Venables J. Introduction to Surface and Thin Film Processes

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i.e. the ﬁnite diﬀerence has been replaced by a partial derivative. In the last two equa-

tions we have replaced the enthalpy h with the internal energy u, since the spreading

pressures in the two phases are the same in (E.12) and the area is constant in (E.13).

When one makes a speciﬁc model of an adsorbed layer, the internal energy includes

lateral interactions. If these vary rapidly with the areal density n, as in a solid phase,

the term in nu/n can be an important component in q

(Price & Venables 1976).

Useful thermodynamic relationships 317

Appendix F

Conductances and pumping

speeds, C and S

Useful formulae: (C, S are measured in liter/s)

Conductances C

in series C

5兺C

, so that S

. (F.1)

Conductances C

in parallel C5兺C

; S5兺S

. (F.2)

In the following conductance formulae, T5temperature (K), M5molecular

weight, tube diameter D and length L are in cm. (Formulae in brackets are for air at

20°C.)

C of an aperture52.86 (T/M)

1/2

·D

;(C59.16 D

). (F.3)

C of tube into large system53.81 (T/M)

1/2

·D

/(L11.33D);

(C512.1 D

/(L11.33D)). (F.4)

Table F1. Conductances (liter/s) in typical situations for standard tube sizes

D (inch) D (mm) Aperture L510 cm (port L51 m

nominal size inside diameter conductance conductance) (no end, per meter)

1.5 36.9 125 40.7 6.0

2.5 61.2 343 153 27.7

4 99.4 905 512 119

6 149.7 2053 1357 406

8 200.4 3679 2657 974

Notes: Columns 3–5 use formulae (F.3) and (F.4) to provide conductance estimates for air at

20°C.

318

Table F2. Typical pump speeds for diﬀerent pump types and sizes

D (inch) D (mm) Turbomolecular Diﬀusion pump Ion or sputter

nominal size nominal size pump 1trap1valve ion pump

1.5 38 — — . 35

2.5 64 50 — . 45

4 100 170–300 32 . 60

6 150 500 200 .110–500

8 200 1400 415 .800

Notes: Columns 3–5 use data from several manufacturers to provide estimates for N

at 20°C;

for particular pumps check performance against speciﬁcation.

Conductances and pumping speeds, C and S 319

Appendix G

Materials for use in ultra-high

vacuum

This appendix gives a few indicators of suitable materials for use in a UHV environ-

ment. The main point is simply to emphasize that the materials need to have low

outgassing rates per unit area exposed, and that they need to be stable at the temper-

atures not only of use, but also during bakeout. Some of the obvious candidates in

the diﬀerent categories are as follows. Much of this information can be gleaned from

talking to practitioners, from vacuum technology books such as Dushman & Laﬀerty

(1992), O’Hanlon (1989), Roth (1990) or from reading between the lines in design

handbooks such as Yates (1997), or increasingly from the web. A page giving

properties and some sources for materials is at http://venables.asu.edu/grad/

appmat1.html

Structural materials

The most widely used structural material is 304 stainless steel, which is used to make

chambers, ﬂanges, etc., and can also be used for stages and other parts of the experi-

ment itself. At very low temperatures this austenitic (largely f.c.c.) 18–20%Cr,

8–10%Ni Fe-based alloy transforms in part to the b.c.c. (martensitic) structure, and

thereby becomes magnetic. If this could be important, then more technical details are

needed, such as would be obtained from ASSDA – the Australian Stainless Steel

Development Association – or AVS – the American Vacuum Society. Aluminum

alloys are used for experimental pieces inside the vacuum system, and have also been

used for whole chambers on occasion. This is the only material which has successfully

achieved UHV pressures without baking, but it needs a special surface treatment

developed in Japan for this to be eﬀective, and the technique has not yet become wide-

spread.

Titanium alloys are expensive, but have been successfully used for small parts, espe-

cially where ﬁne bearing surfaces are required. Copper bronzes (zinc and lead free) are

also useful for stages and related parts. Note that opposite bearing surfaces must be

made of dissimilar materials; in UHV, removal of the oxide or interfacial layers

320

between similar materials results in cold welding. Once this has happened it is too late

to argue that you didn’t know they would.

Electrical conductors

Oxygen-free high-conductivity (OFHC) copper is the standard material for electrical

leads, provided they don’t get too hot; silver (usually as a plating on copper) can be

used to increase the conductivity of surface layers, which can be useful for high fre-

quency applications. The normal 304 stainless steel can be used, but only for low

current applications, possibly at high voltage, as in electron beam heating. The normal

refractory materials are tungsten and tantalum as heater wire and electron source ﬁla-

ments. Often Ta supports are used to hold W ﬁlaments, which prevents the ﬁlaments

welding to the support after use; Ta has the advantage of being less brittle than W.

Thermal conductors

Again OFHC copper is good, and silver, with a special surface treatment developed in

Japan, can be used for low emissivity applications. The combination of high thermal

conductivity with high electrical resistance is provided by sapphire, crystalline Al

This is useful at low temperatures, and provides electrical isolation; this is also a pos-

sible role for diamond in thin ﬁlms. Tantalum has good thermal conductivity to very

high temperatures.

Electrical and thermal insulators

The following materials are discussed in decreasing order of thermal stability. Sapphire

and alumina are useful up to high temperatures. These materials and fused quartz glass

have very low expansion coeﬃcients; fused quartz is an excellent insulator at low tem-

peratures, so it can be used for supporting stable low temperature stages. Borosilicate

glass (Pyrex®) is generally used for UHV windows, whereas fused quartz windows can

be advantageous for special applications, including transmission into the ultra-violet,

and if low birefringence is needed.

Machinable ceramic/glass (with trade names Macor®, Micalex® etc.) outgas more

than the above glasses and so should be used rather sparingly, but they can readily be

made into complex shapes. Various plastics can be used very sparingly, such as

Kapton®, a polyimide polymer with very high dielectric strength. Teﬂon®, which is a

high density PTFE (polytetraﬂuorethylene) can also be used, but tends to degas ﬂuo-

rine and other ﬂuorine compounds. Wires coated with these polymers can be used, but

detailed attention must be paid to bakeout temperatures, as emphasized in section

2.3.4.

Materials for use in ultra-high vacuum 321

Heat and electrical shields

The refractory metals molybdenum, tantalum and tungsten are used as heat shields,

especially in several layers, or in a spiral wrap, because this cuts down substantially on

heat transmission by radiation. Of the three metals, Ta is the most expensive, and Mo

is best for reducing electrical (patch) ﬁelds in the vacuum, especially for low energy

charged particles, as discussed in section 6.1.3.

322 Appendix G

Appendix H

UHV component cleaning

procedures

General precautions

Take care not to damage knife edges, and don’t transport grease and dirt (e.g. from

bolt-holes) from the outside to the inside of the assembly. Clean polyethylene or unpow-

dered PVC gloves should be worn both as safety and contamination protection. More

eﬃcient cleaning results from doing small pieces in batches. Use new solvents for each

piece or set of pieces. Handle parts with cleaned tweezers or tongs as much as is prac-

ticable. Large ﬂanges or assemblies should be held by their outside surfaces only.

Cleaning procedures

The initial decision which has to be made is how dirty the pieces really are and whether

you want to perform what I refer to informally as an ultimate clean or a routine clean.

This diﬀerence can aﬀect both the cost of the operation and the need for special solvent

disposal procedures, with health and safety implications. For these reasons at least, it

is strongly advisable to work closely with your laboratory manager, and to establish

written procedures which are then followed carefully. An inexpensive routine clean with

little or no disposal problems is described ﬁrst, followed by an ultimate clean which is

more expensive, and does have disposal implications.

Routine clean

(1) Prepare a solution of a standard laboratory cleaner in distilled water. Adjust the

strength of the solution depending on how dirty the part is, and the type of con-

taminant. Heating the solution will decrease the necessary soak time, but don’t

exceed 95°C.

(2) Put small parts in a beaker of the cleaning solution and clean ultrasonically for up

to 15 min. Rinse in a beaker of distilled water. Large parts should be swabbed down

with lint-free cloth, and soaked in the cleaning solution and then rinsed under

323

running distilled water to remove most of the loosely attached dirt and oil. If the

parts will ﬁt, they can be put directly into an ultrasonic cleaner tank ﬁlled with

cleaning solution. After this step they should again be rinsed under running dis-

tilled water.

(3) Repeat steps (1) and (2) until the rinse water continues to wet the surface of the

piece as the last trace drains oﬀ. Rinse several times after the last cleaning in the

best quality deionized water you can ﬁnd.

(4) Air dry on a clean surface. Large parts can be dried gently with a clean heat gun or

in a clean oven.

Ultimate clean

If the contaminant on your parts doesn’t come oﬀ with the procedure described above

you may have to resort to organic solvents described below, or even chemical cleaning.

In outline the same process is followed but solvent and rinse chemicals are diﬀerent.

Flammable liquids should not be used in an ultrasonic cleaner and large quantities

should only be used in a high volume fume hood.

A typical procedure is to soak ﬁrst in trichlorethylene, followed by up to 10 min in

an ultrasonic cleaner. This is then followed by repeating the process with acetone, and

then methanol. Finally the parts are dried using a clean air fan, for example a heat gun

or hair dryer with the heat oﬀ.

Storage of UHV parts

Small parts are best stored in clean glassware. Large parts can have their ports covered

with aluminum foil, stretched across them but not touching the sealing surface, and

stored in polythene bags if necessary. All aluminum foil and plastic bags have some

organic or silicone oil on them, which could recontaminate your clean parts, so

beware!

Sample cleaning

The objective of sample cleaning is to prepare a surface with a well-deﬁned chemical

and structural state in a reproducible manner. The particular process used inside the

vacuum system tends to be very material speciﬁc, as discussed in the text. However,

some general types of technique used for preparation of samples are as follows. The

ﬁrst three apply to procedures before the samples are introduced to the vacuum system.

(1) Various forms of mechanical, chemical or electrochemical polishing are used to

make the sample surface as parallel as possible to the desired crystallographic

plane.

324 Appendix H

(2) Solvent cleaning is used to remove as much of the polishing contaminants as pos-

sible.

(3) Chemical cleaning and passivation of the surface is sometimes used with reactive

materials to reduce atmospheric surface contamination.

(4) Heating in the vacuum by resistive means, electron bombardment, or laser anneal-

ing can be used both to evaporate contaminants and to remove crystallographic

imperfections from the surface layers. Vapor pressure versus temperature curves

are very useful in this process.

(5) Ion bombardment or sputtering is used to remove surface material. Heating is used

to anneal out the subsequent damage caused to the structure.

(6) Oxidation is used both to remove contaminants and damaged surface material,

especially in refractory elements.

More details for selected elements can be found in the research literature, including

Musket et al. (1982). I have checked, using the WebofScience™ citation index, that this

reference is still used by workers researching surface and thin ﬁlm processes. We can

therefore use the web, in conjunction with older references, to track down what has

happened more recently, and which papers are thought to be valuable.

UHV component cleaning procedures 325

Appendix J

An outline of local density

methods

Although we introduced density functional theory (DFT) in section 6.1 in the context

of Lang and Kohn’s work on metal surfaces, the concept itself is much broader. It con-

sists of setting up a general single particle method to solve the Schrödinger equation

for the ground state of a many electron system by: (1) showing that the equation can

be solved variationally to give an upper bound to the energy of the system expressed

in terms of the electron density n(r), sometimes written

␳

(r); this theorem was intro-

duced by Hohenberg & Kohn (1964); and (2) proposing practical schemes whereby this

theorem can be implemented as an iterative computational method, starting from a set

of approximate wave functions describing the ground state of the electron system. The

main non-relativistic scheme in use is due to Kohn & Sham (1965). The pervasiveness

of these methods was recognized in 1998 by the award of the Nobel prize for chemis-

try to Walter Kohn (Levi 1998).

Writing down too many equations speciﬁcally here will take too much space, and

may encourage the reader to believe that the method is simpler than it actually is. Some

of the key review articles have been cited in sections 6.1.2 and 7.1.3. So many words

have already be spilt on the topic, the methods are so widespread, and yet no-one can

give a measure of just how good an approximation DFT represents, or say categori-

cally whether further developments such as GGA necessarily improve matters, that

there is no sense in which I should try to confuse you further. Nonetheless, this is a

good topic for an (ongoing) student project, and ﬁgure 6.1 was produced by Ben Saubi

from the original Lang and Kohn output data tables.

The DFT method is based on three coupled equations, and auxiliary ‘orbitals’

␺

which are othogonal to each other, but should not be confused with the real (many

body) wavefunctions of the system. The energy E is expressed as the sum of the electro-

static energy due to the external potential and a functional F[n(r)] of the electron density

n(r) at vector position in the material r. This functional is written as a sum of the kinetic

energy T[n(r)], the Coulomb self-energy of the electrons, expressed as the product

0.5n(r)

␸

(r), which

is integrated over the space d

r, and the exchange-correlation term

326

Here

␸

(r) is the electrostatic potential provided by all the other electrons. This potential is subject to the

consistency check provided by Poisson’s equation

ⵜ

␸

(r)⫹4

␲

n(r)⫽0. Don’t try to check the units, since

most theoretical papers use ‘atomic’ units, in which ប, e and m have all been set equal to 1.