The Photoelectric Effect in Silicon Image Sensors: A Defense [Part: 4 Academic Imaging]
In my previous posts on this topic, [Part 1], [Part 2] and [Part 3] ,we have been discussing the nature of the internal photoelectric effect in silicon. It appears that while there is strong agreement on the physical mechanism and indeed the equations that model the experimental facts, there is some wider debate and disagreement regarding the correct nomenclature.
While parts 1, 2 and 3 have looked at the physical process, some references from literature throughout the web and the opinions of some of the world's largest commercial entities in the field, this blog post will look exclusively at academic literature in the field, and will prove, beyond doubt that the photoelectric effect, or rather its internal rather than external variant is critical for the operation of any semiconductor solid-state photodetector. This includes photodiodes, Schotky diodes, avalanche photodiodes, single-photon avalanche photodiodes, CCD detectors, CMOS Active Pixel imagers and indeed III-V diodes and some of the more unusual detectors such as lead-salt detectors.
Likewise I'll highlight that while one must not rely on a single paper as fact, that if that statement is within 100's of peer reviewed papers, spread over a significant number of decades, has no geographical constraints (i.e. a world wide paradigm) and is the combined thoughts of 1000's if not 100,000's of researchers, professors, R&D team leaders, Ph.D's and indeed journal editors and reviewers, then it represents the current de-facto state of our current best theories in this matter and the de-facto nomenclature of the field.
This part of this blog series looks at and quotes from academic books only, conference slides, conference proceedings and peer-reviewed journal papers containing the nomenclature of the "internal photoelectric effect" will be discussed in forthcoming posts.
So, where to start, well lets start with a few Scientific textbooks in the field:
Source (Book): "Single Photon Imaging", P. Seitz, A. Theuissen (Eds), Springer: Optical Sciences Series, 2011 (Link)
Specifically Chapter 13, Section 13.2, Page 303 Author: Pierre Magnan
CCDs: "CCD imagers for the UV, visible and near-infrared spectral domain (compatible with the Si bandgap energy of 1.13eV)"
Hybrid Detectors: "Hybrid detectors for the short and mid wavelength infrared domain, made of infrared sensitive material (narrow-gap III-V or II-VI semiconductor)"
"Both types of device, that will be shortly reviewed, share the internal photoelectric effect as a photon detection principle..."
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Source (Book): "Advances in Photodiodes", Gian-Franco Dalla Betta (Ed), InTechOpen, 2011 (Link)
Specifically page 332
"Some examples of photo-emissive detectors are photo-multipliers, vacuum photodiodes, and image intensifier tubes. However if there is no emission taking place but the photo generated electron-hole pair is available for the current circulation in an external circuit, then this is called an internal photoelectric effect detector which is the characteristic of all semiconductor photodetectors."
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Source (Book): "High Performance Silicon Imaging", D. Durini (Ed), Woodhead Publishing, 2014 (Link)
This book contains a chapter written by my Ph.D supervisor (Robert Henderson - Edinburgh University), and a chapter by a R. Turchetta from STFC at the Rutherford Appleton Laboratories (Oxford, UK)
Specifically Chapter 1, pages 18/19, Chapter 2 page 26, Chapter 3 page 79 (Author: M. Lesser) and Chapter 10 pages 287, 288
p18 (Durini): "According to the already introduced Rutherford-Bohr model, the individual electrons bound to the nucleus of a certain atom, e.g. silicon, can only possess discrete energy levels separated by forbidden energy gaps. But, if they happen to acquire enough energy to escape the forces that bind them to the atom nucleus, e.g. by absorbing incident radiation on them - which gives birth to the internal photoelectric effect - their behavior will be defined by a new continuum of corresponding energy levels. According to the theory developed by Erwin Schrödinger, which describes how the wave function of a physical system evolves over time, these electrons will become quasi-free and will be able to move around in the silicon crystal within a complex electric field formed by the ions of the crystalline lattice and the valence electrons of the neighbouring atoms. The minimal required energy for the described internal photoelectric effect to take place, defined as the energy-gap energy E g , is less than the work-function energy necessary for the electrons to completely leave the solid, required for the external photoelectric effect."
p19 (Durini): "The internal photoelectric effect manifests itself as a change of the electrical properties of a metal or a semiconductor due to the increase in the amount of excited electrons (i.e. electrons that moved from the valence band into the conduction band of a semiconductor) caused by absorption of the impinging radiation."
p26 (Durini): "If crystalline silicon gets illuminated, in one of all scattering processes that take place between the impinging photons and the silicon crystal, there is an energy transfer between this impinging photon and the one scattered electron within the silicon crystal: the internal photoelectric effect takes place and one electron-hole pair (EHP) gets produced. Apart from the photoelectric effect, often being considered as the first in the line of photon matter interaction phenomena, there exist at least two more important effects: the Compton Scattering and the Pair Production. The probability, expressed as process cross-section in units of square centimeter per gram, of each of the three scattering effects to take place in silicon depending on the energy of the impinging radiation can be observed in Fig. 2.1 (based on the data extracted from Spieler, 1998 )."
p79 (Lesser): "Silicon detectors are sensitive to photons of wavelengths where electrons can be created via the photoelectric effect. This occurs when the photon energy E of wavelength cutoff is greater than the band gap of silicon in order to excite an electron from the silicon valence band to the conduction band. For most CCDs these charge packets are made up of electrons which are generated by the photoelectric effect from incident photons or from an internal dark signal."
p287 (Turchetta): "In the photoelectric effect the photon is absorbed by one of the electrons in silicon. The electron gains the full energy from the photon and travels into the material releasing its energy. In Compton scattering, the photon loses only part of its energy by inelastic scattering with one of the electrons of the material. Part of the photon energy is given to this electron, resulting in an overall reduction in the energy of the incident photon, as well as a change in its travelling direction. Pair creation can only happen for photons with energy higher than two times the rest energy of an electron or 1.02 MeV. In this case, the photon annihilates generating a pair electron-positron."
p288 (Turchetta): "Because of its dominance at low energy, photoelectric effect remains the most important effect for the detection of photons."
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Source (Book): "Optics and Photonics: An Introduction", F. Smith, D. Willkins and T. King, Wiley, 2000 (Link)
Specifically Chapter 21, Page 383
p383: "In all photoemmissive detectors an incident photon frees an electron from a solid by ionisation", and
p391: "Photoelectric detectors have been described so far as single detectors. There are a number of ways in which two-dimensional arrays of detectors can be assembled so that an image may be recorded, as in an electronic camera. An array of photodiodes on a silicon chip, an arrangement which is widely used is the charge-coupled device (CCD)."
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Source (Book): "Radiation Detection and Measurement", Glenn Knoll, 4th Edition, Wiley, 2010 (Link)
Specifically Chapter 11, Section VI.E Page 408 and later page 473
p408: "Even though silicon has a relatively low atomic number of 14, photoelectric absorption of incident photons is still predominant in the soft X-Ray region below 2KeV" (and by extension of being of lower energy also UV and visible photons), and
p473: "In silicon, the photoelectric process is more probable than Compton Scattering for photon energies below 55KeV"
Note that X-Rays are a form of electromagnetic radiation (Link) and are therefore on the same continuum as UV and visible radiation although they differ significantly in energy and wavelength.
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Source (Book): "Concepts of Classical Optics", J. Strong, W. H. Freeman and Company Inc, 1958 (Link)
Specifically Appendix I, Page 493 Author: Harold Yates
"... but results from the increased number of conduction electrons that are freed from bound states by the absorption of incident radiation. The process can be considered as a sort of photoelectric effect in which the absorbed quantum raises an electron from a bound state to the conduction state."
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Source (Book): "Fundamentals of Photonics", B. Saleh and T. Teich (J. Goodman Editor), Wiley Interscience: Series in Pure and Applied Optics, 1991
Specifically Chapter 17, Pages 645 - 648
Both the internal and external photoelectric effects are discussed, for both metals and semiconductors
"The photoeffect takes two forms: external and internal. The former process involves photoelectric emission, in which the photogenerated electrons escape from the material as free electrons. In the latter process, (also called) photoconductivity, the excited carriers remain within the material, usually a semiconductor, and serve to increase its conductivity."
"Many modern photo-detectors operate on the basis of the internal photoeffect, in which the photoexited carriers (electrons and holes) remain within the sample. Photoconductor detectors rely directly on the light-induced increase in electrical conductivity, which is exhibited by almost all semiconductor materials... The application of an electric field to the material results in the transport of both electrons and holes through the material and the consequent production of an electric current in the electrical circuit of the detector."
"The semiconductor photodiode detector is a p-n junction structure that is also based on the internal photoeffect."
The authors discuss the differences between the work function (external) and energy gap (internal) and indeed link the external effect to vacuum technologies
I'm sure there are other books available that cover the "internal photoelectric effect". Likewise I'm sure that depending on their age and scientific focus, there are books that will only list the external photoelectric effect.
For now I'll close this post as the above seven text books, when combined with the previous blog posts, most certainly sets a robust and well referenced rebuttal to the incorrect comment that the "photoelectric effect is irrelevant for semiconductor or solid-state imaging technologies". My next blog post, will look quickly at a number of slides presented at academic conferences, including some slides by radiation detector specialists at CERN. I will also be referencing a number of academic papers (conferences and journals), demonstrating that as a name for the process, as a nomenclature for the fundamental theory, the internal photoelectric effect is indeed is wide spread and continuous use in my field.