S. Lagomarsino1, S. Sciortino, E. Borchi1, R. D’Alessandro2

Modeling of carrier kinetics

in pCVD* diamond detectors

1 INFN and Department of Energetics (Univ. of Florence)

2 INFN and Department of Physics (Univ. of Florence)

*Manufacturer:Element Six, for The RD42 CERN Collaboration

Samples • Polycrystalline detectors from the RD42 CERN Collaboration

(manufactured by DEBID, UK)

Experimentals two types of measurement:

Pumping from the:

• totally depumped state;

• After thermal fading (from the partially depumped state)

pA

90S

r

Persistent current after removal of the source (at differentT )

pA

90S

r

Climatic

chamber

10°C - 40°C

Outline of the presentation:

• Assumptions

• Calculations

• Fit of the experimental data

• Conclusions so far

Aim of the model:

• To evaluate the defect level parameters: capture cross section, concentration, position in the bandgap

• To relate the defect parameters to the device performances

Assumption 1: defect bands We assume the existence of:

• a DONOR centre (sr, Nr)

• and an ACCEPTOR centre (m components: s1,N1,…,si,ni,…sm,Nm),

both with their spread in energy.

The parameters are determined by fitting the experimental data.

The ACCEPTOR CENTRE is BELOW THE DONOR CENTRE in the bandgap, otherwise we should see a different behaviour of the pumping current.

Assumption 2: We neglect interband transitions and

(only in the pumping stage) emission processes

pumping Dynamic equilibrium

•Energy limits of the donor centre (1.7-2.7 eV from VB) determined by

photoconductivity measurements [M. Bruzzi, S. Lagomarsino, S.

Sciortino, et al. Phys. Stat. Sol. (a) 199, #1, 138-144 (2003)]

•Identification of the recombination centre with the luminescence band

A by electroluminescnce measurements [Manfredotti et al., Appl. Phys

Lett. 67 3376 (1995)]

3. Quasi-equilibrium (QE)

approximation

•The population of the VB and CB does not change

significantly with respect to the population of the

defect bands The values of the populations are also negligible

The QE approximation is very well satisfied (a posteriori verification)

5% n, 95% p: 2=1.4

The single-carrier assumption yields the best fit:

From the experimental results of RD42 and the “linear-model”*

* H.Kagan for The RD42 Collaboration NIMA 514 (2003) 79-86

L0 L

The shape of this

dependence is

related to the

relative weight of

electron and holes

conduction

4. Single-carrier approximation

It is well known that material removal from the substrate side of a polycrystalline CVD diamond film produces at first an enhancement, due

to the poorest quality of the near-substrate material,

0

0.05

0.1

0.15

0.2

0.25

0.3 0 0.2 0.4 0.6 0.8 1 L/L0

ccd/L0

then a decrease of the charge collection distance occurs

Assuming a double-

carrier conduction

yields a very poor fit:

50% n, 50% p: 2=11

Rate

equations

QE

approximation

(hypothesis 3)

and

numerical

solution

of the rate

equations

The fit function can be

calculated numerically

Single-carrier approximation (hypothesis 4) and analytical solution of the rate equations

Fit of the experimental data: pumping

A set of m=3 trap

components, and a single

recombination centre, with

cross sections ranging from

10-16 to 10-14cm2, fits very

well to our measurements

(2 4 8)

The stable level value is proportional to the concentration of the recombination centres

Fit of the experimental data: pumping

From 1998 to 2000

•Decrease of the defect concentration

•Same type of defect centres

Thermal fading measurements

Dt is increased

exponentially Dt

Plot the number density of charged traps as a function of

fading time Dt

0

1E-10

2E-10

3E-10

4E-10

5E-10

6E-10

7E-10

0 2000 4000 6000 8000 10000 12000 14000

t (s)

I (A

)

charged traps

concentration

t

The thermal empting of a localized trap level would give an exponential dependence of the population of the level on time (not re-trapping approx. first order kinetics)

Thermal fading analysis pA 90Sr

The analysis of

radiation induced

current after different

times of thermal

fading at room

temperature

As a matter of fact, the experimental dependence is more likely a logarithmic one

+

-

+

20s 1 min

3 min 9 min 27 min

The logarithmic dependence can be explained by

assuming a uniform distribution of level in the band

gap with Esup-Einf>>kT

Einf

Esup

Radiation Induced Current (RIC) pA

90Sr

tkT

dE

dN

t

eekT

dE

dNdE

t

dE

dN

dt

tdq

dEt

dE

dNdEtes

dE

dNtqN

i

ttE

E

ii

E

E

i

E

E

KT

E

iii

1exp

1)(

expexp)(

infsupsup

inf

sup

inf

sup

inf

//

tkTdE

dNAtq ii ln)(

kT

Esi exp

1

pVvNs ii s

Radiation Induced Current:

thermal fading pA

90Sr

kTdE

dN1

The rate of change of the population of empty (charged) states vs. log Dt is proportional, via temperature, to the density of levels per unit energy in the band-gap, and gives a direct measurement of this quantity.

Einf

Esup

Persistent current analysis Persistent current after removal of the source (at room T and near room T )

pA

90Sr

Climatic

chamber

10°C - 40°C

Measurement over 105 s

In a log-log scale

Persistent Induced Current (PIC) pA

90Sr

Persistent Induced Current (PIC)

Fit function

pA

90Sr

A component

In our case

t

With this expression, m=3 trap distributions, corresponding to the

centres found with the Radiation Induced Current analysis, can reproduce the observed behaviour of the Persistent current over 5

decades

1E-13

1E-12

1E-11

1E-10

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05

t (s)

I (A

)

data

simul.

t_A

t_B

t_C

I dark

In this way, the value of

kT

E

Vpt eNvinf

inf

1 s

found by the best fit,

gives the lower energy

Einf of each distribution

Persistent Induced Current. Determination of dN/dE and Einf

0.78eV 0.81eV 0.87eV

• three defect band distributions,

with the same lower limits in all

the samples (within 0.01eV)

• the same cross-section values

(within 20%) 6.10-14cm2

7.10-15cm2

7.10-16cm2

• the same cross section of the

recombination centers (within

50%)

5.10-16cm2 *

Radiation Induced Current (RIC) pA

90Sr

Persistent Induced Current (PIC):

Results

In all the samples under test, we found:

* Good agreement with measurements on natural IIa diamond

Pan L.S. et al, J.Appl.Phys. 73 (6), 15 March 1993 p.2888-2894

pA

90Sr

Persistent Induced Current (PIC)

at near-room temperatures

Climatic

chamber

The analysis performed at room temperature combining RIC and

PIC measurements can be validated by PIC measurements at near-

room temperatures alone

PIC measurements has been

performed on a sample of

the batch CDS106 at

temperatures between 10°C

and 40°C 1.00E-03

1.00E-02

1.00E-01

1.00E+00

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06

t (s)

I/I0

24-Jul-40C

22-Jul-35C

28-jul-30C

14-Jul-25C

31-jul-20C

02-ago-15C

04-ago-10C

The shutter time of the

source is too long, at the

moment, to see the turning

point of the short-lived

component of the current

?

But a dependence on temperature

of the intensity and the turning-off

time of long-lived component is

clearly detectable

pA

90Sr

Persistent Induced Current (PIC)

at near-room temperatures

Climatic

chamber

A simultaneous fit of the PIC currents at different

temperatures gives a good agreement between theory and

experiment:

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06

10C

15C

20C

25C

30C

35

40

fit

The fit of the long-

lived component of

the PIC gives the

following values

for the deeper trap

parameters:

E=0.86 eV

s=7.5.10-16cm2

pA

90Sr

Persistent Induced Current (PIC)

at near-room temperatures

Climatic

chamber

0.78eV 0.81eV 0.87eV

6.10-14cm2

7.10-15cm2

7.10-16cm2

5.10-16cm2

Which are, within the experimental errors, exactly the same values

obtained with RIC and PIC analysis at room temperature

s=7.5.10-16cm2

E=0.86 eV

Summarizing, RIC and PIC measurements allows:

dn/dE s n DE

B1 B2 B3 A

(cm2) (cm-3) (eV)

To separate the band “B” in several

components of given concentration and

capture cross sections

7.10-16

8.10-15

7.10-14 6.1013

3.1014

5.1015

To assign a capture cross section and a

concentration to the recombination centers

of band “A”

5.10-16 5.1015

To find the lower energy of each component

and the density of level per unit energy

6.1014

8.1013

8.1012 0.78

0.81

0.87

Sample

P13 (1998)

Radiation Induced Current (RIC) pA

90Sr

Persistent Induced Current (PIC)

Sample

P13 (1998)

dn/dE s n DE

B1 B2 B3 A

(cm2) (cm-3) (eV) (cm-3eV-1)

7.10-16

8.10-15

7.10-14

5.10-16 6.1014

8.1013

8.1012 0.78

0.81

0.87

A

B

The enhancement in the efficiency

of DEBID detectors from batch

UTS1 to CDS92 (ccd from 130 to

270m):

6.1013

3.1014

5.1015

sample P13

(1998)

sample CDS92

P4 (2000) 5.1015

2.5.1015

5.1015

2.5.1015

3.1014

4.1013

6.1013

2.1013

Radiation Induced Current (RIC) pA

90Sr

Persistent Induced Current (PIC)

RESULTS OF OUR ANALYSIS:

Related to the smallest concentration

of recombination centers and overall

concentration of the traps (reduced of

about one half)

Probably, the diminishing of charged

shallow traps is not intrinsic, but

related to the lower concentration of

recombination centers by compensation

Campione

P13

dn/dE s n DE

B1 B2 B3 A

(cm2) (cm-3) (eV)

7.10-16

8.10-15

7.10-14

5.10-16 6.1014

8.1013

8.1012 0.78

0.81

0.87

A

B

6.1013

3.1014

5.1015

Radiation damage by neutron

with fluence up to 2.1015cm-2

Campione P13

P16 (neutron

irradiated )

8.1012

1.5.1013

8.1013

1.5.1014 6.1014

1.5.1015

7.10-14

4.10-14 6.1013

2.1014 3.1014

2.1014

Radiation Induced Current (RIC) pA

90Sr

Persistent Induced Current (PIC)

RESULTS OF OUR ANALYSIS:

No effects on recombination

centers

General increment of trap level

density per unit energy

Lowering of the cross section

of the low energy tail

Perspectives

• Investigation of the band-gap level structure of monocrystallyne

CVD diamond

• A study of shallower trap levels

structure and the structure of the

recombination “A” distribution: B

A

1 INFN and Department of Energetics (Univ. Of Florence)

2 INFN and Department of Physics (Univ. Of Florence)

Thank you for listening!

S. Lagomarsino1, S. Sciortino1, E. Borchi1, R. D’Alessandro2

Modeling of carrier kinetics

in pCVD diamond detectors

The distributed character of the trap energies is confirmed by measurements of thermal Persistent Induced Currents (PIC)

Persistent Induced Current (PIC) pA

90Sr

1E-13

1E-12

1E-11

1E-10

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05

t (s)

I (A

)

data

1E-13

1E-12

1E-11

1E-10

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05

t (s)

I (A

)

This function is a phenomenological

model whose parameters are not

directly related to the trap parameters

1E-13

5.1E-12

1.01E-11

1.51E-11

2.01E-11

2.51E-11

0.E+00 2.E+01 4.E+01 6.E+01 8.E+01 1.E+02

t (s)

I (A

)

Usually, the Persistent Photocurrents (PPC) are studied by means of a

function called “stretched exponential”

tiiti dark exp)( 0