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Modeling the photon counting and photoelectron counting characteristics of quanta image sensors

Bowen Liu and Jiangtao Xu

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 Corresponding author: Jiangtao Xu, xujiangtao@tju.edu.cn

DOI: 10.1088/1674-4926/42/6/062301

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Abstract: A signal chain model of single-bit and multi-bit quanta image sensors (QISs) is established. Based on the proposed model, the photoresponse characteristics and signal error rates of QISs are investigated, and the effects of bit depth, quantum efficiency, dark current, and read noise on them are analyzed. When the signal error rates towards photons and photoelectrons counting are lower than 0.01, the high accuracy photon and photoelectron counting exposure ranges are determined. Furthermore, an optimization method of integration time to ensure that the QIS works in these high accuracy exposure ranges is presented. The trade-offs between pixel area, the mean value of incident photons, and integration time under different illuminance level are analyzed. For the 3-bit QIS with 0.16 e-/s dark current and 0.21 e- r.m.s. read noise, when the illuminance level and pixel area are 1 lux and 1.21 μm2, or 10 000 lux and 0.21 μm2, the recommended integration time is 8.8 to 30 ms, or 10 to 21.3 μs, respectively. The proposed method can guide the design and operation of single-bit and multi-bit QISs.

Key words: CMOS image sensor, quanta image sensor, photon counting, photoelectron counting, signal error rate, integration time



[1]
Fossum E, Ma J J, Masoodian S, et al. The quanta image sensor: Every photon counts. Sensors, 2016, 16, 1260 doi: 10.3390/s16081260
[2]
Fossum E R. CMOS image sensors: Electronic camera-on-a-chip. IEEE Trans Electron Devices, 1997, 44, 1689 doi: 10.1109/16.628824
[3]
Fossum E R, Hondongwa D B. A review of the pinned photodiode for CCD and CMOS image sensors. IEEE J Electron Devices Soc, 2014, 2, 33 doi: 10.1109/JEDS.2014.2306412
[4]
Fossum E R. What to do with sub-diffraction-limit (SDL) pixels – A proposal for a gigapixel digital film sensor (DFS). Proceedings of Workshop on Charge-Coupled Devices and Advanced Image Sensors, 2005, 214
[5]
Fossum E R. The quanta image sensor (QIS): Concepts and challenges. Proceedings of Imaging Systems and Applications, 2011, JTuE1
[6]
Teranishi N. Toward photon counting image sensors. Proceedings of Imaging Systems and Applications, 2011, IMA1
[7]
Teranishi N. Required conditions for photon-counting image sensors. IEEE Trans Electron Devices, 2012, 59, 2199 doi: 10.1109/TED.2012.2200487
[8]
Fossum E R. Application of photon statistics to the quanta image sensor. Proceedings of International Image Sensors Workshop, 2013, S9-1
[9]
Fossum E R. Modeling the performance of single-bit and multi-bit quanta image sensors. IEEE J Electron Devices Soc, 2013, 1, 166 doi: 10.1109/JEDS.2013.2284054
[10]
Fossum E R. Photon counting error rates in single-bit and multi-bit quanta image sensors. IEEE J Electron Devices Soc, 2016, 4, 136 doi: 10.1109/JEDS.2016.2536722
[11]
Deng W, Starkey D, Ma J, et al. Modelling measured 1/f noise in quanta image sensor (QIS). Proceedings of International Image Sensors Workshop, 2019, R07
[12]
Ma J J, Fossum E R. A pump-gate jot device with high conversion gain for a Quanta image sensor. IEEE J Electron Devices Soc, 2015, 3, 73 doi: 10.1109/JEDS.2015.2390491
[13]
Ma J J, Starkey D, Rao A R, et al. Characterization of quanta image sensor pump-gate jots with deep sub-electron read noise. IEEE J Electron Devices Soc, 2015, 3, 472 doi: 10.1109/JEDS.2015.2480767
[14]
Masoodian S, Rao A R, Ma J J, et al. A 2.5 pJ/b binary image sensor as a pathfinder for quanta image sensors. IEEE Trans Electron Devices, 2016, 63, 100 doi: 10.1109/TED.2015.2457418
[15]
Masoodian S, Ma J, Starkey D, et al. A 1Mjot 1040fps 0.22e- r. m. s. stacked BSI quanta image sensor with cluster-parallel readout. Proceedings of International Image Sensors Workshop, 2017, R19
[16]
Starkey D, Deng W, Ma J, et al. Quanta imaging sensors: Achieving single-photon counting without avalanche gain. SPIE Defense + Security. Proceedings of Micro- and Nanotechnology Sensors, Systems, and Applications X, 2018, 1063, 106391Q
[17]
Dutton N, Parmesan L, Gnecchi S, et al. Oversampled ITOF imaging techniques using SPAD-based quanta image sensors. Proceedings of International Image Sensors Workshop, 2015, S6-4
[18]
Ma J J, Anzagira L, Fossum E R. A 1 μm-pitch quanta image sensor jot device with shared readout. IEEE J Electron Devices Soc, 2016, 4, 83 doi: 10.1109/JEDS.2016.2516026
[19]
Jun O. Smart CMOS image sensors and applications. CRC Press, 2007, 181
Fig. 1.  The QIS conceptual illustration. An 8 × 8 × 4 spatial-temporal data cube of jots in the QIS (left) is reconstructed to a 2 × 2 data plane of pixels in the output image (right). Each data of pixels is equal to the sum of a 4 × 4 × 4 data sub-cube of jots.

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Fig. 2.  The signal chain model of quanta image sensors.

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Fig. 3.  (Color online) The PDF P[URO] as a function of URO on the condition that μe = 2 e- and un = 0.2 e- r.m.s.. N0, N1, N2, and N3 are four quantization levels corresponding to 0, 1, 2, and 3 ADU for a 2-bit QIS. The dashed lines are three quantization boundaries corresponding to 0.5, 1.5, and 2.5 e- for a 2-bit QIS.

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Fig. 4.  (Color online) The ideal D-logH response curves for 1-bit to 5-bit QISs in solid lines. And the ideal linear response curves for 1-bit to 5-bit CISs in dashed lines.

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Fig. 5.  (Color online) The realistic response curves for the 3-bit QIS. The different conditions of curve 1 to 5 are listed in Table 2.

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Fig. 6.  (Color online) The photon counting signal error rate SERph as a function of the mean value of incident photons μph for ideal 1-bit to 5-bit QISs.

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Fig. 7.  (Color online) The photon counting signal error rate SERph as a function of the mean value of incident photons μph for the 3-bit QIS. The five conditions of curve 1 to 5 are listed in Table 2.

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Fig. 8.  (Color online) The photoelectron counting signal error rate SERphe as a function of the mean value of incident photons μph for the 3-bit QIS. The five conditions of curve 1 to 5 are listed in Table 2.

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Fig. 9.  The conceptual illustration of the Airy disk and jot array. The Airy disk diameter DA = 3.8 μm, the jot area Ajot = 1 μm2 (left) and Ajot = 0.25 μm2 (right).

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Fig. 10.  (Color online) The photon counting signal error rate SERph as a function of the mean value of incident photons μph for 1-bit to 5-bit QISs based on the parameters listed in Table 3.

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Fig. 11.  (Color online) The photoelectron counting signal error rate SERphe as a function of the mean value of incident photons μph for 1-bit to 5-bit QISs based on the parameters listed in Table 3.

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Fig. 12.  (Color online) The relationship between jot area Ajot, the mean value of incident photons μph, and integration time τ under different illuminance level Ilux for the 3-bit QIS in Fig. 11. (a) Ilux = 0.1 lux. (b) Ilux = 1 lux. (c) Ilux = 10 lux. (d) Ilux = 100 lux. (e) Ilux = 1000 lux. (f) Ilux = 10 000 lux.

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Table 1.   The parameters of the signal chain model in Fig. 2.

SymbolParameterUnit
kphNumber of photonsphoton, p
kpheNumber of photoelectronselectron, e-
kdNumber of dark signal electronse-
keNumber of total signal electronse-
VCGVoltage-referred jot outputmicrovolt, μV
UCGElectron-referred jot outpute-
VROVoltage-referred readout circuit outputμV
UROElectron-referred readout circuit outpute-
DNADC output digital numbersADU
QEQuantum efficiency of the jote-/p
CGConversion gain of the jotμV/e-
vnVoltage-referred read noise of the readout circuitμV r.m.s.
unElectron-referred read noise of the readout circuite- r.m.s.
vthVoltage-referred quantizer threshold of the ADCμV
uthElectron-referred quantizer threshold of the ADCe-
DownLoad: CSV

Table 2.   Different conditions for realistic QISs in Figs. 5, 7, and 8.

NumberQE (e-/p)μd (e-)un (e- r.m.s.)
Curve 1100
Curve 20.800
Curve 310.010
Curve 4100.3
Curve 50.80.010.3
DownLoad: CSV

Table 3.   The correlation parameters of the QIS chip in Ref. [16].

ParameterValue
Jot size1.1 × 1.1 μm2
Quantum efficiency79% at 550 nm
Dark current0.16 e-/s/jot
Read noise0.21 e- r.m.s.
DownLoad: CSV
[1]
Fossum E, Ma J J, Masoodian S, et al. The quanta image sensor: Every photon counts. Sensors, 2016, 16, 1260 doi: 10.3390/s16081260
[2]
Fossum E R. CMOS image sensors: Electronic camera-on-a-chip. IEEE Trans Electron Devices, 1997, 44, 1689 doi: 10.1109/16.628824
[3]
Fossum E R, Hondongwa D B. A review of the pinned photodiode for CCD and CMOS image sensors. IEEE J Electron Devices Soc, 2014, 2, 33 doi: 10.1109/JEDS.2014.2306412
[4]
Fossum E R. What to do with sub-diffraction-limit (SDL) pixels – A proposal for a gigapixel digital film sensor (DFS). Proceedings of Workshop on Charge-Coupled Devices and Advanced Image Sensors, 2005, 214
[5]
Fossum E R. The quanta image sensor (QIS): Concepts and challenges. Proceedings of Imaging Systems and Applications, 2011, JTuE1
[6]
Teranishi N. Toward photon counting image sensors. Proceedings of Imaging Systems and Applications, 2011, IMA1
[7]
Teranishi N. Required conditions for photon-counting image sensors. IEEE Trans Electron Devices, 2012, 59, 2199 doi: 10.1109/TED.2012.2200487
[8]
Fossum E R. Application of photon statistics to the quanta image sensor. Proceedings of International Image Sensors Workshop, 2013, S9-1
[9]
Fossum E R. Modeling the performance of single-bit and multi-bit quanta image sensors. IEEE J Electron Devices Soc, 2013, 1, 166 doi: 10.1109/JEDS.2013.2284054
[10]
Fossum E R. Photon counting error rates in single-bit and multi-bit quanta image sensors. IEEE J Electron Devices Soc, 2016, 4, 136 doi: 10.1109/JEDS.2016.2536722
[11]
Deng W, Starkey D, Ma J, et al. Modelling measured 1/f noise in quanta image sensor (QIS). Proceedings of International Image Sensors Workshop, 2019, R07
[12]
Ma J J, Fossum E R. A pump-gate jot device with high conversion gain for a Quanta image sensor. IEEE J Electron Devices Soc, 2015, 3, 73 doi: 10.1109/JEDS.2015.2390491
[13]
Ma J J, Starkey D, Rao A R, et al. Characterization of quanta image sensor pump-gate jots with deep sub-electron read noise. IEEE J Electron Devices Soc, 2015, 3, 472 doi: 10.1109/JEDS.2015.2480767
[14]
Masoodian S, Rao A R, Ma J J, et al. A 2.5 pJ/b binary image sensor as a pathfinder for quanta image sensors. IEEE Trans Electron Devices, 2016, 63, 100 doi: 10.1109/TED.2015.2457418
[15]
Masoodian S, Ma J, Starkey D, et al. A 1Mjot 1040fps 0.22e- r. m. s. stacked BSI quanta image sensor with cluster-parallel readout. Proceedings of International Image Sensors Workshop, 2017, R19
[16]
Starkey D, Deng W, Ma J, et al. Quanta imaging sensors: Achieving single-photon counting without avalanche gain. SPIE Defense + Security. Proceedings of Micro- and Nanotechnology Sensors, Systems, and Applications X, 2018, 1063, 106391Q
[17]
Dutton N, Parmesan L, Gnecchi S, et al. Oversampled ITOF imaging techniques using SPAD-based quanta image sensors. Proceedings of International Image Sensors Workshop, 2015, S6-4
[18]
Ma J J, Anzagira L, Fossum E R. A 1 μm-pitch quanta image sensor jot device with shared readout. IEEE J Electron Devices Soc, 2016, 4, 83 doi: 10.1109/JEDS.2016.2516026
[19]
Jun O. Smart CMOS image sensors and applications. CRC Press, 2007, 181

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    Received: 07 October 2020 Revised: 25 October 2020 Online: Accepted Manuscript: 04 December 2020Uncorrected proof: 07 December 2020Published: 01 June 2021

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      Article Navigation >  Journal of Semiconductors  > 2021  >  42(6): 062301
      Bowen Liu, Jiangtao Xu. Modeling the photon counting and photoelectron counting characteristics of quanta image sensors[J]. Journal of Semiconductors, 2021, 42(6): 062301. doi: 10.1088/1674-4926/42/6/062301 ****B W Liu, J T Xu, Modeling the photon counting and photoelectron counting characteristics of quanta image sensors[J]. J. Semicond., 2021, 42(6): 062301. doi: 10.1088/1674-4926/42/6/062301.
      Citation:
      Bowen Liu, Jiangtao Xu. Modeling the photon counting and photoelectron counting characteristics of quanta image sensors[J]. Journal of Semiconductors, 2021, 42(6): 062301. doi: 10.1088/1674-4926/42/6/062301 ****
      B W Liu, J T Xu, Modeling the photon counting and photoelectron counting characteristics of quanta image sensors[J]. J. Semicond., 2021, 42(6): 062301. doi: 10.1088/1674-4926/42/6/062301.
      shu

      Modeling the photon counting and photoelectron counting characteristics of quanta image sensors

      DOI: 10.1088/1674-4926/42/6/062301

      • Tianjin Key Laboratory of Imaging and Sensing Microelectronic Technology, School of Microelectronics, Tianjin University, Tianjin 300072, China

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      • Bowen Liu：received the B.E. degree from the School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian, China, in 2017. Since September 2017, he has been studying for the M.S. degree at School of Microelectronics, Tianjin University. His research interests include the high conversion gain pixel and low noise CMOS image sensor
      • Jiangtao Xu：received the B.E., M.S. and Ph.D. degrees from the School of Electronic Information and Engineering, Tianjin University, in 2001, 2004 and 2007, respectively. From 2007 to 2010 he was a Lecturer and from 2010 to 2018 he was an Associate Professor with the School of Electronic Information Engineering, Tianjin University. Since 2018, he has been a Professor at the School of Microelectronics, Tianjin University. His research interests include CMOS image sensor and image signal processing system
      • Corresponding author: xujiangtao@tju.edu.cn
      • Received Date: 2020-10-07
      • Revised Date: 2020-10-25
      • Published Date: 2021-06-10

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