Exploration Of A Photomultiplier Tube

Exploration of a Photomultiplier tube by David.R.Gilson

Abstract This report details tests performed on a photomultiplier (PM) of unknown specification. The temporal response and signal amplitude are observed for various load resistances and anode capacitances. The built in capacitance is also determined. The spectral response is also investigated, which leads to a conjecture of the actual PM type and construction (according to specifications listed in the Electron Tubes Ltd/Inc "Photomultipliers and accessories" trade catalogue).

Introduction Background Photomultipliers are highly sensitive photon detectors. The word Photomultiplier is actually a misnomer, the device does not multiply photons (like an optical amplifier would), but it actually multiplies electrons (liberated by photons). Unlike many other optoelectronic detectors, PM tubes actually have a resolution down to single photons. This is achieved through an application of the well known Photoelectric Effect (explained by Albert Einstein).

Operation When a photon enters a PM (see fig. 1), through the window (the material of which can effect what is actually detected), it is incident upon the photocathode (k). In accordance with the photoelectric effect, an electron is released from the photocathode. This electron is then accelerated through focusing electrodes into the Electron multiplier Dynodes section of the PM tube. Dynodes are devices which release several electrons when a single electron is incident upon it's surface. This has the (useful) effect of multiplying an electrical current. The anode is placed within the PM tube to bias the dynodes, such that as the electrons are released they are pulled onto the next dynode. This in turn causes the next dynode to release a number of electrons corresponding to the number of electrons incident upon it from the previous dynode.

Figure 1 The amplification, or the gain of the PM tube is derived from a simple argument. If there are δ electrons emitted for every incident electron (on each dynode) and there are N dynodes, then the gain, M, may be expressed as, M = N =

iA iC

(1)

Usually, δ is much greater than one, and since PM tubes can have between 11 and 15 dynodes, therefore very high gains can be achieved. For example, a PM tube with 14 dynodes which releases 5 electrons for every incident electron, detects a single photon (i.e. a single electron is emitted from the photocathode), then there will be 514 or 6.1×109 electrons received at the anode. This clearly shows that PM tubes are ideal detectors for extremely weak optical sources.

Limitations An imperfection all optoelectronic detectors which the PM is particularly susceptible to is the dark current. This rises due to thermal excitations in the detectors which are then recorded as signals. If an electron is thermally emitted from the photocathode or one the early dynodes, an appreciable current can be generated by the time it reaches the anode. In general for detectors, linear signals are favoured. In the PM tube, if the time constant (R'C') is much greater than the shortest temporal feature of an optical pulse, non-linear signals arise. It is therefore imperative that the time constant satisfies the condition R ' C ' t min . Because PM tubes operate on the principal of the photoelectric effect, they have a strong dependence on the wavelength of the incident radiation. Obviously the photons that are to be detected must have an energy greater than the work function of the photocathode. i.e. the wavelength must be greater than the cut-off wavelength. Another wavelength dependent feature is encountered with the window of the PM tube. Different materials have different absorption/transmission characteristics. Hence, depending on the window material, the responsiveness will vary depending on the wavelength of the incident radiation (and this is non-linear relationship). PM tubes are high voltage devices, they can require voltage supplies in the order of kilo-volts. This supply has to be well stabilised because the number of electrons emitted per dynode per incident electron, δ, is a function of bias voltage, so as the supply changes so does the gain. However, if the anode potential is too high, the electrons incident on the dynodes will have so much kinetic energy they will embed themselves several atoms deep in the surface of the dynodes and electron emission will not occur.

R'C' model of PM tube The PM tube (like many other optoelectronic detectors) can be modelled on an resistance-capacitance (R'C') circuit. as shown below.

Figure 2 The output voltage, VL, for a step current switch on can be expressed as,



−t

V L =V 0 1−e RC



(2)

and likewise for a switch off, V L =V 0 e

−t RC

(3)

Where R'C' is the PM's rise time (the time constant), or for equation 3 R'C' is sometimes called the decay time. and R' is the net resistance of the PM and C' is the net capacitance. For both of these we also must consider any other measuring devices connected, as they would have an effect on the readings. This formula can describe the detection of both the switch on of a steady light source and the step up of a pulsed light source.

Good temporal resolution is achieved when t R R' C ' , where tR is the rise time of the pulse. The problem is that for R'C' to be small, the responsiveness (the magnitude of the signal) also decreases. For optimum performance, the time constant (R'C') has to be as small as possible and the responsiveness has to be as large as possible. Note. The terms "time response" and "time constant" are equivalent and can be and shall be used interchangeably!

Procedure For the experiment, the PM was encased in an assembly which contained controls for some of the experimental equipment. The assembly inside, had a constant light source (which the intensity could be controlled). There was also a port on the side so that a purpose strobe light could be fitted. Another part of the PM tube housing was slide mechanism which allowed filters to be placed in front of the PM. Finally the housing was fitted with a screw-on BNC connector. This allowed the anode resistance or capacitance to be altered by fitting the relevant component to this connector. For the experiment, different load resistances were fitted to observe the change in behaviour of the PM. The load resistors were fitted on a BNC T-connector at the CRO input.

Calibration Initially the internal light source was activated and set to an arbitrary intensity. Neutral density gelatin filters (see references) were placed in the PM housing and the output signal was recorded using a DVM (on the 20mV range with 50M ohm impedance). A graph was then plotted of signal versus percent transmittance to check the linearity of the signal as a function of incident intensity (see results). The second calibration check concerned the high voltage (EHT) supply. The introduction discussed the need for a stable power supply, so the PM signal was recorded as a function of EHT supply. A graph was then plotted to determine how well stabilised the EHT supply must be to limit output signal drifts to 1% or less (see results).

Experiment Once calibration was complete, a xenon strobe pulsed light source (which fits in the port mentioned above) was used rather than the internal steady light source (the pulsed light source had a fixed frequency for the experiment). Again, the linearity was tested. This time for the pulsed source. This was also done with the neutral density filters. No load resistance was fitted and the anode resistance was 5M ohms. This configuration gave a high time constant and therefore poor temporal resolution. However the signal was satisfactory. This satisfied this experiment's parameters, since it was only the signal magnitude which was sought. The pulsed light source was use throughout the rest of the experiment. See results. The internal anode capacitance was (at this point) an unknown quantity. Without it, the time constant of the whole assembly including any devices attached (such as a CRO), could not be calculated. The anode capacitance could be calculated from considering the equivalent circuit of the PM and connected CRO.

Figure 3. The net resistance, R', being the parallel combination of RL, RS and RA. subsequently the net capacitance, C', is the parallel combination of CC, CS and CA. The digital CRO (DCRO) used in the experiment was able to calculate values/coordinates from the trace is was displaying on screen. This enabled an accurate measurement of the decay time (which can be regarded as the product, R'C'). Using this value yielded from the DCRO and the known component values the anode capacitance could be calculated. See results. As previously discussed, the conditions for good responsiveness and good temporal response are conflicting. So to find the optimum resistance, the load resistance (still being connected at the Tconnector at the DCRO input) was changed, and signal and rise time recorded. From these values the optimum could be determined. See results. The values of signal and decay time were taken from the DCRO, which displayed them on screen. The DCRO was equipped with an in-built printer, the print out of the signal for each load resistor are supplied in appendix 1. To further investigate the temporal response of the PM tube, the anode resistance was replaced by a capacitance. The screw-on BNC resistor was removed and replaced with a screw-on BNC connector with crocodile clips. The connector allowed standard commercial capacitors to be connected to the PM tube anode. This formed the equivalent circuit, as shown below.

Figure 4 For each capacitor connected, the decay time and the signal amplitude were read by the DCRO. These measurement allowed the theoretical results from equation 3 to be compared to the experimental results and also net charge generated to be estimated. See results. The signals obtained for each capacitor were printed out from the DCRO and are included in appendix 2.

Finally, the spectral response was examined. To control the incident wavelength (from the strobe light), Wratten filters were placed in the slide mechanism (same that used for the neutral filters). Each filter had a different transmission coefficient, so the signal amplitudes were recorded. The signals obtained for each filter, were printed out from the DCRO and are included in appendix 5.

Results Where straight lines have been plotted, the gradients and intercepts (and corresponding errors) were calculated using the Least Square Fit method.

Calibration results For constant illumination, the PM gave a linear signal. This can be seen from figure 5. The gradient was calculated to be (-2.565E-01±1.507E-02) volts and an the intercept was (5.670E-03±7.082E-03) volts. Below are the conditions this test was performed under. Anode resistance (K-Ohms)

200.0

Power Supply (V)

400.0

Light density" of internal light source

PM

tube’s

0.4

DVM range (mV)

20.0

DVM impedance (M-Ohms)

50.0

Table One. Calibration conditions/constants.

Figure 5 The results from the variation if EHT supply is shown in figure 6. The full argument for these results are shown in appendix 3. However it can be shown that none of EHT the voltage ranges have to be very well stabilised to prevent drifts greater than 1% in the output signal. To be brief, the lowest limits of fluctuation was in the 900 to 1000 volt range which permitted drifts of ±12.68%. The EHT voltage supply range which had the greatest allowed range of fluctuation was the 400 to 500 volt range, which had a limit of ±77.76%.

Figure 6 The conditions this test was done under, are shown in the below table. Anode resistance (M-Ohms) Power Supply (V)

5 400

1st DVM range (0-20 mV) 2nd DVM range (20-200 mV) DVM impedance of both ranges (M-Ohms)

20 200 10

Table 2. Conditions for Power supply calibration test.

Experiment results Using the pulsed light source, the output signal was still linear, this is shown in figure 7. The gradient was calculated to be, (0.20497±0.01289) Volts and the intercept was (0.29035±0.00743) Volts.

Figure 7.

To get the anode capacitance, CA, the decay time was found with the DCRO and used with known component values. To make the calculation, the equivalent circuit in figure 3 should be considered. The net resistance, R', can be calculated simply by, R '=

RS RL RA R L R AR A RS R S R L

(4)

and the net capacitance, C', can be calculated by, (5)

C ' =C AC S C C These combine, so we can state, R ' C '=

 C AC S C C  R L RS R A

(6)

R L R A R A R S RS R L

Rearranging this for CA gives,



C A=



R ' C '  R L R AR A RS R S R L  −C S −C C RL R A R S

(7)

Using the following known values, CRO capacitance

24.0pF

Cable capacitance

191.88±0.984pF

Anode resistance

5.000M ohm

DCRO impedance

1.000M ohm

Load resistance

5.287M ohm

Table 3. Component values, used to calculate anode capacitance.

The anode capacitance was calculated to the value, 1.59nF±0.984pF. The next step of the experiment was to determine the optimum load resistance for the best possible combination of responsiveness and time response. Again, the full argument for the following results are detailed in appendix 4. The signal amplitude and response time were recorded for each load resistance (see figures 8 and 9 respectively). Initially the reciprocal of the response time values were taken and then they were transformed by multiplying by 1V.s and them differencing them with the corresponding signal amplitudes. The signal values and then the transformed reciprocal times were differenced, the resistor corresponding to the smallest difference was then selected.

Figure 8 Figure 9 The data from this test are shown below. Load (ohms)

Signal (V)

Response time (s)

Predicted Tr (s)

1/Tr (Hz)

5.287E+06

-3.110E-01

1.440E-03

1.30E-03

6.94E+02

8.270E+05

-2.780E-01

6.760E-04

7.50E-04

1.48E+03

5.106E+05

-2.640E-01

5.430E-04

5.72E-04

1.84E+03

9.903E+04

2.180E-01

1.930E-04

1.60E-04

5.18E+03

5.094E+04

2.000E-01

9.900E-05

8.67E-05

1.01E+04

2.000E+04

1.500E-01

6.240E-05

3.53E-05

1.60E+04

1.602E+04

1.630E-01

8.190E-05

2.84E-05

1.22E+04

1.001E+04

1.370E-01

3.725E-05

1.79E-05

2.68E+04

3.010E+03

7.980E-02

1.574E-05

5.42E-06

6.35E+04

1.007E+03

3.540E-02

7.760E-06

1.82E-06

1.29E+05

Table 4. Data showing variation of signal and time response with load resistance.

After assessing the data, the optimum resistance from this data is the 20K ohm resistor. The predicted values are the time constants calculated using the component values with equation 6 The conditions for this test are shown below.

Anode resistance (ohms)

5.00E+06

Scope resistance (ohms)

1.00E+06

Anode Capacitance (F)

1.59E-09

Scope Capacitance (F)

2.40E-11

Cable Capacitance (F)

1.92E-10

Table 5. Conditions for test.

Figure 10 shows how the signal varies with the net resistance.

Figure 10 When changing the anode capacitance, the first goal was to compare practice with theory. By plotting equation 2 as a function of time for each capacitor, and superimposing the graph using the measured rise time and the theoretical rise time, figures 11,12 and 13 were obtained.

Figure 11

Figure 12

Figure 13 As it can be seen, the theoretical and measured values are very close indeed. The second goal of the anode capacitance testing was to estimate the charge generated at the anode. The relationship between charge and capacitance is well known, Q=CV

(8)

Hence by using the measured signal voltage and the connected capacitance the charge can be calculated, by equation 8. Bellow is a table of data from this test.

470pF

270pF

56pF

Measured rise time (S)

3.380E-03

2.290E-03

1.975E-03

Calculated time (S)

1.914E-03

1.746E-03

1.566E-03

Signal Voltage (V)

1.420E-01

1.840E-01

2.700E-01

Estimated (C)

6.674E-11

4.968E-11

1.512E-11

4.171E+08

3.105E+08

9.450E+07

rise

charge

Estimated charge carriers

Table 6. Data from anode capacitance variation.

As it may be expected, the largest capacitance generates the most charge. The signals obtained from this test are included in appendix 2. When investigating the wavelength dependency of the PM tube, the signal values had to be normalised. This was because the filters used each had different transmission coefficients. So a graph of signal to transmission ratio versus wavelength is plotted. This is shown in figure 14.

Figure 14 We can see from this that signals around 480nm and 552nm are favoured by the PM tube in this experiment. The signals obtained from this test are included in appendix 5.

Conclusion Comparing the spectral characteristics of the PM and comparing with the like in the "Electron Tubes" trade catalogue, an (approximate) match exists, which leads to speculation of the construction and specification of the PM in the experiment. If there is a match then the following may be speculated; It has a model number 9206B, material type S1. It has 11 dynodes. The dynodes are made of BeCu The effective cathode size is 45mm. A peak quantum efficiency of 1%. A gain of 7E+5. A typical dark current of 5µA. It is 140±3 mm long and 51.5 mm in diameter (i.e. cylindrical in shape).

Appendix 1 The attached sheets below are print outs from the DCRO from the load resistance test. These are the original sheets, and the signal amplitude and decay time are actually hand written on the sheets. (Just flip them over to browse through). Note to reader. DCRO printouts are property of the University of Hull's Physics Department and thus not available for this copy. Load Resistance : 5.287M ohms Load Resistance : 827K ohms Load Resistance : 510.6K ohms Load Resistance : 99.03K ohms Load Resistance : 50.94K ohms Load Resistance : 20.0K ohms Load Resistance : 16.02K ohms Load Resistance : 10.01K ohms Load Resistance : 3.01K ohms Load Resistance : 1.007K ohms

Appendix 2 Note to reader. DCRO printouts are property of the University of Hull's Physics Department and thus not available for this copy. The attached sheets below are print outs from the DCRO from the anode capacitance test. These are the original sheets, and the signal amplitude and decay time are actually hand written on the sheets. (Just flip them over to browse through). 470pF capacitor 270pF capacitor 56pF capacitor

Appendix 3 Argument of EHT supply stabilisation limits Consider the graph below,

Figure 15 We can see by taking the error bars, in the y-direction of the point in figure 15 that there is a corresponding x value and corresponding error values on the x-axis. These are related by the curve from which they are traced to the x-axis. Assuming that the part of the curve which the error bars encompass, is locally straight then we can say,

 y=M  x

(9)

Where  y is the width of the y error bars (likewise for  x ) and M is the local gradient of the curve. For a pre-defined value of  y , we can rewrite equation 9 for  x ,  x=

y M

(10)

For the EHT test, the y variable was the output signal and the x variable was the EHT. Now if we want the signal drift to be limited to 1% (or ±0.5%), we can determine the corresponding EHT drift limit. From the data we can calculate the point-to-point gradient, by this formula,  x n=0.01



x n1−x n y n1− y n

Below is a table of values calculated using this value.



(11)

Range (KV)

delta-xn

0.4-0.5

155.52%

0.5-0.6

65.62%

0.6-0.7

38.71%

0.7-0.8

28.35%

0.8-0.9

25.76%

0.9-1.0

25.35%

1.0-1.1

31.11%

1.1-1.2

36.75%

1.2-1.3

42.37%

1.3-1.4

43.10%

1.4-1.5

47.17%

1.5-1.6

46.95%

1.6-1.7

50.25%

Table 7. List of EHT stabilisation limits for various voltage ranges.

For arguments sake, the voltage range with the greatest stabilisation limits was used for the rest of the experiment. The EHT supply was hence set to 450 Volts.

Appendix 4 Argument for determination of optimum load resistance If we consider figures 8 and 9 and table 4. We can see that both the response time (time constant) and signal magnitude increase as load resistance increases. The optimum conditions are the greatest signal magnitude and the smallest time constant. So intuitively, the best resistance to use would be some midvalue, or even an average value. If we were to take the reciprocals of the response time values, we would observe that these new values would decrease as load increases. Hence the gradient of the signal magnitude would be greater than zero and the gradient of the reciprocal times would be less than zero (note, they do not have to be linear, but the sign of the general differential indicates the increasing/decreasing relationships). It can be shown that two functions shall intercept (or get infinitesimally close) if one has a constantly positive gradient and the other has a constantly negative gradient. Following this argument if the signal function has the reciprocal time function (which is transformed by multiplying by 1 V.s) superimposed on it, when they intercept the difference will be zero and we have our optimum performance. i.e. we have the largest possible signal for the shortest possible time constant (or the largest reciprocal time). The load resistance corresponding to this point shall be the optimum load resistance. However with the experimental values these functions would not intercept because they were magnitudes apart. Since it has been hypothesised that we should be looking for a mean value of response time and signal amplitude each set of data was normalised by it's respected mean value. So rather than looking for the smallest difference (zero being the ideal value), the smallest normalised difference was sought. This was done by taking the minimum value from the series,

∣

Vi 1 − −1 V t t  i

∣

(12)

(Note equation 12 is a dimensionless quantity) then simply select the corresponding load resistance. According to the hypothesis, the mean values of the signal and reciprocal time shall meet the reciprocal conditions for optimum performance. We can see that if V i and 1/t i are respectively equal to V and 1/ t than equation 12 reduces to zero, which is the ideal value and the hypothesis holds.

Appendix 5 The attached sheets below are print outs from the DCRO from the spectral response test. These are the original sheets, and the filter number used is actually hand written on the sheets. (Just flip them over to browse through). Note to reader. DCRO printouts are property of the University of Hull's Physics Department and thus not available for this copy. (Note, Wratten filter No. 70 had such a low transmission that all was detected was circuit noise, it is included simply to show that there was hardly any transmission.)

Wratten filter No. 3 - Dominant wavelength is 596.5 nm and 88.30% transmission Wratten filter No. 32 - Dominant wavelength is 551.7 nm and 12.50% transmission Wratten filter No. 47B - Dominant wavelength is 497.8 nm and 0.78% transmission Wratten filter No. 65 - Dominant wavelength is 496.6 nm an 9.60% transmission Wratten filter No. 70 - Dominant wavelength is 675.6 nm and 0.31% transmission Wratten filter No. 74 - Dominant wavelength is 538.6 nm and 4.00% transmission Wratten filter No. 75 - Dominant wavelength is 487.7 nm and 1.90% transmission

References Melles Groit Optics guide and product catalogue. "Photomultipliers and accessories", Thorn EMI, Electron Tubes Ltd/Inc. The Rubber chemicals company book of data and constants. "Optical Radiation Detectors" E Dereniak and D Crowe. Wiley, 1984