Validation of a model for Dark Current Non Uniformity generated by Displacement Damage Dose in irradiated CMOS Image Sensors

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This is an author-deposited version published in: http://oatao.univ-toulouse.fr/

Eprints ID: 17374

To cite this version: Belloir, Jean-Marc and Goiffon, Vincent and Magnan, Pierre and Virmontois, Cédric and Gilard, Olivier and Raine, Mélanie and Paillet, Philippe Validation

of a model for Dark Current Non Uniformity generated by Displacement Damage Dose in irradiated CMOS Image Sensors. (2014) In: Workshop CNES : Radiation Effects on

Optoelectronic Devices, 27 November 2014 (Toulouse, France). (Unpublished) Official URL: http://dx.doi.org/10.1364/OE.24.004299

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Validation of a model for

Dark Current Non Uniformity

generated by Displacement Damage Dose

in irradiated CMOS Image Sensors

J.-M. Belloir, V. Goiffon, P. Magnan, ISAE

C. Virmontois, O. Gilard, CNES

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Outline

1. Introduction

2. Impact of radiation on the dark current of CMOS Image Sensors

3. The existing model of Dark Current Non Uniformity (DCNU)

• Experimental observations

• Modeling

• Link with the Srour’s Universal Damage Factor (UDF)

4. The new photodetector and irradiations

5. Experimental distributions and model results

6. Conclusions

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Outline

1. Introduction

2. Impact of radiation on the dark current of CMOS Image Sensors

3. The existing model of Dark Current Non Uniformity (DCNU)

• Experimental observations

• Modeling

• Link with the Srour’s Universal Damage Factor (UDF)

4. The new photodetector and irradiations

5. Experimental distributions and model results

6. Conclusions

(5)

Introduction :

Context

• Radiation comes from energetic particles which can :  Produce damage at the atomic level

 Degrade the performance of image sensors • The degradation needs to be predicted in order to :

 Set up an appropriate mitigation strategy (shielding, radiation-hardening by design,…) matching the mission constraints

 Respect the mission performance requirements until the end of the mission

• In this work, we focus on the dark current non uniformity (DCNU)

increase in CMOS IS from radiation displacement damage Space and nuclear physics facilities Harsh environment :

 Vacuum

 Extreme temperatures  Electromagnetic fields

 Radiation

Image Sensors (IS) for :

 Acquiring mission data

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• An existing DCNU model (Ph.D Thesis, C. Virmontois, 2012) was previously proposed • We validate the model on :

 A new photodetector using a new technology (different foundry)  A broader range of photodiode depleted volumes

Particle energy (MeV)

14 𝑀𝑒𝑉 500 𝑀𝑒𝑉 100 𝑢𝑚3 200 𝑢𝑚3 16-23 𝑀𝑒𝑉 8 𝑢𝑚3 340 𝑢𝑚3 𝒕𝒉𝒊𝒔 𝒘𝒐𝒓𝒌 𝒑𝒓𝒆𝒗𝒊𝒐𝒖𝒔𝒍𝒚 𝒗𝒂𝒍𝒊𝒅𝒂𝒕𝒆𝒅

Introduction :

This work

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Outline

1. Introduction

2. Impact of radiation on the dark current of CMOS Image Sensors

3. The existing model of Dark Current Non Uniformity (DCNU)

• Experimental observations

• Modeling

• Link with the Srour’s Universal Damage Factor (UDF)

4. The new photodetector and irradiations

5. Experimental distributions and model results

6. Conclusions

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Total Ionising Dose and

Displacement Damage Dose

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Total Ionising Dose and

Displacement Damage Dose

Charged (electrons, protons, ions,…)

Electronic stopping with

target electrons

(LET : Linear Energy Transfer)

Uncharged (neutrons)

Electrons ripped off target atoms

Electron-hole pairs

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Total Ionising Dose and

Displacement Damage Dose

target electrons

Total Ionising Dose (TID)

Coulombic scattering

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Total Ionising Dose and

Displacement Damage Dose

target electrons

Nuclear stopping with target nucleus

(NIEL : Non Ionising Energy Loss)

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Total Ionising Dose and

Displacement Damage Dose

target electrons

Nuclear stopping with target nucleus

(NIEL : Non Ionising Energy Loss)

Atoms ejected from lattice sites

Displaced atoms

Displacement Damage Dose (DDD)

with target nucleus

Elastic Inelastic

displacement interactions

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From Dose, to Damage, to Dark Current

DDD : displacement interactions in some pixels

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From Dose, to Damage, to Dark Current

TID : Electron-hole pairs in all pixels

Progressive degradation of oxide/silicon interfaces

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From Dose, to Damage, to Dark Current

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From Dose, to Damage, to Dark Current

Same DC increase in all pixels

Point defects (PD) Damage cascades (PD + clusters) Formation of stable defects :

 Multi vacancies

 Vacancy-impurity complex  Clusters…

Some defects with an energy level within the bandgap : bulk traps

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From Dose, to Damage, to Dark Current

Same DC increase in all pixels

Point defects (PD) Damage cascades (PD + clusters) Formation of stable defects :

 Multi vacancies

 Vacancy-impurity complex  Clusters…

Some defects with an energy level within the bandgap : bulk traps

Traps in the depleted volume :

generating centers

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Displacement interaction

in a 3T-pixel photodiode

𝑉_𝑑𝑒𝑝 N-type

P-type Depleted volume

Depleted oxide/silicon

interfaces

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Displacement interaction

in a 3T-pixel photodiode

𝑉_𝑑𝑒𝑝 N-type

Depleted oxide/silicon interfaces 𝑉_𝑑𝑒𝑝 Point defects Clusters particle particle interaction oxide

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Displacement interaction

in a 3T-pixel photodiode

Generating centers in 𝑉_𝑑𝑒𝑝 𝑉_𝑑𝑒𝑝 N-type

Depleted oxide/silicon interfaces 𝑉_𝑑𝑒𝑝 𝑉_𝑑𝑒𝑝 Point defects Clusters particle particle interaction oxide

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Dark current distribution evolution

with TID and DDD

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Dark current distribution evolution

with TID and DDD

TID

Total Ionising Dose

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Dark current distribution evolution

with TID and DDD

Displacement Damage Dose

Total Ionising Dose

DC increase in all pixels (gaussian) DCNU increase (hot pixel tail : pixels

with a displacement interaction)

TID

DDD

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Outline

1. Introduction

2. Impact of radiation on the dark current of CMOS Image Sensors

3. The existing model of Dark Current Non Uniformity (DCNU)

• Experimental observations

• Modeling

• Link with the Srour’s Universal Damage Factor (UDF)

4. The new photodetector and irradiations

5. Experimental distributions and model results

6. Conclusions

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The existing DCNU model (Virmontois et. Al)

• The DCNU model aims at predicting the DC distribution after irradiation only from the

DDD deposited in the image sensor (Ph.D Thesis, C. Virmontois, 2012)

• It was modeled from experimental results which showed similarities in radiation-induced DC distributions for:

 Several 3T-pixel image sensors from one foundry (pitch from 7 to 10 µm)  Various neutron and proton irradiations

 Various DDD (doses) from 4 to 1825 TeV/g

−𝟐 𝒔𝒑𝒂𝒄𝒆 𝒏𝒖𝒄𝒍𝒆𝒂𝒓 𝒆𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕𝒔 109 1010 1011 1012 1013 1014 𝟏𝟒 22 50 100 500

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• For low doses and in small pixels (small 𝑽_𝒅𝒆𝒑), the distribution has an exponential

hot pixel tail with a constant slope

First observation : exponential hot pixel tail

at low doses

Distributions normalised by 𝑉_𝑑𝑒𝑝 , the DDD and the number of pixels

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𝒉𝒊𝒈𝒉 𝒅𝒐𝒔𝒆 ∶ 𝒅𝒆𝒇𝒐𝒓𝒎𝒆𝒅

Second observation : Deformation

of the distribution at high doses

• At high doses and in large pixels (large 𝑽_𝒅𝒆𝒑), the distribution is deformed

DC increase (fA) 4 𝑇𝑒𝑉/𝑔 39 𝑇𝑒𝑉/𝑔 365 𝑇𝑒𝑉/𝑔 182 𝑇𝑒𝑉/𝑔 1820 𝑇𝑒𝑉/𝑔 𝑙𝑜𝑤 𝑑𝑜𝑠𝑒 ∶ 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡𝑖𝑎𝑙

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Outline

1. Introduction

2. Impact of radiation on the dark current of CMOS Image Sensors

3. The existing model of Dark Current Non Uniformity (DCNU)

• Experimental observations

• Modeling

• Link with the Srour’s Universal Damage Factor (UDF)

4. The new photodetector and irradiations

5. Experimental distributions and model results

6. Conclusions

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Modeling :

Low doses

• For low DDD and/or small depleted volumes, an exponential distribution is used : 𝐷𝐶 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 ≈ 𝑓_𝜐_{𝑑𝑎𝑟𝑘} 𝐷𝐶 = 1

𝜐_{𝑑𝑎𝑟𝑘} exp −

𝐷𝐶 𝜐_{𝑑𝑎𝑟𝑘} • It is the basic distribution of the model

• 𝜐_{𝑑𝑎𝑟𝑘} is the mean value (the slope) of the exponential measured experimentally :

𝜐

_{𝑑𝑎𝑟𝑘}

≈ 6250 𝑒 −/𝑠

• 𝜐_{𝑑𝑎𝑟𝑘} is the mean DC increase of the pixels impacted by the irradiation • Low dose :

 just a few pixels impacted

 only one interaction per impacted pixel

⇒ 𝝊_{𝒅𝒂𝒓𝒌} can be seen as the mean DC increase produced by one interaction

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Modeling :

Low doses

• For low DDD and/or small depleted volumes, an exponential distribution is used : 𝐷𝐶 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 ≈ 𝑓_𝜐_{𝑑𝑎𝑟𝑘} 𝐷𝐶 = 1

𝜐_{𝑑𝑎𝑟𝑘} exp −

𝐷𝐶 𝜐_{𝑑𝑎𝑟𝑘} • It is the basic distribution of the model

• 𝜐_{𝑑𝑎𝑟𝑘} is the mean value (the slope) of the exponential measured experimentally :

𝜐

_{𝑑𝑎𝑟𝑘}

≈ 6250 𝑒 −/𝑠

• 𝜐_{𝑑𝑎𝑟𝑘} is the mean DC increase of the pixels impacted by the irradiation • Low dose :

 just a few pixels impacted

 only one interaction per impacted pixel

⇒ 𝝊_{𝒅𝒂𝒓𝒌} can be seen as the mean DC increase produced by one interaction

𝝊

_{𝒅𝒂𝒓𝒌}

seems independent on particle and sensor design

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• For high doses and/or big depleted volumes, we have a superposition of several

interactions in each pixel

• We convolute the basic distribution, as proposed by Dale, Marshall and Robbins : 𝐷𝐶 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 = 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 1, 𝝁 ⨯ 𝑓_𝜐_{𝑑𝑎𝑟𝑘}

+ 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 2, 𝝁 ⨯ 𝑓_𝜐_{𝑑𝑎𝑟𝑘} ∗ 𝑓_𝜐_{𝑑𝑎𝑟𝑘} + ⋯

• Convolutions are weighted by coefficients of a Poisson’s law of mean value 𝝁 which is

proportional to DDD and 𝑽_𝒅𝒆𝒑 via a factor γ_{𝒅𝒂𝒓𝒌} :

𝜇 =

γ

_{𝒅𝒂𝒓𝒌}

. 𝑉

_𝑑𝑒𝑝

.

𝐷𝐷𝐷

⇒ 𝝁 can be seen as the mean number of interactions per pixel

Modeling :

High doses

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• For high doses and/or big depleted volumes, we have a superposition of several

interactions in each pixel

• We convolute the basic distribution, as proposed by Dale, Marshall and Robbins : 𝐷𝐶 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 = 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 1, 𝝁 ⨯ 𝑓_𝜐_{𝑑𝑎𝑟𝑘}

+ 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 2, 𝝁 ⨯ 𝑓_𝜐_{𝑑𝑎𝑟𝑘} ∗ 𝑓_𝜐_{𝑑𝑎𝑟𝑘} + ⋯

• Convolutions are weighted by coefficients of a Poisson’s law of mean value 𝝁 which is

proportional to DDD and 𝑽_𝒅𝒆𝒑 via a factor γ_{𝒅𝒂𝒓𝒌} :

𝜇 =

γ

_{𝒅𝒂𝒓𝒌}

. 𝑉

_𝑑𝑒𝑝

.

𝐷𝐷𝐷

⇒ 𝝁 can be seen as the mean number of interactions per pixel

Modeling :

High doses

γ

𝒅𝒂𝒓𝒌

seems independent on particle and sensor design

Second factor of the model

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Modeling :

Dose dependency

𝐿𝑜𝑤 𝐷𝐷𝐷

𝐻𝑖𝑔ℎ 𝐷𝐷𝐷

𝝁 = 𝟎, 𝟑 ≪ 𝟏 𝑬𝒙𝒑𝒐𝒏𝒆𝒏𝒕𝒊𝒂𝒍 𝒅𝒊𝒔𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 𝝁 = 𝟑 > 𝟏 𝑪𝒐𝒏𝒗𝒐𝒍𝒖𝒕𝒆𝒅 𝒅𝒊𝒔𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 Damage event (interaction) Photodiode depleted volume

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Modeling :

Depleted volume dependency

𝑆𝑚𝑎𝑙𝑙 𝑉

_𝑑𝑒𝑝

𝐿𝑎𝑟𝑔𝑒 𝑉

_𝑑𝑒𝑝

𝝁 = 𝟎, 𝟑 ≪ 𝟏

𝑬𝒙𝒑𝒐𝒏𝒆𝒏𝒕𝒊𝒂𝒍 𝒅𝒊𝒔𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏

𝝁 = 𝟑 > 𝟏

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𝝁 𝑝𝑒𝑟 𝝁𝒎𝟑 ⇒ 𝜇 = γ_{𝒅𝒂𝒓𝒌}. 𝑉_𝑑𝑒𝑝 .𝐷𝐷𝐷 𝑤𝑖𝑡ℎ γ_{𝒅𝒂𝒓𝒌} ≈ 𝟑, 𝟎. 𝟏𝟎−𝟓 𝑻𝒆𝑽 𝒈 −𝟏 𝝁𝒎−𝟑 Ph.D Thesis, C. Virmontois, 2012

Modeling :

Experimental estimation of γ

_{𝒅𝒂𝒓𝒌}

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Outline

1. Introduction

2. Impact of radiation on the dark current of CMOS Image Sensors

3. The existing model of Dark Current Non Uniformity (DCNU)

• Experimental observations

• Modeling

• Link with the Srour’s Universal Damage Factor (UDF)

4. The new photodetector and irradiations

5. Experimental distributions and model results

6. Conclusions

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The Srour’s Universal Damage Factor 𝐾

_{𝑑𝑎𝑟𝑘}

𝑉_𝑑𝑒𝑝 𝑁_𝑃𝐷

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The Srour’s Universal Damage Factor 𝐾

_{𝑑𝑎𝑟𝑘} 𝑉_𝑑𝑒𝑝 𝑁_𝑃𝐷 𝑃_𝑒𝑝𝑖

Srour’s hypothesis

mean DC increase

=

𝐾

_{𝑑𝑎𝑟𝑘}

.

𝑉

_𝑑𝑒𝑝

. 𝐷𝐷𝐷

𝐷𝐷𝐷 𝑜𝑓 𝒏𝒆𝒖𝒕𝒓𝒐𝒏𝒔 𝑜𝑟 𝒑𝒓𝒐𝒕𝒐𝒏𝒔

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• 𝐾_{𝑑𝑎𝑟𝑘} is independent on  The particle

 The energy  The NIEL

• The mean DC increase is proportional to 𝑫𝑫𝑫 and to 𝑽_𝒅𝒆𝒑

• For a given image sensor (given 𝑉_𝑑𝑒𝑝), the mean DC increase is proportional to 𝑫𝑫𝑫

The Srour’s Universal Damage Factor 𝐾

_{𝑑𝑎𝑟𝑘}

𝑉_𝑑𝑒𝑝 𝑁_𝑃𝐷 𝑃_𝑒𝑝𝑖

Srour’s hypothesis

mean DC increase

=

𝐾

_{𝑑𝑎𝑟𝑘}

.

𝑉

_𝑑𝑒𝑝

. 𝐷𝐷𝐷

Mean DC increase proportional to

DDD

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Link between the model and 𝐾

_{𝑑𝑎𝑟𝑘}

Number of interactions

per 𝑽_𝒅𝒆𝒑 and per DDD

DC increase for one interaction in a pixel

𝝊

_{𝒅𝒂𝒓𝒌}

(𝑒 −/𝑠)

γ

𝒅𝒂𝒓𝒌

(

𝑇𝑒𝑉

𝑔

−1

𝑢𝑚

−3

)

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Link between the model and 𝐾

_{𝑑𝑎𝑟𝑘}

Number of interactions

per 𝑽_𝒅𝒆𝒑 and per DDD

DC increase for one interaction in a pixel

𝝊

_{𝒅𝒂𝒓𝒌}

. γ

_{𝒅𝒂𝒓𝒌}

is the DC increase

per 𝑽

_𝒅𝒆𝒑

and per

DDD

The product 𝝊_{𝒅𝒂𝒓𝒌} x γ_{𝒅𝒂𝒓𝒌} must be equal to the Srour’s UDF 𝑲_{𝒅𝒂𝒓𝒌}

𝑀é𝑙𝑎𝑛𝑖𝑒 𝑅𝑎𝑖𝑛𝑒 𝑒𝑡 𝑎𝑙. , 𝐼𝐸𝐸𝐸 𝑇𝑁𝑆 𝑣𝑜𝑙. 60, 2013

𝝊

_{𝒅𝒂𝒓𝒌}

(𝑒 −/𝑠)

γ

𝒅𝒂𝒓𝒌

(

𝑇𝑒𝑉

𝑔

−1

𝑢𝑚

−3

)

(42)

Temperature and annealing dependencies

𝑲_{𝒅𝒂𝒓𝒌} : mean DC increase per 𝑽_𝒅𝒆𝒑 and per DDD

𝝊

_{𝒅𝒂𝒓𝒌}

x γ

_{𝒅𝒂𝒓𝒌}

= 𝑲

_{𝒅𝒂𝒓𝒌}

𝝊_{𝒅𝒂𝒓𝒌} : mean DC increase per interaction

γ_{𝒅𝒂𝒓𝒌} : number of interactions

Fixed after irradiation

Same temperature and annealing dependencies : • ↗ with T° (generation rate of traps)

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Temperature and annealing dependencies

𝑲_{𝒅𝒂𝒓𝒌} : mean DC increase per 𝑽_𝒅𝒆𝒑 and per DDD

𝝊

_{𝒅𝒂𝒓𝒌}

x γ

_{𝒅𝒂𝒓𝒌}

= 𝑲

_{𝒅𝒂𝒓𝒌}

𝝊_{𝒅𝒂𝒓𝒌} : mean DC increase per interaction

γ_{𝒅𝒂𝒓𝒌} : number of interactions

Fixed after irradiation

Same temperature and annealing dependencies : • ↗ with T° (generation rate of traps)

• ↘ with annealing (disparition of traps)

⇒ 𝝊

_{𝒅𝒂𝒓𝒌}

has to follow the variations of 𝑲

_{𝒅𝒂𝒓𝒌}

⇒ The 𝝊

_{𝒅𝒂𝒓𝒌}

default value (6250 e-/s) will have to be adjusted in this work

because annealing conditions and testing temperature were different

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Outline

1. Introduction

2. Impact of radiation on the dark current of CMOS Image Sensors

3. The existing model of Dark Current Non Uniformity (DCNU)

• Experimental observations

• Modeling

• Link with the Srour’s Universal Damage Factor (UDF)

4. The new photodetector and irradiations

5. Experimental distributions and model results

6. Conclusions

(45)

The new photodetector and irradiations

• New foundry image sensor comprising four matrices of different pixel pitches :

pixel pitch (µm) PD area (µm²) PD perimeter (µm)

4,5 5 10

7 26 18

9 54 30

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The new photodetector and irradiations

4,5 5 10 7 26 18 9 54 30 14 150 50 𝑉_𝑑𝑒𝑝 varying from ≈ 8,5 𝑢𝑚3 𝑡𝑜 ≈ 340 𝑢𝑚3 (factor 40)

Test the model on a broad range of 𝑽_𝒅𝒆𝒑

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The new photodetector and irradiations

4,5 5 10

7 26 18

9 54 30

14 150 50

Test the model on a

new technology

𝑉_𝑑𝑒𝑝 varying from ≈ 8,5 𝑢𝑚3 𝑡𝑜 ≈ 340 𝑢𝑚3 (factor 40)

Test the model

scaling with 𝑽_𝒅𝒆𝒑

Matrices with different pixel pitches on the same photodetector

(48)

The new photodetector and irradiations

4,5 5 10 7 26 18 9 54 30 14 150 50 𝐸 = 16 𝑀𝑒𝑉 ϕ = 2,14.1011𝑐𝑚2 𝐷𝐷𝐷 = 820 𝑇𝑒𝑉/𝑔 𝐸 = 23 𝑀𝑒𝑉 ϕ = 1,00.1011𝑐𝑚2 𝐷𝐷𝐷 = 400 𝑇𝑒𝑉/𝑔 𝑻𝒘𝒐 𝒏𝒆𝒖𝒕𝒓𝒐𝒏 𝒊𝒓𝒓𝒂𝒅𝒊𝒂𝒕𝒊𝒐𝒏𝒔

CEA DAM UCL

Test the model on a

new technology

𝑉_𝑑𝑒𝑝 varying from ≈ 8,5 𝑢𝑚3 𝑡𝑜 ≈ 340 𝑢𝑚3 (factor 40)

Test the model

scaling with 𝑽_𝒅𝒆𝒑

Matrices with different pixel pitches on the same photodetector

(49)

Outline

1. Introduction

2. Impact of radiation on the dark current of CMOS Image Sensors

3. The existing model of Dark Current Non Uniformity (DCNU)

• Experimental observations

• Modeling

• Link with the Srour’s Universal Damage Factor (UDF)

4. The new photodetector and irradiations

5. Experimental distributions and model results

6. Conclusions

(50)

0 2 4 6 8 10 100 101 102 103 104 Pix el c ount

Results :

Depleted volume estimation

Measurements performed at ISAE (Toulouse)

(51)

0 2 4 6 8 10 100 101 102 103 104 Pix el c ount

Results :

Depleted volume estimation

pixel pitch (µm) Mean DC increase (e-/s)

4,5 730

7 5,600

9 11,800

14 31,800

𝑫𝑫𝑫 = 𝟖𝟐𝟎 𝑻𝒆𝑽/𝒈 Measurements performed at ISAE (Toulouse)

4,5 µm

7 µm

9 µm

14 µm

𝑇 = 22°𝐶

2 𝑤𝑒𝑒𝑘𝑠 𝑎𝑛𝑛𝑒𝑎𝑙𝑖𝑛𝑔 𝑲_{𝒅𝒂𝒓𝒌} = 𝟎, 𝟏𝟏𝟒

(52)

0 2 4 6 8 10 100 101 102 103 104 Pix el c ount

Results :

Depleted volume estimation

pixel pitch (µm) Mean DC increase (e-/s)

4,5 730 7 5,600 9 11,800 14 31,800

𝑉

_𝑑𝑒𝑝

=

𝐷𝐶 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒

𝐾

_{𝑑𝑎𝑟𝑘}

.

𝐷𝐷𝐷

𝑫𝑫𝑫 = 𝟖𝟐𝟎 𝑻𝒆𝑽/𝒈

pixel pitch (µm) Depleted volume (𝒖𝒎𝟑)

4,5 8,7

7 59

9 128

14 346

Measurements performed at ISAE (Toulouse)

4,5 µm

7 µm

9 µm

14 µm

𝑇 = 22°𝐶

2 𝑤𝑒𝑒𝑘𝑠 𝑎𝑛𝑛𝑒𝑎𝑙𝑖𝑛𝑔 𝑲_{𝒅𝒂𝒓𝒌} = 𝟎, 𝟏𝟏𝟒

(53)

Results :

3D effect on the small pixel pitch

pixel pitch PD smallest width (µm) PD area from design (µm²) Depleted volume (µm3, Srour) Depleted depth (µm) = volume / area 4,5 1,4 5 8,7 1,7 7 5 26 59 2,3 9 7,5 54 128 2,4 14 12,5 150 346 2,3

• The depleted depth is smaller for the small pixel pitch (4,5 µm)

• This may come from 3D effects on the depleted volume due to the small width of the

photodiode (1,4 µm) 𝑉_𝑑𝑒𝑝 𝑤_𝑑𝑒𝑝 𝑉_𝑑𝑒𝑝 𝑜𝑥𝑖𝑑𝑒 𝑤_𝑑𝑒𝑝 𝑆𝑚𝑎𝑙𝑙 𝑝𝑖𝑥𝑒𝑙 𝑝𝑖𝑡𝑐ℎ 𝐿𝑎𝑟𝑔𝑒 𝑝𝑖𝑥𝑒𝑙 𝑝𝑖𝑡𝑐ℎ 𝑜𝑥𝑖𝑑𝑒

1,4 𝑢𝑚

≥ 5 𝑢𝑚

(54)

Results :

Calculated distributions

𝑲_{𝒅𝒂𝒓𝒌} = 𝟎, 𝟏𝟏𝟒 𝝊_{𝒅𝒂𝒓𝒌} = 𝐾𝑑𝑎𝑟𝑘

(55)

Results :

Calculated distributions

pixel pitch Depleted volume (𝑢𝑚−3)

4,5 8,7 7 59 9 128 14 346 𝐷𝐷𝐷 = 820 TeV/g 𝑲_{𝒅𝒂𝒓𝒌} = 𝟎, 𝟏𝟏𝟒 𝝊_{𝒅𝒂𝒓𝒌} = 𝐾𝑑𝑎𝑟𝑘 γ_{𝑑𝑎𝑟𝑘} = 𝟑𝟖𝟎𝟎 𝒆 −/𝒔 γ_{𝒅𝒂𝒓𝒌} = 3,0. 10−5

𝜇 = γ

_{𝒅𝒂𝒓𝒌}

. 𝑉

_𝑑𝑒𝑝

.

𝐷𝐷𝐷

(56)

Results :

Calculated distributions

pixel pitch Depleted volume (𝑢𝑚−3)

4,5 8,7

7 59

9 128

14 346

pixel pitch (µm) Poisson’s parameter 𝝁

4,5 0,21 7 1,5 9 3,1 14 8,5 𝐷𝐷𝐷 = 820 TeV/g 𝑲_{𝒅𝒂𝒓𝒌} = 𝟎, 𝟏𝟏𝟒 𝝊_{𝒅𝒂𝒓𝒌} = 𝐾𝑑𝑎𝑟𝑘 γ_{𝑑𝑎𝑟𝑘} = 𝟑𝟖𝟎𝟎 𝒆 −/𝒔 γ_{𝒅𝒂𝒓𝒌} = 3,0. 10−5

𝜇 = γ

_{𝒅𝒂𝒓𝒌}

. 𝑉

_𝑑𝑒𝑝

.

𝐷𝐷𝐷

0 2 4 6 8 10 100 101 102 103 104 P ixe l co u n t

4,5 µm

7 µm

9 µm

14 µm

(57)

0 1 2 3 4 5 6 7 8 9 10 100 101 102 103 104 Pix el c ount

Results :

First irradiation (16 MeV, 820 TeV/g)

Slight overestimation of the small pixel pitch distribution

(58)

0 1 2 3 4 5 6 7 8 9 10 100 101 102 103 104 Pix el c ount

4,5 µm

7 µm

9 µm

14 µm

Slight overestimation of the small pixel pitch distribution

Results :

(59)

𝑉_𝑑𝑒𝑝 particle

Results :

Border effects in the small pixel pitch

• An interaction creates a damage cascade which can spread out of the depleted volume  More pronounced for small volumes

 A part of the damage is lost

 The mean DC increase per interaction is lower (𝝊_{𝒅𝒂𝒓𝒌} is lower)

⇒ Exponential hot pixel tail overestimated by the model for small pixel pitches

(as suggested by P. Marshall and more recently by C. Inguimbert)

interaction

Lost damage

(60)

Outline

1. Introduction

2. Impact of radiation on the dark current of CMOS Image Sensors

3. The existing model of Dark Current Non Uniformity (DCNU)

• Experimental observations

• Modeling

• Link with the Srour’s Universal Damage Factor (UDF)

4. The new photodetector and irradiations

5. Experimental distributions and model results

6. Conclusions

(61)