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Semiconductor Photodetectors

PIN diodes

PIN diodes are semiconductor diodes consisting of a p-type, an intrinsic and an n-type layer. Semiconductors (with four valency electrons) can be doped with 3-valent (acceptor, p-type) or 5-valent (donor, n-type) impurities. This results in the formation of energy levels close to the valence (acceptor, p-type) and conduction (donor, n-type) bands. If we place a pure band between these, the electron-hole pairs are mainly created in the depletion layer where the probability of recombination is low, so the generated charge carriers contribute to the photo current with a high probability. (The energy of visible light is in the order of ~3eV, which is higher than the width of the forbidden band.)
In practice PIN diodes can be used as good photodiodes. They are small, mechanically resistant, used as dosimeters they are compact and not vulnerable, but gamma cameras have also been produced using them (in PET devices good timing would also be required).

APD (Avalanche Photo Diode)

APDs are photodiodes onto which relatively high reverse voltage is connected. Due to the high field strength in the depletion layer an avalanche process can occur (breakdown), the increase of the current is highly nonlinear, this is what the APD uses.
An advantage of APDs is that that they are MR compatible. In the PET-MR brain imaging system by Siemens APDs are used. The drawbacks of APDs are their low gain (\approx 10^3) and the fact that they are highly temperature dependent, thus they need an ASIC (Application Specific Integrated Circuit) as amplifier. At present SiPM seems to be a more promising candidate for creating MR compatible photodetectors.


Silicon Photo Multilpier, or MPPC, or GAPD, or SSPM, or SPAD...
The idea behind this device is biasing the diode in reverse direction instead of using the highly nonlinear signal of the APD, but getting only 1 bit of information from each diode. We give up the amplitude of the signal: if no photons arrive the signal will be zero, whereas if one or more photons arrive the signal will be nonzero. If many small SiPM diodes are placed closely on a surface, expectedly only one photon will hit a SiPM (cell), thus the energy of the sum of their signals can be linear.
The advantage of SiPMs is that they are MR compatible, they have a high gain of ~10^6, no AISC and high voltage are required, but they are not cheap yet and have a high dark current, typically 1 MHz/mm^2, and owing to this it is difficult to add the signals from a large surface. They are sensitive to temperature but this can be calibrated. They can saturate in which case their energy (i.e. the number of photons) in nonlinear, but this can also be corrected easily. Their production is a new and rapidly developing field, which makes it possible for many manufacturers to break the hegemony of Hamamatsu in photodetector production.

The number of excited cells (N_{\mathrm{fired cells}}) can be determined as follows:
A SiPM consists of thousands of cells. Any cell will generate the same signal regardless of the number of photons it is excited by, its dead time is in the order of a microsecond, therefore it is possible that more photons from the same scintillation excite it, since the decay time of a LYSO crystal is ~40 ns. This means that the photons produced in one scintillation arrive in less time than the dead time of a cell. As a result, if more photons hit a cell we can only detect the first one. In this case less photons are observable in the sum signal of the cells of the SiPM than they actually detected. Let us see what this depends on and how.
PDE essentially means the number of photons the SiPM detected out of the total number of photons produced during the scintillation process, where, for example, the ‘total number’ is ~16000 for a LYSO crystal and a 511 keV gamma photon. Let us presume that hitting each cell is equally probable. The probability of the excitation of one cell is
The parameter of the Poisson process in case of a crystal with a light yield of N:
\lambda=\frac{\mathrm{PDE} \cdot \mathrm{N}}{N_{\mathrm{cells}}}
The probability that a cell is excited by one or two or... many photons:
\sum_{k=1}^{N}\frac{\lambda^k}{k!}\cdot e^{-\lambda}\approx 
\sum_{k=1}^{\infty}\frac{\lambda^k}{k!}\cdot e^{-\lambda} =
e^{-\lambda}\cdot \left( \sum_{k=1}^{\infty}\frac{\lambda^k}{k!} + \frac{\lambda^0}{0!} -1 \right)=
e^{-\lambda}\cdot \left( \sum_{k=0}^{\infty}\frac{\lambda^k}{k!} -1 \right)= 
e^{-\lambda} \left( e^{\lambda} -1 \right)=1-e^{-\lambda}
This is the probability of the excitation of a given cell. Since there are N_{\mathrm{c}} cells, the expected value of the number of the excited cells is
N_{\mathrm{fired cells}}=N_{\mathrm{cells}}\cdot (1-e^{-\frac{\mathrm{PDE} \cdot \mathrm{N}}{N_{\mathrm{cells}}}})
This is what we observe when measuring the energy or time resolution, and not the number of photons that hit the cell, so we need to replace the number of photons with this in the formulae. If the number of cells is significantly larger than the number of photons, the value of this is approximately one. However, the SiPM can obviously saturate so we always catch more photons than it is suggested by the resolutions.


The CZT (cadmium-zinc-telluride) is a wide band gap semiconductor (the thermal excitation is 1.5 eV, which causes dark current – the excitation is described by the Arrhenius function –, it operates well at room temperature as well, although it is beneficial if it is cooled a little). Furthermore, it consists of elements with (relatively) high atomic numbers (Z_{Te}=52, Z_{Cd}=48 compared to Z_{Si}=14).
The basic idea is that instead of converting the gamma photons in the scintillation crystal into visible light then getting an electric signal through the photoelectrons generated by the photons reaching the photocathodes, we try to achieve a direct conversion of the gamma photon into an electric signal.
The unit of surface of the CZT is still more expensive than the PMT and its efficiency is low at higher energies (e.g. 511 keV, PET). One advantage is that its energy resolution is very good compared to the PET-scintillation crystal combination (however, it is lower than that of the cooled Ge detectors) and it does not require cooling, at least not liquid nitrogen. The NUCAM3 is a working cardiac SPECT (18.5 x 20.1 cm^2 detector), but there are not many large detectors, since its price per area is still high. The CZT cannot be used in the PET due to its low efficiency, and large surfaces would be needed in gamma cameras and SPECTs.

(Based on the lecture and notes of Péter Major)

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