Contribution from Eg(T) dependence into

parameterization of the bulk generation current of irradiated

Si detectors

Vladimir Eremina, Elena Verbitskayaa,Z. Lib

a. Ioiffe phisiko – technical institute , St. Petersburg , Russiab. Broorhaven National Lab. , Upton, New York, USA

23-th RD50 meeting, CERN, Nov. 13 – 15, 2013

Motivation

1. I(T) parameterization is important for the research in the frame of SWG of RD50 collaboration.

2. Generation of the bulk current in irradiated detectors is a critical process for the electric field distribution in the detector sensitive volume.

3. Physically correct I(T) parameterization is a basis for T-scaling

of the reverse current in irradiated detectors .

V. Eremin, RD50, Nov. 13-17, 2013

2

Energy band gap in semiconductors

V. Eremin, RD50, Nov. 13-17, 2013

Conduction band

Valence band

3

Eg(T=0K) = 1.169 eV

Energy band gap in Silicon

Eg(T = +20C) = 1.125eVEg(T = -20C) = 1.134eV

V. Eremin, RD50, Nov. 13-17, 2013

4

Generation/recombination in a real Si p-n junction

eethe vc

hhthh vc

kTEE

ve tce

ethn exp

kTEE

ve vth

hthh exp

Ge = eent Gh = eh(Nt – nt)Re = ce(N – nt)n Rh = chntp

Ece

h

e

h

Ev

generationrecombination

Et

Ener

gy

V. Eremin, RD50, Nov. 13-17, 2013

U = G - R

5

Simplification for the depleted region:p = 0 and n = 0 …………….since generation in SCR

]exp[]exp[

)( 2

kTEEnpv

kTEEnnv

npnNvvUti

ihthh

iti

ethe

ithth

ethhe

ni = (NcNv)0.5exp(-Eg/2kT)Ei = Eg/2 + kT/2 ln(NV/NC)

Simplification for Si:Ei = Eg/2Nc=2.8e19 cm-3, NV=2.65e19 cm-3 (S.Sze, PSD-3rt edition, 2007)Ei = Eg/2 + 0.0E26/2x0.055 = 1.12 + 0.0007 eV (~0.05% difference)

V. Eremin, RD50, Nov. 13-17, 2013

Solution for the current generation rate 6

Activation form of equitation for the generation rate

kTEE

vkTEv

NNNvvU

tghthh

tethe

vcthth

ethhe

expexp

kTEv

kTEE

vNN

nNvvUth

thhtge

thevc

ithth

ethhe

expexp

2

V. Eremin, RD50, Nov. 13-17, 2013

]exp[]exp[

)( 2

kTEEnv

kTEEnv

nNvvUti

ihthh

iti

ethe

ithth

ethhe

7

Ec=Ege

hEv =0

Et

Ener

gy

kTENNNv

Ut

vcththh

up

exp

kTEENNNv

Utg

vctethe

low

exp

e

hEtEn

ergy Ec=Eg

Ev =0

Single level model

kTEE

vkTEv

NNNvvU

tghthh

tethe

vcthth

ethhe

expexp

V. Eremin, RD50, Nov. 13-17, 2013

UAwIbgen

8

Sub-conclusions1. Transformation of “statistical” form of equitation for the

current generation rate into the “activation” form eliminates parameters which exploit Eg.

2. The temperature dependence of Eg now is substituted by temperature dependence of the position of generation center level in forbidden gap.

3. The temperature shift of the generation center level is not defined theoretically or experimentally and the universal dependence is unknown up to now .

4. The argument against this conclusion can be picked up from any experiment which covers a wide range of temperatures in which the effect dominates.

5. The Ibulk (T) analysis is a proper experiment which can show evidence of Eg (T).

V. Eremin, RD50, Nov. 13-17, 2013

9

# radiation F (cm-2) F (neq/cm2) d (mm) SCSI Vfd Vop (V)

899-82 neutrons 1x1012 200 no 120 140

899-97 neutrons 4.2x1013 200 yes 65 75

899-112 neutrons 2.3x1014 200 yes 200 240

921-D26 protons 5x1012 3.1x1012 188 no 95 110

923-D35 protons 5x1013 3.1x1013 188 yes 50 60

923-D39 protons 2x1014 1.24x1014 188 yes 130 160

0.0025 0.0030 0.0035 0.0040 0.0045 0.0050 0.005510-6

10-5

10-4

10-3

10-2

10-1

100

101

102

I (A

)

T-1 (K-1)

n (n/cm2):

1x1012

4.2x1013

2.3x1014

0.0025 0.0030 0.0035 0.0040 0.0045 0.0050 0.005510-6

10-5

10-4

10-3

10-2

10-1

100

101

102

I (A

)

T-1 (K-1)

eq (neq/cm2):

3.1x1012

3.1x1013

1.24x1014

Samples and I(T) characteristics

V. Eremin, RD50, Nov. 13-17, 2013

10

s(T) dependence

s(T) = so(T/To)m

with 0 > m > -3.

Ec

s(T1)

s(T2)

T1<T2s(T1)>s(T2)

SQR(Nc Nv) ~ T3/2

Vth ~ T1/2

kTENNNv

Ut

vcththh

exp

s(T) ~ T-2

V. Eremin, RD50, Nov. 13-17, 2013

Et(T)-?

11

0.0025 0.0030 0.0035 0.0040 0.0045 0.0050 0.005510-6

10-5

10-4

10-3

10-2

10-1

100

101

102

I (A

)

T-1 (K-1)

eq (neq/cm2):

3.1x1012

3.1x1013

1.24x1014

0.0025 0.0030 0.0035 0.0040 0.0045 0.0050 0.005510-6

10-5

10-4

10-3

10-2

10-1

100

101

102

I (A

)

T-1 (K-1)

experiment calculation:

m = 2 m = 1 m = 0

Neutrons, 4.2e13 cm-2 Protons

-2-10

The activation energy Et for the current generation :in neutron irradiated detector …………….. 0.645 eV in proton irradiated detector …………….. 0.65 eV

Activation energy of reverse current in the frame of SL model

Goal: bulk generation current temperature scaling

V. Eremin, RD50, Nov. 13-17, 2013

12

Two level (TL) approximation for reverse current in irradiated detectors

Goal: bulk generated current scaling + electric field simulation

PTI DL model: Deep acceptor (DA) Ec – 0.525 eV (EDAact = 1.12 – 0.525 = 0.595 eV) Deep donor (DD) Ev + 0.48 eV (EDDact = 1.12 – 0.48 = 0.64 eV)

Proved by : simulation of CCE recovery at low T (Lazarus effect), simulation of DP electric field distribution, simulation of multiplication gain in irradiated detectors.

kTEENNNv

kTE

NNNvUUU

DDg

vcDDethe

DA

vcDAhthh

DDDA

expexp

Ec=Ege

h Ev =0

EDA

Ener

gy

e

hEDDEn

ergy Ec=Eg

Ev =0

Additional parameter is required: ratio: NDD/NDA or

introduction rates : KDD and KDA

V. Eremin, RD50, Nov. 13-17, 2013

13

F (n/cm2) 1x1012 4.2x1013 2.3x1014

Deep level DD DA DD DA DD DA

Et (eV) 0.47 0.6 0.48 0.6 0.47 0.6

se (cm2) 8x10-14 1x10-15 8x10-14 1x10-15 8x10-14 3x10-15

sh (cm2) 1x10-15 5.5x10-15 1x10-15 5.5x10-15 1x10-15 2.5x10-14

Nt (cm-3) 3.5x1010 5.25x1010 4.2x1013 6.3x1013 2.3x1014 3.45x1014

Neutrons, KDD = 1 cm-1, KDA = 1.5 cm-1.

F (neq/cm2) 3.1x1012 3.1x1013 1.24x1014

Deep level DD DA DD DA DD DA

Et (eV) 0.478 0.6 0.48 0.6 0.48 0.6

se (cm2) 8x10-14 1x10-15 8x10-14 1x10-15 8x10-14 1x10-15

sh (cm2) 1x10-15 1.2x10-14 1x10-15 1x10-14 1x10-15 5x10-15

Nt (cm-3) 5x1012 5.5x1012 5x1013 5.5x1013 2x1014 2.2x1014

Protons, KDD = 1 cm-1, KDA = 1.1 cm-1.

Bulk generated current parameterization with TL model

V. Eremin, RD50, Nov. 13-17, 2013

14

0.0025 0.0030 0.0035 0.0040 0.0045 0.0050 0.005510-6

10-5

10-4

10-3

10-2

10-1

100

101

102

I (A

)

T-1 (K-1)

n (n/cm2):

1x1012

4.2x1013

2.3x1014

0.0025 0.0030 0.0035 0.0040 0.0045 0.0050 0.005510-6

10-5

10-4

10-3

10-2

10-1

100

101

102

I (A

)T-1 (K-1)

eq (neq/cm2):

3.1x1012

3.1x1013

1.24x1014

Fit of I(T) curves for detectors irradiated by different fluences with TL model

neutrons protons

V. Eremin, RD50, Nov. 13-17, 2013

15

Proton irradiated detector at V = 300 V, Feq = 1x1015 neq/cm2.

0.000 0.005 0.010 0.015 0.0200

10

20

30

40

E (k

V/c

m)

x (cm)

RT, Ibgen considered

RT, Ibgen disregarded

-20C, Ibgen considered

-20C, Ibgen disregarded

DP electric field distribution modeling with the TL model

V. Eremin, RD50, Nov. 13-17, 2013

16

Conclusions1. Eg (T) is not important for the temperature scaling of

the bulk generated reverse current 2. The influence of T on the position of DL in

semiconductor forbidden gap is not predictable and unknown up to now.

3. Simulation / modeling society should agree the SIG(T) dependence which is not clarified yet due to experimental difficulties. SIG ~ T-2 is proposed.

4. One exponential fit of the I(T) curves can be applied as usually abs(Ei – Et) > kT. This gives a simple and effective way for T-scaling of the current.

V. Eremin, RD50, Nov. 13-17, 2013

17

Thank you for your attention

Generation/recombination in semiconductors

R = Rrec * p * nRecombination rate

Recombination coefficient

Generation rate G = Rgen * p * n

Principe of detailed equilibriumGn = Rn

Gp = Rp

G = Rrec * ni2

Transition rate U = R - G = Rrec(p*n – n2)

V. Eremin, RD50, Nov. 13-17, 2013

Bulk generation current

UAwIbgen

Due to: Ibgen = eniAw/tgen

tihth

ethhe

th

tgevc

bgen NnvvekTE

kTEE

NN

expexp

vciththh

t

up NNnNvkTE

exp

vctethe

tg

low NNNv

kTEE

exp

V. Eremin, RD50, Nov. 13-17, 2013