interpretation of dlts data for silicon detectors irradiated with reactor neutrons

INTERPRETATION OF DLTS DATA FOR SILICON DETECTORS

IRRADIATED WITH REACTOR NEUTRONS

L.F. Makarenko*, F.P. Korshunov**, S.B. Lastovski**, E. Fretwurst***, G. Lindström***

* Belarusian State University, Minsk, Belarus**Institute of Solid State and Semiconductor Physics,

Minsk, Belarus***Hamburg University, Hamburg, Germany

L.F. Makarenko, Belarusian State University 11th RD50 Workshop, November 13, 2007

DLTS is one of the main methods of defect characterization in semiconductor structures. Its application to point defects is well known and described in many reviews and textbooks. However the procedure of DLTS data treatment is not enough elaborated for structures containing defect clusters.

For the purposes of defect engineering of radiation hard Si detectors is necessary to know as the total content of radiation defects so their local distribution.

This work is an attempt to seek proper ways for answering this questions.


• At present two characteristic features of clustered defects in silicon are well established.

• First, it is temperature dependence of the amplitude for some DLTS peaks and closely related to this feature the inequivalent heights of divacancy peaks [1-4].

• And second, the stretched kinetics for filling of clustered traps [3-5]

• 1. I.V. Antonova, A.V. Vasiliev, V.I. Panov and S.S. Shaimeev, Phys. Tekhn. Poluprov. 22, 998 (1988).

• 2. I.V. Antonova and S.S. Shaimeev, Phys. Tekhn. Poluprov. 25, 847 (1991).• 3. M. Kuhnke Microscopic and Electrical Properties of Clustered Divacancies

in n-Type Silicon ROSE/TN/2003-01• 4. E. V. Monakhov, J. Wong-Leung, A. Yu Kuznetsov, C. Jagadish, and B. G.

Svensson, Phys. Rev. B 65, 245201 2002.• 5. R. M. Fleming, C. H. Seager, D. V. Lang, P. J. Cooper, E. Bielejec, and J.

M. Campbell J. Appl. Phys., 102, 043711 (11 pg.) 2007


Part 1. Numerical simulations

• To calculate temperature dependence of any DLTS peak related to a defect in a cluster it is necessary to calculate the distribution of electrical potential inside and around the cluster and then to determine occupancy number of defect under study.

• To calculate the distribution of electrical potential () for spherical cluster one has to solve boundary value problem:

(r) e N n( ) N (r) f N (r) fd VV VV A A

1 d d (r) (r, )2r ,2 dr dr 0r

d0, 0.r 0 rdr


where charge density (r) is,

carrier concentration (n) is related to electrical potential as ( ) exp( )0e

n nk TB

3( )

30 41 exp( ) 0

MN rVV r R R NF

24 ( )0

r N r dr MVV

Gaussian distribution “diffused” Heaviside distribution

2( ) exp( )

23 300

M rN rVV RR


We used two functions to model defect distribution in a cluster

, ,04 3( ) ( ) 004 3303 0, .0

Mfor r R

MRN r H R rVV

Rfor r R

Normalizing factor is chosen in order to fulfill the following condition:

where H(x) is the Heaviside function

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80.01

0.1 =0.1

Gauss distribution Fermi distribution Fermi distribution, step-like

f

distance

=0.3

a

0.0 0.4 0.8 1.2 1.6 2.00.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

=0.1

=0.3

shel

l den

sity

distance

Gauss

step-likeb

Fig.1. Different distribution functions f(r) used for simulation of band bending around spherical cluster. To analyze the contribution to DLTS signal of defects located at different distances from a cluster center the use of shell density 4r2 f(r) is more representative (b).

2( ) 4 ( )n r r N rsh VV


The decrease of DLTS peak amplitude Smax(T) with growing temperature amplitude takes place when there is temperature range of incomplete defect occupation in the central region of cluster.

0 10 20 30 40 50 60 700

1x1010

2x1010

3x1010

4x1010

5x1010

VV= at 155 K

shel

l den

sity

, a.

u.

distance, nm

total density

VV= at 125 K

Fig.2. Distribution of doubly negatively charged divacancies inside a cluster at different temperatures.


110 120 130 140 150 1600.1

0.5

1

delta=0.1 delta=0.3 delta=0.4

S(T

)/S

(125

K)

T, K

Fig.3. Effect of in the “diffused” Heaviside distribution on temperature dependence of VV= peak


110 115 120 125 130 135 140 145 150 155 1600.1

0.5

1

M=5, D=28 nm M=10, D=28 nm M=20, D=28 nm

S

(T)/

S(1

25K

)

T, K220 230 240 250 260

0.0

0.2

0.4

0.6

0.8

1.0

M=10 D=20 nm D=40 nm D-56 nm

S(T

)/S

0

T, K

Fig.4. Temperature dependencies of DLTS peak amplitude for doubly (a) and singly (b) charged divacancy in clusters. The amplitude for doubly charged divacancy is normalized by the amplitude value at 125 K. The amplitude for singly charged divacancy is normalized by the its total number in cluster. Cluster diameter is indicated in figures


M

, a.u

.

D, a.u.

B

110 120 130 140 150 160

0.1

M=5, D=14 nm M=7, D=20 nm M=10, D=28 nm M=14, D=40 nm M=20, D=56 nm

NV

V

=/

NV

V

T, K

Fig.5. Schematic drawing of M/D0 correlation for clusters in neutron irradiated Si [Fleming et al., 2007} (left) and normalized temperature dependencies of DLTS peak amplitude for doubly charged divacancy in clusters with constant ratio of MD0 (right).


It is expected that Smax(T) dependence will be different for silicon diodes with different base doping.

110 115 120 125 130 135 140 145 150 155 1600.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

n=2e14 cm-3 n=2e13 cm-3 n=4e12 cm-3

S(T

)/S

(125

K)

T, K

M=20, D=56 nm

Fig.6. Normalized temperature dependencies of DLTS peak amplitude for doubly charged divacancy in the same clusters located indifferently doped semiconductors.


Part 2. Experimental data

Acronym Resistivity,carrier concentration

Oxygen content

Processed Irradiation fluence

EPI-8364 169 cm, Nd = 2.55x1013 cm-3

lean CiS process 61011 cm-2

MCZ-8556 1090 cm, Nd = 3.96x1012 cm-3

rich CiS process 61011 cm-2

W-337 2090 cm, Nd = 2.6x1012 cm-3

lean STM 31011 cm-2


80 120 160 200 240 2800

10

20

30

40

50

60

S

DL

TS(T

), a

.u.

T, K

E4

E2

E1

E3

100 150 200 250 3000

10

20

30

40

50

12

SD

LTS(T

), a

.u.

T,K

3 4

Fig.7. Comparison of DLTS spectra for epitaxial Si detectors irradiated with neutrons (solid line) and electrons (dashed line). Measurements have been performed at rate window of 95 s-1. Points show DLTS spectra of neutron irradiated diode after 30 min. annealing at 200 C.

Fig.8. Divacancy related peaks (E2 or E024 and E4 or E042) in epitaxial Si detectors irradiated with neutrons measured at different rate windows: 1 – 95 s-1; 2 – 380 s-1; 3—1900 s-1; 4 – 9500 s-1.

However the E024 divacancy peak is temperature dependent even electron irradiated samples (see talks at 8th RD50 workshop, Prague, 2006).


100 120 140 160 180 200 220 240 260 2800.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ub= -5.0 V; U

p= 0 V; t

p= 10 ms

Si based detector diode, CH-1908

El. Irrad., F = 2*1012 cm-2

en, s-1

20 50 80 200 400 1000 2000 5000

C,

pF

Temperature, K

110 120 130 140 150 160 170 180 190 200

0.0

0.2

0.4

0.6

0.8

1.0

Cm

ax(n

om

aliz

ed

)

Tmax

, K

ZamB10 W n=0.9e12 n-2.6e12

Fig. 9. DLTS spectra for Si detectors (=4 kcm) irradiated with electrons (E=3.5 MeV) measured with different rate windows for E024 and E042 peaks of divacancy. Rate windows are shown in the figure. (8th RD50 workshop, Prague, 2006).

Fig. 10. Dependence of DLTS signal amplitude on temperature of DLTS peak appearance for detectors with different doping. ((8th RD50 workshop, Prague, 2006).

Therefore to study cluster effects on DLTS spectra Si diodes with higher doping are preferable.


Comparison with other works

Antonova et al., 1988-1991:

An approximate analytical expression have been obtained to describe Smax(T) dependence for a single clustered defect.

It have been found that the deeper peak (E042) of VV falls with temperature and the shallower one (E024) increases (contrary to our observations)

Fleming et al., 2007:

The step-like distribution have been used in this work to interpret experimental data.

The shallower divacancy peak have been observed to fall with temperature. However its decrease was smaller then ours. This is consistent to our simulation results (Fig.6).

Kuhnke, 2003:

A numerical simulation have been performed for spherical cluster containing purely divacancies with Gaussian distribution. Simulation results are close to ours.


125 130 135 140 145 150 155 1600.0

0.2

0.4

0.6

0.8

1.0

1 - electron-irradiated2 - neutron-irradiated

3 - neutron-irradiated and annealed at 200 oC

Sm

ax(T

max

)/S

max

(12

8K

)

T, K

1

3

2

Fig.11. Amplitudes of the E2 trap measured at different temperatures (Tmax) for epitaxial Si detectors irradiated with electrons (1) neutrons (2, 3). The 3rd curve have been obtained after annealing at 200 C.

The different Smax(T) dependences in as-irradiated and annealed diodes are the consequence of a decrease of cluster charge.


100 150 200 250 3000

20

40

60

80

100

120

140

w=95 s-1 w=380 s-1 w=1950 s-1 w=9500 s-1

S,

fF

T, K

Fig.12. DLTS data for MCZ Si detector irradiated with neutrons measured at different rate windows: 1 – 95 s-1; 2 – 380 s-1; 3—1900 s-1; 4 – 9500 s-1.

Contrary to oxygen lean (STFZ or epitaxial) diodes, DLTS peak of E1 peak (Ec-0.17 eV) is also temperature dependent. It is an evidence of clustered V-O complexes in oxygen rich material.


80 120 160 200 240 280

0

20

40

60

80

100 350 K anneal current injection at 300 K

S, f

F

T, K

Fig.13. DLTS data for MCZ Si detector irradiated with neutrons and annealed at 200 C. Measurements were performed after current injection at 300 K and after subsequent annealing at 350 K. Rate window was 95 s-1.


A new effect related to defect bistability was found in neutron irradiated Si transistors (see R. M. Fleming, C. H. Seager, D. V. Lang, E. Bielejec, and J. M. Campbell Appl. Phys. Lett. 90, 172105 (2007)). The found that current injection at 300 K can change number of defects visible in DLTS spectra.

80 120 160 200 240 280 320-30

-20

-10

0

10

20

30

40 w=9500 s-1 w=1950 s-1 w=380 s-1 w=95 s-1

DLT

S s

igna

l diff

eren

ce

T, K

Fig.14. Difference between DPTS spectra for MCZ Si after current injection at 300 K and after subsequent annealing at 350 K. Measurements were performed at different rate windows: 1 – 95 s-1; 2 – 380 s-1; 3—1900 s-1; 4 – 9500 s-1.


CONCLUSIONS

Temperature dependence of DLTS peak amplitude helps to extract useful information on local distribution of defects in clusters. Though it does not allow to obtain unambiguously both the values of cluster size (D0) and number of defects in a single cluster (M), this dependence may be used for comparative evaluation of different defect clusters.

It has been found that in detectors made on MCZ silicon not only divacancies but also vacancy-oxygen complexes are distributed in the form of clusters.

It has been shown that bistable defects in neutron irradiated and annealed silicon detectors behave similar to divacancies. It suggest that they have two energy levels in the gap.


Acknowledgements

These studies have been done in the framework of WOODEAN Rd50 project.

Authors are indebted to Ljubljana group for neutron irradiation.

interpretation of dlts data for silicon detectors irradiated with reactor neutrons

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