Photomultipler tubes, or phototubes for short, consist of a photocathode (cathodes in any electrical device are ``emitters'' of electrons) coated with alkali metals (see the diagram below). A single photon of light
striking the photocathode liberates an electron from the metal via the photoelectric effect. These electrons are guided and accelerated by an electric potential to a positively charged secondary-emission electrode (dynode), where they free up still more electrons by direct collision and energy loss. These electrons are similarly accelerated to the next dynode where they free up still more electrons (only the first two stages of electron multiplication are shown above). Typically, at each stage, about 4 secondary electrons are emitted for each incident electron. Therefore, large amplification or gain factors are possible with just a few stages of dynodes. Gains as high as 10^8 (i.e. 10 million electrons out for a single photon in) can be achieved with 14 dynode stages. Phototubes are widely used in astronomy for precision measurements of the brightness of stars and galaxies since they provide a pulse for each incident photon. The number of photons detected in a specific time is a measure of the optical targets apparent brightness.
Photomultipliers can be operated in continuous mode (i.e. under constant illumination), or in pulsed mode (e.g. with scintillators). In either mode, if the cathode and dynode systems are assumed to be linear, the current at the output of the phototube will be directly proportional to the number of incident photons. If the phototube is connected to a scintillator whose photon output is proportional to the total energy left by ionization in the scintillator material, then the phototube output is not only capable of detecting the presence of a particle but also the energy it deposits in the scintillator.
The technology advances behind phototubes are driven by their indispensible use in military and scientific applications. The drive is to produce phototubes with fast transit times from the cathode to the output dynode (this is on the order of tens of nanoseconds) with a jitter in the time of much less than 1 nanosecond. There are also strong pushes on to make phototubes physically smaller for the same performance, phototubes with multiple channels that can separately view and amplify small regions of a field of view, operate inside strong magnetic fields, and have high quantum efficiencies. The state-of-the-art today is phototubes with up to 128 separate anodes and those with time jitter less than 100 picoseconds.
The analog output of the phototubes is converted to a digital signal through a chain of amplifiers, discriminators, and either charge to voltage converters or scalers which store the number of photomultiplier pulses of a particular magnitude. The amplifiers serve to magnify and ``clean up'' the phototube pulse outputs. Discriminators reject pulses with amplitude less than a certain threshold and pass on those pulses with amplitudes above this threshold. They thereby discriminate against noise pulses.
A more detailed look at phototubes is offered in the following text. The information is derived from several sources. One of the most authoritative is "Techniques for Nuclear and Particle Physics" by W.R. Leo.
E = h * f - W where E is the electron energy, f is the frequency of the incident light, h is Planck's constant, and W is the work function, or amount of energy necessary to just free an electron from the surface of the material. Because of the non-zero value of W, it is obvious that the efficiency of detecting photons below a certain frequency is zero. Above the minimum frequency, the quantum efficiency is defined as the number of photoelectrons released divided by the number of incident photons. The quantum efficiency is a strong function of the frequency (or conversely, the wavelength) of the incident light. The graph below shows the quantum efficiency vs. wavelength for some of the materials used in phototubes today.
Since it is obvious that only a particular band of wavelengths are efficiently converted for a given material, some care should be used in making sure that the phototube is sensitive in the region where one's signal is being produced. For the case of Cerenkov light, we note that the formula for amount of light produced as a function of light wavelength peaks strongly in the short wavelength regime. We are lucky in that all the materials shown have their highest quantum efficiency in the region around 400 nm, our region of interest.
The accelerating electrode is held at the same potential as the first dynode of the electron multiplier. This accelerating electrode, in conjunction with the focusing electrode on the side of the glass housing of the photocathode, delivers equipotential lines which meet the following criteria:
In order to increase the size of the signal generated by a photon impact, the dynodes must be inside an electric field which both accelerates and guides the electrons along the multiplier. Hence, a dynode consists of a secondary emission material deposited on a conducting material. A common technique is to form an alloy of an alkali or alkaline earth metal with a noble metal. During the mixing process, only the alkaline metal oxidizes, so a thin insulating coating is formed on a conducting support. Materials in common use are Ag-Mg, Cu-Be, and Cs-Sb. All of these have the requirements of a good dynode material:
Most phototubes contain 10 to 14 dynode stages and have overall gains of up to 10^7, i.e. 10 million electrons out for a single photoelectron in.
New materials, such as Gallium Phosphide heavily doped with zinc and a small quantity of cesium, have a negative affinity for electrons. In other words, their work function is negative! A photon simply needs to provide enough energy to get an electron to the surface of the material and it is free! The gain of a dynode made from this material is greatly increased so that fewer stages are needed to get the same degree of gain. This makes for smaller phototube assemblies and smaller time fluctuations for the signals (hence better time resolution) since the cascade path for electrons is shorter.
There are many arrangements of dynodes possible for phototubes. At present, five types of configurations are used:
Below is a picture of the microchannel plate configuration. This is the most popular type of arrangement for modern phototubes.
The primary reasons are time resolution and resistance to magnetic fields. Considering the older types, we find, for example, that the Venitian blind configuration places the dynodes as wide strips at angle of 45 degrees to the electron cascade axis. The arrangement is simple and it offers a large input area to the incident primary electrons. However, it is impossible to prevent a fraction of the primary electrons from going straight through the arrangement. Hence, there are large variations in transit times. The electrons going straight through arrive first while the amplified signal is straggled out over later times.
Development work in image intensifiers, primarily for military applications, led to the development of microchannel plate devices. These consist of a lead glass plate containing a array of microscopic holes or channels, with typical diameters being 10 to 100 microns. The channels are oriented parallel to each other and their inner surfaces are coated with a semiconductor material which acts as a secondary electron emitter. The flat end plates are coated with a metallic alloy so that a potential difference can be maintained along the length of the channels. Electrons which enter a microchannel are accelerated and eventually hit the wall of the microchannel and produce many new electrons. These electrons, in turn, are accelerated along the microchannel until they strike the wall and produce still more electrons as shown in the figure above.
Since each microchannel plate can have between 10^4 and 10^7 holes and provide a gain of 10^3 or 10^4. Two or three plates can be cascaded together to provide a very high overall gain. The small size of the plates means that phototubes based on them can deliver their gain in just a few nanoseconds as opposed to the tens of nanoseconds needed for amplification in a dynode based phototube. Timing resolutions less than 100 picoseconds have been obtained in such phototubes. As an added bonus for particle physics, microchannel plate phototubes are also much less sensitive to magnetic fields than dynode phototubes. The microchannel plate technology forms the heart of the image intensifiers used in military and nighttime surveillance work. Binocular type arrangements can multiply ambient starlight a million times, thereby making what appears to be a pitch-black night as clear a noontime view. The major drawback to this technology is its quite high cost.
To make a quantitative estimate of the gain, we note that the energy of the electrons incident on each dynode stage is a function of the potential difference, V_d, between the dynodes and, therefore, the secondary emission factor, d, can be written as
d = K * V_d
where K is an overall constant. Assuming the voltage is applied equally to all dynodes, the gain, G, is then just
G = d^n = (KV_d)^n
where the number of dynode stages is n. You can now calculate the number of stages needed for a given gain G and a minimum supply voltage V_b
V_b = n * V_d = (n/K)G^(1/n)
This can be minimized with respect to n to find
for operation at a minimum V_b. Generally, you will want to minimize the supply voltage to minimize noise, however, in order to get a smaller time spread in the signal, and for other factors, you will want a larger voltage. An important consideration is the variation in gain with supply voltage. This can be calculated from the formula for gain as follows
dG/G = n dV_d/V_d = n dV_b/V_b
For a 10 stage device, this formula implies a 10 percent change in gain for a 1% change in V_b (i.e. dV_b/V_b = 0.01 generates a dG/G which is 10 times higher if n = 10). Voltage supplies are generally regulated to better than 0.05 percent.
A photomultiplier can be operated at either positive or negative high voltage. The only constraint is that the potential of the dynodes be positive relative to the photocathode. If a positive high voltage is used, the photocathode should be kept at ground potential in order to avoid spurious discharges between the photocathode and the outer envelope of the detector. Grounding the photocathode will also minimize noise from this component. Note that if the photocathode is at a high potential, then the glass covering of the phototube must be kept well insulated in order to avoid large leakage currents between the phototube and the grounded material around it (including you!).
Electrons on the central axis reach the beginning stage dynode before electrons from the edges if they have the same energy simply because the path length is about three times shorter along the central axis than from the edge. In addition, if electrons are emitted with different energies or different initial directions, then their speed components parallel to the central axis will be different as well.
The transit time spread can be calculated as being about half a nanosecond for typical phototube operation. This is comparable to the total transit time of electrons through the entire tube along the central axis. To reduce this effect, the electric field is increased near the outer edges of the photocathode so as to accelerate photoelectrons from there to a higher speed than those from the center. Thus, fast phototubes may have adjustable voltages for the focusing and accelerating electrodes in the electron-optical input system part of the phototube.
I = A * T^2 * exp[-e * phi/(k * T)]
where A is a constant, phi the work function, T the temperature (in units of Kelvin), and k is Boltzmann's constant. It is obvious that lower temperatures lead to a rapid lowering of the current.
Leakage current which go through the electrode supports and the pins on the phototube base also contribute a lot to the dark current. The only means of reducing this contribution is to operate the phototube under reduced atmospheric pressure so that the breakdown voltage is lowered.
Radioactive materials in the glass housing or support materials of the phototube also produce ionizing particles which can cause electron emission from the photocathodes or dynodes. The radioactivity can also produce fluorescence in the glass housing, thereby contributing light which, in turn, produces dark current.
The photocathode should be under high vacuum in order to preserve the photocathode material and to minimize ionization caused by normal electron emission. Any ionized gas atoms will be positively charged (since they lose electrons due to ionization) and therefore accelerate backwards towards the cathode or dynode. Collisions of ionized gas atoms there can cause more electrons to be released. This results in afterpulsing, or pulses occuring after the main pulse of cascaded electrons. The time of the afterpulse is given by the time needed for ions to transit the tube. Under high current, the last stage dynodes can emit electrode glow which travels back to the photocathode and initiates another shower of electrons.
In general, dark currents in phototubes should be, at most, a few nanoamperes.
Statistical fluctuations in the photoelectric emission of electrons from the photocathode comes about due to quantum mechanics and is a fundamental statistical limit. These fluctuation can be calculated for constant illumination by assuming a Poisson distribution for the number of photons incident on the photocathode in a time period, tau, and a binomial distributed probability for the number of photoelectrons released. The root-mean-square deviation is then given by
with I being the cathode current and e the charge of the electron.
There is also noise from the electron-multiplier system due to statistical fluctuations in secondary emission, differences in transit times, nonuniformities in the secondary emission factor over the dynodes, etc.
In general, multiplier noise should not be more than 10 percent of the total statistical noise.