Becker W. Advanced Time-Correlated Single Photon Counting Techniques

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224 6 Detectors for Photon Counting

6.2.3 Signal Transit Time

The signal transit time is the time from the absorption of a photon at the photo-

cathode to the corresponding pulse at the anode of a PMT. The transit time is

almost entirely determined by the transit time of the electrons through the PMT. It

is therefore proportional to the reciprocal square root of the supply voltage. Typi-

cal transit times for a number of frequently used PMTs are shown in the table

below.

Table 6.2.

Detector Operating voltage

(Gain control voltage)

Transit

Time

Transit Time per %

Change in operating

or gain control voltage

R3809U MCP-PMT 3000 V < 1 ns 3 ps

R7400 and R5600 TO8 PMTs 900 V 5.4 ns 21 ps

H5773 Photosensor module (0.9 V) 5.4 ns 21 ps

H7422 PMT module (0.9 V) 6.5 ns 27 ps

R928 side window PMT 900 V 22 ns 100 ps

XP2020 44 mm linear focused

PMT

2500 V 28 ns 140 ps

The transit time has to be taken into account when choosing the cable

length in the detector and reference signal path of a TCSPC system. More

important than the transit time itself is the variation of the transit time with

the detector supply voltage. To keep the transit time of a conventional

PMT stable within 1 ps a stability of the operating voltage of the order of

0.05% to 0.01% is required.

6.2.4 Transit Time Spread

The transit time between the absorption of a photon at the photocathode and the

output pulse from the anode of a PMT varies from photon to photon. The effect is

called „transit time spread“, or TTS. There are three major TTS components in

conventional PMTs and MCP PMTs – the emission at the photocathode, the trans-

fer of the photoelectron to the multiplication system, and the multiplication proc-

ess in the dynode system or microchannel plate. The total transit time jitter in a

TCSPC system also contains jitter induced by amplifier noise and amplitude jitter

of the SER.

The time constant of the photoelectron emission at conventional photocathodes

is small compared to the other TTS components and usually does not noticeably

contribute to the transit time spread. High efficiency semiconductor photocathodes

of the GaAs, GaAsP and InGaAs type are an exception. These cathodes are much

slower and can introduce a transit time spread on the order of 100 ps.

6.2 Characterisation of Detectors 225

The largest fraction of the total transit time spread results from the different tra-

jectories of the photoelectrons on their way from the photocathode to the first

dynode. The photoelectrons are emitted at random locations on the photocathode,

with random start velocities and in random directions. Therefore, the time they

need to reach the first dynode or the channel plate varies from electron to electron

(see Fig. 6.12).

Photo-

Focusing Electrode

1st. Dynode

2nd. Dynode

Electron

Trajecories

cathode

Photons

lg N

time

Main Peak

Secondary Peak

Tail or

Pre-Peak

Fig. 6.12 left Different electron trajectories cause different transit times in a PMT. Right:

general shape of the transit time distribution

Moreover, some of the photoelectrons may be reflected at the first dynode, re-

turn a few hundred ps or a few ns later, and release secondary electrons. These

electrons cause a tail or secondary peaks in the transit time distribution. Another

peak can appear before the main peak. This usually results from photoelectron

emission at the first dynode. Transit time distributions for a number of detectors

are shown under Sect. 6.4, page 242.

Unfortunately the resulting transit time spread depends on the wavelength.

With decreasing wavelength, i.e. increasing photon energy, the start velocity and

the velocity dispersion of the photoelectron increases, which causes changes in the

transit time distribution.

In fast PMTs the transit time spread is minimised by using a spherical

photocathode, by placing one or several focusing electrodes between the cathode

and the first dynode, and by making the dynodes in a curved shape. Of course, a

short distance between the cathode and the first dynode and a strong electrical

field are important as well. The distance is especially short for MCP-PMTs and

miniature PMTs with metal-channel dynodes, which have a correspondingly short

TTS. The transit-time spread is proportional to the reciprocal square root of the

voltage between the cathode and the first dynode. This can be exploited to im-

prove the time-resolution of PMTs in TCSPC applications; see Fig. 6.37, page

248. The maximum voltage is limited by possible dielectric breakdown in the tube

or by an increase of the background count rate.

As for the photoelectrons at the cathode, different start velocities of the secon-

dary electrons at the dynodes result in different transit times. However, because

the number of secondary electrons is larger, time-dispersion in the dynode system

results in pulse broadening rather than in transit-time jitter.

226 6 Detectors for Photon Counting

TTS exists also in single photon avalanche photodiodes (SPADs). The source

of TTS in SPADs is the different depth at which the photons are absorbed, and the

nonuniformity of the avalanche multiplication efficiency. This results in differing

delays in the build-up of the carrier avalanche and in different avalanche transit

times. Consequently the TTS depends on the wavelength and the voltage. More-

over, if a passive quenching circuit is used, the reverse voltage may not have com-

pletely recovered from the breakdown of the previous photon. The result is an

increase of the TTS width or a shift of the TTS with the count rate.

6.2.5 Pulse Amplitude Jitter

The secondary emission coefficient at a particular dynode depends on the dynode

material and energy of the primary electrons. For typical interdynode voltages

used in PMTs, the secondary emission coefficient, n, is between 4 and 10. Be-

cause the secondary emission is a random process the number of the generated

secondary electrons varies from electron to electron. The width of the distribution

can be expected at least of the size of the standard deviation, n

1/2

, of a poissonian

distribution of the secondary emission coefficient, n. Therefore the single-photon

pulses obtained from a PMT have a considerable amplitude jitter. For TCSPC

applications it is important that the pulse amplitudes of the majority of the pulses

are well above the unavoidable noise background.

Because the gain of a PMT may vary over a wide range, the total width of the

distribution may vary for different tubes and different supply voltages. However,

despite the different materials and shapes of the dynodes in different PMTs, the

general shape of the distribution is more or less similar. There is a broad peak at

high amplitudes and a secondary peak at low pulse amplitudes. The high ampli-

tude peak contains the regular single-electron pulses. The low-amplitude peak is at

least partially related to the light. Its relative height does not appreciably depend

on the count rate. It is possibly caused by photoelectrons scattered at the first dyn-

ode and reaching the second dynode without amplification. Another source of the

small-amplitude peak is photoelectron emission on the first dynode. For some

photomultipliers a „peak to valley“ ratio is specified, which indicates how much

higher the main peak is compared to the valley between the main and the secon-

dary peak.

If the discriminator threshold is set low enough an extremely high peak appears

at very low amplitudes. This peak does not originate in the PMT but is caused by

electronic noise of the preamplifier and noise pickup from the environment. Some

typical pulse amplitude distributions are shown in Fig. 6.13.

6.2 Characterisation of Detectors 227

Fig. 6.13 Distribution of the single-photon pulse amplitude of different PMTs and different

gain at a count rate of 10

/s. Upper row: R5600P01, H5773P03. Lower row: Two speci-

mens of the R740002

The narrow peak at the left is the electronic noise. In the upper two tubes the

main peak and the low-amplitude peak are clearly separated from the electronic

noise peak. In the lower left tube, the peaks can be separated at maximum gain; in

the lower right tube the gain is insufficient to separate the pulse distribution from

the electronic noise background.

The pulse height distribution at high detector gain often shows a structure,

probably due to the discrete numbers of secondary electrons emitted at the first

dynode. An example for an H7422P

40 module is shown in Fig. 6.14.

228 6 Detectors for Photon Counting

Fig. 6.14 Pulse amplitude distribution of a H7422P40 for different gain. At high gain the

distribution develops a substructure, probably due to the discrete numbers of secondary

electrons emitted at the first dynode

Figure 6.15 shows that the shape of the main peak of the amplitude distribution is

the same for the photon pulses and the dark pulses. This is not surprising because

the secondary emission process makes no difference between electrons emitted at

the cathode thermally or optically. However, the secondary peak at low ampli-

tudes is more pronounced for the dark pulses, probably because some of the ther-

mal electrons are emitted at the dynodes.

Fig. 6.15 Pulse amplitude distribution for dark pulses and photon pulses of an R5600P01

PMT

For reasonable TCSPC operation, a discriminator threshold must be found that

rejects the electronic noise background and the pulses in the low-amplitude peak,

but counts as many of the regular photon pulses as possible. Moreover, the thresh-

old should be considerably higher than the electronic noise level so that the small-

est detected pulses will still have a good signal-to-noise ratio. For photon counting

it is therefore essential that a sufficient gain can be achieved within the permissi-

ble operating voltage of the PMT.

It is often believed that the width of the pulse amplitude distribution depends on

the cathode material. Certainly there are differences in the peak ratios of the main

6.2 Characterisation of Detectors 229

and the low-amplitude peak, and in the peak-to-valley ratio. However, the differ-

ences are not very large (see Fig. 6.13), and the relative width of the main peak

does not vary appreciably. It seems that detectors of different cathode type differ

mainly in gain, rather than in the shape of the distribution. Consequently, the prob-

lem of most PMTs of poor photon counting performance is lack of gain, not so

much an odd shape of the amplitude distribution.

The amplitude jitter of the single-photon pulses as well as the noise background

induce additional timing jitter in the CFD of a TCSPC device. In practice this jitter

is hard to distinguish from the TTS of the detector. The general advice is to oper-

ate the detector at a gain as high as possible. Higher amplitudes reduce the effect

of the electronic noise on the timing, and the CFD performance usually improves

at higher pulse amplitudes.

6.2.6 Cathode Efficiency

Several different definitions are used to specify the efficiency of a PMT cathode.

Often the sensitivity of a PMT is specified in units of „cathode luminous sensitiv-

ity“. This is the cathode current per lumen incident light from a tungsten lamp

operated at a temperature of 2,856 K. Because the intensity maximum of the lamp

is at about 1,000 nm, the luminous sensitivity may not represent the efficiency at a

given wavelength. Photocathodes of different spectral sensitivity are therefore not

directly comparable. Moreover, the cathode luminous sensitivity does not include

the efficiency of the electron transfer from the cathode into the dynode system and

the possible loss of photon pulses due to incomplete resolution of the pulse height

distribution (see Fig. 6.27, page 241).

In the test sheets of PMTs, the manufacturers occasionally specify the meas-

ured „anode luminous sensitivity“ instead of the cathode sensitivity. The anode

sensitivity is the cathode sensitivity (including the electron transfer efficiency)

multiplied by the gain of the tube. Because almost any gain can be obtained by

increasing the supply voltage, the anode luminous sensitivity cannot be used to

compare the photon counting performance of PMTs.

The „cathode radiant sensitivity“ is the cathode current per watt of incident power

at a given wavelength. It is usually given as a plot versus the wavelength. The cathode

radiant sensitivity does not include the efficiency of the electron transfer from the

cathode into the dynode system or the possible loss of photon pulses due to poor reso-

lution of the pulse height distribution. Nevertheless, the cathode radiant sensitivity

is useful for comparing different detectors and different cathode versions.

The most useful parameter for characterising the efficiency of a photon-

counting detector is the quantum efficiency. The quantum efficiency,

QE, of a

photocathode is the probability of the emission of a photoelectron per incident

photon. It is directly related to the radiant sensitivity,

1024.1

6



SQE

(6.3)

with

h = Planck constant, e = elementary charge,

= Wavelength, c = velocity of

light.

230 6 Detectors for Photon Counting

Usually quantum efficiencies given for detectors refer to the emission of a pho-

toelectron or, in avalanche photodiodes, the generation of an electron-hole pair.

The „detection efficiency“ in PMTs is smaller for the reasons mentioned above:

Not all photoelectrons cause a detectable anode current pulse in a PMT, and not

all electron-hole pairs trigger an avalanche in a SPAD.

The general wavelength dependence of the radiant sensitivity for some com-

monly used photocathodes is shown in Fig. 6.16.

300 400 500 600 700 800 900

100

1000

mA/W

Wavelength

Cathode Sensitivity

bialkali

multialkali

QE=0.2

GaAsP

QE=0.5

GaAs

QE=0.1

300 400 500 600 700 800 900

100

1000

mA/W

Wavelength

Cathode Sensitivity

QE=0.2

QE=0.5

QE=0.1

Ext. Red

High Eff.

multialkali

Fig. 6.16 Spectral sensitivity of photocathodes, after [210, 214]

The QE of the conventional bialkali and multialkali cathodes reaches 20 to 25%

between 400 and 500 nm. A considerably higher efficiency is achieved by GaAsP

and GaAs cathodes. The GaAsP cathode reaches a QE of 40% in the visible re-

gion. The GaAs cathode has a high NIR sensitivity and is a good replacement for

the multialkali cathode above 600 nm.

Unfortunately, GaAsP and GaAs cathodes are intrinsically slow and contribute

with typically 100 ps to the TTS of the PMT. A short TTS in combination with

sensitivity up to 1,100 nm is obtained from the S1 cathode (Fig. 6.16, right). How-

ever, the S1 cathode delivers an extremely high dark count rate and is therefore

rarely used for TCSPC. A good solution to fast measurements in the NIR is the

„extended red“, or S25 cathode. Recently a „high efficiency extended red“ cath-

ode has become available. Up to 750 nm the specified radiant sensitivity is almost

the same as for the GaAs cathode.

The radiant sensitivity of different PMT types of the same cathode material can

vary considerably, especially for NIR-sensitive tubes. Reflection-type cathodes are

usually a bit more efficient than transmission type photocathodes. Even tubes of

the same type and cathode material differ noticeably in their radiant sensitivity.

Compared to PMTs, single photon avalanche photodiodes (SPADs) have a con-

siderably higher efficiency in the near infrared. Figure 6.17 compares the QE of a

silicon SPAD module [408] with the QE of a GaAsP PMT [214].

6.2 Characterisation of Detectors 231

300 400 500 600 700 800 900 1000 nm

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

wavelength

GaAsP

Si APD

Fig. 6.17 Quantum efficiency vs. wavelength for a SPAD, compared with a PMT with

GaAsP cathode. After specifications given by manufacturers [214, 408]

The QE of the SPAD follows the typical QE curve of a silicon photodiode and

reaches almost 80% at 700 nm. However, the active area of the SPAD is only

0.18 mm wide. Therefore the high efficiency of a SPAD can be exploited only if

the light can be concentrated in a small area.

The measurement of absolute detector efficiencies is anything but simple. It is

therefore not surprising that there is some scatter in the values given by different

manufacturers and for different detectors. An overview of the measurement of

PMT parameters is given under Sect. 6.3, page 234.

6.2.7 Dark Count Rate

The dark count rate of the detector sets a limit to the sensitivity of a photon count-

ing system. The dark count rate of a PMT depends on the cathode type, the cath-

ode area, and the temperature. The dark count rate is highest for cathodes with

high sensitivity at long wavelengths. Typical dark count rates for the commonly

used photocathodes are

Table 6.3.

Cathode Type Spectral Range nm Dark Count Rate s

-1

, at 22 °C

Bialkali 180 to 650 10 to 100

Multialkali 180 to 850 80 to 500

Multialkali extended red 180 to 900 2000 to 6 000

GaAs 350 to 900 20000

GaAsP 250 to 700 2000 to 6 000

232 6 Detectors for Photon Counting

The dark count rate decreases by a factor of 3 to 10 for a 10 °C decrease

in temperature. Cooling is therefore the most efficient way to keep the dark

count rate low. Figure 6.18 shows the dark count rate versus temperature

for different cathode versions of the Hamamatsu R3809U MCP PMT

[211].

Fig. 6.18 Dark count rate of the Hamamatsu R3809U versus temperature for different

cathode versions. From [211], S20 = Multialkali, S25 = extended red multialkali

As can be seen in Fig. 6.18, even moderate cooling has a large effect on the

dark count rate. The usual problems associated with cooling, like fogging of the

entrance window or dew condensation on the tube, can often be avoided by cool-

ing just 10

15 degrees below the ambient temperature. Of course, any heating of

the PMT should be avoided. Typical heat sources are the voltage divider resistors,

amplifiers integrated in the PMT housing, or the coils of a shutter in front of the

PMT. The power dissipation of these components should either be kept low or the

heat must be efficiently dissipated via the PMT housing or another heat sink.

The dark count rate of a PMT can increase dramatically after the photocathode

has been exposed to daylight. For traditional cathodes the effect is reversible, but

full recovery can take several hours. An example for a Hamamatsu H5773P

01

(multialkali cathode) photosensor module is shown in Fig. 6.19. To show the full

size and duration of the recovery effect, the experiment was performed at an am-

bient temperature of 5° C.

If the cathode of an

operating PMT is exposed to daylight or another strong

source of light, the dark count rate can be permanently increased by several orders

of magnitude. The tube can be damaged beyond recovery.

6.2 Characterisation of Detectors 233

Fig. 6.19 Decrease of the dark count rate (in counts per second) of a H5773P01 PMT

module after the cathode was exposed to daylight. The detector was cooled down to 5°C.

The peaks are caused by scintillation effects. Total time scale 11 hours

PMTs can produce random single pulses of extremely high amplitude or bursts

of pulses with extremely high count rate. Such bursts cause the spikes in Fig. 6.19.

The bursts can originate from radioactive decay and scintillation effects in the

vicinity of the tube, in the tube structure itself, or from cosmic ray particles. An-

other source of high-amplitude pulses are tiny electrical discharges in the cathode

region of the tube. Therefore not only the tube, but also the materials in the cath-

ode region, must be suspected to be the source of the effect. Generally, there

should be some millimeters clearance around the cathode region of the tube.

Bursts can also be a sign of beginning instability, see 7.2.12.

6.2.8 Afterpulsing Probability

Photon-counting detectors have an increased probability of producing background

pulses within the microseconds following the detection of a photon. These after-

pulses are detectable in almost any conventional PMT. It is believed that they are

caused by ion feedback, or by luminescence of the dynode material and the glass

of the tube.

Afterpulsing can be a problem in high-repetition rate TCSPC applications, es-

pecially with Ti:Sapphire lasers or diode lasers, as well as in fluorescence correla-

tion experiments. At a high repetition rate, the afterpulses from many signal peri-

ods pile up and cause a considerable signal-dependent background (see Fig. 7.31,

page 294). In fluorescence correlation spectra, afterpulsing results in a typical

„afterpulsing peak“ at times shorter than a few µs. The amount of afterpulsing

depends on the PMT gain. It can be reduced, yet not entirely removed, by decreas-

ing the operating voltage of the PMT and using a preamplifier of a correspond-

ingly higher gain. The measurement of the afterpulsing probability versus time is

described under Sect. 6.3, page 234.