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

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

Semiconductors Compounds

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

Semiconductors  Thermal excitations make the electrons “jump” to higher energy levels, according to Fermi-Dirac distribution:  1 exp[(

E



E f

) /

kT

exp(  )

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  k 2 ≈k 1 •useful to remember: )  1240  (

nm

) (T=300K) E gap (eV) λ gap (nm) Ge Si GaAs 0.66

1.11

1.42

1880 1150 870

Intrinsic Semiconductors  Charge carriers concentration in a semiconductor without impurities:

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

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

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

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: 1. larger electric field in the junction 2. extended space charge region

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

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

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

Detectors: Quantum Efficiency  The probability that a single photon incident on the detector generates a signal 

R

   

d

)]   Losses: • reflection •nature of absorption • a fraction of the electron hole pairs recombine in the junction

Detectors: Quantum Efficiency  Wavelength dependence of α:

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

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.

Avalanche photodiode P-N photodiode Avalanche photodiode

Summary: APD    High reverse-bias voltage, but breakdown voltage.

incident photon flux below High gain (~100), weak signal detection (~20 photons) Average photocurrent is proportional to the (linear mode) the

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

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

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).

Silicon Photomultipliers   SiPM is an array of microcell avalanche photodiodes (~20um) operating in Geiger mode, made on a silicon substrate, with 500-5000 pixels/mm 2 . Total area 1x1mm 2 .

The independently operating pixels are connected to the same readout line

SiPM: Examples

Summary: SiPM    Very high gain (~10 6 ) Dark counts: 1MHz/mm 2 (~20C) to 200Hz/mm 2 Correction factor (other than G-APD) (~100K)

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

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

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

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.

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

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

End of 1 st part !

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

Hanbury Brown-Twiss Experiment (2)

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.

Coherence time   The coherence time τ c is originated from atomic processes Intensity fluctuations of a beam of light are related to its coherence

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?)

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

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 :

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

Summary: correlations in classical light

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

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

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

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

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

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)