1. Single Photon Detectors
By: Kobi Cohen
Quantum Optics Seminar
25/11/09

2. Outline A brief review of semiconductors Photodiode
P-type, N-type
Excitations
Photodiode
Avalanche photodiode
Geiger Mode
Silicon Photomultipliers (SiPM)
Photomultiplier
Superconducting Wire
Characterization of single photon sources
HBT Experiment
Second order correlation function

3. Semiconductors
Compounds

4. Semiconductors
electrons and “holes”: negative and positive charge carries
Energy-momentum relation of free particles, with different effective mass

5. Semiconductors
Thermal excitations make the electrons “jump” to higher energy levels, according to Fermi-Dirac distribution:

6. Semiconductors
Excitations can also occur by the absorption of a photon, which makes semiconductors suitable for light detection:
Energy conservation
Momentum conservation
photon momentum is negligible  k2≈k1
useful to remember:
(T=300K)
Egap(eV)
λgap(nm) Ge
0.66
1880 Si
1.11
1150
GaAs
1.42
870

7. Intrinsic Semiconductors
Charge carriers concentration in a semiconductor without impurities:

8. N-type Semiconductor
Some impurity atoms (donors) with more valence electrons are introduced into the crystal:

9. P-type Semiconductor
Some impurity atoms (acceptors) with less valence electrons are introduced into the crystal:

10. The P-N Junction
Electrons and holes diffuse to area of lower concentration
Electric field is built up in the depletion layer
Drift of minority carriers
Capacitance

11. Biased P-N junction
When connected to a voltage source, the i-V curve of a P-N junction is given by:
We’ll focus on reverse biasing:
larger electric field in the junction
extended space charge region

12. The P-N photodiode
Electrons and holes generated in the depletion area due to photon absorption are drifted outwards by the electric field

13. The P-N photodiode
The i-V curve in the reverse-biased P-N junction is changed by the photocurrent
Reverse biasing:
Electric field in the junction increases quantum efficiency
Larger depletion layer
Better signal

14. The P-I-N junction Larger depletion layer allows improved efficiency
Smaller junction capacitance means fast response

15. Detectors: Quantum Efficiency
The probability that a single photon incident on the detector generates a signal
Losses:
reflection
nature of absorption
a fraction of the electron hole pairs recombine in the junction

16. Detectors: Quantum Efficiency
Wavelength dependence of α:

17. Summary: P-N photodiode
Simple and cheap solid state device
No internal gain, linear response
Noise (“dark” current) is at the level of several hundred electrons, and consequently the smallest detectable light needs to consist of even more photons

18. Avalanche photodiode
High reverse-bias voltage enhances the field in the depletion layer
Electrons and holes excited by the photons are accelerated in the strong field generated by the reverse bias.
Collisions causing impact-ionization of more electron-hole pairs, thus contributing to the gain of the junction.

19. Avalanche photodiode
P-N photodiode
Avalanche photodiode

20. Summary: APD
High reverse-bias voltage, but below the breakdown voltage.
High gain (~100), weak signal detection (~20 photons)
Average photocurrent is proportional to the incident photon flux (linear mode)

21. Geiger mode
In the Geiger mode, the APD is biased above its breakdown voltage for operation in very high gain.
Electrons and holes multiply by impact ionization faster than they can be collected, resulting in an exponential growth in the current
Individual photon counting

22. Geiger mode – quenching
Shutting off an avalanche current is called quenching
Passive quenching (slower, ~10ns dead time)
Active quenching (faster)

23. Summary: Geiger mode High detection efficiency (80%).
Dark counts rate (at room temperature) below 1000/sec. Cooling reduces it exponentially.
After-pulsing caused by carrier trapping and delayed release.
Correction factor for intensity (due to dead time).

24. Silicon Photomultipliers
SiPM is an array of microcell avalanche photodiodes (~20um) operating in Geiger mode, made on a silicon substrate, with pixels/mm2. Total area 1x1mm2.
The independently operating pixels are connected to the same readout line

25. SiPM: Examples

26. Summary: SiPM Very high gain (~106)
Dark counts: 1MHz/mm2 (~20C) to 200Hz/mm2 (~100K)
Correction factor (other than G-APD)

27. Photomultiplier
Photoelectric effect causes photoelectron emission (external photoelectric effect)
For metals the work function W ~ 2eV, useful for detection in the visible and UV. For semiconductors can be ~ 1eV, useful for IR detection

28. Photomultiplier
Light excites the electrons in the photocathode so that photoelectrons are emitted into the vacuum
Photoelectrons are accelerated due to between the dynodes, causing secondary emission

29. Summary: Photomultiplier
First to be invented (1936)
Single photon detection
Sensitive to magnetic fields
Expensive and complicated structure

30. A remark – image intensifiers
A microchannel plate is an array consists of millions of capillaries (~10 um diameter) in a glass plate (~1mm thickness).
Both faces of the plate are coated by thin metal, and act as electrodes.
The inner side of each tube is coated with electron-emissive material.

31. Superconducting nano-wire
Ultra thin, very narrow NbN strip, kept at 4.2K and current-biased close to the critical current.
A photon-induced hotspot leads to the formation of a resistive barrier across the sensor, and results in a measurable voltage pulse.
Healing time ~ 30ps

32. SSPD – meander configuration
Meander structure increases the active area and thus the quantum efficiency

33. End of 1st part !

34. Hanbury Brown-Twiss Experiment (1)
Back in the 1950’s, two astronomers wanted to measure the diameters of stars…

35. Hanbury Brown-Twiss Experiment (2)

36. Hanbury Brown-Twiss Experiment (3)
In their original experiments, HBT set τ=0 and varied d.
As d increased, the spatial coherence of the light on the two detectors decreased, and eventually vanished for large values of d.

37. Coherence time
The coherence time τc is originated from atomic processes
Intensity fluctuations of a beam of light are related to its coherence

38. Correlations (1)
We shall assume from now on that we are testing the spatially-coherent light from a small area of the source.
The second order correlation function of the light is defined by:
(Why second order?)

39. Correlations (2)
For τ much greater than the coherence time:

40. Correlations (3)
On the other and, for τ much smaller than the coherence time, there will be correlations between the fluctuations at the two times. In particular, if τ=0 :

41. Correlations: example
If the spectral line is Doppler broadened with a Gaussian lineshape, the second order correlation functions is given by:

42. Summary: correlations in classical light

43. HBT experiments with photons
The number of counts registered on a photon counting detector is proportional to the intensity

44. Photon bunching and antibunching
Perfectly coherent light has Poissonian photon statistics
Bunched light consists of photons clumped together

45. Photon bunching and antibunching
In antibunched light, photons come out with regular gaps between them

46. Experimental demonstration of photon antibunching
Antibunching effects are only observed if we look at light from a single atom

47. Experimental demonstration of photon antibunching
Antibunching has been observed from many other types of light emitters

48. Bibliography Fundamentals of Photonics, Saleh & Teich, Wiley 1991
Quantum Optics: An introduction, Mark Fox, Oxford University Press 2006
Hamamatsu MMPC datasheet (online)
PerkinElmer APCM datasheet (online)
Golts’man G., SSPD, APL 79(6),2001,
Hanbury Brown, R. , and Twiss, R. Q. , Nature, 177, 27 (1956)
Hanbury Brown, R. , and Twiss, R. Q. , Nature, 178, 1046 (1956)