Alexandr A. Ezhevskii*, Andrey V. Soukhorukov*, Davud V. Guseinov*, Sergey A. Popkov*, Anatoliy V.

Gusev†, Vladimir A. Gavva†

 1Department of Physics, Lobachevsky State University, Nizhniy

Novgorod, 603950 Russia†Department of Semiconductor Materials, Institute of Chemistry

of High Purity Substances RAS, Nizhniy Novgorod, 603950 Russia

 e-mail: ezhevski@phys.unn.ru

Isotopic Effects in Spin Resonance of Electrons with Different Localization in

Silicon

Electron Spin Resonance for spin systemS=1/2, I=1/2

826 828 830 8320,0

0,2

0,4

0,6

0,8

1,0

EP

R S

ign

al (a

rb. u

nits)

Magnetic field (mT)

IASIBgBgSH NNB

�� ˆ

3330 3340 3350 3360 3370 3380 3390

-200000

-150000

-100000

-50000

0

50000

100000

150000

200000

EP

R S

igna

l

Magnetic field, Gs

P-donor in Si

826 828 830 8320,0

0,2

0,4

0,6

0,8

1,0

EP

R S

ign

al (a

rb. u

nits)

Magnetic field (mT)

S=1/2, I=1/2),()( rr jj

j

)exp()()()( 0 rikrurFr jjjj

First observation by G. Feher (1958):Electron paramagnetic resonance spectra of phosphorus in silicon-28 FWHM = 0.022 mT. Natural silicon, FWHM = 0.29 mT

826 828 830 8320,0

0,2

0,4

0,6

0,8

1,0

EP

R S

ign

al (

arb

. u

nits

)

Magnetic field (mT)

830 832 834 8360,0

0,2

0,4

0,6

0,8

1,0

EP

R S

ign

al (

arb

. u

nits

)

Magnetic field (mT)

V.V. Emtsev Jr., C.A.J. Ammerlaan, A.A. Ezhevskii, A.V. Gusev, Physica B 376-377 (2006) 45

Isotopic Effects in ESR in Silicon

Isotopic effects are caused by changing of nuclear mass:

a) Phonon’s frequency shift

b) Broadening of spectra is caused by isotopic disordering of the crystal.

(In ESR it could contribute to spin-lattice relaxation)

C

phon

• Isotopic effects are caused by changing of nuclear spin I to I≠0 which leads to hyperfine interaction: where

a) Hyperfine Fermi–Contact interaction of

b) Anisotropic part of hyperfine interaction.

i

ziziNNCF ISrggH 2

)(3

8

IASH�

ˆ

35

0 IS)rI)(rS(3

4IBS

rrgg NNB

�

BaA���

1

Feher (1958)

Isotopic Effects in ESR in Silicon

Natural abundances of isotopes for Si, Ge and GaAs

Si: 28Si =92.27%, I=0 29Si =4.68% I=1/2 30Si =3.05% I=0

Ge: 70Ge =20.55% 72Ge =27.37% 73Ge =7.67% I=9/2 74Ge =7.67% 76Ge =7.67%

Ga: 69Ga =60.2% I=3/2 71Ga =39.8% I=3/2

As: 75As =100% I=3/2

P: 31P =100% I=1/2

N: 14N =99.636% I=1 15N =0.038% I=1/2

Spin-less GaAs, GaP, GaN (InAs, InP, InN ) couldn’t be obtained!

Isotopic Effects in ESR of Donors in Silicon

Deep Donors Centers

(Strongly localized electrons)

Shallow Donors Centers

(electrons localized on

hydrogen-like orbital)

Low Temperature

(T<20K)

Shallow Donors Centers

(electrons localized on

hydrogen-like orbital)

Higher Temperatures

(20<T<100K)

Hopping

Conduction Electrons

(electrons delocalized into

c-band

Nd<nc

(T<100K)

Conduction Electrons

(electrons delocalized into

c-band

Nd ≥ nc

3d, 4d, 4f,

Vacancy-type

Defects,

Complexes,

etc.

P, As, Sb, Bi,

Li, N, etc.

P, As, Sb, Bi,

Li, N, etc.

P, As, Sb, Bi,

Li, N, etc.

P, As, Sb, Bi,

Li, N, etc.

Learning the structure of defects with higher accuracy Determining the hyperfine

contribution to the spin-relaxation

?

0.01 0.1 1 10 1001E-4

1E-3

0.01

0.1

1

FW

HM

, mT

Concentration of 29Si, %

P

Fe+

Dependence of the full width at half maximum (FWHM) of EPR lines of deep and shallow donor centers in silicon on magnetic nuclear 29Si concentration.

0.01 0.1 1 10 100

0.01

0.1

1

10

FW

HM

, G

s

Concentration of 29Si, %

V-

Fe+

Cr+

Bi

iIsh gamBBi

0

D.V. Guseinov, A.A. Ezhevskii, C.A.J. Ammerlaan, Physica B 381 (2006) 164 D.V. Guseinov, A.A. Ezhevskii, C.A.J. Ammerlaan, Physica B 395 (2007) 65

(ΔB)n = (ΔBsh)n + (ΔBrel)n + (ΔBrest)n,

(ΔBsh)2 = (2ln2/g2μB2)Σl,iαal,i

2.

3240 3245

-60000

-40000

-20000

0

20000

40000

EP

R S

ign

al

Magnetic field, Gs

T=30K

High resolution EPR spectra of Fe0 in silicon enriched by 28Si isotope

3241.1 3241.15 3241.2 3241.25 3241.3 3241.35

B, Gauss

EP

R in

ten

sit

y

3243

3243,05

3243,1

3243,15

3243,2

3243,25

3243,3

3243,35

3243,4

3243,45

0 20 40 60 80Angle, deg

Mag

netic

fiel

d,G

s

-2,3

-1,8

-1,3

-0,8

-0,3

0,2

0,7

1,2

1,7

2,2

0 20 40 60 80 100 120

Angle,deg

Lin

e-p

ea

k p

os

itio

n

Li donors in Si-28Li-O

Conduction electrons in silicon.Spin relaxation. g-factor behavior.

0 40 80 120 160 200 240 2800.0

0.5

1.0

1.5

2.0

100 120 140 160 180 200 220

5 28Si:P 1,5x1018cm-3

Si:P 3,3x1018cm-3

Si:P 9,1x1018cm-3

28Si:P 1,1x1019cm-3

Si:N ~1019cm-3

Si:Li 3,7x1018 cm-3

28Si:Li ~1018 cm-3

28Si:Li ~1016 cm-3

29Si:Li 4x1018 cm-3

29Si:P 3x1018 cm-3

H,

mT

T, K

Si:As 8,4x1018 cm-3

H,

mT

T, K

0 40 80 120 160 200 240 280

1.9968

1.9972

1.9976

1.9980

1.9984

1.9988

1.9992

1.9996

0 40 80 120 160 200

1.9968

1.9972

1.9976

1.9980

1.9984

1.9988

1.9992

1.9996 28Si:Li ~1016 cm -3

g - f

acto

r

T, K

28Si:P 1,5x1018cm-3

Si:P 3,3x1018cm-3

Si:As 8,4x1018

Si:P 9,1x1018cm-3

28Si:P 1,1x1019cm-3

Si:N ~1019cm-3

Si:Li 3,7x1018 cm-3

28Si:Li ~1018cm-3

28Si:Li ~1016 cm-3

29Si:Li 4x1018 cm-3

29Si:P 4x1018 cm-3

g - f

acto

r

T, K

2/5

22

2

2/3

*22/1

kTm

uB

s

0 50 100 150 200 250 300 350 4001.9975

1.9980

1.9985

1.9990

1.9995

2.0000

g -

fact

or

T, K

gg

pg

312

)1()0(

2

2

22

2)1( 1

2 drVd

rcm

kThx 2/

2/1

0

32)0()0(

1

mx

x dxe

xT

Dependencies of the impurity spin-orbit contribution to the g – factor of conduction electrons on concentration and atomic number of donor

0 10 20 30 40 50

1.984

1.986

1.988

1.990

1.992

1.994

1.996

1.998

2.000

g -

fact

or

Atomic number of donor

1,9970

1,9975

1,9980

1,9985

1,9990

1,9995

2,0000

1E+13 1E+15 1E+17 1E+19

Nd, cm-3

g- fa

ctor

Electron on the spin diffusion length Lsd, scattered by the n donors, each time getting a g - factor shift g, such that(g)2 = n (g)2, where Nd1 - number of atoms per unit length.

3/11 dsddsd NLNLn

Hyperfine contribution to the spin relaxation of conduction electrons

0 20 40 60 80 100

0.000

0.004

0.008

0.012

0.016

0.020

Hhf, m

T

29Si izotope content, %

Experiment

Corrected Pershin-Privman (Hhf~2/3)

Pershin-Privman (Hhf~1/3)

v

NA

t

tAT a

3/13/1222221 2424

242cosln2 at

at

s

tga NB 2

03

81

20

2

0

2/ bu

t sec/10~ 7 cm

v

NAT a

3/23/23221 24 t/t1, 3/13/1

aNN

For high concentration of nuclei 29Si when the electron wave packet covers several nuclei t becomes meaningless parameter and relaxation rate should be multiplied by the number of nuclei that located within the wave packet.

121860

2

0 u

121860

2

0 u

Measurements were done on Bruker EMX plus 10/12 spectrometer with helium cryostat (3.8-300К) ER 4112 HV.

Thank you for your attention

Зависимость ширины линии ЭПР электронов проводимости от температуры для образцов кремния обогащенного изотопом Si-29, легированного фосфором

0

0.5

1

1.5

2

2.5

3

3.5

0 20 40 60 80 100

T,K

B

,Ga

us

s

имплантация ионов дозой 6x1012 см-2 (d=1mkm, Nd=6x1016cm-3) дозой 3x1013 см-2 (d=1mkm,

Nd=3x1017cm-3)

Saturation curves for EPR lines of conduction electrons for phosphorus doped silicon samples (Si-28 and natural isotopic abundance).

1.00E+05

1.00E+06

1.00E+07

0510152025

MW Power, dB

4,2

10

20

30

50

95K

1.00E+05

1.00E+06

1.00E+07

0510152025

MW Power, dB

4,2

10

20

30

95K