Analytical Model Progress

8/6/2019 Analytical Model Progress

1/22

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Analytical Model Progress

Andr Sopczak

Lakhdar Dehimi,Salim Aoulmitand Khaled Bekhouche


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OUTLINE

Introduction

Updated analytical model for CP-CCD

Comparison with full simulations Effect of edges (suggestions)

Conclusion


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Introduction

Models:Hardy model

with assumption

Where

temit is the total emission time from the previous packet=tw

tjoin is the time during which the charges can join their parent packet

ec

( )eemittejoints

t een

NCTI

= 2

Improved Hardy model : include capture time

( )( )eemittejointcshts

t eeen

NCTI

= 12

tsh is the shift time, that is the time spend under each node


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Updated CTI Analytical Model

The fraction of filled traps(rf):

s

f

ce

f

c

ffrrr

dt

dr

=

= 11

( ) ( )c

s

sc

s

ff

trtr

+

= exp0

( ) ( ){ }0ff

s

t rtr

N

NCTI =

t

f

fN

nr =

Where

nf is the density of filled traps

Nt is the density of traps


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Model for CP-CCD (2-phase)

rf1A

is the fraction of filled trap under node1 during time t1(when

signal packet is present).

( ) ( )c

s

s

t

c

sfrt

Afr

+=

1exp011

( ) ( )

=

e

AfBf

ttrtr

2

1121exp

rf1B is the fraction of filled trap under node1 during time t2 (when

signal packet is present under the second node).

(1)

(2)


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( ) ( )c

s

sc

s

fBf

trtr

+

= 2

22exp0

( ) ( ) = eBfCf ttrtr

1

2212 exp

rf2B is the fraction of filled trap under node2 during time t2 (when signal

packet is present).

rf2C is the fraction of filled trap under node2 during time t1 (when signal

packet is present under the first node of the next pixel).

(3)

(4)


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So the CTI is the sum of the CTI under each node

21 CTICTICTI +=( ) ( ) ( ){ }02

1221 fCfBf

s

t rtrtrn

NCTI +=

rf(0) is defined by considering the fact that initially all taps

are filled and emit during the waiting time and then:

( )

=

e

w

f

t

r exp0

(5)

(6)

(7)


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Case of t1=t2 =t

+

+=

e

wt

e

t

es

t

s

t

e

s

ec

t

sn

tN

CTI

expexp

11

exp1

exp1

21

exp12


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Comparison with Full SimulationsComparison of AM, Updated, Full simulations Glasgow and Lancaster for the 0.17 eV trap

100 120 140 160 180 200 220 2400

0.05

0.1

0.15

0.2

0.25

Temperature(K)

CTI(%)

ImpAM

UpdatedAM

Full SimGlasgow

Full SimLancaster

0.17eV50MHz

1e12/cm 3

Occ=1%


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Comparison of AM, Updated, Full simulations Glasgow and Lancaster for the 0.44 eV trap

200 250 300 350 400 450 500 5500

0.02

0.04

0.06

0.08

0.1

0.12

Temperature(K)

CTI(%)

ImpAM

UpdatedAM

Full SimGlasgow

Full SimLancaster

0.44eV50MHz

1e12cm -3

Occ=1%


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Comparison Updated Model with Full

Simulation (Dima) for 0.17 eV at 10 MHz

100 120 140 160 180 200 220 2400

0.1

0.2

0.3

0.4

0.5

0.6

Temperature(K)

CTI(%)

UpdatedAM

Full Sim

0.17eV10MHz

1e12cm -3

Occ=1%


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100 120 140 160 180 200 220 2400

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Temperature(K)

CTI(%)

UpdatedAM

Full Sim

0.17eV15MHz

1e12cm -3

Occ=1%


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100 120 140 160 180 200 220 2400

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Temperature(K)

CTI(%)

UpdatedAM

Full Sim

0.17eV25MHz

1e12cm -3

Occ=1%


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Edges Effect

Substrate

x

n p

wp0-wn -xt1

EC

EV

EFi

-xt2

V2

V1

Ef

Et1

Et2

Et1,2 are the trap energy levels,

EC and EV are respectively the conduction and the valence band,

Efand EFi are respectively Fermi level and intrinsic Fermi level,

wn and wp are the edges of the depletion region,xt1,2 are the intersection points of Fermi level with trap energy level.

1 m

Gate

Insu

lat

or


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Xt is not the same for both traps (0.17,

0.44 eV) depending on the energy level.

Volume is then calculated by means of Xt

for each trap.


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Conclusion

Updated model is a systematicdevelopment from Hardy original model.

Updated model agrees better with Full

Simulation. As the frequency is increasing the fast

and full simulation agree better.

Volume of the ionised traps depends ontrap level (Effect of volume changeunderstudy).


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Next: List of systematic uncertainties

Doping profile, Clock voltage (form and amplitude), we suggest to

use a rectangular or square signal,

Documents

Analytical Model Progress