"Electron Beam Evaporation" in "Handbook of Thin Film Process Technology" [2]

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Introduction and General Discussion

t

A l.O Introduction and General Discussion EB Graper Al.0.0

INTRODUCTION

Thin films, invisibly thin on edge, are at the core of integrated circuits, materials technology, optics and communications. The process for deposition of thin films underlies the production of a vast range of consumer products. This deposition technology is a mix of applied science and art with physics at its core. Understanding, practical application and seldom published technology are the focus of this work.

Al.0.1

VACUUM ENVIRONMENT

The physical vapour deposition processes of interest in this handbook all take place in a vacuum. The vacuum environment is a complex one and is neither a void nor inert. To be successful, thin film deposition must be done with awareness of the effect of the environment upon the vapour flux and growing film. A general understanding of vacuum is of importance and the literature is extensive, most finding its roots in the classic work by Duschman and Lafferty [l]. The three most important aspects of the vacuum environment to thin film deposition are: the pressure, expressed as the mean free path (MFP), the partial pressure of reactive gasses in inert working gasse& Ｎ ［Ｌｩｮ､ ｾ ｴ ｨ ･＠ ｦｩ ｟ ｾｩｮ ｾ＠ ｶ Ｎ ｡Ｌｰｯｵｾ Ｎ＠ ｦｩｬＡｉｶｾ Ｈ ｴｰ Ｎ＠ ｾ ｾｓ ｾｶ･＠ ｾ ｧ｡ｳ＠ impfogement rate ratio. These aspects of vacuum are tabulated against absolute pressure in table 1. Each of these aspects of vacuum has a direct effect on thin film deposition. From table 1 it is seen that at about 1 x 10-5 Torr the mean free path is 5 m or about ten times the usual source to substrate distance for evaporated thin film deposition. This means that at about 1 x 10-5 Torr about 5% of evaporant atoms will undergo a collision during their travel from the source to the substrate giving up energy, being scattered and perhaps reacting with the residual gas, usually water vapour. The mean free path is a particularly significant consideration when scaling up vacuum processes and should be at least ten times the source to substrate distance. When source to substrate distance is increased, the pressure must be decreased proportionally or the evaporant will have more interactions with the residual gas in the vacuum chamber. Table Al.0.1. The effect of vacuum pressure on film vapours. The pressure may be taken as either the total pressure or the reactive gas partial pressure during sputtering.

Pressure (Torr)

Mean free path

Arrival rate ratio*

1010-2 10-3 10-4 10-s 10-6 10-1 10-s 10-9

0.5 mm 5 mm 5 cm 50 cm 5m 50 m 500 m 5 km 50 km

0.0001 0.001

1

O.Ql

0.1 1 10

100 1000 10000

* The ratio of molecular film vapour arrival at 10 the molecular impact rate of the residual gas.

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Als to

Handbook of Thin Film Process Technology

Al.0: 1

Thermal Evaporation

The second significant pressure consideration is the arrival rate ratio: as a film is growing, it is also being bombarded by residual gas. The ratio tabulated is the molecular arrival rate ratio of film vapour at 10 Als to that of residual gas molecules. When this ratio is unity each atom of film is accompanied by one of residual gas. Though the reaction probability of this gas is on the order of 0.1 it is obvious that it is desirable to have significantly more evaporant film vapour arriving at the substrate surface than potentially contaminating gas. In evaporation this residual gas is the total chamber pressure and is predominantly water vapour. In sputtering, the working gas represents nominally 99.9% (10- 3 Torr Ar, with a residual contaminant pressure of 1o- 6 ) of the total pressure. The effect of the residual contaminant pressure on films during sputtering is as severe or more so, as is the total chamber pressure during evaporation because much of the gas is ionized, making it more reactive. Unfortunately, an expensive and complex residual gas analyser with a UHV pressure reducing inlet is necessary to measure this extremely important pressure. The arrival rate ratio can be improved by either reducing the pressure or increasing the film deposition rate. Particular care must be taken when scaling up a process by increasing the source to substrate distance because the deposition rate will fall as the square of the distance. This means increasing the source to substrate distance from 16 in (40 cm) to 25 in (63 cm) requires doubling the deposition rate to maintain the arrival rate ratio (or halving the pressure). Using table 1 the maximum deposition pressure can be established for a thin film process based upon its sensitivity to residual gas. Maintaining film purity during growth of films by MBE, typically done at 10-9 Torr or lower, requires an exceptionally low pressure because of the low (0.1 Als) deposition rate. Maintaining high film purity when sputtering with Ar working gas at 10- 2 Torr and a arrival ratio of 10 requires the total reactive gas partial pressure to be below 10-6 Torr (table 1) during deposition.

Al.0.2

THE VAPORIZATION PROCESS

Vacuum thin film deposition processes generate a source of vapour flux of the desired film material to be condensed upon a substrate. Vaporization of a solid or liquid material is the process of changing its phase to a vapour, driven by the input of energy. Thin film deposition sources are the means to bring about this phase change. The energy input required for vaporization is identical for sputtering and evaporation though the energy sources are very different. The vaporization energy, delivered by the vaporization process consists of the following components. ( 1) Latent heat, the heat necessary to raise the temperature (energy) of the material to that where phase change can occur.

(2) Phase change heat, the heat of vaporization and the heat of fusion (for melting materials). This energy is the dominant energy required for vaporization. (3) Kinetic energy imparted to the vapour in excess of the minimum necessary for phase change. The microscopic process of evaporation, to be rigorously considered, must be understood from a statistical thermodynamic perspective. This is best done by referring to the extensive literature [1]. An important intuitive understanding of vaporization can be developed from two different perspectives depending upon the means of energy input. The first is evaporation and the second sputtering. The ｾｙ Ｎ ｾｰｯ Ｌ ｾｴｩＹＮｮ＠ ｐＮ｜ＺＹｾ Ｍ ･ＬｾＦ Ｌ＠ Ｈｾ＠ the pbas1 .change, using heat, of a solid to a vapour, as occurs in boiling. The difference between vacuum evaporah-on and boiling is that the boiling point is defined as the temperature at which the phase of a material changes from a liquidto a gas at one ｡ｴｲｮｯｳｰｾ･Ｙｦ＠ ｰｲ･ｳＱＺｾＮ Ｌ＠ In thin film · 15·ori "file 'order of-6. i -.:1 ｔｾｲ＠ depending evaporation the pressure of vapour over the' evaporanis ｾｲｦ｡｣･＠ upon the evaporation rate when the phase change occurs. The temperature is therefore much reduced from the boiling point (i.e. Al boils at 2300°C and evaporates at 1080°C at I Torr). From tabulated vapour pressure tables and equations [2] the approximate evaporation temperature of many materials can be determined. The thermal evaporation of a material requires the addition of the heat of fusion and heat of vaporization, and latent heat (for Al heat of fusion = 270 cal/cm 3 , heat of vaporization = 78 kcal cm3 ) and the thermal kinetic energy supplied to the evaporant by the electron beam or hot refractory metal

A 1.0:2

Handbook of Thin Film Process Technology

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1995 IOP Publishing Ltd

Introduction and General Discussion

source. The latent heat and kinetic energy are negligible. Upon condensation this energy is given up to the substrate and represents the principal source of substrate heating [3]. The evaporation temperature determines the median kinetic energy of the evaporant (1000°C = 0.2 eV and 2000°C = 0.4 eV). This energy is a measure of the velocity of the evaporant. In simple evaporation the kinetic energy of the evaporant is limited to thermal energy. Ion plating and ion assisted deposition processes increase this energy by either ionizing a working gas (ion plating) and accelerating it through 100-1000 V or bombarding the growing film from a low energy source using an energetic neutralized ion beam (ion assisted deposition) during growth, adding energy to the growing surface. Both precesses can increase the evaporant energy at the film surface by an order of magnitude or more, sharply improving adhesion and film density (as well as the throw, the ability of the evaporant to uniformly coat into holes and cracks). This added energy also significantly increases the heating of the substrates during deposition.

The energy to vaporize a material being sputtered is delivered by momentum transfer to the target from the energeti.-; working gas ions, usually Ar, rather than heat. These ions of the working gas are accelerated in the sputtering discharge to a few lOOs of electron volts. They give up this energy upon collision with the target surface causing a cascade of collisions within the target. Those surface target atoms receiving sufficient momentum from the sum of the collision cascades will be sputtered, often with significant excess kinetic energy. That energy of the working gas ions not imparted to the sputtered material or retained by the working gas atom as it leaves the target heats the target and represents the majority of the discharge energy. The sputtered atom, on leaving the target, with 10-100 eV of energy enters the working gas plasma and drifts several cm to the substrate. During this drift the target atoms undergo thermalizing collisions with the working gas (mean free path = 1 cm at 5 x 10-3 Torr) reducing their energy to 1-10 eV. Upon impacting the substrate the target atoms condense, giving up their energy as heat, and forming more adherent films than those grown by evaporation. The sputtering plasma additionally offers the opportunity, by properly biasing the substrates, for ion bombardment of the growing film, driving reactions, improving density and adhesion. These energetic deposition processes, as in ion assisted evaporation, sharply increase the energy input to the substrates during film growth, making control of the substrate temperature difficult.

Al.0.3 DEPOSITION OF ALLOYS Alloys and mixtures of materials find wide technical application but are difficult to deposit as thin films. No method easily deposits all alloys while preserving their composition. Sputtering is the deposition method of choice for alloys but secondary effects and large expensive targets are a limitation. Using evaporation, the constituents of alloys (with rare exceptions) evaporate at different rates, due to their different vapour pressures, producing films of variable composition. Evaporation or sputtering of the constituents of alloys from individual sources is versatile but difficult to control and, because the sources cannot be co-located, films of varying or layered composition result. This can be used to advantage where a range of alloy compositions is required for study. Sputtering can, in theory, produce films identical in composition to those of the target. The sputtering process vaporizes the alloy target quantitatively, atom by atom. Good practical results are obtained with two limitations . .First, the sputtering yield (film material vaporized from the target per Ar ion impact-see section A3) differs greatly between metals requiring long target conditioning to develop the target surface composition to the inverse of the sputtering yield. It has also been measured that different metals leave the target surface at different average angles causing composition variations across the substrate surface [4]. Composite targets of sectors of each alloy component can give good results, using a rotating substrate table. Evaporation of alloys is only practical for those having similar vapour pressures. The interactions of the components of alloys during evaporation are complex. Theories of alloy evaporation have been successfully developed [5] but do not find direct application in film production. Alloys will virtually never evaporate with exact composition. Only if, at evaporation temperature, the vapour pressures of the components of an alloy are identical will the film composition be nearly that of the starting alloy. Practical alloy

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Handbook of Thin Film Process Technology

Al.0:3

Thermal Evaporation

evaporation requires using an evaporant alloy with the composition chosen to yield a film of the desired composition. The composition of this 'special alloy', selected by trial and error to be one yielding films of the correct composition, is approximately the inverse of the volatility of the alloy components. The evaporant inventory in the source must also be kept constant, to maintain constant composition, by frequent replenishment with alloy matching that of the film. For example, at 1mm vapour pressure Al and Cu have temperatures of 1082°C and 1142°C respectively and Al-Cu alloys evaporate well, but are Al rich. A 'special alloy' of Al-4%Cu alloy will yield approximately Al- 2% Cu films. A film of 95% Pb (627°C at 1 mm)-5% Sn (1092°C at 1 mm) solder is much more difficult to evaporate. A 'special alloy' of about 95% Sn is required due to the preferential evaporation of the Pb. The alloy composition will change rapidly as the small amount of Pb in it is evaporated. This alloy must, therefore, be replenished continuously to a constant volume with material matching the film composition. Alloys can also be flash evaporated from a hot, essentially dry source. This technology is limited to alloys available as gas free wire that melt at a high enough temperature to permit feeding onto the hot flash evaporation source.

Al.0.4

DISTRIBUTIONS

A principal requirement of all thin films is that they coat the substrate uniformly. Unfortunately, in evaporation, the approximate point source of evaporant, is intrinsically non-uniform. To mitigate this non-uniformity, one uses understandin·g-of the physics of distributions to design tooling that supports the substrates to receive uniform coating or uses tooling that is distribution independent. Evaporant distribution variations can be divided into two classes, those due to variation in source to substrate geometry and those caused by the evaporant flux. At a microscopic level the flux from all emitters can be treated as a series of cosine point sources (figure Al.0.1). The cosine emitter, rooted in statistical thermodynamics, describes the flux from a small emitter (a pinhole) on a evaporating ｳｵｲｦ｡｣･ Ｚ ｾ Ｂ＠ This ·ideal ·ernittei:has·-a. ··flux · of .. ... . (Al.0.1) f (0) =cos() ｾ｟ＬＮＭ

ＭＮ

ｾＧＺＮ

ﾷ ＢＧＺ［＠

.

ｾ＠

and will deposit a uniform film on the inside of a sphere tangent to the emitter.

( b)

Figure Al.0.1. The distribution of a vapour flux as (a) a single cosine from a point and (b) as the sum of the cosines over an extended source. Note that the direction of the extended emitters is normal to the emitting surface.

In the simplest uniform isotropic case, a series of equal cosines covering a point source in space, the cosines sum to a uniform evaporant flux in all directions. Taking a real example (figure Al.0.2) the cosines radiate isotropically about the axis of the coil creating a cylindrically uniform source. The distribution parallel to the axis of a coil, assuming uniform loading, is uniform over the length of the coil, diminishing at the ends. One can see that, for a point source, a substrate holder that is a fixed spherical section, centered on the source, will yield uniform films. It is also apparent that even for a simple real case, a coil, this solution fails in one axis. As a result, non-uniformity must be tolerated or tooling that averages the evaporant flux by moving the substrate must be used. Before presenting specific types of tooling, understanding a simple isotropic, cosine and general case of a summed cosine distribution, as represented by electron beam guns is important.

Al.0:4

Handbook of Thin Film Process Technology

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1995 IOP Publishing Ltd

Introduction and General Discussion

Figure Al.0.2. The evaporant distribution from a coil.

The distribution describes the evaporant flux intensity and direction from the source. This flux is a function of source design, evaporation rate, source fill, evaporant material and chamber pressure (vacuum). Three effects combine to determine the film thickness on a substrate; the source to substrate distance,the evaporant fiims a ｾ ｩｯｾ､ ＭＧ ﾷ ＺＮ＠ distribution from the source and the angle of incidence on the substrate. To receive. ｵ ｾ ｩ ｦ ｯｾ＠ 0 substrates "rnust be shapea or moved-in-such ｴ ｨｾｴ Ｍ ｴｨ ﾷ ｾ＠ ｾ Ｎ＠ ［ ｲ ｾ｡ｰｯｲｮｴ＠ flux over all the substrates is equal at the completion of the deposition. Ｐ

a'\vay.

The effect of source to substrate distance on film thickness is accurately described by ｾ＠ &quare law-. The film flux through -a--given-solid angle' is the same whether that flux is passing through a small area close to --tl1e-source ·br ·a larger area farther away. The exact relation can be developed from the ratios of the areas subtended by a constant solid angle of evaporant flux as follows.

Substrate

I

A

(b) Source

Source

ｉｮ｣ｩ､･ｾ＠

I /

for a small solid angle of radius a

I ( c)

Source

Figure Al.0.3. The geometric relations of (a) a radiating source, (b) a source on a flat substrate, and (c) the details of the incident flux on a flat substrate showing the circular and elliptic area of incidence at points A and B.

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Handbook of Thin Film Process Technology

Al.0:5

Thermal Evaporation The area of spherical zone centred upon the source (figure Al.0.3(a)) can be expressed as follows: A = 2rrd 2 (1 - cos e)

' areas' at tw-o ､ ｳｴｾＮｮｧｩ

from basic geometry. Taking the ratio ｊｦＮ Ｐ ｴｨｾ＠

(Al.0.2)

Ｎ ･ｳｽｆ｡ｲｩ

Ｑ

ｃ ｴｬＧｦ･

ﾷ Ｎｓ Ｎ ｾＩｕｲ｣･＠

.

"

/. A1 = 2rrd?O - case) = df

r })

di

''

A1

2rrdi(l - cos e)

di and d1

(Al.0.3)

In equation (A 1.0.2) we see the area Js proportional to the square of the distances from the source. That is, if one doubles the source to substrate distance, the area is four times as large.

The thickness of the film deposited by an evaporant flux is inversely it is deposited: T = 1/A ,,,..,,;:4

ｰｲｯＮｾｮ｡ｬ＠

to the area upon which i

.

(Al.0.4)

( / " ,,/

That is, combining equations (Al.0.3) and (Al.0.4)

\ ｜Ｎ｟ＬｾＭﾷＧＢ＠

1

;.,

(Al.0.5) Real films follow this square law accurately except where the pressure is high enough to cause scattering, ·thu;s '(foubil.ri'g the ·aisfanc·e ·yields a filrri. f/4'".as thick. It is illustrative to develop the ratio of the flux at the centre (point A) and edge or corner (point B) of a flat substrate (figure Al.0.3(b)) assuming uniform (isotropic) emission from the source, using the inverse square law. From equation (Al.0.4) we know that the evaporant flux is a inverse function of the square of the source to substrate distance. That is the flux (rate, R) at A and B are: (Al.0.6) Assuming an isotropic distribution the function f (e) is independent of(} and identical at A and B so the relative flux at the edge of a flat plate is given by Ra

df

-

=-

di

RA

=cos

2

e.

(Al.0.7)

Taking f (e) =cos e to describe the flux from a simple cosine point emitter and again taking the ratio of the rate R at points A and B: (Al.0.8) The function f (e) =cos e at point A (e = 0°) is 1 so Ra

df case

RA=

di

From the isotropic case (equation Al.0.7), substituting Ra

-

RA

(Al.0.9)

d?f d'f. = cos 2 e we have

=cos

3

e.

(Al.0.10)

The relative flux (rate) at the edge versus centre of a flat substrate is of only limited interest. This is because, for the foregoing to be useful, the rate must be equal to the thickness at points A and B. That is, the film must impact the substrate nominal to its surface. This is, of course, not true at point B. To expand this example for film thickness we must consider the effect of the angle of incidence of the film flux at points A and B. If we examine a small circular area (solid angle) point, A, over the source and a similar solid angle of flux at the edge of the substrate, B, we find that the one at the edge appears as an ellipse on the substrate surface (figure Al.0.3(c)).

Al.0:6

Handbook of Thin Film Process Technology

@ 1995 IOP Publishing Ltd

Introduction and General Discussion The ellipse has an area Jr

As= -ab 4

with major axis, b, given by

a

b=--. cos()

The area of the ellipse can now be written as 1L

a2

As=---. 4 cos8

Taking the ratio of the area coated at A, a circle diameter a, and the ellipse at B AA As

(rr/4)a 2

= (rr /4)(a 2 /cos(}) = cose.

Combining this with equations (A!.0.7) and(Al.0.10) using T = Rate/Area = R/ A, we find thickness variation across a flat substrate of a film from an isotropic source given by Ts 3 - =cos 8 TA

(Al.0.11)

and for a cosine source by Ts 4 (Al.0.12) - =cos 8. TA In the general case for evaporant distribution f (8) on a a flat substrate holder, the thickness distribution is given by . Ts - = 2 cos8/(·9) (Al.0.13) TA dB

dx

with 8 being the angle between the substrate and evaporant flux at B. In a typical evaporation system (37 mm (15 in) source to substrate distance, flat substrate holder 25 mm (10 in) diameter) the angle (} = 18° (cos 18° = 0.949) yielding a thickness at the edge (cos(} = 0.949) 3 of 0.85 times (cos 3 8) that in the centre for an isotropic source and 0.81 (cos4 (}) times that at the centre for a cosine. The distribution from an isotropic or cosine emitter represents that from ideal sources. Unfortunately, real sources are much more complex. Each resistance heated source has a unique distribution (figure Al.0.4) and the only published measurement of these, the Sloan notebook, is long out of print. The empirical description of the flux from real electron beam heated sources [6] is given by: /((}) = (1 - a) cosn (}+a

ａ ｾ _,

(Al.0.14)

exponent. The distribution function (equation where a is the isotropic component and n is the__｢･ｾｭｩｮｧ＠ ;; . .｡ｮ､ｾ Ｍ .(ii"gure Al.0.5). These functions describe a (Al.0.14)) contains two rate ､･ｰｃｮｯＧｩｴｚｾ｣ｦｳ＠ beaming or focused component (cosn 8) of the flux derived from the hot, slightly concave, central emitting area of an electron beam heated source and an isotropic component, a, originating from the high pressure (low mean free path, viscous flow) gas cloud on the surface of the evaporant. This description reduces to ｴｄｾ＠ _isotropic for \ ; and _ _ __case _ ......--:::: to the often referred (j f (.,to 'cosine emitter' for n = 1.

s·

ｯｏｾ＠

ｲ･｡ｾｳｯｵ｣＠

Taking the description from (equation (Al.0.14)) and substituting it for the angle independent isotropic distribution in equation (Al.0.6) 1

RA= 2[(1 - a)cosn 8 +a] dA

at A, (} = 0°

(vertical)

(Al.0.15)

- d2

A

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Handbook of Thin Film Process Technology

CDs &

Al.0:7

Thermal Evaporation 1

Ra= 2[(1- a)cosn ()+a].

da

The relative rate at B (equation (Al.0.7)) for a real source is: Ra

- = RA

d1[(1 - a) cosn B +a] 2 B[(l = cos - a ) cos n () + a ] . dB2

(Al.0.16)

RA and Rs are now general terms for the flux at points A and B on (figure Al.0.3) any flat substrate holder.

(al

15

15

"O

c

;;

cu

0 u

c

0 u

cu

VI

ｾ＠

VI

10

'-

Cl.

VI

VI

E

E

- s· 0

0

'-

.!::

VI

VI

C1I

O"

c

.E

c ..9

cu

OJ

-

e::::

e::::

15

15

( c)

c

80 100 120 140 160 1'00 Degrees

(d)

QJ

QJ

VI

.,,. ,,-

10

Cl.

VI

E 0 '..._

I

/

"'"'

""

I

I

5

''

cu

'

''

cu

10

ｾ＠

VI

\

'

E

0 '-

\

VI O"

\

c

5

E

QJ

\

l

d

\

e::::

'

' 0

'-

' ....

\

I I

.......

I I

I

er::

VI

I

I

VI

ｾ＠

40 60

0 u

0 u

.E

20

:0c

"O

C1I

0

20 40 60 80 100 120 140 160 180 Degrees

0

c

5

ｾ＠

d

cu

10

cu

Cl.

'-

(bl

\ \

20

40 60 80 100 120 140 160 18 0 Degrees

0

20

40 60 so 100 120 140 160 1'00 Degrees

Figure Al.0.4. Evaporant distributions from (a) a dimple boat with a 40 mm x 10 mm dimple, (b) a dimple boat with a 10 mm diameter x 3 mm deep dimple, (c) a coil 40 mm long with 6, 10 mm turns and (d) a crucible 10 mm inside diameter and 12 mm high (solid line-longitudinal axis).

From the foregoing, it is seen that the farther from the source (smaller angle B) a substrate is placed, the more uniform the distribution. Unfortunately, the deposition rate falls as the square of the source to

Al.0:8

Handbook of Thin Film Process Technology

@ 1995 IOP Publishing Ltd

Introduction and General Discussion

-ｾ＠

/

c

Ｎ ｾ＠

u

ｾ＠

1

8

-s c:

c

QI

c.

4

x

QI

1000

100

10

Deposition rate at 20 cm

(A

s-

1

)

Figure Al.0.5. The distribution coefficients defining the measured evaporant flux for aluminum in an electron beam heated source.

substrate distance. Long distances yield low rates and a long path for the evaporant. This increases the opportunity for the evaporant vapour or the slower growing film to react with the vacuum environment. Linear scaling requires constant rate at the substrate and a constant mean free path to source/substrate distance ratio to maintain the deposition environment when increasing source to substrate distance. The thickness distribution on any substrate holder can be calculated in the same manner as that for a flat plate using the general distribution function (equation (A 1.0.14)). Though analysis using this function is useful its value is limited by the variability of the distribution (figure Al .0.6). For this reason the design of substrate holders to match specific distributions is uncommon except where one must coat large substrates with unusual curvatures such as spacesuit visors. Instead, substrate holders are empirically designed to make them distribution independent. ｾ＠ ::>-.

6 5

.c

E 4 VI

.«:= c 0

ｾ＠ ::::J

.a

ﾷ ｾ＠

Ci

10

30 20 Angle from normal (degrees)

40

50

Figure Al.0.6. Distribution instability expressed as the standard deviation of measured thicknesses for aluminum evaporated from an electron beam heated source.

Al.0.5 SUBSTRATE HOLDERS The complex and variable evaporant distribution of all sources (equation (Al.0.14)) requires well thought requirements. e out substrate holders to obtain films of sufficient uniformity to meet normal ｦｵｮ｣ｴｩｾ｡ｬ＠

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Handbook of Thin Film Process Technology

Al.0:9

Thermal Evaporation substrates must be positioned to receive a uniform film, or moved such that all receive a comparable integrated evaporant flux. Uniform coating of c.urved substrates (lenses and mirrors) often depends upon experience and cannot be ｡｣ｨｩ･ｶ ｾ＠ by" ｾｯ ｰ･ ｲ＠ ci1o!ce_qf aｳ ｟ ｾ ｢ｳｴｾ ｾ ｴ ･＠ ho_lder alone. Of particular importance is the positfon ofthes ourc-erelative to the substrates as discussed in the following section on source/substrate ｧ･ｯｭｴｲｹ ｾ＠ The r an"ge ofs ubstrate holder designs is boundless but among the most common are shown in figure Al.0.7 .

I

Source (a) Flat plate

Source {b} Dome

Source ( c) Flat planetary Source ( d) 0 om e p I an eta r y

Source

f e) Drum Figure Al.0.7. Common substrate holders.

Flat Plate: As a fixed or rotating holder, flat plates are inexpensive, and all very large substrates act as flat plates. With a included evaporant angle of 30° and a cos 1 () (simple cosine) source distribution the best case uniformity will be ±10%. The techniques in the following section on source/substrate geometry enable substantially better uniformity to be obtained using off-axis sources and rotated flat substrate holders.

Domes: The substrate holding dome is the most common simple substrate holder. Spherical domes (or planetaries) with a radius equal to the source to substrate distance eliminate geometric distribution errors. The evaporant flux is normal to the surface, improving pattern mask resolution. This leaves only the source flux introduced thickness non-uniformity of ±5% for a simple cosine (cos 1 0) source flux and a 36% included angle. The uniformity of the film deposited on a spherical dome can always be improved

Al.0:10

Handbook of Thin Film Process Technology

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1995 IOP Publishing Ltd

Introduction and General Discussion

,/

by moving the dome farther from the source. Domes are a good compromise between the complexity of a planetary and the poor uniformity of a fiat plate. Planetaries: Where film uniformity of better than ±3% is required a planetary substrate holder is the only option. Though not geometrically perfect, planetaries regularly produce films as uniform as ±1 % [7]. A large amount of complexity, loss of reliability and cost must be justified to obtain this uniformity. Most planetaries use 3 dome planets positioned on a spherical surface or 5 ft.at round planets in a plane over the source. As the name implies, the individual planets rotate while the entire set is rotated above the source. This rotation requires a powerful motor drive and numerous bearings within the hot part of the coating chamber. Though a planetary will yield substrates with films of uniform thickness, the cyclic rate variation due to the planetary motion during coating can be extremely large. Rate variations of a factor of 9 (3-27 Als with an average of 9 Ais) have been measured for a common high capacity dome type planetary with a included angle of 100°. Planetaries also introduce a range of operational problems. They are complex to handle for loading because of the required substrate retaining clips and are quite difficult to heat. Vigorous cleaning often bends the planets causing jamming. If large substrates (more than 50% of the planet diameter) are coated in a dome planetary, non uniformity will be seen across the substrates to the extent that they flatten the dome. Drums: These ferris wheel like holders offer extraordinary capacity while remaining mechanically fairly simple. The uniformity of a drum with a centrally located source is similar to that of a fiat plate in one axis and a dome in the other. This can be sharply improved by installing masks on both sides of the source to reduce the thickness along the centerline. Good uniformity is obtained without masks in large multiple source drums. Exceptional economy can be obtained, as in decorative coating, by centrally locating an array of isotropic emitting resistance sources within a large drum.

Al.0.6

SOURCE/SUBSTRATE GEOMETRY

In all systems with rotated substrate holders and having the source centred under the axis of rotation, the

film is thickest in the centre of the holder. This is because sources radiate in a beam (equation (Al.0.14)) subtending a narrow angle. The uniformity can be sharply improved by moving the source from beneath the axis of rotation out toward the edge of the holder. Laboratory experience shows that a film uniform to ±3% can be deposited on a fiat plate holder from a electron beam heated source at approximately the outer edge of the holder and one plate holder radius from the source. A similar optimal off centre source position exists for domes and planetaries. The uniformity on a planetary with optimally located sources can exceed the limits of measurement (±0.5% ). In addition to improved film uniformity, off centre location of evaporation sources significantly simplifies the vacuum system layout. There is no longer only one source position but a annular ring yielding uniform films. As a result several sources can be located on this ring. The thickness monitoring head located at the edge of the substrate holder can now be positioned more nearly over the source, improving thickness measurement repeatability. Off centre sources provide better step coverage on planetary substrate holders but, conversely cannot be used for lift off or with pattern delineation masks because of the widely varying evaporant angle of incidence. Off centre sources and reduced source to substrate distance can deposit uniform films on convex optics. Unfortunately, at this time, no known software provides a good solution to the distribution problem, so experience and trial and error must be used. Off centre sources potentially introduce several process problems. When the source is not on the axis of rotation the evaporant rate varies even more than for a axially positioned source. This can cause problems with reactively evaporated or rate dependent films. In addition, this angle of incidence varies with each rotation of the substrate holder across the source. In the case of large dome planetaries the angle of incidence can vary from normal (90°) to 25° for a source located half way between the rotation axis and the edge of the planetary during each rotation. It is well established that the columnar growth direction of films is toward the evaporation source. Recent measurements also show that significant changes in index of refraction occur at beyond an angle of incidence of 30° [8]. In addition, the evaporant from off-centre sources is less efficiently captured by the substrates, reducing the average deposition rate and increasing ' evaporant cost. 1 /

©

1995 IOP Publishing Ltd

Handbook of Thin Film Process Technology

Al.0:11

Thermal Evaporation

Al.0.7

EVAPORATION MATERIALS

The selection of evaporation material is the critical process choice as it will be the thin film. Two principal factors govern evaporability: ( 1) Bound gas

(2) Chemical stability. Assuming no significant source interactions, evaporant purity per se does not affect evaporability so long as the 'impurity' causes no energetic reactions. Material manufacturer specified purities seldom, if ever, include gas, oxide, or organic impurities. A thin film is usually first visualized as a function like a conducting surface on a substra . Then a material, Al, Au or Ni for example, is selected for this film based on perceived film properties (cost, adhesion, toughness; colour). From the perspective of selecting an evaporation material Al, Au and Ni provide"fOrins uc 1ve comparison. Al and Ni can be very inexpensive but are both expensive as high purity materials. Al and Au both evaporate easily from a wide range of sources, but gold films are soft and adhere poorly. N! fil!_lls are tough, but ｾｩ＠ forms an alloy with resistanct'. s_ources and, without careful ('spits') Ni droplets endlessly upon first melting in an evaporation system. Al vacuum degassing, ｾｰｲ｡ｹｳ＠ is often the material -of clioi·ce-due- o 1 s evapora 1 1ty, good adhesion and modest cost. A material, no matter how attractive as a thin film, is useless if it cannot be acquired in an evaporable form. For electron beam guns this means large gas-free chunks or chips. Resistance heated sources require wire or small chips. In general the lowest possible volume-to-surface area ratio is desired to minimize surface absorbed gas (principally water vapour). Powder, without premelting, is almost always difficult or impossible to evaporate, particularly in an electron beam gun. Today a number of suppliers offer 'evaporation grade' materials for thin film deposition. These materials are, ostensibly, tested for evaporability and should yield defect free films of the nominal composition. The 'evaporation grade' of the most common thin film metals, Al, Au and Cr which usually yield defect free films, work very well. Unfortunately this is not true for many less common metals, such as Fe, Ni, Pt, Si and Ti. These metals absorb gas during purification, mostly H and 0. Upon heating to evaporation temperature, this gas is liberated driving droplets of metal from the evaporant. This 'spitting' is the principal cause of film defects. Though most 'evaporation grade' metals are vacuum melted, this does not heat them to as high a temperature as does evaporation and often does not begin to drive off the spit causing absorbed gas. 'Conditioning' metal evaporants to drive off bound gas is seldom a problem with resistance evaporation because of the small capacity of most sources and the limited range of metals evaporated. Electron beam heated sources however may hold 10-30 cm3 of poorly degassed evaporant in a water cooled hearth in which it is impossible to melt the entire charge. This combination of a large evaporant inventory and limited conditioning ability melt temperature because of the hearth cooling makes some electron beam melts into time bombs of unconditioned evaporant. The deposition of films of compounds finds wide application, particularly in optics. When evaporating a compound one is, unlike with chemical elements, not assured the film is of the same composition as the evaporant. Developing the technology of compound deposition is the subject of intense continuing research [9]. The 'evaporation grade' compounds of the major suppliers will usually perform better than the metals. This is because simple air melting or furnace degassing of the common optical thin film materials is satisfactory. To prepare a laboratory grade powder or granular material for evaporation, under a hood, with eye protection, place the material on a 100 mm square of 0.2 mm (0.01 in) Mo plate and gently melt it with a propane torch. Allow the molten evaporant to drip off one corner of the Mo plate onto a cooled Cu collector or into a boat or electron beam gun hearth liner. Powders that will not melt at red heat will often evaporate satisfactorily after heating. Unfortunately, many materials (compounds of Pb, S, Se, Ti, Zn) are too volatile to condition with a torch, and most oxides melt at temperatures beyond that of a propane torch. The deposition of compounds assumes the compound is stable at evaporation temperature. Many materials of interest (CaF, CeF, MgF) are quite stable. Unfortunately, the most useful optical materials, oxides, have widely variable compositions which produce films of similarly variable properties. Suboxide formation is

A 1.0: 12

Handbook of Thin Film Process Technology

©

1995 IOP Publishing Ltd

/

Introduction and General Discussion minimized by introducing, during coating, a partial pressure of oxygen (on the order of 2 x 10- 4 Torr) into the coating chamber (excluding oxygen if the suboxide is desired as with SiO) or oxygen ion bombardment of the films along with slow (1-5 A s- 1 ) well controlled evaporation and a suitable elevated substrate temperature (usually -over 200°C). Exact deposition processes are among the most proprietary technology of ｳｵ｣ｾｦｬ＠ optical thin film fabricators. As a result of the difficulties evaporating some important materials, thin film materials suppliers have developed proprietary new materials. These materials are usually made of the 'desired' material, i.e. ZrO, and a stabilizing 'impurity', ZrTi04 . The only drawbacks of proprietary materials are their cost and their specialty nature, limiting the applicability of some film design software and current film deposition technology research. The evaporation of alloys is complex and a complete treatment [5] is beyond the scope of this work. A first order analysis shows each component of an alloy evaporates as if it were the only material present. This means that two materials of similar vapour pressure (i.e. Sn and Cu) will evaporate approximately in the ratio of the starting material. Unfortunately, most alloys of importance [NiCr, Inconel™ (Ni 72%, Cr 16%, Fe 8%)] are made up of metals of significantly different vapour pressures. As a result, 80%Ni20%Cr, will start out evaporating very Cr rich and as the Cr is consumed slowly the composition will pass through 80:20 to nearly pure Ni. Films of the desired composition can be deposited by: (a) Co-evaporating the alloy constituents from independently controlled sources. (b) Depositing from a pool, continuously replenished with the desired film alloy by wire or rod feed, of a suitably composed 'special alloy'. The starting 'special alloy' is empirically chosen to yield the film desired composition.

(c) Evaporating a small per cent (thin film) of the contents of a large pool of 'special alloy' and maintaining the pool volume constant by frequent small additions of the desired film alloy. (d) Flash evaporating continuously fed wire or granules of the desired film alloy.

These techniques all add complexity or have limitations. All will work with metals differing in temperature at a vapour pressure of 10-4 (a better visualized way to present vapour pressure) of less than 200°C. For alloys having great differences in vapour pressure only co-evaporation provides completely independent control of the film constituents. A final evaporation material consideration is when to replenish and when to replace evaporant charge. An electron beam gun can hold in excess of 20 cm3 (15 gm of Al, 50 gm of Ni) worth $50-$100. Even a small resistance boat holds in excess of $100 worth of gold. This makes charge replacement a significant economic consideration. As this evaporant is consumed, the material is replenished, reconditioned and used, concentrating low volatility impurities. The principal reason to discard an evaporant charge is concern about film composition or purity. In addition, oxide impurities from reaction with the vacuum environment and refractory metal dissolved from the boat or hearth liner contaminate the evaporant. The evaporation of compounds introduces decomposition as a limit on evaporant charge life. This is a particular problem with oxides where suboxide formation (Tii0 3 and Ti02) and residual fully oxidized material (Si0 2 in SiO) cause gradual index of refraction shifts in optical films. Operating experience also shows that old evaporant charges, though of low purity are well degassed, often yield films with fewer defects. Three principles guide the replenishment and replacement of evaporant charges: (1) Replenish the charge frequently and replace it on a regular schedule.

(2) Where minimum film defects are the critical process parameter, replace the charge very seldom. (3) Where film functional properties (index of refraction, etch residue, conductivity) are critical, measure

the property with reference to evaporant charge age and replace the charge with one half the age showing property deterioration.

© 1995 IOP Publishing Ltd

Handbook of Thin Film Process Technology

Al.0:13

Thermal Evaporation

REFERENCES [1] Dushman Sand Lafferty J 1992 Scientific Foundations of Vacuum Technique (New York: Wiley) O'Hanlon J F 1980A A User's Guide to Vacuum Technology (New York: Wiley-Interscience) [2] Dushman S 1992 Scientific Foundations of Vacuum Technique (New York: Wiley) pp 691-737 [3] Breitweiser G, Varadarajan B N and Wafer J 1969 Influence of film condensation and source radiation on substrate temperature J. Vac. Sci. Technol. 7 (1) 274-77 [4] Harper J M E, Berg S, Nender C et al 1992 Enhanced sputtering of one species in the processing of multielement thin films J. Vac. Sci. Technol. A 10 (4) 1765-71 [5] Santalia T 1970 Kinetics and thermodynamics in continuous electron-beam evaporation of binary alloys J. Vac. Sci. Tech. 7 (6) S22-S29 [6] Graper E B 1973 Distribution and apparent source geometry of electron-beam heated evaporation sources J. Vac. Sci. Technol. 10 (1) 100-103 [7] Behmdt K H and Doughty R W 1966 Fabrication of multilayer dielectric films J. Vac. Sci. Technol. 3 (5) 264-72 [8] Flory F 1993 Anisotropy in thin films Appl. Opt. 32 (28) 5649-59 [9] Chow R, Falabella S, Loomis G E et al 1993 Reactive evaporation of low-defect density hafnia Appl. Opt. 32 (28) 5567-73

A 1.0: 141

Handbook of Thin Film Process Technology

©

1995 IOP Publishing Ltd

Thermal Evaporation

Name

Symbol

Acustic Temperature ( •q Impedance t1,. ........ ,.. o .......... ro •• ,....,,, Melting Bulk Ratio, lo ·• lo ·• Point Density 1 •c a/cm Torr Torr 725

J . 51

Biirium Chloride

961

J. 86

Barium Fluoride

1280

4. 89

Barium

Ba

Source

Material

Index of Refraction @ microns

］ＶｾＰ＠

Good

Boat

Mo

l. 74 @ . 58

Use gentle preheat to outgas.

"480

Good

Boat

Mo

l .'51 l. 40

Sublimes . Density rate dependent.

Poor

Boat

Pt

l.98 @ .5 9

Decomposes slightly .

Boat

Mo

2.16@ . 59

Sublimes.

Bao

192 J

5 . 72

"1300

Bas

1200

4 . 25

1100

1620

5. 85

. 32

1283

l. 85

. 55

Beryllium Chloride

440

l . 90

"150

Beryllium fluoride

800

l. 99

"480

. 85

2. 4

decomposies ...

. 50

. 27 10. 3

@ •8

w Be

Beryllium Oxide

BeO

Bismuth Bisir.uth fluoride

710

1000

2 575

3. 01

Bi

271

9 . 80

Bif 1

727

5 . 32

Bismuth Oxide

811

8.9

Bismuth Selenide

710

7 . 66

::650

Bismuth Telluride

585

6. 82

"600

1900 . 81

330

520

Xlnt.

Good

Ta

Boat

Ho

Boat

Mo

1.33@ . 59

Very toxic, sublimes.

.SS

Powders very toxic . No decomposition from EB guns.

2. 5 @ • 5

Very toxic.

Good

Boat

Ta

Xlnt.

Boat

Mo

. 82 4.5

.35 l.O

Vapors are toxic. High resistivity.

Poor

. 19

Crucible

c

l. 74 l.64

1.0 10

Toxic, sublimes. App . Opt. 18, 105 (1979).

Boat

w

2.48

.58

Vapors are toxic. JVST12, 63 (1975).

Toxic. Sputter or co-evaporate .

Good Boat

Toxic . Sputter or co-evaporate.

Mo

Toxic . Decomposes. Sputter or co-evaporate in io" Oz-

7. 39

Toxic.

2100

2. 34

Material explodes with rapid cooling. Forms

2350

2. 52

2300

2. 25

"1600

Poor

460

2 . 46

"1400

Good

Boat

Mo

310

l. 55

800

321

8. 65

Fair

Boat

Mo

685

Boron

Metal powder and oxides very· toxic. Wets W/Mo/Ta.

Boat

decomposes

Bismuth Sulfide

Decomposes, yields free Ba ; sputter or co-evaporate .

1.82 1.72

:0300

Bismuth Titanate

Toxic . Wets w/o alloying, reacts with ceramics.

Mo

Barium Sulfide

Beryllium

Remarks

Boat

7J5

Barium Oxide

Barium Titanate

ｬＭ｟ｊｂＮ･ｩＱＴｴ｡ｲＺｾＬ＠

fair

545

. 90

Electron Beam

. 45

1278

1797

Poor

2500

2650

Xl nt .

Crucible

l"".::llrh'rio

uit-h

rnnt-:::11 ' nn.-

Boron

Carbide

Similar to chromium. Sputtering pref.

Boron

Nitride

BN

Decomposes. 'TUC'T'

J.Ci.(4\

1C.DC.

/10.D"1\

Boron

Cx ide

l . 46

Boron

Sulfide

Poisons vacuum systems,

-: admium

Cd

.6

64

180

1.13@ .6

low sticking coefficient. '''""""'

Cadmium Antimonide

Cd Sb

Cadmium Arsenide

456

6. 92

7 21

6 . 21

Boat

Mo

Boat

Mo

Mn

F.

R

1 · ... .,..,..

Toxic.

Cadmium Bromide

567

5. 19

:,300

Cadmium Chloride

960

4 . 05

"400

1100

6 . 64

"600

7

5. 67

"250

1430

8 . 15

Sublimes. Sublimes .

ｾ｡､ｭｩｵ＠

Fluoride

Cadmium Iodide Cadmium Oxide

)8

CdO

Inficon Z-Ratio 0

= acoustic impedance ratio, Z-Ratio 0

Al.0:16

Leybold Inficon

Handbook of Thin Film Process Technology

l . 56 @ • 58

2.49@ .67

Disproportionates .

Maxtec Inc. Acoustic Impedance (A . I.): 8.83.;. z

© 1995 IOP Publishing Ltd

Introduction and General Discussion

Name

Symbol

Cadmium serenide

Cd Se

Cadmium Silicide

CdSi0 2

Cadmium Sulfide

eds

Cadmium Telluride

Cd Te

Calcium

Ca

Calcium Fluoride

Acustic Temperature ( 'C) Impedance u,.. ... ,,. ..... o ｾＧＢＬＮﾰ＠ Mel ting Bulk Ratio , io · 8 10 · 4 Point Density z Torr Torr •c a/cm 1 l 3 51

5 80

5. 79

Electron Beam

Index of Refraction ＱＭ｟Ｎ］ｩＺﾵｬｊｾ＠

Source

Material

Good

Box

Mo

Good

Box crucible

Ho Quartz

2 . 4 3 @ • 67 2 . 31 @ l. 4

Sublimes. Sticking coeff . affected by sub temp . Comp.

Box Boat

Mo Ho

? ?7 a 7 n 2. 68 @ 4. 0 2. 51 @ 3 2

Toxic . Stoichiometry depends on substrate temp.

Poor

Boat

Mo

. 29 @ • 58

Xlnt .

Boat

Ho

l . 47 l . 32

Boat

w

l.84 @ . 59

2.4

" 600

1750

4. 82

550

l . 02

1041

6. 20

. 98

845

1. 55

2. 36

car,

1360

3. 18

. 85

Calcium Oxide

cao

2580

-3. 38

Calcium Silicate

CaO•Sio,

1540

2. 90

Calcium Sulfide

CaS

subl.

2.5

Remarks

P microns @

. 58

Toxic,

l . 69

450

ｶｾ

ﾷ ｾｨｬａ＠

.TU2000

3.7 0

... " nn

Electron ＱＭ］ｾ｣Ｎｬ＼ｉｊｗｏｓＬ｟ｪ＠ Beam

Source

Boat

1500

Material Ta

Index of Refraction @ microns 1.88

@ •

58

2 . 11 @ • 59

Remarks Sublimes . Reacts with Mo and

w.

Decomposes. Toxic .

Sulfur

2 . 07

115

Supermalloy

Ni / Fe/ Mo

1410

8. 9

Tantalum

Ta

2996

16. 6

3000

11. 15

2. 29

57

1J

Po or

Boat

Mo

Poisons va c uum system .

Sputtering preferred ; or co-evap . from 2

Good

ｄｾｲｭ［Ｑｯｬｮｶ＠

Tantalum Bo ride Tantalum Carbide

Tac

3880

14. 65

Tantalum Nitride

TaN

3J60

16 . JO

Tantalum Oxide

1800

8 . 74

Tantalum Sult ide

1300

2200

1960

2 5 90

2 . 05 @ • 58

Xlnt .

Mo ［ＱＮｮｾ＠

Forms good films.

JVST 12 , 811 ( 1975) .

" 2 500

Reactive; evaporate Ta 10. 3 N • 2

. JO

19 20

1570

2 090

Good

Boat

Ta

Box

Mo

2 . 28

. 40

2. 0

1. 5

Slight decomposition : evap .

ＡｾｮｬｏＺ［ｯｲＹ＠

ｯｦｬｾ［＠

11oan\

Tc

Teflon

PTFE

3JO

2 . !:I

Tellurium

Te

452

6. 2 5

. SJ

157

2 77

Poor

Boat

Mo

Terbium

Tb

1357

8. 2 7

. 64

80 0

1150

Xlnt .

Boat

Ta

Boat

Mo

Boat

Ta

Partially decomposes.

Tb 4 0 7

Boat

Ta

Films TbO.

Tl

Boat

Mo Mo

2 . 65 2.J2

. 44 24

Toxic, sublimes.

.75 12

Toxic, sublimes.

.75

Toxic, sublimes.

Terbium Fl uoride

1176

Terbium Oxide

2)87

Thallium

11. 5

1550

Technetium

Terbium Oxide

:::000

7. 87

JOl

11. 89

lJOO

1. 58

280

480

Poor

Baffled source. Film struci:ure doubtful. 4.9

@

6.0

Toxic . Wets w/ o alloying.

Wets freely, very toxic .

Thallium Bromide

Tl Br

480

7. 56

1. 77

"200

Boat

Thalium Chloride

Tl Cl

430

7. 00

l. 21

::: 150

Boat

Mo

2 . 20 2. 6

Thal 1 ium Iodide (B)

TlI

440

7. 09

"200

Boat

Mo

2.78

717

9 . 65

J50

Boat

Mo

Toxic . Goes to Tl 2 at 85o 0 c.

1875

11. 7

Boat

w

Toxic, radioactive .

Boat

Mo

2 . 47 • 5

Ta

1.52 1.25

.40 12

Radioactive. Heat substrate to above 150°c .

1. 8 1. 75

• 55 2.O

Radioactive.

Thallium Oxide Thorium

Th

Thorium Bromide

ThBr 4

Thorium carbide

ThC 2

. 54

14JO

1925

Xlnt .

5. 67

277J

8 . 96

Thorium Fluoride

ThF 4

900

6 . 32

Thorium Ox ide

Tho 2

J050

9. 86

Thorium Oxy fluoride

ThOF 2

Thorium Sulfide

ThS 2

1925

6 . 80

Thulium

Tiii

1545

9 . J2

Thulium Oxide

Tm20l

@

" 2J OO . 74

Radioactive, sublimes. Radioactive.

,,,750

Fair

Boat

:: 2100

Good

Boat

ｔｕｾＢ＠

900

Inficon Z-Ratio 0

f\.1.0:24

. 26

9. 1

Boat

Mo

1. 52

1')

Q1Q

fln""TC:

Radioactive. Films often ThF4 •

, ___

. 52

461

acoustic impedance ratio, Z-Ratio 0 Leybold Inficon

Handbook of Thin Film Process Technology

w

Radioactive . Sputtering preferred; or co-evaporate

8 . 90

-

. 02

680 1500

Good

, --··----

Boat

Ta

Sublimes .

Boat

Ir

Decomposes.

Maxtec Inc. Acoustic Impedance (A. I.)= 8. BJ

©

1995 IOP Publishing Ltd

Introduction and General Discussion

Name

Symbol

..

Acustic Temperature ( 'C) ,,.. · ............. _._ ·Impedance V;iinnr P ｾＢ｣ＺＮＱｲ＠ Melting Bulk Ratio, lo·• 10·' Point Density E 1 e ct r on >--___J;DU: o.,:u..: c· µ.g.W