I04_Single Photon Imaging

International Image Sensor Workshop 2011

Single Photon Imaging

Peter Seitz

CSEM SA, Nanomedicine Division, CH-7302 Landquart, Switzerland

EPFL STI IMT NE, Federal Institute of Technology, CH-2000 Neuchâtel, Switzerland

phone: +41 81 307 8101 ; e-mail:

1. Introduction

Electromagnetic radiation can be successfully modelled as a stream of particles with zero rest-mass, the so-called photons. For this reason, the holy grail of image sensing is a two-dimensional array of photodetectors, capable of sensing each individual incident photon. Despite the simplicity of this demand, it is surprising to realize how many different solutions to the single-photon imaging problem exist today [1]. The present work provides a concise categorization of the various single-photon imaging techniques, offering a systematic approach to the methodical selection of the optimum single-photon imaging solution for given boundary conditions.

2. Solid State Photosensing

Because of their superior sensitivity and stability, only solid state photosensors are considered here, either in the form of a metallic or a semiconducting material. In both cases, the energy of incident photons is employed for the creation of mobile charge carriers, see also Fig. 1. If the energy of an incident photon is larger than the so-called work function EW of a metallic material, then an electron can be removed from the material surface for subsequent detection. In the case of a semiconductor, the incident photon’s energy must be larger than the bandgap EG for the creation of a mobile electron-hole pair, which can be subsequently detected. If a semiconductor is employed as photocathode, the total energy EG+EA is required to lift an electron from the edge of the valence band to the vacuum level. EA is called the electron affinity.

The first class of solid state photosensors includes a large family of photocathode materials whose properties have been carefully tuned for low work function, low dark current density and high quantum efficiency [2]. Obvious-ly, the ubiquitous CCD and CMOS image sensors belong to the second class of solid state photosensors.

The performance of a photosensor is described by three main parameters:

- Quantum efficiency, defined as the fraction of free or mobile charge carriers created per incident photon. The quantum efficiency tends to zero (the material starts to become transparent) once the energy of the incident photon falls below EW or EG - Dark current density, describing the number of free or mobile charge carriers per surface area and per unit time, created due to thermal excitation under dark conditions.

- Electronic charge detection noise, defined as the input-referred charge noise of the electronic circuit employed for the detection of the photogenerated free or mobile charge carriers.

3. Dark Current Density

In a semiconductor, the dark current density jdark consists of three major parts, see [3] and [4]: the recombination current jrec in the space charge region, the diffusion current jdiff describing the thermal generation of charge pairs within a diffusion length from the space charge region, and the surface dark current density jsurf generated by traps at the semiconductor-oxide interface:

jqni

qndark jrec jdiff jsurf w i2D

NL

qniS (1)

with unit charge q=1.602×10-16 As, intrinsic carrier con-centration ni, width of the space charge region w, genera-tion lifetime , diffusion constant D, doping concentration N, minority carrier diffusion length L and surface gene-ration velocity S.

The intrinsic carrier concentration ni depends exponen-tially on the bandgap energy EG and the inverse absolute temperature 1/T:

3EGni T2

e

2kT

(2) The thermionic emission jmet from a metallic surface, however, exhibits a different temperature dependence [5]: jmet T2

e

EWkT

(3) Finally, the thermionic emission from the surface of a semiconducting photocathode is given by [5]:

EA jsem T2

e

EG2kT (4)

In Fig. 2, the lowest dark current densities known to the author for various photodetector materials at 250C are plotted as a function of the bandgap energy EG. The mate-rials include silicon [6], germanium [7], InGaAs [8] and the two photocathode materials S-20 and S-24 [5]. The straight line corresponds to the exponential energy depen-dence of the intrinsic carrier density ni, as described by Eq. (2), and the vertical offset has been chosen so that the line crosses exactly the measurement point for silicon [6]. The main conclusion from this graph is that very low dark current densities (below fA/cm2) can be achieved at room temperature, provided one accepts a lower wavelength cutoff and one is willing to employ detection methods involving photocathodes.

4. Electronic Charge Detection Noise

Today it is believed that the ultimate precision with which an electronic circuit can determine the size of a charge packet is limited by thermal (Johnson) noise in the channel of the circuit’s input transistor. Provided that this

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