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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: [email protected]
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