cp-ccd comparisons of full and analytic simulations

8/6/2019 CP-CCD Comparisons of Full and Analytic Simulations

1/27

120 140 160 180 200 220 2400

0.05

0.1

0.15

0.2

0.25

Temperature (K)

CTI(%)

Full Sim Glasgow

Full Sim Lancaster

50 MHz

0.17 eV1e12/cm3Occ=1%

CP-CCD Comparisons of Full and Analytic Simulations

13-7-2007

1) Introduction

This report describes the comparisons of full and fast analytic simulations for the

prototype CP-CCD. The influence of frequency is studied and compared to the full

simulation done by Lancaster and Glasgow group. Systematic uncertainties for the

fast analytic model are studied by means of occupancy, shift time and joining time.

The effects of radiation damage in a particular detector are studied by examining two

electron trap levels: the 0.17 eV and 0.44 eV below the bottom of the conduction

band.

2) Comparisons of Different Full Simulations

a) Glasgow-Lancaster 0.17eV Traps

Fig 1 a: CTI vs Temperature for full simulation results of lancaster and Glasgow

for 0.17 eV at 50 MHz

1


2/27

250 300 350 400 450 500 5500

0.02

0.04

0.06

0.08

0.1

0.12

Temperature (K)

CTI(%)

Full Sim Glasgow

Full Sim Lancaster

0.44 eV1e12/cm3

50 MHzOcc=1%

b) Glasgow-Lancaster 0.44eV Traps

Fig 1 b: CTI vs Temperature for full simulation results of lancaster and Glasgow

for 0.44 eV at 50 MHz

3) Analytical model

a) General Model

The model considers the effect of a single trapping level and include the emission

time only in the following differential equation:

The traps are initially filled for this model and (Hardy) . Neverthless, to be

consistant with the DESSIS simulations(that use partially filled traps) the analytical

model uses a time constant between the filling of the traps such that the traps remain

partially filled when the new electron packet passes through the CPCCD. In the

analytical model , so we include the capture process in the model neglected in

Hardy model. Therefore the solution of this differential equation leads to an estimator

of the CTI.

Where

temit is the total emission time from the previous packet=tw, which means

waiting time between two charges packets related to the mean occupancy of

pixels in the device.

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

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

The 2 factor means here we considered that the same phenomena happens at each

node, such as, shift time is the same.

2

( )( )etemitetjoincsht

s

eeen

NtCTI

=12

trapsfilledofdensitytheisnwheret

e

ttn

dt

dn

=shct


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We consider one pixel:

( ) ( )c

s

s

t

c

s

f

rt

Af

r

+=

1exp0

11(6)

( ) ( )

=

e

AfBf

ttrtr

2

1121exp (7)

( ) ( )c

s

sc

s

fBf

trtr

+

= 2

22exp0 (8)

( ) ( )

= eBfCf

t

trtr

1

2212 exp (9)

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

21CTICTICTI += (10)

( ) ( ) ( ){ }021221 fCfBf

s

t rtrtrN

NCTI += (11)

rf(0) is defined by considering the fact that initially all taps are filled and emit during

the waiting time and then:

One pixel

0

t1

t2

t

A

B

1 2

C

4


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( )

=

e

w

f

tr

exp0 (12)

From equations 6 to 12 we obtain:

+

+

+++

=

es

es

c

s

e

w

tt

tt

t

e

t

s

t

e

t

s

t

sN

tN

C T I

12

21

e x pe x p1

e x pe x p1

e x p212

e x p21

e x p

(13)

In the case where the time spending under each node is the same (t1=t2) we have

+

+=

e

wt

e

t

es

t

s

t

e

s

ec

t

sn

tN

CTI

expexp

11exp1

exp1

21exp12

14)

5


6/27

100 120 140 160 180 200 220 2400

0.5

1

1.5

2

2.5x 10

-3

Temperature (K)

CTI

Analytical Model Occ=1%

Imp AM

Full Sim

6


7/27

200 250 300 350 400 450 500 5500

0.2

0.4

0.6

0.8

1

1.2x 10

-3

Temperature (K)

CTI

Analytical Model Occ=1

IMp AM

Full Sim

7


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80 100 120 140 160 180 200 2200

0.05

0.1

0.15

0.2

0.25

Temperature (K)

CTI(%)

ImpAM

AM0.17 eV1e12/cm350 MHzOcc=1%

80 100 120 140 160 180 200 2200

0.15

0.1

0.15

0.2

0.25

Temperature (K)

CTI(%)

ImpAM

AM

Lancs Full Sim

0.17 eV1e12/cm350 MHzOcc=1%

250 300 350 400 450 500 5500

0.05

0.1

0.15

0.2

0.25

0.3

Temperature (K)

CTI(%)

ImpAM

AM

0.44eV1e12/cm350 MHzOcc=1%

c) omparison with Full Simulations 0.17eV Traps.

Fig2.a: CTI vs temperature for Analytical model(AM) and the Improved

Ananlytical model (ImpAM),for the 0.17 eV trap at 50MHz.

Fig2.b : CTI vs temperature of Analytical model(AM), Improved model (ImpAM) and Lancaster

full simulation for the 0.17 eV trap at 50MHz.

d) Comparison with Full Simulations 0.44eV Traps

8


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250 300 350 400 450 500 5500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Temperature (K)

CTI(%)

ImpAM

AM

Lancs Full Sim


Fig3.a : CTI vs temperature for Analytical model(AM) and the Improved model (ImpAM)

for the 0.44 eV trap at 50MHz.

Fig3.b : CTI vs temperature of Analytical model(AM), Improved model (ImpAM) and Lancaster full

simulation for the 0.44 eV trap at 50MHz

For 0.17 eV the analytical Improved model agree well with lancaster full

simulation as in fig2.b.

For 0.44 eV the analytical Improved model agree well with lancaster fullsimulation as in fig3.b.

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1010

1011

1012

10-3

10-2

10-1

50 MHz

0.17 eV

Occ= 1%

CTI(%)

Trap concentration (cm-3)

T=160K

T=185K

We can see clearly from fig2.a and fig 3.a, that the main diffrence is from peak

temperature.

e) CTI vs Trap concentration

Fig4: CTI vs Trap concentration for two different temperatures

Figure 4 shows the CTI against concentration traps for the 0.17 eV at 50 MHz for twodifferent temperatures. The CTI varied linearly with a factor of 1 with trap

concentration.

f) Variation of Frequency

10


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80 100 120 140 160 180 200 2200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Temperature (K)

CTI(%)

ImpAM 50 MHz

ImpAM 25 MHz

ImpAM 10 MHz

0.17 eV1e12/cm3Occ=1%tjoin=2tsh

80 100 120 140 160 180 200 2200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Temperature (K)

CTI(%)

ImpAM 50 MHz

ImpAM 25 MHz

ImpAM 10 MHz

0.17 eV1e12/cm3Occ=1%tjoin=tsh

250 300 350 400 450 500 5500

0.05

0.11

0.15

0.2

0.25

0.3

0.35

Temperature (K)

CTI(%)

ImpAM 50 MHz

ImpAM 25 MHz

ImpAM 10 MHz0.44 eV1e12/cm3Occ=1%tjoin=tsh

Fig 5 a: CTI vs temperature for different frequencies for 0.17 eV .

Fig 5.b: CTI vs temperature for different frequencies for 0.17 eV .

Figure 5.a and figure 5.b show the frequency effect on the CTI with tjoin as

parameter.The CTI peak increase and shift to low temperature as the frequency

decrease. The tjoin affect only the region from peak temperature and reduc the CTI

value.

11


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250 300 350 400 450 500 5500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Temperature (K)

CTI(%)

ImpAM 50 MHz

ImpAM 25 MHz

ImpAM 50 MHz0.44 eV1e12/cm3Occ=1%tjoin=2tsh

80 100 120 140 160 180 200 2200

0.05

0.1

0.15

0.2

0.25

Temperature (K)

CTI(%)

ImpAm Occ=0.1%

ImpAm Occ=1 %

ImpAm Occ=5 %

0.17 eV1e12/cm350 MHztjoin=tsh

Fig 6.a: CTI vs temperature for different frequencies for 0.44 eV .

Fig 6.b: CTI vs temperature for different frequencies for 0.44 eV .

Figure 6.a and figure6.b show the frequency effect on the CTI with tjoin as

parameter.The CTI peak increase and shift to low temperature as the frequency

decrease. The tjoin affect only the region from peak temperature and reduc the CTI

value.

g) Variation of Occupancy Level

12


13/27

80 100 120 140 160 180 200 2200

0.05

0.1

0.15

0.2

0.25

0.3

Temperature (K)

CTI(%)

ImpAM Occ=0.1%

ImpAM Occ=1%

ImpAM Occ=5%

0.17 eV1e12/cm325 MHztjoin = tsh

80 100 120 140 160 180 200 2200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.2

0.45

Temperature (K)

CTI(%)

lmpAM Occ=0.1%

lmpAM Occ=1%

lmpAM Occ=5%

0.17 eV1e12/cm310 MHztjoin=tsh

Fig7.a: CTI vs temperature for different occupancy for 0.17 eV at 50 MHz.

Fig7.b: CTI vs temperature for different occupancy for 0.17 eV at 25 MHz.

13


14/27250 300 350 400 450 500 550

0

0.05

0.1

0.15

0.2

0.25

0.3

Temperature (K)

CTI(%)

ImpAM Occ=0.1%

ImpAM Occ=1%

ImpAM Occ=5%


Fig7.c: CTI vs temperature for different occupancy for 0.17 eV at 10 MHz.

The effect of occupancy on CTI is shown in figure 7a,b,c for the 0.17 eV with

tjoin equal tshift (tjoin=tsh). As the occupancy decreases the CTI peak

temperature increases and become larger with increasing frequency.

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250 300 350 400 450 500 5500

0.05

0.1

0.15

0.2

Temperature (K)

CTI(%)

ImpAM Occ=0.1%

ImpAM Occ=1%

ImpAM Occ=5%


250 300 350 400 450 500 5500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Temperature (K)

CTI(%)

ImpAM Occ=0.1%

ImpAM Occ=1%

ImpAM Occ=5%


Fig8.a: CTI vs temperature for different occupancy for 0.44 eV at 50 MHz.

Fig8.b: CTI vs temperature for different occupancy for 0.44 eV at 25 MHz.

15


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fig8.c: CTI vs temperature for different occupancy for 0.44 eV at 10 MHz.

Same effect of occupancy on CTI is shown in figure 8a,b,c for the 0.44 eV with

tjoin equal tshift (tjoin=tsh). As the occupancy decreases the CTI peak

temperature increases and become larger with increasing frequency.

16


17/27100 120 140 160 180 200 220 240

0

0.05

0.1

0.15

0.2

0.25

Temperature (K)

CTI(%)

tjoin=0.5 tsh

tjoin=tsh

tjoin=2 tsh

0.17 eV1e12/cm350 MHzOcc= 1%

0 1 2 3 4 5

40

50

60

70

80

90

100

W

idth(K)

Occupancy (%)

0.17 eV

0.44 eV

0 1 2 3 4 5

0.25

0.30

0.35

0.40

CTImax(%)

Occupancy (%)

0.17 eV

0.44 eV

Fig9: Width vs Occupancy for both traps 0.17 eV and 0.44 eV at 10 MHz.

Figure 9 show the width at half way versus occupancy for both traps (0.17 eV and0.44 eV), the width decrease as occupancy increase, that means traps mainley

filled as occupancy increases

Fig10: CTI max vs Occupancy for both traps 0.17 eV and 0.44 eV at 10 MHz.The amplitude of CTI max decrease with the incresing occupancy (Fig10).

h) Systematic Unvertainties

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100 120 140 160 180 200 2200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Temperature (K)

CTI(%)

ImpAM tjoin=0.5 tsh

ImpAM tjoin=tsh

ImpAM tjoin=0.5 tsh

0.17 eV1e12/cm325 MHz

Occ= 1%

80 100 120 140 160 180 200 2200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Temperature (K)

CTI(%)

ImpAM tjoin=0.5tsh

ImpAM tjoin=tsh

ImpAM tjoin=2tsh

0.17 eV1e12/cm310 MHzOcc= 1%

Fig11.a: CTI vs temperature for different tjoin for 0.17 eV at 50 MHz.

Fig11.b: CTI vs temperature for different tjoin for 0.17 eV at 25 MHz.

18


19/27250 300 350 400 450 500 550

0

0.05

0.1

0.15

Temperature (K)

CTI(%)

ImpAM tjoin=0.5 tsh

ImpAM tjoin=tsh

ImpAM tjoin=2 tsh

0.44 eV1e12/cm350 MHzOcc= 1%

100 120 140 160 180 200 2200

0.05

0.1

0.15

0.2

0.25

Temperature (K)

CTI(%)

Imp AM tjoin=0.5 tsh

Imp AM tjoin=tsh

Imp AM tjoin=2 tsh

Lancs Full Sim


Fig11.c: CTI vs temperature for different tjoin for 0.17 eV at 10 MHz.

Fig12.d: CTI vs temperature for different tjoin compared with Lancaster Full

Simulation for 0.17 eV at 50 MHz.

For the 0.17 eV, figure 12.d, shows that the analytical improved model agree well

with Lancaster full simulation for the tjoin equal one shift time (tjoin=tsh).

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250 300 350 400 450 500 5500

0.05

0.1

0.15

0.2

0.25

Temperature (K)

CTI(%)

ImpAM tjoin=0.5 tsh

ImpAM tjoin=tsh

ImpAM tjoin=2 tsh

0.44 eV1e12/cm325 MHzOcc= 1%

250 300 350 400 450 500 5500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Temperature (K)

CTI(%)

ImpAM tjoin=0.5tsh

ImpAM tjoin=tsh

ImpAM tjoin=2tsh

0.44 eV1e12/cm310 MHzOcc= 1%

Fig13.a: CTI vs temperature for different tjoin for 0.44 eV at 50 MHz.

Fig13.b: CTI vs temperature for different tjoin for 0.44 eV at 25 MHz.

20


21/27250 300 350 400 450 500 550

0

0.02

0.04

0.06

0.08

0.1

0.12

Temperature (K)

CTI(%)

ImpAM tjoin=0.5tsh (AM)

ImpAM tjoin=tsh

ImpAM tjoin=2tsh

Glasg Full Sim


250 300 350 400 450 500 5500

0.05

0.1

0.15

Temperature (K)

CTI(%)

ImpAM tjoin=0.5 tsh (AM)

ImpAM tjoin=tsh

ImpAM tjoin=2 tsh

Lancs Full Sim


Fig13.c: CTI vs temperature for different tjoin for 0.44 eV at 10 MHz.

Fig13.d: CTI vs temperature for different tjoin compared with Lancaster FullSimulation for 0.44 eV at 50 MHz.

For the 0.44 eV, figure 13.d, shows that the analytical improved model agree well

with Lancaster full simulation for the tjoin equal two shift time (tjoin=2tsh).

21


22/27100 150 200 250

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

Temperature (K)

Constanttime(s)

Emission time

Capture time

Shift time

0.17 eV1e12/cm350 MHz

Peakposition

Fig13.e: CTI vs temperature for different tjoin compared with Glasgow Full

Simulation for 0.44 eV at 50 MHz.

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23/27

250 300 350 400 450 500 55010

-9

10-8

10-7

10-6

10-5

10-4

10-3

Temperature (K)

Constanttime(s)

Emission time

Capture time

Shift time

0.44 eV1e12/cm350 MHz

Peakposition

80 100 120 140 160 180 200 2200

0.05

0.1

0.15

0.2

0.25

Temperature (K)

CTI(%)

ImpAM tsh1=tsh2=0.5/f (AM)

ImpAM tsh1=2/3f tsh2=1/3f


0.17 eV1e12/cm350 MHzOcc= 1%

Fig14.a : Time constant vs temperature for 0.17 eV and 50 MHz.

Fig14.b : Time constant vs temperature for 0.44 eV and 50 MHz.

In ordre to explain the change of tjoin with trap level. Figure 14a,b show time

constant versus temperature, we can observe quickly that the the capture time is

about twice for 0.44eV (toc=3.226e-8)than that of 0.17 eV (1.51e-8).

The raio 89.144.044.0

17.017.0

=

ce

ce

. The emission time is closer to capture time for 0.44

eV than that of 0.17 eV, So the charges losses for 0.44 eV need more time to join

their parent packet. Because of the uncertainty of the partition function

(HARDY), we will assume that the time period during which the charges can join

their parent packet s different. We may think that the real vale of tjoin for 0.44 eV

is (1


24/27

80 100 120 140 160 180 200 2200

0.05

0.1

0.15

0.20

0.25

0.30

Temperature (K)

CTI(%)

ImpAM tsh1=tsh2=1/2f (AM)

ImpAM tsh1= 2/3f tsh2=1/3f


Lancs Full Sim

0.17 eV1e12/cm350 MHzOcc 1%

Fig15.a: CTI vs temperature for different shift time for 0.17 eV at 50 MHz.

Fig15.b: CTI vs temperature for different shift time for 0.17 eV at 50 MHz compared

to Lancaster full simulation.

We see from figure15, for 0.17 eV, that the case where the fast simulation agree better

for improved model at tsh1=2/3f and tsh2=1/3f (concept of considering shift time

under each node is different) with Lancaster full simulation.

24


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250 300 350 400 450 500 5500

0.05

0.1

0.15

Temperature (K)

CTI(%)



ImpAM tsh1= 3/4f tsh2=1/4f

50 MHz0.44 eV1e12/cm3Occ= 1%

250 300 350 400 450 500 5500

0.05

0.1

0.15

Temperature (K)

CTI

(%)




Lancs Full Sim

50 MHz0.44 eV1e12/cm3Occ= 1%

Fig16.a: CTI vs temperature for different shift time for 0.44 eV at 50 MHz.

Fig16.b: CTI vs temperature for different shift time for 0.44 eV at 50 MHz, compared

to Lancaster full simulation.

We see from figure16, for 0.44 eV, that the case where the fast simulation agree better

for improved model at tsh1=2/3f and tsh2=1/3f (concept of considering shift time

under each node is different) with Lancaster full simulation

0.17eV

50 MHz 25 MHz 10MHz

25


26/27

Occ Amp CTImax

Peak temperature

(K)

Amp CTI

max

Peak temperature

(K)

Amp CTI max Peak temperature

(K)

0.1 % 0.001998 145 0.002993 135 0.004055 125

1 % 0.001983 150 0.00295 145 0.003958 135

5 % 0.001812 165 0.002698 155 0.003565 145

Table1.a: Amplitudte CTI max and peak postion for different Ocuupancy for 0.17 eV

at different frequency

0.17eV

50 MHz 25 MHz 10MHz

Tjoin Amp CTImax

Peak temperature

(K)

Amp CTI

max

Peak temperature

(K)Amp CTI

max

Peak temperature

(K)

0.5 0.002027 155 0.003018 145 0.00403 135

1 0.001983 150 0.00295 145 0.003958 1352 0.001909 150 0.002847 140 0.003818 135

Table1.b: Amplitudte CTI max and peak postion for different joining time for 0.17 eV


0.44eV

50 MHz 25 MHz 10MHz

Occ Amp CTImax

Peak temperature(K)

Amp CTImax

Peak temperature(K)

Amp CTI max Peak temperature(K)

0.1 % 0.001094 350 0.001863 330 0.00317 310

1 % 0.001068 370 0.00181 350 0.003043 330

5 % 0.009057 400 0.001532 380 0.002538 360

Table2.a: Amplitudte CTI max and peak postion for different Ocuupancy for 0.44 eV


0.44eV

50 MHz 25 MHz 10MHz

Tjoin Amp CTI

max

Peak position

(K)

Amp CTI

max

Peak position

(K)

Amp CTI

max

Peak position

(K)

0.5 0.001135 380 0.001917 360 0.003216 340

1 0.001108 370 0.001872 360 0.003143 340

2 0.001068 370 0.00181 350 0.003043 330

Table2.b: Amplitudte CTI max and peak postion for different joining time for 0.44 eV


4) Conclusions

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27/27

CTI decrease with increasing frequency.

Occupancy increases CTI decreases in the amplitude.

Occupancy decreases the width of the curve increases and peak become flat.

Assumption of the joining time (Uncertainty).

As tjoin increases the CTI reduced and shifted down starting from the peak

postion,for both traps.

For 0.17 eV ImpAM agree well for tjoin=tsh.

For 0.44 eV ImpAM agree well for tjoin=2tsh.

Some of the charge trapped will also join their parent packet (they must be

included in calculation of CTI). Because of the uncertainty we will assume

that the time during which charge can join the parent packet is Tjoin .

The Tjoin parameter affect the CTI curves for both traps after the peak

position.

cp-ccd comparisons of full and analytic simulations

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