Ghodssi R., Lin P., MEMS Materials and Processes Handbook

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974 P. Lin e t al.

Table 13.5 Properties of some commercial optical glasses [ 109]

Type n

α (10

−6

/K) T

(

◦

C) d (g/cm

)HKT

BK7 1.51680 1.52283 1.51432 64.17 7.1 559 2.51 520 0.991

K5 1.52249 1.52910 1.51982 59.48 8.2 543 2.59 450 0.984

BaK1 1.57250 1.58000 1.56949 57.55 7.6 602 3.19 460 0.976

SK4 1.61272 1.62059 1.60954 58.63 6.4 643 3.57 500 0.973

KF6 1.51742 1.52492 1.51443 52.20 6.9 446 2.67 420 0.985

SSK4 1.62765 1.62611 1.61427 55.14 6.1 639 3.63 460 0.972

LaK8 1.71300 1.72298 1.70898 53.83 5.6 640 3.78 590 0.950

: index at helium d line (587.5 nm); n

: index at hydrogen f line (486.1 nm)

: index at hydrogen c line (656.3 nm); α: thermal expansion coefﬁcient

: Abbe V-number (reciprocal relative dispersion), V

= (n

− 1)/(n

− n

)

: glass transition temperature; d: density; HK: Knoop hardness

: internal transmittance at 0.4 μm for a thickness of 25 mm

Table 13.6 Properties of some crystalline materials [109]

Material

Transmission

range, nm Index Applications

Crystal quartz (SiO

) 120–4500 1.544 Birefringence

Calcite (CaCO

) 200–5500 1.658 Birefringence

Rutile (TiO

) 430–6200 2.62 Birefringence

Sapphire (Al

) 140–6500 1.834

Strontium titanate (SrTiO

) 400–6800 2.490 IR immersion lens

Magnesium ﬂuoride (MgF

) 110–7500 1.378 IR optics, low reﬂection

coatings

Lithium ﬂuoride (LiF) 120–9000 1.429 Prisms, windows,

apochromatic lens

Calcium ﬂuoride (CaF

) 130–12,000 1.442 Prisms, windows,

apochromatic lens

Barium ﬂuoride (BaF

) 250–15,000 1.512 windows

Sodium chloride (NaCl) 200–26,000 1.791 Prisms, windows

Silver chloride (AgCl) 400–28,000 2.096

Potassium bromide (KBr) 250–40,000 1.590 Prisms, windows

Potassium iodide (KI) 250–45,000 1.922

Cesium bromide (CsBr) 300–55,000 1.709 Prisms, windows

Cesium iodide (CsI) 250–80,000 1.806 Prisms, windows

Silicon (Si) 1200–15,000 3.498 IR optics

Germanium (Ge) 1800–23,000 4.102 IR optics

Zinc selenide (ZnSe) 500–22,000 2.489

Zinc sulﬁde (ZnS) 500–14,000 2.292

AMTIR (Ge/As/Se) 700–14,000 2.606

Gallium arsenide (GaAs) 1000–15,000 3.317

Cadmium telluride (CdTe) 200–30,000 2.307

Magnesium oxide (MgO) 250–9000 1.722

13 Surface Treatment and Planarization 975

Table 13.7 Properties of some optical polymers [109, 110, 177]

Material n

Light

transmitance

(%)

3mm

Deﬂection

temperature

(

◦

C) ASTM

D648

Tensile

Modulus

(MPa)

Density

(g/cm

)

Water

Absorption

(%) 24 h,

◦

Coefﬁcient of

thermal

expansion,

(

−5

)1/k

Suitability for

vacuum

coating

Poly

(methylmetharcrylate)

(Plexiglas 7 N)

1.491 58 92 95 3200 1.19 0.3 6.8 No

Polycarbonate

(Makrolon LQ2647)

1.585 30 91 124 2400 1.2 0.12 6.6 Yes

Polycyclooleﬁn

(Topas 5013)

1.533 58 92 123 3100 1.02 <0.01 6 Yes

Polysulfone

(Udel P-1700)

1.634 23 84 174 2480 1.24 0.3 5.6 Unknown

Polyethersulfon

(Ultrason E2010)

1.65 80 208 2700 1.37 2.1 5.5 Yes

Polyamide

(Trogamid CX 7323)

1.516 45 89 122 1400 1.02 0.3 9 Yes

SU-8 3050 (UV) 1.57 93 200 73 1.15 0.55 5.2 Yes

PMMA (x-ray) 1.491 92 180 3240 1.19 2 6.8 Yes

NOA 63 (UV) 1.56 99 1655 1.2 Unknown

AZ 9620 (UV) 1.07 No

JSR THB-130 N (UV) 1.4 Yes

Photoresist for different spectrum

UV curable material

976 P. Lin e t al.

Wavelen

Index

Absorption band

Fig. 13.31 Index dispersion of an optical material [108]. Reprinted with permission. Copyright

2002 Addison Wesley

of light, E,inthey direction is expressed by the following equation with a complex

refractive index:



E =



−ωn

y/c

iω(t−n

y/c)

(13.20)

where n

and n

are the real and imaginary parts of the refractive index, respectively.

Thus, when the wave progresses into a conductor, the amplitude



−ωn

y/c

is expo-

nentially attenuated and the penetration depth y = c/2ωn

becomes very shallow.

For copper, for example, the penetration depth is about 3 nm when the wavelength

is about 500 nm. Since the incident waves cannot effectively penetrate the material,

bulk metal materials are opaque. However, light can partially penetrate metal when

the metal ﬁlm is thin enough.

For thin ﬁlms, the dispersion equation for metal becomes:

(ω) = 1–

(13.21)

At high frequencies, the free electrons and positive ions in a metal will carry out

many oscillations between each collision and can be thought of as a plasma with a

density oscillating at a natural frequency of ω

= (Nq

/ε

)

1/2

. Therefore, when

the index of the metal becomes complex in the case of ω<ω

the transmission of

the light wave drops off exponentially, and the reﬂection from the surface greatly

increases. In contrast, metal becomes transparent when ω>ω

, e.g. when X-rays

are encountered. Since the index of refraction of a metal is usually complex, incident

light will also encounter a frequency dependent absorption when impinging on a

metal.

13.6.1.2 Fresnel Equation for Reﬂection [108]

Reﬂection from a Dielectric

The relationships between electric ﬁelds for reﬂection and transmission are shown

in Fig. 13.32.

13 Surface Treatment and Planarization 977

→

(a)

→

(b)

Fig. 13.32 The reﬂection and transmission of an electromagnetic wave incident on an optical

material with electrical ﬁeld (a) normal to, or (b) in the plane-of-incidence

The reﬂectance R is deﬁned as

R ≡

Acosθ





= r

(13.22)

where I is the i ntensity of light, r is the reﬂection coefﬁcient, and θ

and θ

are

incident and transmission angles, respectively. The transmittance T is deﬁned as

T ≡

cosθ





cosθ

(13.23)

where t is the transmission coefﬁcient. Assuming no absorption, it can be simply

expressed as R + T = 1. It can also be expressed in component form as

⊥

= r

⊥



sin(θ

− θ

)

sin(θ

+ θ

)



(13.24)

= r



tan(θ

− θ

)

tan(θ

+ θ

)



(13.25)

⊥



cosθ



⊥



cosθ



2sinθ

cosθ

sin(θ

+ θ

)



(13.26)



cosθ





cosθ



2sinθ

cosθ

sin(θ

+ θ

)cos(θ

− θ

)



(13.27)

where r

⊥

, r

are the reﬂection coefﬁcients in the normal/parallel directions and t

⊥

are the transmission coefﬁcients in the normal/parallel directions to the plane-of-

incidence, respectively. The reﬂectance R and transmittance T are functions of the

angle of incidence θ

, angle of transmissionθ

, and the indices of the two media, n

and n

Furthermore, reﬂectance and transmittance also have the following relationship

⊥

+ T

⊥

= 1 and R

+ T

= 1 (13.28)

978 P. Lin e t al.

If the incident light is non-polarized and can be represented by two orthogonal,

incoherent, and equal-amplitude plane polarized light components, the amount of

energy in either of the two states is the same as that in the other. Therefore, the

reﬂectance in natural light, R = I

, becomes

R =

rll

+ I

r⊥

+ R

⊥

) (13.29)

When the incident angle θ

is zero, the reﬂectance and transmittance are

R = R

= R

⊥



− n

+ n



(13.30)

T = T

= T

⊥

+ n

)

(13.31)

Reﬂection from a Metal

When a light wave propagates at some angle to the normal of a high-conductivity

metal surface, the wave fronts align with the surface of constant amplitude. As a

result, in a good conductor the transmitted wave propagates in a direction normal t o

the interface regardless of the incident angle. The reﬂectance R of normal incidence

on a metal becomes:

R =

− n

)

+ n

)

+ n

(13.32)

where n

and n

are the real and imaginary parts of the refractive index.

If the conductivity of the material is zero, i.e. n

= 0, the reﬂectance is the same

as that of a dielectric material. However, in a good conductor, in which n

is large

and n

is small, the reﬂectance is large. For example, at an incident wavelength of

= 589.3 nm, n

and n

for bulk tin are 1.5 and 5.3, respectively, giving an R

value of 0.8. The reﬂectance R is also frequency dependent. For example, gold and

silver can transmit at wavelengths well below 530 and 316 nm, respectively.

13.6.1.3 Principle of Antireﬂection (AR) [108]

Antireﬂection by Thin Film Coatings

Figure 13.33 shows a plot for a linearly polarized light incident on a thin dielectric

ﬁlm (with reﬂective index n

) between two semi-inﬁnite transparent media (n

and

In the case of normal incidence of light, i.e. θ

= θ

tII

= 0, the reﬂectance

can be simpliﬁed to

13 Surface Treatment and Planarization 979

tII

Fig. 13.33 Passage of light

through a thin ﬁlm

− n

)

cos

h + (n

− n

)

sin

+ n

)

cos

h + (n

+ n

)

sin

(13.33)

where k

is 2π/λ

and h is the thickness of the ﬁlm. When k

h = π/2, the optical

thickness h of the ﬁlm is an odd number of quarter wavelengths (h = λ

/4), and the

reﬂectance reduces to

− n

)

+ n

)

(13.34)

If a zero reﬂection from the surface is desired, the required reﬂective index is

√

(13.35)

Thus the ﬁrst and simplest way to create an antireﬂection surface is to choose a

coating material with its index equal to the geometric mean of the top and bottom

media (n

and n

, respectively), and to use a coating thickness of one quarter wave-

length. For an antireﬂection coating layer on a glass plate of index 1.5, the required

index of the AR layer is

√

1 × 1.5 = 1.225. However, this value is much below that

of commonly used low index materials, such as MgF

, which has an index of 1.38.

As a result, a single antireﬂection layer of MgF

cannot thoroughly eliminate reﬂec-

tion from the glass surface. The reﬂectance is around 10%, according to Equation

(13.34) at normal incidence. Multiple layer coatings can be used to further reduce

the reﬂection from the surface. For a double layer (with indices n

and n

for the

ﬁrst and second layers), the reﬂectance at normal incidence becomes:

− n

)

+ n

)

(13.36)

For zero reﬂection, R

must vanish and thus we require:



(13.37)

If the same n

and n

values are used as previously mentioned, n

must equal

1.225. In this case, it is much easier to ﬁnd a proper set of n

and n

instead of

searching for only one value as in the single layer case. The two-layer system is a

980 P. Lin e t al.

(glass)-(high index)-(low index)-(air) system, and the two coating materials may be

selected from many different choices, as shown in Table 13.4. For example, we can

select hafnium oxide (HfO

, n

= 2.05) as the high index material, and aluminum

oxide (Al

, n

− 1.62) as the low index material. The index ratio n

for these

choices is 1.265, much closer to 1.225 than the single layer index of 1.38 (for MgF

)

considered earlier. R

is reduced to 0.107%.

Using a similar concept, one can establish a quarter-wave stack by stacking

a number of quarter-wave layers, such as the (glass)(HL)

(air) system shown in

Fig. 13.34. Here p indicates the number of pairs of stacks. With proper design,

the reﬂectance can be further reduced for broader wavelength regions and incident

angles. The coating can also be tailored for high pass ﬁlters (e.g. attenuating lower

frequencies, such as (glass)(0.5L)(HL)

(0.5L)(air) system) or low pass ﬁlters (such

as (glass)(0.5H)(HL)

(0.5H)(air) system) [111, 112]. An example is also provided

in Section 13.6.2.1.

Antireﬂection by Nano-scale Surface Structures: Moth Eye Structures

In addition to the use of multiple ﬁlm coatings as antireﬂection (AR) layers, the fab-

rication of submicron structures on a dielectric/polymer surface can also effectively

eliminate reﬂective light from the surface in a wide viewing angle and broad spec-

trum [113]. These structures were ﬁrst observed on the eyes of some night-ﬂying

moths, on which thousands of rows of bump-like protrusions around 200–300 nm

in height and pitch are accommodated inside hexagonal sectors [113, 114]. These

nanostructures reduce light reﬂection by creating a refractive index gradient between

the air-eye interface, which can gradually change the light speed from the airside to

the eye side and hence eliminate reﬂection. The low reﬂection from the moth’s eyes

enables the moth to effectively protect itself from predators as it ﬂies in the moon-

light. The moth eye has motivated many AR applications recently, including solar

panels, windows, computer screens, ﬂat-panel displays, vehicle dashboards, and

optical elements [115]. Usually AR structures accompany a hydrophobic surface

(Glass)(HL)(Air)

(Glass)(HL)

(Air)

Fig. 13.34 Stacks of quarter layers for antireﬂection coatings. (a) A double layer quarter

wavelength antireﬂection coating (b) a six-layer antireﬂection coating

13 Surface Treatment and Planarization 981

coating to prevent environmental contamination such as dust, bacteria, and aerosols

[115].

The continuous nanostructures on moth eyes can be modeled as a s tack of many

layers, with each layer having a slightly different refractive index as a result of

the fractional area each layer occupies on the s ubstrate material [116–118], as

shown in Fig. 13.35. In the limit of a continuously varying surface proﬁle, the

nano-scale structures are analogous to a coated ﬁlm with a continuous variation

of index from that of the surrounding medium to that of the underlying substrate.

The nanostructures can also be considered as an impedance matching material at

optical wavelengths [116]. The spacing, depth, and cross-sectional geometry of the

nano-scale layered structures determine the AR properties and the band width for

operation [116–118].

(A)

(B)

gradient-index

(A)

(B)

Fig. 13.35 Model of moth eye structures (a) continuous moth eye nano structure (b) discretized

stacking structure (n

: index of substrate, n

: i ndex of medium, n

: index of each stacking

layer)

Moth eye structures can be designed using different materials for the spectrum

in ultraviolet, visible, or infrared region. Three important rules need to be followed

for the design of effective AR structures [116]. First, to avoid signiﬁcant diffraction

and surface scattering effects, the period (P) of the nano-structures must be smaller

than the shortest wavelength of operation (λ

min

) divided by the index of refraction

of the substrate (n

)[116].

P ≤

min

(13.38)

This means that only the zeroth order reﬂected and transmitted waves can prop-

agate into the substrate with no aberration or distortion. If the pitch is too large,

the structures will behave like a conventional diffraction grating and scatter most of

the light into higher orders. Second, the height (h) of the nano-structures needs to

be at least 40% of the longest operating wavelength λ

max

[116–118]. Note that the

optimum depth is a function of the substrate material index and the reﬂectance will

increase quickly when the depth is larger than λ

max

[117].

0.4λ

max

≤ h ≤ λ

max

(13.39)

982 P. Lin e t al.

This criterion is a rough estimate for cases with light normally incident on a

surface with continuous surface area variation, and might be varied with different

viewing angles, surface structures, and spectrums [116]. Third, the optimal proﬁle

will be close to a pyramid structure with straight or curved sidewalls [116].

13.6.1.4 Principle of Absorption [108, 109]

The transmission of a material usually involves two effects. The surface transmis-

sion T

occurs at the interface and is affected by the reﬂection at the material surface.

The internal transmission T

occurs within the material and is affected by the absorp-

tion of light. The total transmission T of the material can be expressed as the product

of the surface and internal transmissions.

The surface transmission T

can be estimated from Equation (13.31) for nor-

mal incident light. For light transmitting from air into the material, the surface

transmission will be

(n + 1)

(13.40)

The internal transmission, usually correlated to the absorption, can be formulated

= t

(13.41)

where t is the transmission of a unit thickness of material, and x is the thickness. For

example, if a 1 mm thick layer of a material has a transmission efﬁciency of 30%

for red light, a 2 mm thickness of this material will give 0.3

= 9% transmission.

If the light transmitted through the ﬁrst surface of the material is partially trans-

mitted at the second interface, and partially reﬂected and transmitted in the material

several times, the resulting maximum transmission T

max

for a non-absorbing plate

will be:

max

+ 1)

(13.42)

The reﬂection of the uncoated plate of index n will be

R = 1 −T

max

(n − 1)

+ 1)

(13.43)

It is also noted that the transmission of a material is a wavelength-dependent

property, and cannot be treated as a simple value over a large spectrum.

13 Surface Treatment and Planarization 983

13.6.1.5 Surface Plasmon Resonance

A special phenomenon in optical reﬂection called surface plasmon resonance (SPR)

has been reported as a sensitive technique for surface change monitoring [119]. As

mentioned previously, light reﬂects and transmits at the interface of two transparent

media. Total internal reﬂection occurs if the light approaches from the side of high

reﬂective index with an incident angle higher than the critical angle. One popular

setup for SPR, proposed by Krestchmann [120] in 1971, involves depositing a thin

metal ﬁlm on top of a prism, as shown in Fig. 13.36a. As the angle of the incidence

changes, the intensity of the reﬂected light reaches a dip (minimum) at a speciﬁc

angle called the SPR angle (Fig. 13.36b). This minimum occurs when photons of p-

polarized light interact with the free electrons of the metal layer, introducing charge

density oscillations (called plasmons) and thus reducing the intensity of the reﬂected

light. Surface plasmons (or surface plasmon polaritrons, SPP) are surface electro-

magnetic waves that propagate in parallel along a metal/dielectric interface. When

a light beam impinges onto a metal ﬁlm at a speciﬁc (resonance) angle, the surface

plasmons are set to resonate with the light. The fully reﬂected beam leaks an electri-

cal ﬁeld intensity (i.e. evanescent ﬁeld wave) a short distance (tens of nanometers)

into a medium of a lower refractive index (Fig. 13.36a).

SPR has been shown to be sensitive to very low levels of material adsorbed onto

a surface (much less than a monolayer). Typical metals that support surface plas-

mons are silver and gold. A SPR-based biomolecular interaction monitoring system

was ﬁrst demonstrated by Liedberg [122]. The monitoring of the surface plasmon

Angle

TIR

SPR

angle

Reflectivity

SPP

Metal

Laser light

Air or water

Electric field

amplitude

Detector

(A)

(B)

Metal

Glass

Fig. 13.36 Reﬂectivity of the

exciting beam for surface

plasmon resonance [ 121];

(a) schematic drawing of SPR

measurement setup; (b)the

reﬂectivity. Reprinted with

University Press, Cambridge