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

  2. Outline • A brief review of semiconductors • 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. Compounds Semiconductors

  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. Energy conservation • Momentum conservation • photon momentum is negligible  k2≈k1 • useful to remember: Semiconductors • Excitations can also occur by the absorption of a photon, which makes semiconductors suitable for light detection:

  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 500-5000 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, 705-707 • Hanbury Brown, R. , and Twiss, R. Q. , Nature, 177, 27 (1956) • Hanbury Brown, R. , and Twiss, R. Q. , Nature, 178, 1046 (1956)