Mean free path [PDF]

Vacuum Technology

Text books: (1)

A User’s Guide to Vacuum Technology Author: F. O’Hanlon ISBN: 0471270520 Publisher: Wiley –Interscience; 3rd edition (2003)

(2)

真空技術與應用(Vacuum Technology & Application) Authors: 行政院國家科學委員會 ISBN: 9570286768 Publisher: 精密儀器發展中心

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

Vacuum Application -

To create a new gaseous environment, e. g. to remove gas in a distillation process. To prevent a clean surface from contamination by air. To prevent a particle beams from colliding with air molecules. An essential part of, e. g., mass spectrometer, electron microscope, far-IR and far-UV spectrometers.

Energy Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

Vacuum Application

半導體製程學程 半導體製程概論

真空技術

蝕刻製程

薄膜製程

擴散製程

微影製程

Vacuum technology

Etch

Thin film

Diffusion Lithography Ion implantation

半導體元件物理 材料分析

-- flat-panel -- solar manufacturing -- scientific instrumentation -- solid-state lighting  More than 70 industrial application

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

Vacuum Application - Semiconductor Industry

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

Vacuum Application

http://www.electroiq.com/inde x/display/articledisplay.articles.solid-statetechnology.semiconductors.su bsystems.currentand_future.QP129867.dcmp=r ss.page=1.html

2007 US$ 6 Billion Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

ITS BASICS 1. Vacuum Technology

4. Gas Release from Solids

1.1 Unit of Measurement

4.1 4.2 4.3 4.4 4.5

2. Gas Properties 2.1 Kinetic Picture of a Gas 2.2 Gas Laws 2.3 Elementary Gas Transport Phenomena

3. Gas Flow 3.1 3.2 3.3 3.4 3.5 3.6 3.7

Flow Regimes Throughputs, Mass Flow, and Conductance Continuum Flow Molecular Flow The Transition Region Models Spanning Several Pressure Ranges Summary of Flow Regimes

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

Vaporization Diffusion Thermal Desorption Stimulated Desorption Permeation

1. Vacuum Technology 1643 1644 1650 1874 1905 -

Torricelli, understanding vacuum within a mercury column. Viviani, performing the first experiment. Otto von Guericke’s, piston vacuum pump. McLeod, mercury pressure gauge. Gaede, rotary pump sealed with mercury.

Thermal conductivity gauge, diffusion pump, ion gauge, ion pump, helium refrigerator pump, organic pump fluid, etc.  Applications from light bulbs to space simulations.

“One man’s vacuum is another man’s sewer.” -----

-N. Milleron(1970)

The nature of a vacuum. The limitation of a vacuum apparatus. Economic constraints to build a vacuum equipment. Choose compatible vacuum components for a vacuum equipment.

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

1. Vacuum Technology ** From atmospheric pressure to vacuum, 　  A molecule from one wall can travel to another without a collision. The increment of its mean free path. ** Many effects become possible: -- Metals can be evaporated from a pure source without reacting in transit.　  Metal deposition -- Molecules or atoms can be accelerated to a high energy and sputter away, or to be implanted in the bombarded surface.　  Ion implantation, Ar sputtering. -- Electrons or ions can be scattered from surfaces and be collected. The energy changes used to probe or analyzed the surface or underlying layers.　  CD SEM, SIMS.

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

1. Vacuum Technology Definition of “vacuum”

1.3 x 104 Pa ~ 100 torr 1.3 Pa ~ 0.01 torr 1.3 x 10-7 Pa ~ 10-9 torr

-- 1 bar = 105 Pa -- 1 atm = 101325 Pa = 760 torr = 760 mmHg -- 1 torr = 133.32 Pa Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

1. Vacuum Technology ** Vacuum requirements: Low vacuum – epitaxial growth of semiconductor films, laser etching of metals. Medium vacuum – sputtering, plasma etching and deposition, LP CVD, ion plating. High vacuum –microwave, power, cathode ray, PMT, ion implantation, etc. Very high vacuum (HV) – Electron microscopy, mass spectroscopy, crystal growth, x-ray and e-beam lithography. Ultrahigh vacuum (UHV) – surface analysis, material research, EUV lithography. • Number density (N/V) at 1 atom (760 torr) at 20ºC, pV= nRT

 1 atm = (n/V) mol L-1(0.08206 atm L K-1mol-1)(293.15 K) K　  n/V = 4.16 x 10-2 mol L-1　  N = N/V = 2.5 x 1025 molec m-3

under 1 atm.

• Number density (N/V) at 10-7 Pascal (~10-9 torr) at 20ºC, 10-7 Pa = (n/V) mol m-3 (8.314 J K-1 mol-1)(293.15 K) 　

n/V = 4.1 x 10-11 mol m-3　

13 molec m-3 N = N/V = 2.5 x 10 Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

under 10-7 Pa

1. Vacuum Technology Evacuation

Air  Molecules desorbed from the walls, mainly water.  H2

1. Displacement pump to remove the air from the chamber and expels it to the atmosphere.: Rotary and piston pump, sorption pump. 10-1–10-3 Pa (mtorr range). 2. Displacement pump to reach low pressures: Diffusion pump, turbomolecular pump. Need “backing”(fore) pump. 10-4 – 10-7 Pa (10-6 – 10-9 torr). (high backing pressure  an additional lobe blower in between) 3. Capture pump effective to remove gas from a chamber at low pressure: Cryogenic pump, getter pump, ion pump. < 10-8 Pa (10-10 torr)

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

1. Vacuum Technology Evacuation

Air  Molecules desorbed from the walls, mainly water.  H2

** Water pressure is not a constant, it is temperature dependent. ** At 20°C, the relative humidity of water of 50% ~ 1165 Pa (8.75 torr). (third largest constituent of air) Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

1. 1 Units of Measurement MKS system Meter – Kilogram – Second Length: m Pressure: Pa Time: s

SI base units: m (meter) kg (kilogram) s (second) A (ampere) K (Kelvin)

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

2 Gas Properties 2.1 Kinetic Picture of a Gas Assumption: (i) A large number of molecules / unit volume. At 22°C, 105 Pa, N = 2.5 x 1025 m-3 10-7 Pa, N = 2.5 x 1013 m-3

** Molecules evenly distributed throughout the volume:

3.26 * 1016 cm-3 torr-1

(ii) Adjacent molecules (d ~ 2 –6 x 10-10 m) are relatively far apart. At 105 Pa, adjacent molecules are 3.4x10-9 m apart = 6 –15 times of the diameter. (iii) Molecules are in a constant state of motion. Equal partition in x, y, and z directions, all velocities are possible. (iv) Molecules exert no force on one another except when they collide. Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

2.1.1 Velocity Distribution **

Maxwell – Boltzmann distribution of particle velocities:

3/ 2

 m  2  mv 2 / kT f ( v ) 4 v exp     ** Distribution of speed: 2 kT    Peak velocity (the most probable velocity) = (2kT/m)1/2 Mean velocity = (8kT / πm)1/2 1.128 1.225 Root mean square velocity = (3kT / m)1/2 Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

½ m = 3kT/2

2.1.1 Velocity Distribution ** Maxwell –Boltzmann distribution of particle velocities: Example: The mean (average) velocityof a molecule for air at 20°C, Mean velocity = (8kT/πm)1/2 = (8RT/πM)1/2 = (8 x 8.314 x 297.15/(πx 0.0288))1/2 = 467 m s-1 ~ 0.5 km s-1

- The Maxwell – Boltzmann distribution is quite broad, over 5% of the molecules travel at velocities greater than two times the average velocity. Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

3/ 2

4  m  2 mv dn  1/ 2   ve dv   2kT 

2.1.2 Energy Distribution dE = d( ½ mv2) = mv dv 3

dn 4 N 1  m  2 2  mv  1/ 2   ve dE  mv  2kT 

1/ 2

E  1  E  ( kT ) a   e  kT  kT 

2

/ 2 kT

2

/ 2 kT

2 N E 1/ 2  E / kT  1/ 2 3/ 2 e  kT  The most probable energy: d(dn/dE) = 0  Emost probable = kT/2

** Both Emost probable and Eaverage are dependent on temperature only, and are independent on the molecular mass. Example: Gases in Figure 2.2, having the same average temperature, have the same energy distribution.

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

2.1.3 Mean Free Path (MFP)

** Collision frequency Z = σvrelN = 2 Nπd2 vavg = σvrel p/kT ** Time between collision = 1/Z ** Mean free path = λ= vavg/ Z =

vrel = (8kT/πμ)1/2 N = nNA/V = NAp/RT = p/kT

kT 1  2 2d p 2d 2 N

λ: gas density and temperature dependent. Example: For air at room temperature, (P. 467, dair = 0.372 nm) λ(m) = 0.0067 / P(Pa), λ(cm) = 0.67 / P(Pa), or λ(cm) = 0.005 / P(torr) Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

2.1.3 Mean Free Path (MFP) ** The distribution of free paths: N’= N e-x/λ 0 ≤x ≤λ, 63% of the collisions λ≤x ≤5λ, 37% x > 5λ, < 0.6% ** The mean free path of a in b: -- Collision frequency

Zb  vrel ,a b N b



d

4 2 Za  vrel ,a a N ad a

 db  a

-- Time between collision = 1/(Za + Zb) -- Mean free path = λa = vavg,a/ (Za + Zb)



8kT vrel  ma  mb  ma  mb

2

1

1/ 2   1/ 2  ma  1 2 2 2  N b  d a  d b  2 N ad a  1  4  mb   

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

2.1.4 Particle Flux ** Collision frequency per unit area:

Γ = Nvavg/ 4 s-1m-2 = N(kT/2πm)1/2 = p/(2πmkT)1/2

Number of collisions 

 NAt 0 vx f (vx )dx

Example: Assume unit sticking probability and a molecular diameter d = 3 x 10-8cm: 1. To cover 1 cm2 surface by the closest pack arrangement requires: 1 cm2/{ 1 molec* 31/2 r2 cm2 molec-1} = 1.3 x 1015 (molecules) 2. The number of collision per 1 cm2 surface: Γ= 3.3 x 1016 molec cm-3 torr-1 x p torr x 46700 cm s-1 x 1 cm2/ 4 = 3.9 x 1020 s-1 x p (torr) 3. Time required to form a monolayer of adsorbed air molecules at 20°C:　  t = 1.3 x 1015/ {3.9 x 1020 s-1 x p( in torr)} = 3.3 x 10-6/ { p ( in torr)} second

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

2.1.4 Particle Flux ** Collision frequency per unit area:

Γ = Nvavg/ 4 s-1m-2 = N(kT/2πm)1/2 = p/(2πmkT)1/2

Number of collisions 

 NAt 0 vx f (vx )dx

** Time required to form a monolayer of adsorbed air molecules at 20°C:　  t = 3.3 x 10-6/ { p ( in torr)} second

2.1.5 Monolayer Formation time 1 4 tml  2  2 d 0 Nvavg d 0 Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung

** Sticking coefficient

2.1.6 Pressure ** From the “Kinetic Molecular Theory”, ** The total translational energy of a molecule, ** The ideal gas law,

1 2 P  Nmvrms 3 1 2 3 E  mvrms  kT 2 2 P  NkT

Grace H. Ho, Department of Applied Chemistry, National University of Kaohsiung