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SEMI E78-1102 © SEMI 1998, 2002 17 at a distance r = R from the center of the wafer. R1-2.2.2.4 For a co nductive wafer, or for a wafer with localized regions of charge, the electric field will vary over the surface, cau…

SEMI E78-1102 © SEMI 1998, 2002 16

a charged particle by a charged surface. This is the only

electrostatic effect considered here.

For particles of one diameter, d, and one charge, q, the

particle deposition flux, j, (the number of particles

deposited per unit area per unit time) is the product of

aerosol particle number concentration, c; particle

charge, q; the electric field created by the charged

wafer, E; and particle mechanical mobility, B (terminal

velocity per unit external force):

j = cqEB (1

)

The group qEB is the “electrostatic deposition

velocity”, v

elect

= qEB =

c (2)

The variables q and E are those containing the electrical

parameters that affect the magnitude of v

elect

; B depends

on particle diameter but not electrical properties.

It is the v

elect

values that will be calculated for

comparison with those of v

diff

, the particle deposition

velocity attributable to particle diffusion. Values of E

for which v

elect

< v

diff

will be those deemed tolerable in

wafer manufacturing.

Note that the total number of particles, N, deposited on

a wafer, obtained by integrating Equation (1) over the

wafer area, A, and the time of exposure, t, depends on c

as well as the deposition velocity:

= cqEBAt o

= ctv

elect

(3)

Reducing c obviously reduces N, but the relative

importance of the differing deposition mechanisms and

the values of the deposition velocities associated with

these mechanisms are assumed to not depend upon c, at

least to a first-order approximation (see, for example,

Peters and Cooper, 1991).

R1-2.2.1 Effect of the Particle Charge, q — There are

many charging and discharging mechanisms for

particles, so q is hard to predict and likely to be highly

variable. In a normal atmosphere the positive and

negative air ions tend to have roughly equal

effectiveness in charging particles, so that the number

of positively charged particles is roughly equal to the

number of negatively charged particles. Thus, about

half the particles will be attracted and half repelled by a

net charge on the wafer. Special circumstances, such as

corona discharge ionizers that are not balanced, could

alter this conclusion. Without ionizers, cleanrooms tend

to have relatively low levels of ions compared to the

outdoor or other indoor atmospheres, because the

HEPA/ULPA filters efficiently remove ions from the

recirculating air.

R1-2.2.1.1 A Boltzmann charge equilibrium, the

charge distribution approximated by aerosol particles

exiting a radioactive neutralizer, is a plausible lower

limit for particle charge and will be assumed in the

calculations of v

elect

, using an improved version of this

distribution developed by Fuchs (1964). Upper limits

on particle charge are determined by ion emission limits

or, in the case of water droplets, the Rayleigh limit.

However, assuming higher particle charge distributions

usually means that v

elect

> v

diff

for virtually any value of

E > 0 and that the only method for avoiding

electrostatically enhanced particle deposition is to

reduce wafer charge to zero. Thus, the Fuchs charge

distribution will be assumed in calculating v

elect

even

though it represents the most favorable particle charge

distribution for minimizing electrostatically enhanced

particle deposition. Under many practical circumstances

the particle charge will be greater and the maximum

tolerable electrostatic field will be lower than that

calculated for the Fuchs charge levels.

R1-2.2.2 The Electrostatic Field, E, Induced by the

Wafer Surface Charge — The electrostatic field will

depend on the charge on the wafer divided by a quantity

with the units of length squared; either a distance

squared (far from the wafer) or an area (close to the

wafer) or some combination at intermediate distances.

While field is not properly measured as a voltage,

measuring the voltage, V, at a fixed distance, s, from the

wafer allows inferring the field from V/s and the

appropriate geometric and dimensional factors. The

electrostatic field to be used in Equation (2) can be

estimated from the ratio of the wafer charge to the

wafer surface area, or the average field near the surface

at the center, E

R1-2.2.2.1 Very far from the wafer, many wafer

diameters away, the field created by the net wafer

charge, Q, will be similar to that from a point charge:

= k

(4)

where k

depends on the system of units used; and r is

the distance from the center of the wafer to the particle.

R1-2.2.2.2 Very close to the wafer, a fraction of a

wafer diameter away, the field created by the net wafer

charge is:

= k

′ Q r

(5)

where Q' is the net wafer charge, assumed to be

uniformly distributed, contained within the intersection

of a sphere of radius, r, and centered on the point of the

wafer closest to the particle.

R1-2.2.2.3 This equation indicates that the charge

distribution on the wafer can make a difference close to

the wafer. For an insulating wafer with a uniform

charge and a radius, R:

= E

= k

(6)

SEMI E78-1102 © SEMI 1998, 2002 17

at a distance r = R from the center of the wafer.

R1-2.2.2.4 For a conductive wafer, or for a wafer with

localized regions of charge, the electric field will vary

over the surface, causing greater and lesser deposition

velocities. A conductive wafer will have the charge

concentrated near the edges, producing a relatively high

field there and much lower fields as the center is

approached.

R1-2.2.2.5 Note that both E

and E

are proportional to

Q and therefore, other variables being equal,

electrostatic deposition is expected to be proportional to

Q. Thus, the criterion to be specified is not the tolerable

charge on the wafer but the tolerable electrostatic field

near the wafer surface (such as that evaluated at a

distance of one radius perpendicular to the wafer

surface above its center), E

. A maximum tolerable

value of E

will be estimated by calculating the

maximum E

values for which v

elect

< v

diff

, assuming a

Fuchs distribution for the particle charge.

R1-2.3 Tolerable Electrostatic Field

R1-2.3.1 Particle Deposition Velocity Attributable to

Convective Diffusion (vdiff) — In a microelectronics

cleanroom, airflow is generally laminar

(“unidirectional”) downward at about 50 cm/sec (100

ft/min). If the flow is perpendicular to a surface, such as

a wafer of diameter, Dw, a boundary layer forms across

which particles diffuse to the surface. Liu and Ahn

(1987) adapted the correlation of Sparrow and Geiger

(1985) and obtained a correlation for the average

diffusive deposition velocity as:

diff

= 1.08 Sc

D * D

(7)

where Sc =

D * is the Schmidt Number

is the gas viscosity

is the gas density

and D*= kTB is the particle diffusivity

k is the Boltzmann constant

T is the absolute temperature and

B is the particle mobility

and Re =

is the Reynolds number

U is the gas velocity and

is the wafer diameter

Bae et al. (1994) reviewed the experimental work of

others and presented their own, supporting this

correlation; Cooper et al. (1990) obtained a similar

equation by a somewhat different method. Oh et al.

(1996) summarized prior experimental and theoretical

work and extended the numerical analysis with a

turbulent transport properties model, finding a small

increase in deposition for the conditions modeled.

These authors’ publications support the approximation

that the diffusional deposition velocity is about 0.006

cm/sec at particle diameter of 0.25 µm and about 0.03

cm/sec at particle diameter of 0.01 µm, or:

diff

(0.03 cm / sec)/(d /0.01

(8)

for 0.01 µm ≤ d ≤ 0.3 µm in cleanroom air.

R1-2.3.2 Particle Deposition Velocity Attributable to

Electrostatic Forces (v

elect

) — Using a power law to

approximate the Fuchs particle charge distribution

yields the following approximation for electrical

mobility (Cooper et al., 1990):

(0.002 cm /

)/(d /0.01

m)(1 V / cm) (9)

from which the deposition velocity attributable to

electrostatic forces becomes:

elect

(0.002 cm

)[

cm)]/(d

0.01

m) (10)

Setting v

elect

diff

= 1 results in the following expression

for tolerable E

[(E

/(V /cm)]

15 [d /(0.01

m)]

(11)

Table R1-2 lists the values of tolerable electrostatic

field adjacent to a wafer surface as calculated from

Equation (11). Note that the electrostatic fields are

calculated at a distance of one wafer radius from the

center of the wafer. E

is the value of electric field at

which electrostatically enhanced particle deposition is

estimated to match the particle deposition velocity

attributable to diffusion, assuming a Fuchs charge

distribution on the particles. This charge distribution

represents a minimal particle charge. With most particle

charge distributions to be encountered in practice, even

lower values of electrostatic fields will produce

enhanced deposition. A safe conclusion is that there is

no safe value of electrostatic field that will avoid

enhanced particle deposition unless neutralization of

particle charge has been achieved, in which case the

very modest values of electrostatic fields calculated

from Equation (11) and tabulated in Table Rl-2 should

be tolerable.

SEMI E78-1102 © SEMI 1998, 2002 18

Table R1-2 Tolerable Levels of Electrostatic Field at

a Distance of One Radius from the Center of a

Wafer, Assuming a Fuchs Charge Distribution on

the Particles

Minimum Particle Diameter d in

µm

Tolerable Field E

, in

Volts/cm

0.01 15

0.02 21

0.03 26

0.05 34

0.10 47

0.20 67

0.30 82

R1-2.4 Conclusions — As indicated in Table R1-2, the

calculated value of tolerable electrostatic field (the

value of electrostatic field above which electrostatic

particle deposition becomes the dominant mechanism

of particle deposition) is just 47 V/cm for particles of

0.1 µm diameter when the particle electrical charge is

that described by the Fuchs charge distribution, a

minimum value of particle charge that is normally

exceeded in most environments. In most realistic

environments the particle charge will be greater and the

tolerable electrostatic field, even lower. Hence the

conclusion that in all practical processing environments

electrical forces will be the dominant mechanism of

particle deposition on wafers.

R1-2.4.1 In a Federal Standard 209E Class 1

environment (c ≤ 0.00124 particles/cm

) with v

elect

, ~

0.01 cm/s (the value predicted by Equation 10 for a 0.1

µm particle in an electric field of 47 Volts/cm) the

target areal particle densities (N/A = 0.016 particles/cm

for the 0.25 µm technology of 1998) specified in the

National Technology Roadmap for Semiconductors

(NTRS, 1994) will be reached after an exposure time of

about 1300 seconds, assuming c is at its maximum

allowed concentration.

R1-2.4.2 With less favorable electrical conditions, or

higher particle concentration, the maximum allowed

exposure time becomes shorter. In addition, the target

values for N/A continue to decrease with each

technology generation. Fortunately, one or more of the

parameters, particle concentration in the ambient, the

charge level on a surface, or the time a charged surface

is exposed to a given particle ambient, can be

controlled.

R1-2.4.3 Charge Neutralization — Achieving the

Fuchs charge distribution by means of radioactive

isotopes or balanced corona neutralizers — is the first

step in controlling particle deposition on wafers. This

step, while clearly necessary, is unlikely to be sufficient

to guarantee meeting the NTRS requirements of the

future. Steps to minimize environmental particle

concentration, c, and time of exposure, t, will have to be

part of the strategy for creating acceptable processing

environments. Minimizing these variables reduces

particle deposition attributable to all mechanisms, not

just electrostatic deposition.

R1-2.4.4 Contemporary standards recognize the need

for reduced particle concentrations in wafer

environments. For example, the classification ISO Class

1 (of the proposed international standard for classifying

cleanrooms according to concentration of airborne

particulate cleanliness) describes an environment in

which the concentration of particles > 0.1 µm is 10

-5

particles/cm

or less. In an environment of this quality,

wafer exposure can be as long as 10

seconds at the

deposition velocity predicted for neutralized 0.1 µm

particles (~0.01 cm/s) and still meet the target defect

density that the NTRS recommends for the 0.1 µm

technology anticipated in 2007. Fractional increases in

the electric field above 47 Volts/cm will decrease the

allowed exposure time by that same fraction (Equations

10, 12) — an electric field of 94 Volts/cm reduces the

allowed exposure time to 5 × 10

seconds, etc.

R1-2.5 References

Bae, G.N., Lee, C. S., and Park, S. O., “Measurement of

Particle Deposition Velocity Toward a Horizontal

Semiconductor Wafer by Using a Wafer Surface

Scanner”, Aerosol Science Technology 21: p. 72–82

(1994)

Cooper, D. W., Miller, R. J., Wu, J. J., and Peters, M.

H., “Deposition of Submicron Aerosol Particles During

Integrated Circuit Manufacturing: Theory”, Particulate

Science Technology 8 (3 and 4): p. 209–224 (1990)

Fuchs, N. A., The Mechanics of Aerosols, Pergamon

Press, Oxford (1964)

Liu, B. Y. H., and Ahn, K. H., “Particle Deposition on

Semiconductor Wafers”, Aerosol Science Technology 6:

p. 215–224 (1987)

National Technology Roadmap for Semiconductors,

Semiconductor Industry Association, 4300 Stevens

Creek Boulevard, Suite 271, San Jose, CA 95129, 1994

Oh, M. D., Yoo, K. H., and Myong, H. K., “Numerical

Analysis of Particle Deposition onto Horizontal

Freestanding Wafer Surfaces Heated or Cooled”,

Aerosol Science Technology 25: p. 141–156 (1996)

Peters, M. H., and Cooper, D. W., “Approximate

Analytical Solutions for Particle Deposition in Viscous

Stagnation-Point Flow in the Inertial-Diffusion Regime

with External Forces”, J. Colloid Interface Science

142(1): p. 140–148 (1991)