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The effects of linear strain on the electronic properties of glow discharge amorphous silicon
Journal of Non-Crystalline Solids 77 & 78 (1985)495-498 North-Holland, Amsterdam
495
TIIE EFFECTS OF LINEAR STRAIN ON THE ELECTRONIC PROPERTIES OF GLOW DISCHARGE AMORPHOUS SILICON M. HEINTZE and W.E. SPEAR
Carnegie Laboratory of Physics, U n i v e r s i t y of Dundee, Dundee, Scotland The c o n d u c t i v i t y of n- and p-type a-Si specimens has been i n v e s t i g a t e d as a function of t e n s i l e and compressive s t r a i n s . All changes were r e v e r s i b l e . For a given type of s t r a i n a u n i d i r e c t i o n a l movement o f ~ f takes place in both n- and p-type specimens. The dependence of the e l a s t o - c o n d u c t i v i t y on ~.-E~ can be i n t e r p r e t e d mainly in terms of changes in the c o n d u c t i v i t y p~e--~actor~ o . I.
INTRODUCTION In c r y s t a l l i n e semiconductors, such as Si or Ge, the e f f e c t of u n i - a x i a l
s t r a i n on the t r a n s p o r t p r o p e r t i e s is c l o s e l y r e l a t e d to the d e t a i l s of t h e i r band structure I and the experimental work in t h i s f i e l d has led to useful fundamental i n f o r m a t i o n . little
As f a r as a-semiconductors are concerned, comparatively
is known about the e f f e c t of s t r a i n on e l e c t r i c a l p r o p e r t i e s ;
previous
work 2,3 has been confined to evaporated f i l m s and i t appeared t h e r e f o r e of i n t e r e s t to return to t h i s
problem using w e l l - c h a r a c t e r i s e d material such as
glow discharge a-Si, in which the Fermi level p o s i t i o n can be c o n t r o l l e d throughout the m o b i l i t y gap. 2.
SPECIMENSAND EXPERIMENTAL ARRANGEMENTS Most of the experiments were c a r r i e d out on doped and undoped specimens,
between O.51Jm and 5~m t h i c k . slides f i t t e d
They were deposited on 2cm x 4.5cm Corning glass
at t h e i r centre with a I c m 2 i n t e r d i g i t a l electrode p a t t e r n .
imens were mounted in vacuum on the apparatus shown in f i g .
I.
Spec-
The s t a i n l e s s
steel shaft E, r o t a t i n g about an S
I
o f f - c e n t r e axis, applied a periodic
E
, t
,
i
~ I j
bending couple at about 3Hz to the clamped substrate and f i l m which could be r e l a t e d to a t e n s i l e s t r a i n S = mg/g across the c o n d u c t i v i t y cell.
For measurements under com-
pressive s t r a i n the s l i d e was reversed in the holder H. FIGURE 1 Experimental arrangements f o r applying a periodic strain.
using phase s e n s i t i v e detection
0022-3093/85/$03.30 © Elsevier Science Publishers B.V,
(North-Holland Physics Publishing Division)
Conductiv-
i t y measurements were c a r r i e d out
496
M. Heintze, I¢.E. Spear / The effects o f linear strain
f o r strains of up to 10-3 i
at room temperature the results were c l o s e l y
s i m i l a r to those from steady bending experiments.
All c o n d u c t i v i t y changes
were reversible and i t is u n l i k e l y that the moderate values of S introduced additional permanent defects.
In subsidiary experiments on O.Imm glass sub-
s t r a t e s , i t was deduced from the d i s t o r t i o n of the glass that deposited f i l m s were subject to an internal compressive strain of about 5 x 10-3 . 3.
EXPERIMENTAL RESULTS The results have been evaluated in terms of the e l a s t o - c o n d u c t i v i t y parameter
~.=
~ $
/xO-" o-
(1)
K is related to the n~eas~red conductance r a t i o ~ G / G by K = -(]/S)(~G/G)+(I+2~), where the Poisson r a t i o ~ ( ~ 0 . 2 f o r glass) accounts f o r the l a t e r a l change in specimen dimensions. Fig. 2 is a graph of~G/G vs. S f o r a l i g h t l y doped n-type specimen (ec-6f) o ~ 0.69eV and a heavily doped p-type sample (~c-ef)o ~ 1.55eV).
The
stress is applied in the d i r e c t i o n of current flow and S is p o s i t i v e f o r t e n s i l e and negative f o r compressive applied s t r a i n s . The graph indicates that f o r a g i v e n specimen K is i d e n t i c a l f o r both types of s t r a i n , but in a l l experiments i t has been found to be negative for n-type specimens and p o s i t i v e f o r p-type m a t e r i a l . 20
:/°
compressive -6
-/
I
[
u'
I
54x10-3
AG/G
-8
r
i-
:
n-type
'7'L;o, '
'
'
s'
-2 -3
~,
"1]
I
//.k,/.
0"4
OB
"~- I p-type
-5 0
1"2
1'6
(~c-Ef)o (eV) FIGURE 2 Change in conductance r a t i o ~ G / G with S f o r an n- and p-type specimen
FIGURE 3 Experimental K-values p l o t t e d against (~c-ef)o. Broken l i n e : calculated from eqns. (2) and (3) w i t h e s = O. 52eV/unit s t r a i n .
M. Heintze, W.E. Spear / The effects o f linear strain
497
The important conclusion is therefore that a tensile strain w i l l always moveEf towardsEc, both in n- and p-type a-Si, whereas compressive strain produces a ~ f in the opposite direction. I t should be noted that with the small observed conductance changes ~ e f ~ 10-3eV. Contrary to e a r l i e r results on evaporated a-Si 3, but in agreement with the work on a-Ge2,
K is found to depend on the angle 0 between current and S.
occurs at 8 = O, 180° , and Kmin at 90 ° and 270 ° . doping.
KII/K ~ 1 . 6 ,
K max depending on
In f i g . 3 K-values for a range of n- and p-type specimens are plotted against (Ec-Ef)o, determined from the activation energy of O~(T). The interesting features are: (i) the rapid change in sign of K at (6c-6f) o = 0.875eV, the centre of the mobility gap, ( i i ) the peaks at O.6eV and l.OeV, and ( i i i ) the rapid decrease in K when ~ f approaches the t a i l states.
Very similar
results have been obtained when Ef is moved by the f i e l d effect instead of by doping. 4.
DISCUSSION Neglecting any effect of the strain on carrier mobility, i t can be shown
from the normal expression for the activated conductivity that {< = -- ~ I<=
Cl(Ec_6~)o]
~
---r'Ctl~O'-o -~
i
~ ( z _ _
9 ) for n-type specimens, (~)
for
specimens.
K is therefore determined by the strain c o e f f i c i e n t =° r. = -~(ec-Ef)~S__ and by '
'~ I
(~cmF~ 10 5
I'
!
I
i
the dependence of the preexponential conductivity factor
I
on (ec-Ef) o. Fig. 4 shows a graph of log O~o vs. (Ec-Ef) ° based on experimental results from about
104 I
103
lO0 specimens produced in the same plasma unit. The graph emphasises the remarkably rapid changes i n ~ o between O.6eV and l.OeV, the
10 2 _ _
-
=
I
eNc.Pc'10 I I
I
O'2
'
I
OZ.,
0'6
II
0"8
reasons for which are not f u l l y understood. As
I
1"0
12
1"4 1"6 1£,c-Cf)o leVI
FIGURE 4 Dependence o f ~ n on (6 - ~ ) o ' from experimental results o~ a~out lO0 specimens.
~O = eNcHc exp (=~T/k), where ~ = -~(Ec-Ef)o/~T and eNc~c ~ 40(1)cm)- I , the ~-'o behaviour can formally be
M. Heintze, I¢.E. Spear / The effects o f linear strain
498
attributed to a large temperature coefficient ~ ,
varying rapidly with~c-~f
in the central region of the mobility gap. The results of f i g . 4 can be used to check the consistency of the analysis. The broken line in f i g . 3 shows the K-dependencecalculated from eqs. 2 and 3 I
for a constant ~s = O.52eV/unit strain.
The main features of the experimental
results are reproduced, demonstrating that the characteristic dependenceof K is largely determined b y e ,
particularly in the centre of the gap. The calculated
f i t can be improved by allowing ~s to have some dependenceonEf.
I t is appar-
ent that ~s w i l l have to decrease considerably as~f approaches the valence band t a i l states. We have shown that the effect of small externally applied strains can be accounted for by a unidirectional movemento f ~ f .
The r e v e r s i b i l i t y of the
measurements suggests that S causes primarily a perturbation in the disorder within the t a i l states, which could s l i g h t l y modulate their extent.
This in
turn w i l l affect the balance of the charge distribution in gap states and thus the Fermi level position.
I t is not surprising that the most pronounced effects
are observed when~f lies in the central region of the gap, because here even a small perturbation in the overlapping charge distribution can lead to the maximum movementof Ef. the magnitude o f ~ 6 f .
In this connection, prominent defect centres may determine I t could therefore be relevant that the peaks in f i g . 3
coincide almost exactly with the D° and D- energies recently determined from transient lifetime measurements4.
I f such an interpretation can be substan-
tiated, i t is possible that the close connection of the strain experiments to the coefficient ~ T ( i . e . f i g . 4) could lead towards a better understanding of the ~o problem. REFERENCES l) C.S. Smith, Phys. Rev. 94 (1954) 42; (1960) 149.
R.W. Keyes, Solid State Phys. II
2) R. Grigorovici and A. Devenyl, Proc. of the 9th International Conference on the Physics of Semiconductors, Moscow, 1968 (p. 1267). 3) W. Fuhs, Phys. Stat. Sol. A, lO, (1972) 201. 4) W.E. Spear, H.L. Steemers and P.G. LeComber, Phil. Mag. B 50 (1984) L33.
495
TIIE EFFECTS OF LINEAR STRAIN ON THE ELECTRONIC PROPERTIES OF GLOW DISCHARGE AMORPHOUS SILICON M. HEINTZE and W.E. SPEAR
Carnegie Laboratory of Physics, U n i v e r s i t y of Dundee, Dundee, Scotland The c o n d u c t i v i t y of n- and p-type a-Si specimens has been i n v e s t i g a t e d as a function of t e n s i l e and compressive s t r a i n s . All changes were r e v e r s i b l e . For a given type of s t r a i n a u n i d i r e c t i o n a l movement o f ~ f takes place in both n- and p-type specimens. The dependence of the e l a s t o - c o n d u c t i v i t y on ~.-E~ can be i n t e r p r e t e d mainly in terms of changes in the c o n d u c t i v i t y p~e--~actor~ o . I.
INTRODUCTION In c r y s t a l l i n e semiconductors, such as Si or Ge, the e f f e c t of u n i - a x i a l
s t r a i n on the t r a n s p o r t p r o p e r t i e s is c l o s e l y r e l a t e d to the d e t a i l s of t h e i r band structure I and the experimental work in t h i s f i e l d has led to useful fundamental i n f o r m a t i o n . little
As f a r as a-semiconductors are concerned, comparatively
is known about the e f f e c t of s t r a i n on e l e c t r i c a l p r o p e r t i e s ;
previous
work 2,3 has been confined to evaporated f i l m s and i t appeared t h e r e f o r e of i n t e r e s t to return to t h i s
problem using w e l l - c h a r a c t e r i s e d material such as
glow discharge a-Si, in which the Fermi level p o s i t i o n can be c o n t r o l l e d throughout the m o b i l i t y gap. 2.
SPECIMENSAND EXPERIMENTAL ARRANGEMENTS Most of the experiments were c a r r i e d out on doped and undoped specimens,
between O.51Jm and 5~m t h i c k . slides f i t t e d
They were deposited on 2cm x 4.5cm Corning glass
at t h e i r centre with a I c m 2 i n t e r d i g i t a l electrode p a t t e r n .
imens were mounted in vacuum on the apparatus shown in f i g .
I.
Spec-
The s t a i n l e s s
steel shaft E, r o t a t i n g about an S
I
o f f - c e n t r e axis, applied a periodic
E
, t
,
i
~ I j
bending couple at about 3Hz to the clamped substrate and f i l m which could be r e l a t e d to a t e n s i l e s t r a i n S = mg/g across the c o n d u c t i v i t y cell.
For measurements under com-
pressive s t r a i n the s l i d e was reversed in the holder H. FIGURE 1 Experimental arrangements f o r applying a periodic strain.
using phase s e n s i t i v e detection
0022-3093/85/$03.30 © Elsevier Science Publishers B.V,
(North-Holland Physics Publishing Division)
Conductiv-
i t y measurements were c a r r i e d out
496
M. Heintze, I¢.E. Spear / The effects o f linear strain
f o r strains of up to 10-3 i
at room temperature the results were c l o s e l y
s i m i l a r to those from steady bending experiments.
All c o n d u c t i v i t y changes
were reversible and i t is u n l i k e l y that the moderate values of S introduced additional permanent defects.
In subsidiary experiments on O.Imm glass sub-
s t r a t e s , i t was deduced from the d i s t o r t i o n of the glass that deposited f i l m s were subject to an internal compressive strain of about 5 x 10-3 . 3.
EXPERIMENTAL RESULTS The results have been evaluated in terms of the e l a s t o - c o n d u c t i v i t y parameter
~.=
~ $
/xO-" o-
(1)
K is related to the n~eas~red conductance r a t i o ~ G / G by K = -(]/S)(~G/G)+(I+2~), where the Poisson r a t i o ~ ( ~ 0 . 2 f o r glass) accounts f o r the l a t e r a l change in specimen dimensions. Fig. 2 is a graph of~G/G vs. S f o r a l i g h t l y doped n-type specimen (ec-6f) o ~ 0.69eV and a heavily doped p-type sample (~c-ef)o ~ 1.55eV).
The
stress is applied in the d i r e c t i o n of current flow and S is p o s i t i v e f o r t e n s i l e and negative f o r compressive applied s t r a i n s . The graph indicates that f o r a g i v e n specimen K is i d e n t i c a l f o r both types of s t r a i n , but in a l l experiments i t has been found to be negative for n-type specimens and p o s i t i v e f o r p-type m a t e r i a l . 20
:/°
compressive -6
-/
I
[
u'
I
54x10-3
AG/G
-8
r
i-
:
n-type
'7'L;o, '
'
'
s'
-2 -3
~,
"1]
I
//.k,/.
0"4
OB
"~- I p-type
-5 0
1"2
1'6
(~c-Ef)o (eV) FIGURE 2 Change in conductance r a t i o ~ G / G with S f o r an n- and p-type specimen
FIGURE 3 Experimental K-values p l o t t e d against (~c-ef)o. Broken l i n e : calculated from eqns. (2) and (3) w i t h e s = O. 52eV/unit s t r a i n .
M. Heintze, W.E. Spear / The effects o f linear strain
497
The important conclusion is therefore that a tensile strain w i l l always moveEf towardsEc, both in n- and p-type a-Si, whereas compressive strain produces a ~ f in the opposite direction. I t should be noted that with the small observed conductance changes ~ e f ~ 10-3eV. Contrary to e a r l i e r results on evaporated a-Si 3, but in agreement with the work on a-Ge2,
K is found to depend on the angle 0 between current and S.
occurs at 8 = O, 180° , and Kmin at 90 ° and 270 ° . doping.
KII/K ~ 1 . 6 ,
K max depending on
In f i g . 3 K-values for a range of n- and p-type specimens are plotted against (Ec-Ef)o, determined from the activation energy of O~(T). The interesting features are: (i) the rapid change in sign of K at (6c-6f) o = 0.875eV, the centre of the mobility gap, ( i i ) the peaks at O.6eV and l.OeV, and ( i i i ) the rapid decrease in K when ~ f approaches the t a i l states.
Very similar
results have been obtained when Ef is moved by the f i e l d effect instead of by doping. 4.
DISCUSSION Neglecting any effect of the strain on carrier mobility, i t can be shown
from the normal expression for the activated conductivity that {< = -- ~ I<=
Cl(Ec_6~)o]
~
---r'Ctl~O'-o -~
i
~ ( z _ _
9 ) for n-type specimens, (~)
for
specimens.
K is therefore determined by the strain c o e f f i c i e n t =° r. = -~(ec-Ef)~S__ and by '
'~ I
(~cmF~ 10 5
I'
!
I
i
the dependence of the preexponential conductivity factor
I
on (ec-Ef) o. Fig. 4 shows a graph of log O~o vs. (Ec-Ef) ° based on experimental results from about
104 I
103
lO0 specimens produced in the same plasma unit. The graph emphasises the remarkably rapid changes i n ~ o between O.6eV and l.OeV, the
10 2 _ _
-
=
I
eNc.Pc'10 I I
I
O'2
'
I
OZ.,
0'6
II
0"8
reasons for which are not f u l l y understood. As
I
1"0
12
1"4 1"6 1£,c-Cf)o leVI
FIGURE 4 Dependence o f ~ n on (6 - ~ ) o ' from experimental results o~ a~out lO0 specimens.
~O = eNcHc exp (=~T/k), where ~ = -~(Ec-Ef)o/~T and eNc~c ~ 40(1)cm)- I , the ~-'o behaviour can formally be
M. Heintze, I¢.E. Spear / The effects o f linear strain
498
attributed to a large temperature coefficient ~ ,
varying rapidly with~c-~f
in the central region of the mobility gap. The results of f i g . 4 can be used to check the consistency of the analysis. The broken line in f i g . 3 shows the K-dependencecalculated from eqs. 2 and 3 I
for a constant ~s = O.52eV/unit strain.
The main features of the experimental
results are reproduced, demonstrating that the characteristic dependenceof K is largely determined b y e ,
particularly in the centre of the gap. The calculated
f i t can be improved by allowing ~s to have some dependenceonEf.
I t is appar-
ent that ~s w i l l have to decrease considerably as~f approaches the valence band t a i l states. We have shown that the effect of small externally applied strains can be accounted for by a unidirectional movemento f ~ f .
The r e v e r s i b i l i t y of the
measurements suggests that S causes primarily a perturbation in the disorder within the t a i l states, which could s l i g h t l y modulate their extent.
This in
turn w i l l affect the balance of the charge distribution in gap states and thus the Fermi level position.
I t is not surprising that the most pronounced effects
are observed when~f lies in the central region of the gap, because here even a small perturbation in the overlapping charge distribution can lead to the maximum movementof Ef. the magnitude o f ~ 6 f .
In this connection, prominent defect centres may determine I t could therefore be relevant that the peaks in f i g . 3
coincide almost exactly with the D° and D- energies recently determined from transient lifetime measurements4.
I f such an interpretation can be substan-
tiated, i t is possible that the close connection of the strain experiments to the coefficient ~ T ( i . e . f i g . 4) could lead towards a better understanding of the ~o problem. REFERENCES l) C.S. Smith, Phys. Rev. 94 (1954) 42; (1960) 149.
R.W. Keyes, Solid State Phys. II
2) R. Grigorovici and A. Devenyl, Proc. of the 9th International Conference on the Physics of Semiconductors, Moscow, 1968 (p. 1267). 3) W. Fuhs, Phys. Stat. Sol. A, lO, (1972) 201. 4) W.E. Spear, H.L. Steemers and P.G. LeComber, Phil. Mag. B 50 (1984) L33.