Lecture 3 Vacuum Science and Technology

Transcription

1 Lecture 3 Vacuum Science and Technology Chapter 3 - Wolf and Tauber 1/56

2 Announcements Homework will be online from noon today. This is homework 1 of available marks (distributed as shown). This contributes 25% of homework grade. 7.5% of class grade. Please hand in at the start of class next Thursday (5 th October 10am). I will give your homework back at the start of class Thursday 12 th October. The solutions will go online at noon on the 12 th. 2/56

3 Announcements Office hours this Monday (2 nd October) will be moved to: 2pm 3pm. 3/56

4 Why Vacuum Science and Technology? It is a large subject area. There is a journal Vacuum Science and Technology A good vacuum is crucial in semiconductor processing. There are a range of pumps and approaches. Useful knowledge for when you break your advisors pumps. 4/56

5 Lecture 3 Kinetic Theory of Gases. Types of Vacuum Pump. Pressure Gauges. Residual Gas Analyzers. 5/56

6 Kinetic Theory of Gases 6/56

7 Kinetic Theory of Gases Kinetic theory provides us with a model (or a way of thinking about) the gas phase processes in Si manufacturing. It invokes atomic theory: all matter is made up of discrete atoms or molecules. Liquids and solids: atoms are closely spaced relative to their size. Gases: atoms or molecules are far apart. There are still lots of molecules in a gas (2.7 x cm -3 at 1 atm). Si processing mainly deals with vacuum processes (others at 1 atm), can assume ideal gas behavior. Ideal gas: gases consist of infinitely small rigid spheres which only interact with each other during the period of direct collision. 7/56

8 Brownian Motion Molecule in motion in a gas colliding with other molecules in its path; all other molecules are also in motion. 8/56

9 Kinetic Theory of Gases Perpetual motion of collisions on a atomic scale. The degree of motion is determined by the macroscopic variable: Temperature. E = 1 2 mc2 = 3 2 k BT E: Energy. m: Particle mass. c: Particle velocity. k B : Boltzmann Constant Note, we don t use v T: Temperature. Through elastic collisions, the speeds of the molecules become randomized, i.e., different molecules have different speeds. While the speed of a given molecule may change via collision, the entire population of molecules obtains a fixed distribution of velocities (or equivalently energies) at equilibrium. 9/56

10 Maxwell-Boltzmann distribution This distribution is characterized by the Maxwell-Boltzmann distribution function: P c = 4 π m 2k B T Τ 3 2 c 2 exp m 2k B T c2 P: Probability. m: Mass. k B : Boltzmann Constant. T: Temperature. c: Particle speed. 10/56

11 Maxwell-Boltzmann Distribution Most probable velocity: cҧ Argon at 300 K c m c m c cc rms rms c m = 2k BT m Average (mean) velocity P(v) P c c ҧ = 8k BT πm Root-mean Squared velocity: c rms = 3k BT m cv (cm/s) 11/56

12 P c P c Maxwell-Boltzmann Distribution T=300K 4 He 20 Ne 40 Ar 132 Xe T=900K 4 He 20 Ne 40 Ar 132 Xe 12/56

13 Important Parameters Pressure, P: The force per unit area on the walls of a container associated with the elastic bouncing of molecules from a wall: P = nk B T Collision frequency, ν: The number of collisions a molecule undergoes per unit time. nu v n: Particle number density Mean free path, λ: The distance, on average, a molecule goes between collisions. (63% of collisions occur within λ, 36% occur between λ and 5 λ.) λ = 1 2πd 0 2 n d 0 : Molecular diameter Impingement Rate or Flux, J A : # molecules A that hit a surface per area per time: J A = 1 4 n Acҧ 13/56

14 Pressure Pressure has many units, and many are commonly used. Pascal is the SI unit, but few vacuum equipment manufactures use pascals as a pressure scale. These conversions are linear: Unit Pascals 1 Pascal 1 1 Torr Bar atm /56

15 Example 1 Determine the mean free path of Ar atoms at a pressure of 10-4 Torr at 300K. Determine the mean free path of Ar atoms at a pressure of 1 Torr. We need to know: λ = 1 2πd 0 2 n Boltzmann Constant: m 2 kgs -2 K -1 Molecular diameter of Ar = 4Å. 1 Torr in Pascals: 1 Torr = 133 Pa. 15/56

16 Example 1 First we need to know the number density of particles at this pressure: P = nk B T n = P k B T We are given the pressure in Torr, so need to convert to SI units (Pa): P pascals = P torr P torr = 10 4 P Pa 16/56

17 Example 1 The number density is therefore: n = P m 2 kgs -2 K -1 k B T n = m Pa 300K We know the molecular diameter of Ar is 4Å. λ = 1 2πd 0 2 n m m 3 λ = 0.44 m 17/56

18 Ar at 300 K Calculate the mean free path for various pressures. Remember to convert to SI units! Molecular diameter of Ar = 4Å. n = P k B T λ = 1 2πd 0 2 n P (Torrr) P(Pascal) n (m -3 ) λ (m) , /56

19 Example 2 What is the impingement rate (flux to a surface) of Ar at 300 K and 10-6 torr? We need to know: Mass of Ar: m= amu Atomic mass unit = 1 amu = kg Boltzmann Constant: m 2 kgs -2 K -1 1 Torr in Pascals: 1 Torr = 133 Pa. Quantity / area / time J A = 1 4 ncҧ We need to find n and c. ҧ 19/56

20 Example 2 First determine n: P = nk B T n = P k B T We need pressure in SI units (Pascals): P pascals = P torr P torr = 10 6 P Pa 20/56

21 Example 2 Argon concentration is therefore: n = P m 2 kgs -2 K -1 k B T n = m Pa 300K We also need the average particle velocity: c. ҧ c ҧ = 8k BT πm We need to know the mass of Ar atoms. 21/56

22 Example 2 Mass of Ar atom is: m = amu 1 amu = kg m = kg m = kg Now determine average velocity: c ҧ = 8k BT πm 300K c ҧ = 399 m/s 22/56

23 Example 2 Now we can determine the impingement rate: m 3 J A = 1 4 ncҧ 399 m/s J A = m 2 s 1 J A = cm 2 s 1 23/56

24 Example 3 With the impingement rate known, determine the amount of time required to form a monolayer on a substrate. We need to know: The impingement rate: J A = cm 2 s 1 Sticking coefficient: S c = 0.1. Atomic diameter of Argon: d A =4Å Probability of atom sticking to substrate. 24/56

25 Example 3 Determine areal density of a monolayer of Ar. Assume atoms pack on surface as simple 2D array: d A Ar d A Area occupied per atom is: A = d a 2 A = m 2 A = m 2 = cm 2 25/56

26 Example 3 Determine areal density of a monolayer of Ar. Areal density: n 2D = 1 A cm 2 n 2D = cm 2 Remember: A impingement rate (J A ) of 1 cm -2 s -1, means that 1 particle per cm 2 hits the surface every second. If the impingement rate is cm 2 s 1 then an area of 1 cm 2 will receive particles every second. 26/56

27 Example 3 Therefore to form a layer with a density of n 2D = cm 2, at an impingement rate of J A = cm 2 s 1, we would have to wait t seconds: cm 2 s 1 t = n 2D J A S c 0.1 t = 19.5 s cm 2 27/56

28 Types of Vacuum Pump 28/56

29 Vacuum System A typical vacuum system is made of four parts 1) Gas supply 2) Reaction chamber 3) Pumping system 4) Gauges and control Reaction Chamber Gas Supply Gauge P Pumping System Exhaust 29/56

30 Gas Flow Mean free path Representative dimensions of chamber Viscous Flow: (λ<<d) collisions between atoms dominate collisions with wall. There are two main types: Laminar Flow: characteristic of lowers flow rates where fluid stream lines move parallel to each other; typical for vacuum systems. Turbulent Flow: characteristic of higher flow rates where eddies form Molecular Flow: (λ >>d) collisions with wall dominate collisions between atoms. Characteristic of high vacuum. Transition Flow: (λ = d) collisions with wall roughly equal to collisions between atoms. Knudsen Number, Kn: Single parameter (not K n) Kn = λ d 30/56

31 Pumping Speed & Pressure Pumping speed. Pumping speed refers to the gas flow rate through the system. Larger pumps give higher pumping speed. Choice of pump size and type determines pumping speed of gas. Ultimate and operating pressure. Different types of pumps are able to achieve different pressures. Choice of pump type determines the ultimate and operating pressure. Pumping speed depends on pump size and type Ultimate & operating pressure depend on pump type. 31/56

32 Vacuum Pumps Pumps used to achieve low vacuum (750 to 10-3 torr) are called low vacuum pumps. The dry mechanical pump and the Roots blower are examples of low vacuum pumps. Pumps used to achieve high vacuum (1 to torr) are called high vacuum pumps. The turbo pump and the cryo pump are examples of high vacuum pumps. 760 torr 10-3 torr torr Low Vacuum High Vacuum Atmospheric pressure 32/56

33 Viscous Flow Viscous flow is possible when there is a lot of gas (high pressure.) If part of the bulk is moved in one direction, the remaining bulk comes in to fill its space. It is like pumping water. Tank (B) Tank (A) Pump 33/56

34 Molecular Flow Molecular flow occurs at high vacuum. At high vacuum there are so few molecules in the gas that it does not behave like a bulk. The molecules behave like individual particles that need to be moved individually. It is like the flow of gravel from ground to the truck shown below. Collect individual stones into a pile Bulk mover moves the gravel to the truck 34/56

35 Rotary Pump Widely employed and cheap. Inlet Outlet Employed to reduce pressure from atmosphere (10 5 Pa) to medium range: Pa. Rotor Vanes Housing Spring 35/56

36 Rotary Pump a: b: c: d: e: f: 36/56

37 Diffusion Pump Developed 1913; used extensively in the early years of semiconductor processing. No moving parts. Require a backing (rotary) pump. Pressure range: 10-1 to 10-4 Pa. Downside: oil contamination. 37/56

38 Diffusion Pump Chamber Jet caps Cooling coils Backing pump Used in conjunction with a backing pump (e.g. rotary pump) to draw gas through the diffusion pump. Oil is heated up to boiling point, and vapor rises up the chimney. The vapor direction is reversed by a jet cap. Heaters Oil Bath The lower pressure of the jet caps the oil acquired supersonic speed. This means it leaves directionally downwards, rather than isotopically. 38/56

39 Diffusion Pump Chamber Gas from chamber is pulled through diffusion pump. Cooling coils Backing pump On average particles from the chamber (black dots) will acquired momentum from the oil, taking them towards to walls of the diffusion pump. The oil (and particles from chamber) then condenses and heads back towards the oil bath. Heaters Oil Bath 39/56

40 Cryogenic Pump Works in a similar way to a conventional refrigerator: Refrigerant is compressed, then allowed to expand, reducing its temperature. Cryopumps use He in the gas phase (20K). Require a backing (rotary) pump. Pressure range: 10-1 to 10-7 Pa. Performance depends on gases present. Less susceptible to damage if exposed to atmospheric pressure. 40/56

41 Cryogenic Pump Chamber 77K refrigerant Gas is pulled through cryogenic pump by backing (rotary) pump. Condensing arrays (static) Backing pump 20K refrigerant Water molecules condense onto first stage (77K refrigerant). N, O and Ar condense onto second stage (20K refrigerant). H, He, Ne are adsorbed onto the second stage. H 2 O N O Ar H He Ne 41/56

42 Turbomolecular Pump Require a backing (rotary) pump. Cannot run until low pressure is achieved blades will be damaged. Pressure range: 10-1 to 10-9 Pa. Commonly employed. 42/56

43 Turbomolecular Pump Chamber Turbine blades Stator blades (static) Backing pump Blades are designed to transfer momentum to molecules, forcing them downwards. Molecules preferentially hit the lower side of the blades ~10k rpm. Needs low vacuum or blades can be damaged. 43/56

44 Pressure Gauges 44/56

45 Capacitance Manometer For high pressures. Range from above atmosphere (760Pa) to 10 Pa. Useful for gloveboxes for example. One side is evacuated, the other is exposed to the vacuum chamber. A diaphragm will move an change its distance from the electrodes. This is detected as a change in detected capacitance. Diaphragm Electrodes Evacuated Chamber 45/56

46 Thermocouple Gauge Useful for backing pump pressure ranges: 100 to 0.1 Pa. A filament is heated with electrical current. A thermocouple then detects the temperature of the filament. The filament temperature will depend on the pressure in the chamber. Heater filament Chamber Thermocouple wire 46/56

47 Ionization Gauge Useful for high vacuum: 0.1 Pa to 10-8 Pa. Hot filament is used to create electrons. Electrons are attractive to grid. These electrons ionize gas molecules. These ions flow to cathode and can be detected as current. 47/56

48 Residual Gas Analyzers 48/56

49 Residual Gas Analyzers Sometimes we wish to know the content of gas. Residual gas analyzers (RGAs) identify the gases present in vacuum environments. Basically they are a type of mass spectrometer. Gas molecules are ionized when they enter RGA. They are then deflected by a magnetic field. Their mass / charge ratio is then detected. Relative intensities of each molecule are reported. 49/56

50 Residual Gas Analyzers Detector Gas enters residual gas analyzer from chamber. Magnetic Field Hot filament generated directed electrons. H 2 O + O 2 + N 2 + etc. e - e - e - N 2 O 2 H 2 O etc. Gas molecules are ionized when they enter RGA. They are then deflected by a magnetic field. Their mass / charge ratio is then detected. Relative intensities of each molecule are reported. 50/56

51 Quadrupole RGAs Quadrupole residual mass spectrometers are commonly used for this application. 4 cylindrical rods are present in the quadrupole RGA. 51/56

52 Quadrupole RGAs A combination of AC and DC signals are applied to the cylinders. 52/56

53 Quadrupole RGAs For a set combination of frequencies and biases, only ions of a particular mass-to-charge ratio are able to pass through a filter, to the detector. 53/56

54 Quadrupole RGAs Provides much better sensitivity to the ions of interest. 54/56

55 RGA Spectra Base conditions Flowing Ar 55/56

56 RGA Spectra SiH 4 in chamber ionizer off plasma on 28 Si + 29 SiH + 30 SiH SiH SiH /56