1

Simulation of electric field profile Simulation of electric field profile in Si irradiated detectors in Si irradiated detectors

with a consideration of carrier with a consideration of carrier generation parametersgeneration parameters

E. Verbitskaya, V. EreminIoffe Physical-Technical Institute of Russian Academy of Sciences

St. Petersburg, Russia

21 RD50 Collaboration WorkshopCERN, Geneva, Nov 14-16, 2012

2

Outline

♦ Goals

♦ Model of E(x) profile in Si heavily irradiated detectors developed in PTI

♦ Alternative methods of simulation

♦ Comments on lifetime

♦ Results on I, gen, Neff and E(x) based on PTI approach

♦ Impact of bulk generation on E(x) profile

Conclusions

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

3

Goals

Goals:   Analysis of the impact of carrier generation (bulk generation current) on the electric field profile in Si irradiated detectors Finding the correct approach for E(x) simulation Importance: Correct E(x) is required for adequate calculation of CCE

Earlier/Related results:

Temperature dependences of reverse current: activation energy of generation current of 1 MeV neutron and 23 GeV proton irradiated detectors was estimated as 0.65 eV (E. Verbitskaya, et al., 20 RD50 workshop) Recent results on I(T) scaling: simulation and experiment; A. Chilingarov, RD50 notes and presentation at 18 RD50 workshop, May 2011, Liverpool Presentations in Bari on electric field simulation

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

4

Global result of RD50 collaboration

Linear fit of I(F) is a strong argument to use linear dependence of the concentration of energy levels, which act as generation centers, on Feq

/Vol = Feq

= 3.7x10-17 A/cm

G. Lindström, NIM A 512 (2003) 30

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

5

Approach for calculation of E(x) profile (PTI model)

We consider two independent processes which control E(x) profile

1. Equilibrium carrier generation (bulk generation current, gen):

Ibgen = eniVol/gen

Generation occurs in SCR via effective generation level (0.65 eV),

introduction rate Mj = 1 cm-1, e = h = 1x10-13 cm2, (T) = o(T/To

)-2

(defined from our I(T) data)

divJgen = G; G = ni/g

G – generation rate jgen ~ Gxdepth Electron and hole components je(x) = Gx; jh(x) = G(d – x)

This level does not contribute to Neff

p+ n+

jh(x) je(x)

p+ n+

Neff

p+ n+

E(x)

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

At F > FSCSI

6

Approach for calculation of E(x) profile

2. Trapping to deep levels

DDs: Ev + 0.48 eV; DAs: Ec – (0.5250.005) eV – midgap levels used in all PTI simulations and fits

Filling factors are calculated for DDs and DAs which charged fractions contribute to Neff

No contribution of DDs and DAs to generation current!

Then Poisson equation:

dE/dx = -eNeff/o → E(x)

Method: Numerical simulation (EXCEL)

E(X), F eq = 1ex1015 cm-2, V = 500 V, T = 260K

0

10000

20000

30000

40000

50000

60000

0 0.005 0.01 0.015 0.02 0.025 0.03

x (cm)

E (

V/c

m)

p-on-n

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

Double Peak (DP) E(x) profile

7

Alternative issues: comments

Recently: Simulation of detector characteristic using standard simulating software (ISE-TCAD, Atlas (Silvaco), etc.)

Pres. at 20 RD50 workshop, Bari: R. Eber, Karsruhe, KIT; M. Miñano, IFIC, Valencia; also results from Deli University group

Main features

DDs and DAs are implemented (the same levels as in PTI model) which are considered as traps and generation levels Disagreement in current when calculating with standard simulator, no DP E(x) To agree with expected current calculated from and F, tuning of initial parameters is done

(suggested: cross-sections, reduced lifetime, introduction rate)

Question: lifetime – is it recombination lifetime as in Simulator Standard physics model for a sensor with no radiation damage? Value?

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

8

Alternative issues: comments

Igen(V) ~ V0.5 (w ~ V0.5) Igen(T) ~ exp(-Eg/2kT) - plot I-V in log-log scale Idif (V) = Is at V > 2kT/e Idif(T) ~ exp(-Eg/kT)

Also, generation and diffusion have different dependences on V and T

This may be the most probable reason for necessity to make tuning/tailoring//adjustment of initial parameters for simulation (e.g., , K) in standard software

(see presentations on Simulation mentioned above and at 21 RD50 workshop)

At F beyond SCSI → p-Si in base region,electrons are minor carriers which diffuse towards SCR

Idif depends on Ldif = (Dec)0.5 to (d-W) ratio

In SCR DivJdr e,h = 0Je_dr = enve_dr = Je_dif = const

If so, no DP E(x) arises!

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

p+ n+

Base, diffusion-V

SCR, generation

Jdr e

Jdr h

main junction

If recombination is considered:

9

S. M. Sze. Physics of Semiconductor Devices

Generation-recombination currents are described by Sah-Noyce-Shockley modelWhen pn<ni

2, generation rate U:

Generation: If n=p=ni gen_min 2rec

Trapping – controls CCE; all levels contribute to since pulse signal is measured within = 25 ns that is far less than detrapping time constant for larger energy gap (at RT)

Relationship between different lifetimes

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

Uncertainty in lifetime may be the most probable reason for necessity to make tuning/tailoring/adjustment of initial parameters for simulation in standard software (see presentations on Simulation mentioned above and at 21 RD50 workshop)

10

Generation lifetime vs. F

Ibgen = eniVol/gen; Ibgen = FVol

gen = (eni /F-1

gen 15tr

gen = 4.32x107/Feq

tr_e = 3.1x106/Feq

tr_h = 2.9x106/Feq

For Feq = 1x1014 cm-2

gen = 4.3x10-7 s

whereas lifetime used in Silvaco

≈ 1x10-7 s – recombination lifetime?

How to insert (F) in standard software?

I. Mandić, et al., NIM A 612 2010) 474

e = 3.2x10-16 cm2ns-1; e = 3.5x10-16 cm2ns-1

For trapping: 1/tr = Feq

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

gen vs. F

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E+12 1.0E+13 1.0E+14 1.0E+15 1.0E+16

F eq (n/cm2)

(s

)

tau_gen from RD50I(F) dependence

tau_gen from PTImodel

11

Another trend in alternative issues: implementation of multiple traps

Feq ~ 1014 cm-2 DLs: DD, DA, VV-

NVV = 1x1014 cm-3 NVV = 1x1016 cm-3

NVV = 1x1017 cm-3

In plots: concentration of charged DLs and total Neff

-6.E+12

-4.E+12

-2.E+12

0.E+00

2.E+12

0 50 100 150 200 250 300 350

Nd

d+

, N

da-

, N

eff

(c

m-3

)

T (K)

DD(0.48eV)

DA(V-V)

DA(0.53eV)

Neff

-4.E+12

-2.E+12

0.E+00

2.E+12

0 50 100 150 200 250 300 350

Nd

d+

, N

da-

, N

eff

(c

m-3

)

T (K)

DD(0.48eV)

DA(V-V)

DA(0.53eV)

Neff

-4.E+12

-2.E+12

0.E+00

2.E+12

0 50 100 150 200 250 300 350

Nd

d+

, N

da

-, N

eff

(cm

-3)

T (K)

DD(0.48eV)

DA(V-V)

DA(0.53eV)

Neff

Deep levels with Ea ~ 0.4 eV (VV, Ci-Oi) hardly affect current

DLs with Ea ~ 0.4 eV affect:♦ space charge region depth (at very high F);♦ trapping time constant

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

12

Reverse current simulation using PTI

model Carrier generation via single effective level 0.65 eV Ngen vs. fluence dependence

Linear dependence of Ngen vs. F agrees with data on I(F)

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

No adjustment of parametersIs required

RD50 parameterization: = 3.7x10-17 A/cmPTI model gives = 4x10-17 A/cm

0.0E+00

2.0E+14

4.0E+14

6.0E+14

8.0E+14

1.0E+15

1.2E+15

0.00E+00 1.00E+14 2.00E+14 3.00E+14

F (neq/cm2)N

ge

n (

cm-3

)

protons

neutrons

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+12 1.0E+13 1.0E+14 1.0E+15 1.0E+16

F (neq/cm2)

I/V

ol

(A/c

m3)

RD50parameterizationPTI model

13

Results on simulated Neff(x) and E(x)

Neff(x), 290K , 300 V

-1.4E +13

-1.2E +13

-1E +13

-8E +12

-6E +12

-4E +12

-2E +12

0

2E +12

4E +12

6E +12

0 0.005 0.01 0.015 0.02 0.025 0.03x (c m)

Neff

(cm

-3)

1.00E +13

1.00E +14

3.00E +14

5.00E +14

E (x), 290K , 300 V

0

10000

20000

30000

40000

0 0.005 0.01 0.015 0.02 0.025 0.03x (c m)

E(x

) (V

/cm

)

1.00E +13

1.00E +14

3.00E +14

5.00E +14

Neff(x), 290K , 5e14 c m-2

-1.4E +13

-1.2E +13

-1E +13

-8E +12

-6E +12

-4E +12

-2E +12

0

2E +12

4E +12

6E +12

0 0.005 0.01 0.015 0.02 0.025 0.03x (c m)

Neff

(cm

-3)

200 V

300 V

500 V

1000 V

E (x), 290 K , 5e14 c m-2

0

10000

20000

30000

40000

50000

60000

0 0.005 0.01 0.015 0.02 0.025 0.03x (c m)

E(x

) (V

/cm

)

200 V

300 V

500 V

1000 V

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

14

Simulation of Igen using two levels

E. Verbitskaya, et al., presented at 20 RD50 workshop, Bari, May 30 – June 1, 2012

Bulk generation current may be simulated using two levels (TL): – two independent processesDDs: Ev + 0.48 eV; DAs: Ec – (0.5250.005) eV

NDA/NDD = 1.2; kDD = 1

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

0.0025 0.003 0.0035 0.004 0.0045 0.005 0.0055

I (m

A)

1/T

protons, TL simulation

5E+12

simul.

5E+13

simul.

2E+14

simul.

kDD and kDA are different for neutrons and 23 GeV protons; cross-sections should be tuned

→ Using a single generation level for Igen calculation is more simple and unambiguous

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

15

Impact of Ibgen on E(x) profile

Key parameters for adequate E(x) description: bulk generation current and deep traps

Impact of Igen – double peak E(x) Simulation without current – no DP E(x)

0.0E+00

1.0E+04

2.0E+04

3.0E+04

4.0E+04

5.0E+04

6.0E+04

0 0.005 0.01 0.015 0.02 0.025 0.03

E (V

/cm

)

x (cm)

293K, current

293K, no current

253K, current

253K, no current

Igen is important parameter since it gives correct E(x) reference to other characteristics (CCE, tdr)

0.0E+00

5.0E+03

1.0E+04

1.5E+04

2.0E+04

2.5E+04

3.0E+04

3.5E+04

4.0E+04

0 0.005 0.01 0.015 0.02 0.025 0.03

x (cm)

E (

V/c

m)

PTI model, Kdd,da = 1

Igen = 0, Kdd,da = 1

PTI model, Kdd,da = 0.8

Igen = 0, Kdd,da = 0.8

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

16

Conclusions

PTI model considers E(x) profile formation in irradiated Si detectors caused by two independent processes: carrier generation via effective level with Ea = 0.65 eV and carrier trapping to midgap DDs and DAs.

This model gives nice agreement of the current with I(F) dependence

Therefore,Consideration on contribution of bulk generation current gives adequate description of irradiated detector characteristics

The nature of lifetime used in standard simulation software should be clarified

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN

17

Acknowledgments

This work was made in the framework of RD50 collaboration and supported in part by:

• Fundamental Program of Russian Academy of Sciences on collaboration with CERN, • RF President Grant # SS-3008.2012.2

Thank you for attention!

E. Verbitskaya, V. Eremin, 21 RD50 workshop, Nov 14-16, 2012, CERN