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Deuteron and proton NMR in plasma-deposited amorphous silicon
Journal of Non-Crystalline Solids 66 (1984) 121-126 North-Holland, Amsterdam
121
DEUTERON AND PROTON NMR IN PLASMA-DEPOSITED AMORPHOUS SILICON D. J. Leopold, B. S. Coughlan, P. A. Fedders, and R. E. Norberg* Washington U n i v e r s i t y , St. Louis, Missouri 63130, U.S.A. J. B. Boyce and J. C. Knights Xerox Palo Alto Research Center, Palo A l t o , C a l i f o r n i a 94304, U.S.A. Nuclear resonance l i n e shapes and spin r e l a x a t i o n rates have been measured f o r deuterons and protons in f i v e a-Si samples plasma-deposited from SiH,/Dz and SiD4/Ar gas mixtures. Some samples show s p i n - l a t t i c e relaxat i o n rates which increase exponentially with temperature above 50K to sharp maxima near 400 K. In a l l f i v e samples one component of the nuclear s p i n - l a t t i c e r e l a x a t i o n proceeds via d i l u t e molecular D2 and H2 r e l a x a t i o n centers. The corresponding temperature v a r i a t i o n s of molecular e l e c t r o n i c r e l a x a t i o n rates are given by CE*T.2 where C varies systematically with sample preparation conditions. We have made NMR measurements between 14.4 and 92.5 MHz on f i v e a-Si samples plasma-depositedI from I00% SiH4, 5% SiH4/D 2, and 5% SiD4/Ar gas
mixtures.
Substrate temperatures varied from 298 to 503 K and r f power levels ranged from 2 to 18W onto 20 cm2 cathode and anode surfaces. of the c h a r a c t e r i s t i c of these a-Si samples.
Table I summarizes some
The indicated proton and deuteron
concentrations have been determined by c a l i b r a t e d NMR spin counts. Table l :
Sample preparation conditions and r e s u l t i n g H and D concentrations determined by NMR spin counts
Sample
I
Gas Mixture
5%SiH4/D2
Substrate Temperature (C) Substrate RF Power (W)
----~
25 Cathode
25 Cathode
ITI~--~ lO0%SiH4 230 Anode
18
2
2
n(H) (%)
7
12.8
10.9
n(D) (%)
24
I0.5
V
5%SiD4/Ar 25 Cathode 15
230 Anode 15
3.3
1.4
13.4
I0.3
Figurel shows the quadrupole echo FTDMR spectra for sample #I at 4.2 and 39K.
The resonance shows a w e l l - d e f i n e d quadrupolar doublet with a zero
asymmetry parameter and an area which corresponds 2 to a 21 at.%D f r a c t i o n of t i g h t l y bound deuterium (TBD). The f u l l s p l i t t i n g between the main peaks of the doublet is 6 6 ± I . 0 kHz and corresponds to a deuteron quadrupole coupling *Supported in part by NSF Low Temperature Physics Grants 82-04166 and 83-04473. 0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
122
D.J, Leopold et al. / Deuteron and proton NMR
constant of 8 8 ± 1 . 3 kHz in a-Si.
I f the c o r r e l a t i o n between ~ q and force constant reported 3 f o r DMR in diatomic molecules is v a l i d in a - S i , then the above ~ co-responds to an i n f r a red s t r e t c h i n g mode absorption a t 1 4 6 0 ± l O c m -I. q The quadrupole-broadened central l i n e in Fig. 1 has a temperature-dependent l i n e - w i d t h which varies from 10 -4 to 2 x 1 0 -3 sec between 4.2 and 300 K.
•• 200 k H z
~'1
FIGURE l Fourier transforms of 30.0 MHz deuteron 90°-z-90°90o quadrupole echoes at 39 and 4 . 2 K forSample I. The resonance doublet has a f u l l width s p l i t t i n g between the main peak of 66 1 kHz. Also v i s i b l e is a narrow component which broadens with reduced temperature.
200 k H z
33R
~1
FIGURE 2 Fourier transforms of deuteron 90°-z-9090 o quadrupole echoes at 33, 23 and 14 K f o r Sample V.
Figure 2 shows s i m i l a r DMR l i n e shapes f o r Sample V at 14, 23, and 33 K. The 66 kHz doublet again is apparent and corresponds to a 2.1% TBD f r a c t i o n in t h i s sample.
The narrow spike at the center corresponds to a small f r a c t i o n
which has l i n e - w i d t h s which correspond c l o s e l y with the narrow central l i n e in Fig. I .
In Sample V there also is a t h i r d component to the DMR, a broad central
f e a t u r e with a resonance h a l f width near 30 kHz and l i t t l e
temperature dependence
between 14 and 33 K. Spin l a t t i c e
r e l a x a t i o n data f o r four Samples are summarized in Fig. 3.
Samples I I and I I I
show TI(H) minima near 30 to 40K which are t y p i c a l of those
which r e f l e c t r e l a x a t i o n by spin d i f f u s i o n to f a s t - r e l a x i n g o-H 2 molecules. Sample I contained r a t h e r large amounts of D (24at.%)
and D2 (670ppm), with
D.J. Leopold et al. / Deuteron and proton ~W/R
123
much of the l a t t e r presumably coming from the D2 in the o r i g i n a l gas mixture. In order to examine this question, Samples IV and V were prepared by plasma deposition from a gas mixture of 5% SiD4 and 95% argon.
However, our NMR
measurements show 3.3 and 1.4% components in these two samples and so the gas mixture apparently contained a s i g n i f i c a n t hydrogen impurity• TIB(D) for the TBD doublet is shown for Samples IV and V as circles and dots at the top of Fig. 3. squares.
TI(D ) for the central lines are shown as triangles and
There is a small TI(D) minimum v i s i b l e in these central WBD data.
There is no corresponding TI(H) minimum below I00 K for Sample V, presumably because the sample contains very l i t t l e
H2. TI(D)(30.0)
IOC
~
0
o
o \ioo++ L ~--
" : ~ ' ~ o o "" ~ I ~ ,
°°%8~,
TI(H) o (92.5)
~. ~'
~
= (46.0) (30.0)
-
0.1 -
~,.
in ,~ (91.8) J
I
i
V 0 (30.0) • (92.5) I
I0
I
T(K)
I
,
~ I
0
I00
Figure 3 TI(H) and TI(D ) in f i v e a-Si Samples The WBD TI(D) results for Samples IV and V can be analyzed by reciprocal subtraction of the non-D2-related TIB(D) for the TBD doublet to y i e l d the molecular-D2-related component TI~(D): I ] _ : I___ 1 TI~ T1 T1B
(1)
The resulting TI~(D ) show a minimum near 47 K and have been optimally f i t t e d to the expression
D,J. Leopold et al. / Deuteron and proton NMR
124
Tim(D) : ATl(D 2) + B
(2)
with A =13800 and B=16 sec for Sample IV and A=16500 and B=64 sec for Sample V.
The A term r e f l e c t s rapid spin d i f f u s i o n to D2 relaxation centers and B is
a spin d i f f u s i o n bottleneck term. Equation (2) can be analyzed to y i e l d n(D2) and the spin d i f f u s i o n coeff i c i e n t DD. In the rapid spin d i f f u s i o n l i m i t and neglecting intermolecular EQQ interactions and para-ortho conversion, we have T1 (D) .
(3)
The bottleneck term corresponds to TI(D) = B = 3/[4/~Dn(D2)b ]
(4)
Some of the results deduced from our analyses of relaxation minima which occur via molecular hydrogen in the f i v e samples along with corresponding conclusions about the TI(H) minima in three samples reported 4'5 by Carlos and Taylor are summarized in Table I I . minations of DH and DD show l i t t l e Table 2:
I
Except for H in Sample I , the nine deterv a r i a t i o n among the highly clustered samples
Molecular H2 and D2 related relaxation f i t s and corresponding results.
134 TI(D2)+0.13
3.0
670
l . l xlO -12
IV
13800 TI(D2) +16
2.7
5.9
1 . 3 x l O -12
V
16500 T1 (D2) + 64
2.1
3.8
4 . 9 x i 0 -13
S-a~pl=e ---~llc~~ I II Ill IV V
( s e c ) . . . . n-(=H~-(a-t-.~)-=n(H-2)- (p-p;m)-
4590 T1 (H2) + 0.25
7.0
542 TI(H2) +1.8
12.8
120
2 . 5 x i 0 -13
78 Tl (H2) + 0.22
I0.9
700
3 . 5 x i 0 -13
-
3.3
-
l .4
RCA #1
76 TI(H2) +0.16
lO.O
RCA #2
127 TI(H2) +0.27
BNL #94
25 TI(H2) +0.28
7.6
- SH-~CC~/sec~ -
<0.2 <0.2
2.8xi0 -II
-
660
5 . 0 x l O -13
12.0
470
4.1 xlO -13
6.0
1200
1 . 6 x l O -13
From the relaxation times TI(D2) and TI(H2) we can determine the molecular electronic correlation frequencies F2(T) for the d i l u t e p-D2 and o-H 2 molecules in the various amorphous s i l i c o n samples. The angular-averaged, no-symmetry, r = 0 relaxation equation 6 is
D.J. Leopold et al. / Deuteron and proton NMR
I : 6~[F2(wo ) + 2F2(2Wo)] T1 5
125
(5)
Here we use6'7 F2(~) =?2/(W2-?~), Wd(H2) =3.624x105sec I andwd(D2)=l.588xlO5sec! ?2 values can be calculated for each T1 data point. These F2 results are plotted in Fig. 4 for samples I, I I , and IV. For comparison, the curved lines indicate F2 results for dilute o-H 2 in solid neon and argon. '
'
•
I
.
.
.
.
I
•
o e
;.7
,o
N e ~ T~2 i e,, 7. . "
T2
,o9
/
108
t.a,q
II.' r/.'i. /.o
o Sample I • Sample II 17 Sample IV
l
/ / .:
107 '
'
I
]
I0
I
I
T (K)
I
I
i
I
I00
FIGURE 4 Molecular correlation frequencies 2 for a-Si:(D,H) Sample I, I I , and IV calculated from TIm(D) and TI~(H) data. The curved lines represents ?2 for ortho-H 2 in solid neon and argon for comparison. The molecular relaxation of dilute J = l o-H 2 and p-D2 in non-magnetic solid hosts can be described via a phonon-Raman process. It is anticipated 9'I0 that F2 = C E*(T*)T .2
(6)
where E*(T*) is the tabulated g Van Kranendonk function and T* is a reduced temperature T/@c. E* is nearly independent of temperature for_T*>l and there F2=T .2. For T*<0.02 the quantity E* is proportional to T.5 and thus F2~T .7. The characteristic temperature @c has been found 8 to be 40±2K for. o-H2 in solid neon and argon. The ?2 points plotted in Fig. 4 have not involved any
126
D.J. Leopold et al. / Deuteron and proton NMR
assumptions about the magnitude of @c" The results however can be f i t t e d very well by Eq. (6) with @c=40 K. There is an evident chemical trend in the sample-dependence of the molecular 2 F2 data plotted in Fig. 4 and reported e a r l i e r • The F2 curves systematically s h i f t downward ( i . e . , C, reduces) as one progresses towards host materials with larger p o l a r i z a b i l i t i e s .
There is in addition an apparent d i s t r i b u t i o n among
the ?2 results for a-Si samples (Fig• 4).
Those samples deposited more slowly
at lower power levels show larger coefficients C.
The results may be approxi-
mately described by the r e l a t i o n C =p-O'5, where P is the deposition power density. Above 50K the T1 results (Fig. 3) for Samples IV and V are d i f f e r e n t from those for the other samples described here•
Both TI(D) and TI(H ) decrease
rapidly with increasing temperature and TI(H ) shows a minimum near 380 K.
It
is probable that this additional r e l a x a t i o n arises from interaction with electron magnetic moments.
I f the r e l a x a t i o n r e f l e c t s contact interaction
with mobile c a r r i e r s , then one expects the r a t i o T1 (D) [ ~_~12 T I ~ = Iv(D)] = 42.44
(7)
and, for a semiconducting sample, I/T1 = ¥2 N ~
(8)
where the number of c a r r i e r s , N, may be exponentially thermally activated• In Fig• 3 a solid l i n e has been drawn through the 92.5 MHz TI(H ) data for Sample V.
The upper solid l i n e is 42.44 times the lower TI(H) l i n e •
Equation
(8) applied to the data yields an a c t i v a t i o n energy of 37 meV. REFERENCES I)
R. A. Street, J. C. Knights, and D. K. Biegelsen, Phys. Rev. B18,1880(1978).
2)
D. J. Leopold, J. B. Boyce, P. A. Fedders, and R. E. Norberg, Phys. Rev. B 26, 6053 (1982).
3)
M. Mokarrsm and J. L. Ragle, J. Chem. Phys. 59, 2770 (1973). W. E. Carlos and P. C. Taylor, Phys. Rev. B 26, 3605 (1982).
4)
5)
W. E. Carlos and P. C. Taylor, private communication. P• A. Fedders, Phys. Rev. B 20, 2588 (1979). N. F. Ramsey, Molecular Beams (Oxford University Press, London, 1956),p. 235. 8) M. S. Conradi, K. Luszczynski,and R. E. Norberg, Phys. Rev. B 2_0_0,2594 (1979). 9) a. Van Kranendonk, Physica (Utrecht) 20, 871 (1954). I0) a. Van Kranendonk and M. B. Walker, Can. J. Phys. 46, 2441 (1968). 6) 7)
121
DEUTERON AND PROTON NMR IN PLASMA-DEPOSITED AMORPHOUS SILICON D. J. Leopold, B. S. Coughlan, P. A. Fedders, and R. E. Norberg* Washington U n i v e r s i t y , St. Louis, Missouri 63130, U.S.A. J. B. Boyce and J. C. Knights Xerox Palo Alto Research Center, Palo A l t o , C a l i f o r n i a 94304, U.S.A. Nuclear resonance l i n e shapes and spin r e l a x a t i o n rates have been measured f o r deuterons and protons in f i v e a-Si samples plasma-deposited from SiH,/Dz and SiD4/Ar gas mixtures. Some samples show s p i n - l a t t i c e relaxat i o n rates which increase exponentially with temperature above 50K to sharp maxima near 400 K. In a l l f i v e samples one component of the nuclear s p i n - l a t t i c e r e l a x a t i o n proceeds via d i l u t e molecular D2 and H2 r e l a x a t i o n centers. The corresponding temperature v a r i a t i o n s of molecular e l e c t r o n i c r e l a x a t i o n rates are given by CE*T.2 where C varies systematically with sample preparation conditions. We have made NMR measurements between 14.4 and 92.5 MHz on f i v e a-Si samples plasma-depositedI from I00% SiH4, 5% SiH4/D 2, and 5% SiD4/Ar gas
mixtures.
Substrate temperatures varied from 298 to 503 K and r f power levels ranged from 2 to 18W onto 20 cm2 cathode and anode surfaces. of the c h a r a c t e r i s t i c of these a-Si samples.
Table I summarizes some
The indicated proton and deuteron
concentrations have been determined by c a l i b r a t e d NMR spin counts. Table l :
Sample preparation conditions and r e s u l t i n g H and D concentrations determined by NMR spin counts
Sample
I
Gas Mixture
5%SiH4/D2
Substrate Temperature (C) Substrate RF Power (W)
----~
25 Cathode
25 Cathode
ITI~--~ lO0%SiH4 230 Anode
18
2
2
n(H) (%)
7
12.8
10.9
n(D) (%)
24
I0.5
V
5%SiD4/Ar 25 Cathode 15
230 Anode 15
3.3
1.4
13.4
I0.3
Figurel shows the quadrupole echo FTDMR spectra for sample #I at 4.2 and 39K.
The resonance shows a w e l l - d e f i n e d quadrupolar doublet with a zero
asymmetry parameter and an area which corresponds 2 to a 21 at.%D f r a c t i o n of t i g h t l y bound deuterium (TBD). The f u l l s p l i t t i n g between the main peaks of the doublet is 6 6 ± I . 0 kHz and corresponds to a deuteron quadrupole coupling *Supported in part by NSF Low Temperature Physics Grants 82-04166 and 83-04473. 0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
122
D.J, Leopold et al. / Deuteron and proton NMR
constant of 8 8 ± 1 . 3 kHz in a-Si.
I f the c o r r e l a t i o n between ~ q and force constant reported 3 f o r DMR in diatomic molecules is v a l i d in a - S i , then the above ~ co-responds to an i n f r a red s t r e t c h i n g mode absorption a t 1 4 6 0 ± l O c m -I. q The quadrupole-broadened central l i n e in Fig. 1 has a temperature-dependent l i n e - w i d t h which varies from 10 -4 to 2 x 1 0 -3 sec between 4.2 and 300 K.
•• 200 k H z
~'1
FIGURE l Fourier transforms of 30.0 MHz deuteron 90°-z-90°90o quadrupole echoes at 39 and 4 . 2 K forSample I. The resonance doublet has a f u l l width s p l i t t i n g between the main peak of 66 1 kHz. Also v i s i b l e is a narrow component which broadens with reduced temperature.
200 k H z
33R
~1
FIGURE 2 Fourier transforms of deuteron 90°-z-9090 o quadrupole echoes at 33, 23 and 14 K f o r Sample V.
Figure 2 shows s i m i l a r DMR l i n e shapes f o r Sample V at 14, 23, and 33 K. The 66 kHz doublet again is apparent and corresponds to a 2.1% TBD f r a c t i o n in t h i s sample.
The narrow spike at the center corresponds to a small f r a c t i o n
which has l i n e - w i d t h s which correspond c l o s e l y with the narrow central l i n e in Fig. I .
In Sample V there also is a t h i r d component to the DMR, a broad central
f e a t u r e with a resonance h a l f width near 30 kHz and l i t t l e
temperature dependence
between 14 and 33 K. Spin l a t t i c e
r e l a x a t i o n data f o r four Samples are summarized in Fig. 3.
Samples I I and I I I
show TI(H) minima near 30 to 40K which are t y p i c a l of those
which r e f l e c t r e l a x a t i o n by spin d i f f u s i o n to f a s t - r e l a x i n g o-H 2 molecules. Sample I contained r a t h e r large amounts of D (24at.%)
and D2 (670ppm), with
D.J. Leopold et al. / Deuteron and proton ~W/R
123
much of the l a t t e r presumably coming from the D2 in the o r i g i n a l gas mixture. In order to examine this question, Samples IV and V were prepared by plasma deposition from a gas mixture of 5% SiD4 and 95% argon.
However, our NMR
measurements show 3.3 and 1.4% components in these two samples and so the gas mixture apparently contained a s i g n i f i c a n t hydrogen impurity• TIB(D) for the TBD doublet is shown for Samples IV and V as circles and dots at the top of Fig. 3. squares.
TI(D ) for the central lines are shown as triangles and
There is a small TI(D) minimum v i s i b l e in these central WBD data.
There is no corresponding TI(H) minimum below I00 K for Sample V, presumably because the sample contains very l i t t l e
H2. TI(D)(30.0)
IOC
~
0
o
o \ioo++ L ~--
" : ~ ' ~ o o "" ~ I ~ ,
°°%8~,
TI(H) o (92.5)
~. ~'
~
= (46.0) (30.0)
-
0.1 -
~,.
in ,~ (91.8) J
I
i
V 0 (30.0) • (92.5) I
I0
I
T(K)
I
,
~ I
0
I00
Figure 3 TI(H) and TI(D ) in f i v e a-Si Samples The WBD TI(D) results for Samples IV and V can be analyzed by reciprocal subtraction of the non-D2-related TIB(D) for the TBD doublet to y i e l d the molecular-D2-related component TI~(D): I ] _ : I___ 1 TI~ T1 T1B
(1)
The resulting TI~(D ) show a minimum near 47 K and have been optimally f i t t e d to the expression
D,J. Leopold et al. / Deuteron and proton NMR
124
Tim(D) : ATl(D 2) + B
(2)
with A =13800 and B=16 sec for Sample IV and A=16500 and B=64 sec for Sample V.
The A term r e f l e c t s rapid spin d i f f u s i o n to D2 relaxation centers and B is
a spin d i f f u s i o n bottleneck term. Equation (2) can be analyzed to y i e l d n(D2) and the spin d i f f u s i o n coeff i c i e n t DD. In the rapid spin d i f f u s i o n l i m i t and neglecting intermolecular EQQ interactions and para-ortho conversion, we have T1 (D) .
(3)
The bottleneck term corresponds to TI(D) = B = 3/[4/~Dn(D2)b ]
(4)
Some of the results deduced from our analyses of relaxation minima which occur via molecular hydrogen in the f i v e samples along with corresponding conclusions about the TI(H) minima in three samples reported 4'5 by Carlos and Taylor are summarized in Table I I . minations of DH and DD show l i t t l e Table 2:
I
Except for H in Sample I , the nine deterv a r i a t i o n among the highly clustered samples
Molecular H2 and D2 related relaxation f i t s and corresponding results.
134 TI(D2)+0.13
3.0
670
l . l xlO -12
IV
13800 TI(D2) +16
2.7
5.9
1 . 3 x l O -12
V
16500 T1 (D2) + 64
2.1
3.8
4 . 9 x i 0 -13
S-a~pl=e ---~llc~~ I II Ill IV V
( s e c ) . . . . n-(=H~-(a-t-.~)-=n(H-2)- (p-p;m)-
4590 T1 (H2) + 0.25
7.0
542 TI(H2) +1.8
12.8
120
2 . 5 x i 0 -13
78 Tl (H2) + 0.22
I0.9
700
3 . 5 x i 0 -13
-
3.3
-
l .4
RCA #1
76 TI(H2) +0.16
lO.O
RCA #2
127 TI(H2) +0.27
BNL #94
25 TI(H2) +0.28
7.6
- SH-~CC~/sec~ -
<0.2 <0.2
2.8xi0 -II
-
660
5 . 0 x l O -13
12.0
470
4.1 xlO -13
6.0
1200
1 . 6 x l O -13
From the relaxation times TI(D2) and TI(H2) we can determine the molecular electronic correlation frequencies F2(T) for the d i l u t e p-D2 and o-H 2 molecules in the various amorphous s i l i c o n samples. The angular-averaged, no-symmetry, r = 0 relaxation equation 6 is
D.J. Leopold et al. / Deuteron and proton NMR
I : 6~[F2(wo ) + 2F2(2Wo)] T1 5
125
(5)
Here we use6'7 F2(~) =?2/(W2-?~), Wd(H2) =3.624x105sec I andwd(D2)=l.588xlO5sec! ?2 values can be calculated for each T1 data point. These F2 results are plotted in Fig. 4 for samples I, I I , and IV. For comparison, the curved lines indicate F2 results for dilute o-H 2 in solid neon and argon. '
'
•
I
.
.
.
.
I
•
o e
;.7
,o
N e ~ T~2 i e,, 7. . "
T2
,o9
/
108
t.a,q
II.' r/.'i. /.o
o Sample I • Sample II 17 Sample IV
l
/ / .:
107 '
'
I
]
I0
I
I
T (K)
I
I
i
I
I00
FIGURE 4 Molecular correlation frequencies 2 for a-Si:(D,H) Sample I, I I , and IV calculated from TIm(D) and TI~(H) data. The curved lines represents ?2 for ortho-H 2 in solid neon and argon for comparison. The molecular relaxation of dilute J = l o-H 2 and p-D2 in non-magnetic solid hosts can be described via a phonon-Raman process. It is anticipated 9'I0 that F2 = C E*(T*)T .2
(6)
where E*(T*) is the tabulated g Van Kranendonk function and T* is a reduced temperature T/@c. E* is nearly independent of temperature for_T*>l and there F2=T .2. For T*<0.02 the quantity E* is proportional to T.5 and thus F2~T .7. The characteristic temperature @c has been found 8 to be 40±2K for. o-H2 in solid neon and argon. The ?2 points plotted in Fig. 4 have not involved any
126
D.J. Leopold et al. / Deuteron and proton NMR
assumptions about the magnitude of @c" The results however can be f i t t e d very well by Eq. (6) with @c=40 K. There is an evident chemical trend in the sample-dependence of the molecular 2 F2 data plotted in Fig. 4 and reported e a r l i e r • The F2 curves systematically s h i f t downward ( i . e . , C, reduces) as one progresses towards host materials with larger p o l a r i z a b i l i t i e s .
There is in addition an apparent d i s t r i b u t i o n among
the ?2 results for a-Si samples (Fig• 4).
Those samples deposited more slowly
at lower power levels show larger coefficients C.
The results may be approxi-
mately described by the r e l a t i o n C =p-O'5, where P is the deposition power density. Above 50K the T1 results (Fig. 3) for Samples IV and V are d i f f e r e n t from those for the other samples described here•
Both TI(D) and TI(H ) decrease
rapidly with increasing temperature and TI(H ) shows a minimum near 380 K.
It
is probable that this additional r e l a x a t i o n arises from interaction with electron magnetic moments.
I f the r e l a x a t i o n r e f l e c t s contact interaction
with mobile c a r r i e r s , then one expects the r a t i o T1 (D) [ ~_~12 T I ~ = Iv(D)] = 42.44
(7)
and, for a semiconducting sample, I/T1 = ¥2 N ~
(8)
where the number of c a r r i e r s , N, may be exponentially thermally activated• In Fig• 3 a solid l i n e has been drawn through the 92.5 MHz TI(H ) data for Sample V.
The upper solid l i n e is 42.44 times the lower TI(H) l i n e •
Equation
(8) applied to the data yields an a c t i v a t i o n energy of 37 meV. REFERENCES I)
R. A. Street, J. C. Knights, and D. K. Biegelsen, Phys. Rev. B18,1880(1978).
2)
D. J. Leopold, J. B. Boyce, P. A. Fedders, and R. E. Norberg, Phys. Rev. B 26, 6053 (1982).
3)
M. Mokarrsm and J. L. Ragle, J. Chem. Phys. 59, 2770 (1973). W. E. Carlos and P. C. Taylor, Phys. Rev. B 26, 3605 (1982).
4)
5)
W. E. Carlos and P. C. Taylor, private communication. P• A. Fedders, Phys. Rev. B 20, 2588 (1979). N. F. Ramsey, Molecular Beams (Oxford University Press, London, 1956),p. 235. 8) M. S. Conradi, K. Luszczynski,and R. E. Norberg, Phys. Rev. B 2_0_0,2594 (1979). 9) a. Van Kranendonk, Physica (Utrecht) 20, 871 (1954). I0) a. Van Kranendonk and M. B. Walker, Can. J. Phys. 46, 2441 (1968). 6) 7)