperture is defined as NA = nsinmax where max is the maximum half-angle of the diffracted light that can enter the objective lens, and n is the refractive index of the medium between the mask and the lens.


7

Objective Lens

Mask (Object)

Wafer (Image)

Entrance Pupil

Exit Pupil

Figure 2.7 Formation of an aerial image: a pattern of lines and spaces produces a diffraction pattern of discrete diffraction orders (in this case, three orders are captured by the lens). The lens turns these diffraction orders into plane waves projected onto the wafer, which interfere to form the image.


8

fx

Am

plit

ud

e

0 p

1p

2

p3

p1

p2

p3

0.5

Figure 2.8 Graph of the diffraction pattern for equal lines and spaces plotted out to ±3rd diffraction orders. For graphing purposes, the delta function is plotted as an arrow, the height equal to the amplitude multiplier of the delta function.


9

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

lativ

e In

ten

sity

N = 1 N = 3 N = 9

Figure 2.9 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.


10

Figure 2.10 Ideal point spread function (PSF), the normalized image of an infinitely small contact hole. The radial position is normalized by multiplying by NA/.

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 N

orm

aliz

ed

In

ten

sity


11

m

Entrance Pupil

Refractive index on mask side = nm

Refractive index on wafer side = nw

Exit Pupil

Aperture Stop

w

Figure 2.11 An imaging lens with reduction R scales both the lateral dimensions and the sine of the angles by R.


12

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.2 0.4 0.6 0.8 1.0

sin(angle)

Pu

pil

Tra

nsm

ittan

ce

Figure 2.12 A plot of the radiometric correction as a function of the wafer-side diffraction angle (R = 4, nw/nm = 1).


13

1.00

1.04

1.08

1.12

1.16

1.20

1.24

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Wa

fer

Pla

ne O

pe

n F

ield

In

ten

sity

Partial Coherence

0.9

Figure 2.13 One impact of the radiometric correction: the intensity at the wafer plane for a unit amplitude mask illumination as a function of the partial coherence factor (R = 4, NA = 0.9).


14

Diffraction Pattern

Lens Aperture

Mask Pattern (equal lines and spaces)

Figure 2.14 The effect of changing the angle of incidence of plane wave illumination on the diffraction pattern is simply to shift its position in the lens aperture. A positive illumination tilt angle is depicted here.


15

Mask Pattern (equal lines and spaces)

Diffraction Pattern

Lens Aperture

Figure 2.15 The diffraction pattern is broadened by the use of partially coherent illumination (plane waves over a range of angles striking the mask).


16

-1st 0th +1st

Lens Aperture

-1st 0th +1st

Lens Aperture

Figure 2.16 Top-down view of the lens aperture showing the diffraction pattern of a line/space pattern when partially coherent illumination is used: a) = 0.25; and b) = 0.5.

(a) (b)


17

-1st order +1st order 0th order

Figure 2.17 Example of dense line/space imaging where only the zero and first diffraction orders are used. Black represents three beam imaging, lighter and darker grays show the area of two beam imaging.


18

Quadrupole Annular Conventional Dipole

Figure 2.18 Conventional illumination source shape, as well as the most popular off-axis illumination schemes, plotted in spatial frequency coordinates. The outer circle in each diagram shows the cut-off frequency of the lens.


19

-1.0 -0.5 0.0 0.5 1.0 -1.0

-0.5

0.0

0.5

1.0

X Pupil Position

Y P

upil

Pos

itio

n

-1.0 -0.5 0.0 0.5 1.0 -1.0

-0.5

0.0

0.5

1.0

X Pupil Position Y

Pup

il P

ositi

on

(a) (b)

Figure 2.19 Examples of measured annular source shapes (contours of constant intensity) from two different lithographic projection tools showing a more complicated source distribution than the idealized ‘top-hat’ distributions.


20

+1st order -1st order

Lens Pupil

Figure 2.20 Annular illumination example where only the 0th and ±1st diffracted orders pass through the imaging lens.


21

Mask

Mask

Illumination Wavefront

Objective Lens

(a) (b)

Figure 2.21 The impact of illumination: a) when illuminated by a plane wave, patterns at the edge of the mask will not produce diffraction patterns centered in the objective lens pupil, but b) the proper converging spherical wave produces diffraction patterns that are independent of field position.


22

Mask

Entrance Pupil

Objective Lens

Source

Figure 2.22 Köhler illumination where the source is imaged at the entrance pupil of the objective lens and the mask is placed at the exit pupil of the condenser lens.


23

fx 0 f

NA

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

f/(2NA/)

MT

F

(a) (b)

Figure 2.23 The MTF(f) is the overlapping area of two circles of diameter NA/ separated by an amount f, as illustrated in a) and graphed in b).


24

X Position (nm)

-1000 -500 0 500 1000

-600

-400

-200

200

400

600

0

Y P

ositi

on (

nm

)

-1000

-500

500

1000

0 Y

Posi

tion (

nm

)

X Position (nm)

-1000 0 1000

Figure 2.24 Some examples of two-dimensional aerial image calculations (shown as contours of constant intensity), with the mask pattern on the left (dark representing chrome).


25

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

-0.8 -0.4 0.0 0.4 0.8 1.2 1.6

Horizontal Position (xNA/)

Re

lativ

e In

ten

sity

= 0 = 0.3 = 0.6 = 0.9

Figure 2.25 Aerial images of an isolated edge as a function of the partial coherence factor.

Documents

Figure 2.1 Block diagram of a generic projection imaging system