# Basics of Vacuum Systems

The primary source of knowledge for this post is the first lecture of Experimental Condensed Matter which was delivered by Peter Grütter.

The primary things he wants to teach us in this section are:

1. Basic factors determining pump down times and ultimate pressure achievable for physical vacuum systems.
2. Material choices in vacuum applications. These can be important for many reasons. An example would be the necessity of high-temperature tolerance in those situations where we need to achieve very high vacuum since that is only possible if we ‘bake the system’. More on this later.
3. Some basic hands-on demonstrations of these concepts.

He believes that memorizing big formulas is not a high priority. His position is that the information is available as long as you know your basic concepts well enough to know that you should go look it up. When designing physical systems, we need to know the right questions to ask.

Vacuum systems are utilized for a wide variety of scientific and industrial applications. Some things brought up were signal to noise ratios for sensitive instruments, crystal formation, and insulating devices. This list is severely incomplete even as an outline of the applications that he spoke about in class.

## Mean Free Path

The mean free path of a particle is the average distance travelled by a particle between successive collisions. These collisions can be with other gaseous particles or with the walls of the containing vessel (if there is one).

If we need a molecule to land on a specific surface with a well-defined energy, we need to maximize its mean free path so that the other gas particles are not colliding with it and thus changing its energy. When creating layers of materials on top of a substrate, it is often necessary to hit the surface with molecules of a specific energy.

## Well-defined surfaces

On every surface, there is always contamination from the atmosphere. Much of this contamination is in the form of water. Water is polarized, so it will stick to anything. Tens of nanometers of water can build up! Even on hydrophobic surfaces there is a layer of water. We use high vacuum to help make a clean surface.

Contamination, even with water, can be bad for many reasons. For example, the surface tension of water (because it is so strong) can damage instruments such as a scanning tunneling microscope. You may also end up measuring the first layer of water and other deposited materials instead of the primary material of your surface.  The layer of water can also cause warping in thin films of material. You usually have to bake a vacuum system to get the water layer off of the surfaces.

To keep a surface clean for longer than a few seconds, you need a very high vacuum. Even millibars of atmosphere will deposit all kinds of junk.

The atomic version of sandpapering is shooting ions at the surface. This can actually damage the underlying surface as well, so you need to heat it again and anneal it to restore the structure.

Dr. Grütter talked about the following process flow in surface science:

1. Clean surface
2. Anneal it
3. Characterize it
4. Do experiment
5. Write paper
6. Graduate (Or get a raise.)

Even one part in a million for a surface layer can be a lot of impurity. Sometimes we do the first two steps: “clean surface” and “anneal it” in a cycle for weeks or months before we will have a clean crystal or surface.

## Question: How long does it take to cover a clean surface with 1ML?

First of all, the ML is a monolayer (one layer of material). Our class answered this question with estimates between 10s and 1 microsecond. These were just guesstimates. A closely related question is: How many atoms z strike a surface area per unit time at a given pressure?

$$z = \frac{1}{6}(1/6) u n$$

Where we have velocity u and particle density n. Writing this in more a more useful way gives us:
$$z = \frac{1}{6} p \sqrt{2N_A / (MkT)}$$
Where $$p$$ is pressure, $$N_A$$ is Avogadro’s number, $$M$$ is the molar mass, $$k$$ is Boltzmann’s constant, and $$T$$ is the temperature.

Our back of the envelope calculation in class was a demonstration of a rule of thumb in vacuum system design:

It takes about 1 second to absorb one monolayer at one microbar of pressure with a thermalized gas.

Aside: Adsorb is not a typo, this is referring to the process by which another atom or molecule becomes attached to a surface. Wikipedia defines it in terms of adhesion to a surface.

Under these conditions, we would need to do our experiment very quickly if it was sensitive to a monolayer of atoms on the surface. Having to do experiments quickly is problematic because the signal to noise ratio goes down.

Surface properties can become very important at nano scales. For example, nano wires might have as many surface atoms as bulk atoms!

Second layer and deeper layers can be very different than the first layer (and often are). This depends on a number of factors including the sticking characteristics of the layers.

## Basic components of a vacuum system

Here we look at a very simple layout for a complete vacuum system.

1. Pressure sensor
2. Vacuum system – the containment vessel for the vacuum.
3. Pump

We will look into some of the following topics in more detail later on.

The connectors between the parts of the vacuum system are very important. The width of the connecting tubes has a great effect on the effectiveness of the pump in terms of maximum vacuum attainable and pumpdown time (the length of time it takes to create a vacuum of a given level).

Which of these components leak, and how much?

Long pipes can also be problematic. Length of pipe linearly reduces the effectiveness of the pump for creating vacuum.

Location of the vacuum gauge matters. If you buy a system, where were they measuring its specifications? Manufacturers will often measure its statistics right at the mouth of the pump, while what you care about primarily is the effective vacuum that the pump can create in your vacuum system. For a real measurement, you would place the gauge in the evacuated space (the experimental space) rather than in the connecting tube.

## Pressure Units

Definition: 1 Standard Atmosphere: 760 TORR or 1013 millibar (mbar) at sea level 0ºC and 45º latitude.

Many people don’t distinguish between TORR and mbar, despite the ~30% difference between them. Why? The performance of these systems depends very strongly on the specific gases inside. The calibration curves generally do not take into account the composition of the gas. The error is usually about 25% for the calibration of vacuum systems. This is why it often does not matter very much whether you consider the units of pressure to be TORR or mbar.

Where does TORR come from? 760 mm of mercury is one atmosphere.

### Partial pressure

Each component gas in the atmosphere (or any contained gas) has its own pressure. The sum of all the partial pressures gives you the total pressure. In the atmosphere, some amount of the total pressure is due to each of: Nitrogen, Oxygen, Argon, CO2, etc.

Pressure sensors can sometimes detect certain types of gas more than others. Dr. Grütter mentions that Xenon and Oxygen might be detected differently with the same apparatus. Instruments may not be able to measure pressures accurately in all cases. This must be taken into account.

### Vapour Pressure

We look at the vapour pressure of water at various temperatures. Even ice at 0ºC has some non-zero equilibrium vapour pressure. This means that it off-gasses water molecules. This means that even ice in your vacuum system will emit vapour. This will stop you from achieving ultra high vacuum conditions.

### General pressure ranges

Rough (Low) Vacuum: 759 to 10-3 mbar
High Vacuuum: 1×10-3 to 10-8 mbar
Ultra High Vacuum less than 10-8 mbar

The difference between high and ultra high is essentially the fact that these systems need to be baked to get out the residual water molecules. Thus, the material choices are much more limited if you need to reach ultra high vacuum since they will need to be capable of withstanding temperatures of 100-200ºC.

If you want to do surface science, high vacuum is generally not good enough. You need ultra high vacuum.

## How do we create a vacuum

Here we discuss gas flow conductance where we draw an analogy between gaseous flow and electric current flow.

### Viscous and Molecular Flow

Viscous (or turbulent) Flow is characterized by momentum transfer between molecules. What is most important is how the molecules interact with each other.

Molecular Flow is the state where molecules flow essentially independently of one another. Typical collisions are with the walls rather than with other molecules. Here we can treat molecules independently.

Consider gas conductivity as analogous to electrical conductivity because we can add up resistances in parallel, series, etc in a similar fashion.

Mean Free path and Molecular Density at various pressures. In air under standard conditions, the mean free path is about a micron. Under ultra high vacuum we can reach mean free paths of 50+km.

Interplanetary space is high vacuum. Interstellar space is very high vacuum.

Mean free path over the characteristic dimension of the containment vessel is a useful quantity for defining various flow regimes. If the mean free path is the same as or longer than the characteristic dimension, we have molecular flow. If it is shorter, then we are in the realm of viscous/turbulent/laminar flow.

### Conductance

Conductance for Viscous flow in a cylindrical pipe: The conductance is inversely related to pipe length and proportional to the 4th power of diameter!!! This means that under viscous flow, doubling the pipe diameter will increase the conductance 16 times.

Conductance in molecular flow (long round tube) equation:
$$C = 3.81 \frac{d^3}{l} \sqrt{T/M}$$
T is temperature, M is A.M.U., D is diameter in cm, l is length in cm, C is in litres per second. If you want to see the derivation of this formula, there is a paper online that has it.

Pumps will have a given pressure p and pump speed S. The throughput of the pump is Q = pV/t = pS where t is time. The effective pressure $$p_{eff}$$ is not equal to the pump pressure p.

1. $$S = Q/p$$
2. $$S_{eff} = Q/p_{eff}$$
3. $$C = \frac{Q}{(p_{eff} – p)}$$
4. $$\frac{1}{C} = \frac{1}{S_{eff}} – \frac{1}{S}$$
5. $$\frac{1}{S_{eff}} = \frac{1}{C} + \frac{1}{S}$$
6. $$S_{eff} = \frac{SC}{S+C}$$

This means that S_eff ~ C for C << S. This condition is common. This means that the connection is usually the limiting piece, not the pump. This effect is noticeable in terms of both pumping speed and maximum vacuum attainable.

### Pumpdown time

The pumpdown time for a given volume $$V$$, with an effective pump speed $$S_{eff}$$, an effective pressure $$p_{eff}$$, and a starting pressure of $$p_{start}$$.

$$t = 2.3 (\frac{V}{S_{eff}}) log_{10} (\frac{p_{eff}}{p_{start}})$$

The 2.3 came from converting ln to log10.

Gas load is the sources of gas in the vacuum system. It is usually written as Q, and is expressed in mbar litres per second. The gas load for a typical system is due to:

1. Out-gassing of surface atoms.
2. Permeation from outside. Nothing is perfectly impermeable.
3. Leaks (both real and virtual). What is a virtual leak? It is a trapped volume of gas due to bad design of the system. For example, some gas can be trapped in a screw hole below the bottom of a screw.  Screws are usually put in during 1 ATM. Screws may be put in very tightly, but the trapped gas can slowly leak. This can be fixed by drilling the hole right through. Bigger hole means that the gas can move out more effectively, leading to higher vacuum because there is less flow ‘resistance’. Alternatively you can drill an extra angled hole as a shunt.
4. Diffusion
5. Backstreaming from the pump side.  Pumps aren’t perfect. They allow some gas to escape back into the system.

## Troubleshooting a Vacuum System

You had a working vacuum system, you shut it down, change some small things, and fire it up again. Now your vacuum is nowhere near as good as it was. What happened? What can you do?

Even a single fingerprint can have huge consequences for vacuum systems. Consider the number of fatty (oil) atoms from a fingerprint that is a few microns deep. These atoms can be a big problem if you are trying to achieve ultra high vacuum.

One major troubleshooting tool is the pumpdown curve. The pumpdown curve is a graph of pressure vs time. To see an example of one, see here.

The key facet to this analysis is that different types of gas load have different signatures on the pump down curve. The initial volume of gas in the vessel is typically gone quickly. Then we see the effects of surface desorbation, diffusion, and permeation in that order. Permeation never goes away because it is constant.

## Hands-on

### O-ring seal

The O-ring seal, or ‘quick flange’ is a typical easy-to-use seal. It involves 2 pieces, an O-ring, and a clamp. The clamp closes on the flange, pressing on the angled metal sides, causing the sealing action.

Not much force is actually needed to seal these, despite what people tend to think.

Scratches are the most major problem. A single scratch that crosses the O-ring area will leak atmosphere. Tightening the O-ring will not stop the leak from a scratch. The only way to fix it is to either polish the surface again or get another piece.

Vacuum grease is used a lot for quick flanges. Dr. Grütter isn’t a big fan of vacuum grease because it tends to acquire dust particles when it is in normal air. Dust particles are often silicone dioxide, an incredibly hard substance. Apparently it is harder than the metals that form the O-ring seal, because use and re-use of vacuum grease can lead to scratches from the dust particles.

### CF (Conflat) Seal

The CF or Conflat seal uses a copper ring that is squeezed between two metal pieces that have small knife edges on them. The knife edges cut into the copper, creating an incredibly good seal. These seals can be used for achieving ultra high vacuum.

Overtightening can be very bad, since the knife edges can sometimes hit each other after they have cut through the copper.

The copper rings are generally not reusable, but they cost only about \$1 each so they are cheap to replace.

The bolts must be tightened in a pattern similar to that for tightening bolts on a car.

How do you mount it sideways? Find a way to hold the ring in place while you put on the other side of the seal. Dr. Grütter says you can use a bit of scotch tape to hold it there while you put the seal together. Once you have the seal together, take off the scotch tape. If you bake the system you will have melting/burning scotch tape to deal with. Another technique is to use a gold loop to hold the ring up while you seal it.