Becker W. Advanced Time-Correlated Single Photon Counting Techniques

Подождите немного. Документ загружается.

214 6 Detectors for Photon Counting

Light

D10

Light

Circular

Linear focused

Fine Mesh Venetian Blind Metal Channel

Fig. 6.2 PMT dynode geometries. Circular dynode arrangement, linear focused, fine mesh,

venetian blind, metal channel type. C Cathode, D dynodes, A anode, F focusing electrode,

S screen

Of special interest for time-correlated single photon counting are the „linear fo-

cused“ dynodes, which give fast single electron response and low transit-time

jitter, and the „fine mesh“ and „metal channel“ types, which offer position sensi-

tivity when used with an array of anodes. Moreover, PMTs with fine-mesh and

metal channel dynodes can be made extremely small, which results in low transit

time, low transit-time jitter, and a fast single-electron response.

The gain systems used in photomultipliers can also be used to detect electrons

or ions. The detectors are then called „Electron Multipliers“. The particles to be

detected are fed directly into the dynode system.

6.1.2 Channel and Microchannel PMTs

The gain effect of secondary electron emission is also used in the Channel PMT

and in the Microchannel Plate (MCP) PMT (Fig. 6.3). These PMTs use channels

with a conductive coating. A high voltage is applied along the channels. The

channel walls act as secondary emission targets. When a photoelectron enters the

channel it bounces between the walls and causes secondary electron emission. The

principle can be used in a single macroscopic channel or a microchannel plate

[297, 298]. The microchannel plate contains a large number of microscopically

small channels. Typical channel diameters are from 3 to 10 µm. Two or three

microchannel plates can be used in series to achieve a high gain. The distance

between the first microchannel plate and the cathode can be made very small. This

results in a transit time spread of the photoelectrons as short as 25 ps. The output

pulse width is of the order of a few hundred ps. Currently MCP PMTs are the

fastest commercially available single photon detectors.

6.1 Detector Principles 215

Cathode

Anode

Conductive Channel

Electrical Field

cathode

Channel

Plates

Anode

electron

Photo-

Channel plate

Electrons

Anode

Electrical Field

Photo-

from

Photo-

cathode

Fig. 6.3 Channel PMT (left) and microchannel PMT (right)

Like conventional PMTs, channel PMTs and MCP PMTs can also be used for

the detection of single electrons or ions. The particles are fed directly into the

input of the multiplication channels.

6.1.3 Position-Sensitive PMTs

To obtain position sensitivity, the single anode can be replaced with an array of

individual anode elements [297, 298]; see Fig. 6.4. The position of the correspond-

ing photon on the photocathode can be determined by individually detecting the

pulses from the anode elements. Multianode PMTs are particularly interesting in

conjunction with the multidetector capability of advanced TCSPC techniques.

Cathode

Metal channel or fine mesh dynodes

Array

anodes

Cathode

Microchannel plates

Array

Anodes

Fig. 6.4 Multianode PMT with metal channel dynodes (left) and multianode MCP-PMT

(right)

A version of the multianode PMT uses a system of crossed wires as the anode

[297]. In principle, individual wires could be connected to a TCSPC device via a

router as in the case of the multianode PMT. Another way to obtain the X-Y in-

formation is to connect the wires via two resistor chains, as shown in Fig. 6.5, left.

The spatial coordinates of the photons are then determined by measuring the pulse

amplitudes at the ends of the resistor chains.

Virtually continuous X-Y information can be obtained from an MCP-PMT with

a resistive anode [311, 312, 361] (Fig. 6.5, right). TCSPC operation of these detec-

tors is described under Sect. 3.5, page 39.

216 6 Detectors for Photon Counting

Multichannel

plates or

Cathode

Crossed

Wires

finemesh dynodes

Timing

Multichannel

Plates

Cathode

Resistive

Anode

Timing

Fig. 6.5 Position-sensitive PMT with crossed-wire anode (left) and resistive anode (right)

The drawback of any resistive network used at the MCP output is that it intro-

duces additional noise into the position signals. The thermal noise current is pro-

portional to the reciprocal square root of the resistance. To obtain X-Y resolution

of the order of 1,000

u 1,000 pixels, the resistance is usually kept in the 100 k:

range. However, the high resistance reduces the signal bandwidth, and conse-

quently the useful count rate.

Noise from a resistive output structure is avoided in the wedge-and-strip anode.

The structure is shown in Fig. 6.6.

Multichannel

plates

Cathode

Timing

Fig. 6.6 MCP-PMT with wedge-and-strip anode

The anode consists of a system of interlaced wedges and strips. The width of

the strips gradually increases in the X direction. An electron cloud originating

from a single photoelectron is split into three charge components, A1, A2, and A3.

The ratios of A1, A2, and A3 depend on the X-Y position of the photoelectron. A

typical micromachined wedge-and-strip anode contains hundreds of wedges and

strips considerably smaller than the size of an electron cloud from a single photon.

Therefore, the X-Y information is virtually continuous.

The wedge-and-strip anode does not introduce resistive noise into the position

signals. However, the capacitance between the outputs is of the order of 100 pF.

To avoid capacitive crosstalk between the position signals, charge-sensitive ampli-

fiers with a virtual input impedance close to zero must be used. The high capaci-

tance increases the noise gain of the amplifiers. If the amplifiers are made fast, the

signal-to-noise ratio decreases. Therefore, the wedge-and-strip anode also requires

6.1 Detector Principles 217

making some tradeoff between the maximum count rate and the obtained spatial

resolution.

A problem shared by the crossed-wire anode detector with resistor chain, the

resistive-anode detector and the wedge-and-strip detector is that ratios of the pulse

amplitudes have to be calculated. However, it is difficult to calculate ratios with

high speed, no matter whether analog or digital calculation is being used (see

Sect. 3.5, page 39).

Ratio calculation is avoided by using a delay line as an anode of an MCP-PMT

[247, 248] (Fig. 6.7). The location along the delay line is obtained by measuring

the delay between the outputs at both ends of the delay line.

Multichannel

plates

Cathode

Delay Line

Timing

Fig. 6.7 Position-sensitive MCP-PMT with delay-line anode

The drawback of the delay-line-anode detector is that one or two additional

TACs and ADCs are required to obtain the X or X-Y information. The electronics

for data acquisition are therefore complicated and expensive. This problem may be

solved, with some loss in spatial and temporal resolution, by using TDC-based

electronics for data acquisition.

6.1.4 Single-Photon Avalanche Photodiodes

PMTs use the emission of photoelectrons from a photocathode, i.e. the „external

photo effect“, as a primary step of detection. The drawback of the external photo

effect is that the photoelectrons are emitted in all directions, including back into

the photocathode. Therefore the quantum efficiency, i.e. the probability that a

photon releases an photoelectron, is smaller than 0.5. The best cathodes reach a

quantum efficiency of about 0.4 between 400 and 500 nm [214].

Semiconductor detectors use the „internal photo effect“. That means that the

photons generate electron-hole pairs inside the semiconductor. Theoretically the

internal photoeffect works with a quantum efficiency of 1. In practice the quantum

efficiency of a good silicon photodiode reaches 0.8 around 800 nm. In photodi-

odes and photoconductors an electrical field separates the electrons and holes, so

that a photocurrent flows through the device when it is illuminated. Of course, the

photocurrent caused by a single electron-hole pair is far too small to be recorded

directly. Single photons can therefore be detected only if the semiconductor detec-

218 6 Detectors for Photon Counting

tor has an internal gain mechanism that does not introduce any thermal noise

background. A suitable gain mechanism exists in the „avalanche effect“. A photo-

diode is operated at a reverse voltage so high that the carriers moving through the

semiconductor break off new electron-hole pairs from the lattice of the semicon-

ductor material. This avalanche effect is used in standard avalanche photodiodes

(APDs) and delivers a stable gain on the order of 10

to 10

A gain of 10

is, however, too low to detect single photons with the time resolu-

tion required for TCSPC. Unfortunately, higher gain normally results in instabil-

ity, i.e. the avalanche becomes self-sustaining and destroys the diode. Neverthe-

less, photon-induced avalanche breakdown can be used for single photon

detection. The reverse voltage of the diode is set several volts above the break-

down voltage. To avoid the avalanche destroying the diode, an active or passive

quenching circuit restores normal operation after each photon. The principle is

often termed „Geiger mode“ [113, 115, 302], beause of the similarity with the

Geiger-Müller counter. The principle of a single photon avalanche photodiode

(SPAPD or SPAD) operating in the Geiger mode is shown in Fig. 6.8.

Avalanche

Photon

200 to

Output

Avalanche Photodiode

300V

Avalanche

Quenching Circuit

Photon

200 to

Output

Avalanche Photodiode

300 V

Fig. 6.8 Single photon avalanche photodiode (SPAD). Left Passive quenching, right active

quenching

Passive quenching is obtained by operating the diode via a series resistor, R

which is typically a few hundred k

:. C

is the stray capacitance of R

and the

diode leads to ground, or an additional capacitor of a few pF. When an avalanche

breakdown occurs, C

is discharged within a time on the order of a nanosecond.

The discharge current flows through the diode and the load, producing a corre-

spondingly short output pulse. Simultaneously the voltage across the diode drops

below the breakdown voltage and the avalanche stops. The voltage across the

diode then increases and eventually reaches the supply voltage. The time constant

of this recovery process is

)(

dssr

CCRT  (6.1)

with

being the diode junction capacitance.

is typically a few hundred nano-

seconds to a few microseconds. As long as the reverse voltage of the diode re-

mains below the breakdown voltage, a new avalanche cannot be triggered. After

the breakdown voltage is reached, the detection probability gradually rises to the

original level. Full recovery of the detection probability and timing performance

6.1 Detector Principles 219

takes 3 to 5

. Consequently, passive quenching can be used only at count rates

far below 1 MHz, and some count-rate dependence of the timing performance and

efficiency must be expected.

Active quenching uses an electronic quenching circuit [113, 116, 158, 302].

When a breakdown occurs, the output pulse of the diode triggers the quenching

circuit, which reduces the reverse voltage of the diode below the breakdown level

for a time of typically 20 to 50 ns. After the quenching pulse the reverse voltage is

restored within a few ns, and the diode resumes normal operation. Thus a much

higher count rate can be obtained than for passive quenching. However, in practice

it is difficult to apply the quenching pulse to the high-voltage side of the diode

without using a coupling capacitor or a transformer. Consequently, the diode volt-

age swings slightly above the steady state level after the quenching pulse, and then

settles with the coupling time constant. Thus also actively quenched photodiodes

often show some count-rate-dependent timing shift and change in efficiency. Dif-

ferent quenching circuits are discussed in detail in [116].

The reverse voltage applied to a SPAD can be as high as 200 to 500 V. The

power dissipation in the diode during the avalanche breakdown is therefore con-

siderable. In passively quenched APDs the average diode current is limited by the

series resistor, R

. This gives inherent safety against damage. In an actively

quenched APD the current is not automatically limited. Therefore some kind of

overload protection must be implemented to avoid damage to the diode from ex-

cessive detection rates.

APDs suitable for single photon detection must be free of premature breakdown

at the edge of the junction or at local lattice defects. So far, only selected silicon

APDs can be operated in the passive or active quenching mode, and only a few

single photon APD detectors are commercially available [245, 354, 408].

For detection in the infrared region the situation is even less favourable. A few

TCSPC applications of liquid-nitrogen cooled Ge APDs have been reported [391],

but have not resulted in commercially manufactured detectors. InGaAs APDs

suffer from strong afterpulsing which has prevented continuous quenched opera-

tion so far.

A variant of active quenching is

gated detection of single photons. For gated

detection, the reverse voltage of the diode is pulsed above the breakdown voltage

for a time of 1 to 100 ns. If a photon is detected within this time, an avalanche is

triggered. For short gate pulses at low duty cycle there is no problem with after-

pulsing. Gated avalanche detection therefore works also with InGaAs APDs.

Gated APDs are commonly used for experiments of quantum key distribution.

They can also be used for low-intensity gated photon counting at low pulse repeti-

tion rate.

At first glance, gated operation appears applicable to TCSPC at low pulse repe-

tition rate. TCSPC records only one photon per signal period. Consequently, the

APD could be gated „on“ shortly before the light pulse to be recorded, and gated

„off“ after the time interval of interest. However, in actuality ripple on the gate

pulse and transients induced by the leading edge of the gate pulse cause large

timing errors and poor differential nonlinearity.

Passively and actively quenched single-photon APDs must normally be cooled.

Except for diodes of extremely small area the thermal carrier generation rate at

220 6 Detectors for Photon Counting

room temperature is so high that the device is useless or may not work at all. Even

if the diode is cooled to –30° C, the dark count rate per mm

of active area is much

higher than for a PMT. Interestingly, the dark count rate increases more than pro-

portionally with the area [246]. Consequently, SPADs are made only with small

active diameters on the order of 10 to 200 µm. The small detector area has to be

taken into account when the use of a SPAD is considered.

A problem associated with quenched breakdown operation is light emission

from the diode. Light emission can be a problem for correlation experiments and

quantum cryptography [299, 515] (see Fig. 5.105, page 175).

An overview of currently available SPAD technologies is given in [117]. The

SPCM-AQR modules of Perkin Elmer [408] are based on diodes manufactured in

a dedicated technological process [127]. The depletion region of the diodes is 30

to 40 µm deep. This results in an exceptionally high quantum efficiency in the

NIR, but also in a high breakdown voltage, poor timing stability, and relatively

large timing jitter.

A better timing performance is achieved with diodes built in a planar epitaxial

process. The diodes are characterised by a small thickness of the depletion region

and a breakdown voltage of only a few 10 V. The small thickness results in low

timing jitter [115]. The quenching amplitude is of the order of a few V, and the

quenching pulse can be coupled directly to the diode. Fully integrated quenching

circuits can be used; the quenching circuit can even be integrated on the same chip

with the diode [245]. The direct coupling of the quenching pulse keeps count-rate

dependent timing shifts and IRF changes small. The drawback of the thin deple-

tion region is a reduced quantum efficiency in the near infrared. Moreover, pho-

tons passing the depletion layer may cause a wavelength-dependent tail in the

response (see Fig. 6.58, page 261). Planar epitaxial APDs are compatible with

standard manufacturing processes used for high-speed CMOS circuits [245, 246,

354, 424, 459]. The technique may reduce the price of SPADs considerably and is

a possible way to produce SPAD arrays.

Recently silicon APDs with a stable gain of 10

to 10

have been developed

[294]. The diodes behave more or less like a PMT, i.e. the gain is a continuous func-

tion of the operating voltage. The output pulses have a duration of the order of a few

hundred ps and an amplitude of a few 10 mV. It is likely, but not proved yet, that

timing stability or light emission will no longer be a problem with these diodes.

6.1.5 Hybrid PMTs

Hybrid PMTs accelerate the photoelectrons emitted by a photocathode to an en-

ergy of 5 to 10 keV. The electrons are directed into a silicon PIN or avalanche

photodiode. The principle is shown in Fig. 6.9.

When an accelerated photoelectron hits the silicon diode it generates a large

number of secondary electrons. Therefore a large part of the gain is obtained in a

single step, with a correspondingly narrow amplitude distribution of the single-

photon pulses at the output of the device. By measuring the pulse amplitude, hy-

brid PMTs can therefore be used to distinguish between one, two, or even more

photons detected simultaneously [314, 315].

6.1 Detector Principles 221

Photocathode Focusing

Electrode

PIN Diode

APD or

-5 to -10 kV

Ground

Fig. 6.9 Hybrid photomultiplier

Currently manufactured hybrid PMTs have gains of the order of 10,000. There-

fore electronic noise from the matching resistor and from the preamplifier impairs

the time resolution of single photon detection. The relatively large distance be-

tween the photocathode and diode chip may also cause transit-time spread. In

practical applications, the extremely high operating voltage also causes problems.

Currently hybrid PMTs are not routinely used for TCSPC experiments.

The principle of the hybrid PMT is also used in electron-bombarded (EBD)

CCDs. In these devices the diode is replaced with a CCD image sensor. Electron

multiplication results in a considerable gain effect so that EBD-CCDs are able to

detect single photons. However, the quantum efficiency of the photocathode is

lower than the optical quantum efficiency of a CCD sensor. If an acquisition time

of a few ten seconds can is acceptable it is often better to detect the photons di-

rectly in a cooled CCD.

6.1.6 Other Detector Principles

X-ray photons can be detected directly by PIN photodiodes. A single high energy

X-ray photon absorbed in the diode generates a large number of electron-hole

pairs. The resulting current pulse can be detected by a charge amplifier. Due to the

limited speed of the amplifier these detectors have a time resolution in the us

range and do not reach high count rates. They can, however, distinguish photons

of different energy by the different amount of charge generated. Energy-resolved

X-ray imaging with single photon sensitivity can be achieved even by CCD ar-

rays. When a single X-ray photon is absorbed it generates a number of electron-

hole pairs much higher than the readout noise of the CCD device. The number of

carriers is proportional to the energy of the X-ray photon. If the CCD device is

read out at a sufficiently high rate, the spatial position and the energy are obtained

for individual X-ray photons [392].

Recently CCD image sensors with internal amplification have been developed.

These devices have a readout noise of the order of one photoelectron or less [244].

They are, therefore, able to detect single photons, but not with the time resolution

required for TCSPC.

There are other single photon detection techniques, e.g. devices based on su-

perconductivity [359] and quantum dots. These techniques have not yet led to

commercially available detectors.

222 6 Detectors for Photon Counting

Interestingly, the detection threshold of the rod cells in the human retina is

close to the single photon level [427]. Most likely the sensitivity of the eye of a cat

is even better. Unfortunately, most cats are not interested in serious scientific

work, and it remains an open question whether they see individual photons or not.

6.2 Characterisation of Detectors

6.2.1 Gain

The gain of a photomultiplier tube changes strongly with the operating voltage.

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

of the dynodes and the energy of the primary electrons. For typical interstage

voltages of the order of 100 V the secondary emission coefficient, n, is between 4

and 10 and changes with the 0.7th to 0.8th power of the voltage [219]. For a 10

stage PMT the total gain increases with the 7th or 8th power of the total voltage.

It should be pointed out that the gain mechanism in a PMT tube operates as a

random process. The number of secondary electrons is different for each primary

electron. The relative width of the distribution can be expected at least of the size

of the standard deviation of a poissonian distribution, n

1/2

, of the secondary emis-

sion coefficient, n, at the first dynode. Therefore the single-photon pulses obtained

from a PMT have a considerable amplitude jitter, see Sect. 6.2.5, page 226.

PMTs of the same type but with different cathodes may differ considerably in

gain. The reason is that the cathode is formed inside the tube. During the manufac-

turing process the cathode material spills into the dynode system. This can even be

intentional, because the cathode materials are efficient secondary electron emitters.

High PMT gain is essential for TCSPC applications. A good timing stability

can only be obtained if the gain is high enough to obtain single photon amplitudes

considerably above the noise of a subsequent amplifier.

6.2.2 Single-Electron Response

The output pulse of a detector for a single photoelectron is called the „Single-

Electron Response“ or „SER“. Some typical SER shapes for different detectors are

shown in Fig. 6.10.

Standard PMT High Speed PMT MCP-PMT

t, 1ns/div

Iout

t, 1ns/div t, 1ns/div t, 1ns/div

SPAD

Iout

Vout

Fig. 6.10 Single electron response (SER) of different detectors

6.2 Characterisation of Detectors 223

Due to the random nature of the detector gain, the amplitude of the single-photon

pulses of PMTs and MCP-PMTs varies from pulse to pulse. The pulse height

distribution can be very broad, up to 1:5 to 1:10. Figure 6.11 shows the SER

pulses of an R5600 PMT recorded by a 1-GHz oscilloscope.

Fig. 6.11 Amplitude jitter of SER pulses. R5900 PMT at –900 V. Scale 5 mV and 1 ns per

division

The current amplitude, I

SER

, of the SER is approximately

SER



(6.2)

with

G = PMT Gain, e = 1,60210

-19

As, T

SER

= SER pulse width (fwhm). The table

below shows some typical values.

SER

is the average SER peak current and V

SER

the

average SER peak voltage when the output is terminated with 50

:. I

max

is the

maximum permitted continuous output current of the PMT.

Table 6.1.

PMT GT

SER

(50 :) I

max

(cont)

Standard 10

5 ns 0.32 mA 16 mV 100 uA

Fast PMT 10

1.5 ns 1 mA 50 mV 100 uA

MCP PMT 10

0.36 ns 0.5 mA 25 mV 0.1 uA

An important conclusion may be drawn from this table: If the PMT is

operated near its full gain, the peak current I

SER

is much higher than the

maximum continuous output current, I

. Consequently, the PMT delivers

a train of random pulses rather than a continuous signal (see Fig. 1.1, page

2). Because each pulse represents the detection of an individual photon, the

pulse density, rather than the pulse amplitude, is a measure of the light

intensity at the cathode of the PMT [297]. Obviously, the pulse density is

measured best by counting the PMT pulses within successive time inter-

vals. Therefore, photon counting is a logical consequence of the high gain

and the high speed of photomultipliers.