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Analysis of SCLC curves in a-Si:H by a new direct method
Journal of Non-CrystallineSolids 77 & 78 (1985) 347-350 North-Holland,Amsterdam
347
ANALYSIS OF SCLC CURVES IN a-Si:H BY A NEW DIRECT METHOD
C. MANFREDOTTI, L. MONTALDI I s t i t u t o di Fisica Superiore, Corso M. D'Azeglio 46, I0125 Torino, I t a l y and S. GALASSINI Dipartimento di Fisica, Via Arnesano, 73100 Lecce, I t a l y By this method, density-of-states (DOS) d i s t r i b u t i o n is calculated d i r e c t l y from derivatives of I-V SCLC curves, under reasonable assumptions and without a-priori hypothesis concerning DOS d i s t r i b u t i o n i t s e l f . The method is applied to LPCVD a-Si:H films and a certain s i m i l a r i t y of conduction band t a i l with GD samples is found. The DOS d i s t r i b u t i o n seems to be thickness-dependent. I. INTRODUCTION SCLC has been proved to be a good technique for investigation of DOS d i s t r i bution in the mobility gap of a-Si. Generally, GD a-Si:H films are used in n+.i.n+ geometry and a-priori models for DOS are assumed in data analysis, p a r t i c u l a r l y + of exponential type. A precise control of n - i interface is clearly needed, in order to define the electrical sample thickness, together with the certainty that Fermi level EF lies r e a l l y in band t a i l s . In the present work, a different approach is t r i e d I which leads d i r e c t l y to DOS d i s t r i b u t i o n , whichever i t is, under normal SCLC assumptions ( mobility and trap density s p a t i a l l y homogeneous,e l e c t r i c a l length l bias-independent ). This approach has been applied to LPCVD a-Si films obtained by SiH4 and Si2H6 p y r o l i sis at r e l a t i v e l y low temperatures 2. 2. THE METHOD Neglecting diffusion currents and starting from Poisson's equation under normal SCLC conditions, the following relationships are obtained for free electron density
at the anode na l
d(I/j)
na : e~ d(Vl.-~)3 and for the t o t a l electrical charge density at the anode p c d d(V/j 2 ) p a 12 d ( I / j ) d(I/j) 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
(I)
(2)
C Manfredotti et al. / Analysis o f SCLC curves
348
Eq.(1) is used to obtain Fermi level at the anode EF N kT c EF = kT In - - ~ a where Nc = 102] cm-3eV-I in the conduction band states density and EF is taken from m o b i l i t y edge Ec. By d i f f e r e n t i a t i n g
Pa with respect to EF, under the hy-
pothesis t h a t trapped and i n j e c t e d c a r r i e r concentrations are p r a c t i c a l l y equal and much l a r g e r than f r e e c a r r i e r c o n c e n t r a t i o n , and assuming as usual a stepwise Fermi f u n c t i o n , DOS d i s t r i b u t i o n g(E) is e a s i l y obtained. Obviously, g(E), which requires a d i f f e r e n t i a t i o n
of a second-order d e r i v a t i v e , w i l l
show f l u c -
t u a t i o n s and, consequently, a p a r t i c u l a r smoothing procedure has been used 3 2 which searches f o r a minimum s t r u c t u r e g(E) g i v i n g a value of p a × compatible with the value determined by Eq. (2). As i t could be e a s i l y observed, the method needs a value f o r ~ and N and a cerc t a i n sample homogeneity, in order to extend the r e s u l t s to the whole f i l m . The first
two c o n d i t i o n s , however, enter only in EF determination, which is r e p l a -
ced by the t r a p level energy E as p r e v i o u s l y v e r i f i e d 4. I t may be noted t h a t the present method, in i t s s i m p l i f i e d version n
a
jl 2~ V
2
(3)
2EV
= 12
(4)
is exactly the step-by-step method of den Bo~r5 and that Eqs. (3) and (4) are practically equal to Eqs. (7) and (9) of ref. 4. 3. EXPERIMENTAL LPCVD a-Si f i l m s are deposited on n c-Si 3" substrates (
of the oder of Rcm)
which are e s s e n t i a l l y used as i n j e c t i n g e l e c t r o n contacts. All the deposition d e t a i l s are given in r e f . 2. Evaporated Al dots are used both as anodes and as contacts on c - S i . The good behaviour of contacts is demonstrated by the ohmic c h a r a c t e r i s t i c s at low voltages, by the high values of current density obtained at r e l a t i v e l y
low e l e c t r i c a l
fields,
which well compare with l i t e r a t u r e data 4
and by the absence of breakdowns even of small e x t e n t . As a matter of f a c t , the scaling law j / d = f(V/d 2) independently of thickness d, is reasonably s a t i s f i e d f o r sample thicknesses l a r g e r than 0.6 um ( see Fig. 1 ). Below t h a t value, the
C Manfredotti et al. / Analysis o f SCLCcurves
349
J/d ( A Cm-3 )
103
SiH 4 A A A ~
8(E) (cm-3eV"I )
o•
i~
lO19
102
•
~
~
°°
I0
/:
~o
o.~
oA •A •
.• e,A
o° •
•
1018
I
;
• •
% •
•
•
i0 -2
• •
o~o o
ee •
•
•
•
o•
o
•• o • e'
I
lO6
• o°
1017
o
%
i
•A
.6
•
%
I
iOI0
; %0 o°
~ d:1.15um
°ooo• I
I
V/d2 (Vcm-2)
• • •
•
o d:0.6.m o
o o
1016 I
• •
•
o 1.15 .m
108
#
O~rO
o
•
~m
•
d=0 33~. ~e d=O.17."
•
o
•
~m
%
eeee. el • •
o o o o• o o o o • o
• .33 ~m
• i0 -3
.17
• • • •
•'~ e . 1 1 i~m
/
•
e o
•
i0 "I o° • o°o o
•
O&
• o° • o° o•
l
d=O.llum
%
o•
0.4
I
0.5
I
0.6
i
ECeV}
Fig. 1 Fig. 2 The s c a l i n g law f o r samples obtained from DOS d i s t r i b u t i o n g(E) f o r samples of SiH 4 at 500°C in d i f f e r e n t runs. The v a l u - d i f f e r e n t thicknesses obtained from es of d are determined by a t a l y s t e p . SiH 4 at 500°C. d e v i a t i o n from c o r r e c t behaviour seems to increase with decreasing thickness. In our view, since other e l e c t r i c a l
p r o p e r t i e s have been checked to be thickness
independent ( e.g. m o b i l i t y ), t h i s f a c t could be explained by taking i n t o account t h a t v o l t a g e drop at the cathode is estimated to be 0.4 V and i t extends up to 0.2 ~m : t h e r e f o r e ,
samples t h i n n e r than 0.6 ~m s t a r t to be non-homogeneous
with respect to Fermi l e v e l p o s i t i o n in the m o b i l i t y gap. 4. RESULTS AND DISCUSSION The most typical results obtained for films deposited at 500°C from SiH4 are reported in Fig. 2. Three facts seem to be clear : l) DOS distribution for thicker samples resemble very much to FE data6 for GD films deposited at 300°C. The peak increases of importance for thinner samples as the mean g(E) value. FE data show a peak at 0.4 eV: the deviation from this value, i f not a physical one, may be related to Eq. (1) which is used to calculate EF. I f ~ is lower, na increases and consequently EF gets nearer to Ec. Hall mobility 2 in our samples is relatively thickness-independent and i t ranges from O.l to l cm2V-Is- l . The lowest value
350
C. Manfredotti et al. /Analysis o f SCLC curves
3.0 Si2H6
,+~ 2.0
°°oOooo
,?,
~
g~eak(E (c•" eV-l )
Td= 460°C d = 2000 ,~
SiH4
• gpeak(E) fro• SCLC • Spin density N • s normalized to gpea
Ns(C•-3
101
°°°o•
0.5 0.4 0.3
••
1018
\~'--..
°°OOoo/
0.2
I 0.5
l 0.55
I
l
0.6
E(eV)
Fig. 3 Typical DOS d i s t r i b u t i o n for Si2H6 samples
]017
I
thickness
while the peak of g(E) ' becomes more evident. The same p e a k
•
1016
has been used in the present work; 2) g(EF) increases with decreasing
,
o.5
I
i.
d(,•)
Fig. 4 g as derived from Fig 2 and N. eak . " . n~rmallzed to g . as a functlon of thickness d. peak
seem to be less evident in Si2H6 samples ( Fig. 3 ). This r e l a t i v e behaviour is in good agreement with ESR results on the same samples as a function of thickness ( see Fig. 4 ). Constant values are reached above 0.6 ~m. These results can be acconuted for only assuming a non-homogeneoussample, with different dangling bonds densities at the surface and in the bulk. Therefore, thinner samples are more defective; 3) values of g(EF) are very low, while spin densities as deduced from ESR measurements are larger than lO19 cm-3. Therefore, g(EF) value cannot be always used as a key parameter in order to get an idea of f i l m q u a l i t y . In our samples, D states at the midgap are l i k e l y contributing to ESR signal. Finally, band t a i l s in the 0.4-0.7 eV region show kT values of 30 - 60 meV. C
REFERENCES I) C. Manfredotti, C.DeBlasi and S.Galassini, Phys. St. Sol. (a)36 (1976) 569 2) C. Manfredotti, "LPCVD amorphous s i l i c o n " , 6th Int. Conf. on Thin Films, Stockolm, August ]984. 3) B. C. Cook, Nucl. Instr. Methods 24 (1963) 256. 4) K.D.Mackenzie, P.G. LeComber and W.E.Spear, Phil.Mag. B46 (1982) 377. 5) W. den Bo~r, J. Phys. Paris 42, C4 (1982) 451. 6) A. Madan, P.G. Le Comber and W.E. Spear, J. Non Cryst. Solids 20 (1976) 239.
347
ANALYSIS OF SCLC CURVES IN a-Si:H BY A NEW DIRECT METHOD
C. MANFREDOTTI, L. MONTALDI I s t i t u t o di Fisica Superiore, Corso M. D'Azeglio 46, I0125 Torino, I t a l y and S. GALASSINI Dipartimento di Fisica, Via Arnesano, 73100 Lecce, I t a l y By this method, density-of-states (DOS) d i s t r i b u t i o n is calculated d i r e c t l y from derivatives of I-V SCLC curves, under reasonable assumptions and without a-priori hypothesis concerning DOS d i s t r i b u t i o n i t s e l f . The method is applied to LPCVD a-Si:H films and a certain s i m i l a r i t y of conduction band t a i l with GD samples is found. The DOS d i s t r i b u t i o n seems to be thickness-dependent. I. INTRODUCTION SCLC has been proved to be a good technique for investigation of DOS d i s t r i bution in the mobility gap of a-Si. Generally, GD a-Si:H films are used in n+.i.n+ geometry and a-priori models for DOS are assumed in data analysis, p a r t i c u l a r l y + of exponential type. A precise control of n - i interface is clearly needed, in order to define the electrical sample thickness, together with the certainty that Fermi level EF lies r e a l l y in band t a i l s . In the present work, a different approach is t r i e d I which leads d i r e c t l y to DOS d i s t r i b u t i o n , whichever i t is, under normal SCLC assumptions ( mobility and trap density s p a t i a l l y homogeneous,e l e c t r i c a l length l bias-independent ). This approach has been applied to LPCVD a-Si films obtained by SiH4 and Si2H6 p y r o l i sis at r e l a t i v e l y low temperatures 2. 2. THE METHOD Neglecting diffusion currents and starting from Poisson's equation under normal SCLC conditions, the following relationships are obtained for free electron density
at the anode na l
d(I/j)
na : e~ d(Vl.-~)3 and for the t o t a l electrical charge density at the anode p c d d(V/j 2 ) p a 12 d ( I / j ) d(I/j) 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
(I)
(2)
C Manfredotti et al. / Analysis o f SCLC curves
348
Eq.(1) is used to obtain Fermi level at the anode EF N kT c EF = kT In - - ~ a where Nc = 102] cm-3eV-I in the conduction band states density and EF is taken from m o b i l i t y edge Ec. By d i f f e r e n t i a t i n g
Pa with respect to EF, under the hy-
pothesis t h a t trapped and i n j e c t e d c a r r i e r concentrations are p r a c t i c a l l y equal and much l a r g e r than f r e e c a r r i e r c o n c e n t r a t i o n , and assuming as usual a stepwise Fermi f u n c t i o n , DOS d i s t r i b u t i o n g(E) is e a s i l y obtained. Obviously, g(E), which requires a d i f f e r e n t i a t i o n
of a second-order d e r i v a t i v e , w i l l
show f l u c -
t u a t i o n s and, consequently, a p a r t i c u l a r smoothing procedure has been used 3 2 which searches f o r a minimum s t r u c t u r e g(E) g i v i n g a value of p a × compatible with the value determined by Eq. (2). As i t could be e a s i l y observed, the method needs a value f o r ~ and N and a cerc t a i n sample homogeneity, in order to extend the r e s u l t s to the whole f i l m . The first
two c o n d i t i o n s , however, enter only in EF determination, which is r e p l a -
ced by the t r a p level energy E as p r e v i o u s l y v e r i f i e d 4. I t may be noted t h a t the present method, in i t s s i m p l i f i e d version n
a
jl 2~ V
2
(3)
2EV
= 12
(4)
is exactly the step-by-step method of den Bo~r5 and that Eqs. (3) and (4) are practically equal to Eqs. (7) and (9) of ref. 4. 3. EXPERIMENTAL LPCVD a-Si f i l m s are deposited on n c-Si 3" substrates (
of the oder of Rcm)
which are e s s e n t i a l l y used as i n j e c t i n g e l e c t r o n contacts. All the deposition d e t a i l s are given in r e f . 2. Evaporated Al dots are used both as anodes and as contacts on c - S i . The good behaviour of contacts is demonstrated by the ohmic c h a r a c t e r i s t i c s at low voltages, by the high values of current density obtained at r e l a t i v e l y
low e l e c t r i c a l
fields,
which well compare with l i t e r a t u r e data 4
and by the absence of breakdowns even of small e x t e n t . As a matter of f a c t , the scaling law j / d = f(V/d 2) independently of thickness d, is reasonably s a t i s f i e d f o r sample thicknesses l a r g e r than 0.6 um ( see Fig. 1 ). Below t h a t value, the
C Manfredotti et al. / Analysis o f SCLCcurves
349
J/d ( A Cm-3 )
103
SiH 4 A A A ~
8(E) (cm-3eV"I )
o•
i~
lO19
102
•
~
~
°°
I0
/:
~o
o.~
oA •A •
.• e,A
o° •
•
1018
I
;
• •
% •
•
•
i0 -2
• •
o~o o
ee •
•
•
•
o•
o
•• o • e'
I
lO6
• o°
1017
o
%
i
•A
.6
•
%
I
iOI0
; %0 o°
~ d:1.15um
°ooo• I
I
V/d2 (Vcm-2)
• • •
•
o d:0.6.m o
o o
1016 I
• •
•
o 1.15 .m
108
#
O~rO
o
•
~m
•
d=0 33~. ~e d=O.17."
•
o
•
~m
%
eeee. el • •
o o o o• o o o o • o
• .33 ~m
• i0 -3
.17
• • • •
•'~ e . 1 1 i~m
/
•
e o
•
i0 "I o° • o°o o
•
O&
• o° • o° o•
l
d=O.llum
%
o•
0.4
I
0.5
I
0.6
i
ECeV}
Fig. 1 Fig. 2 The s c a l i n g law f o r samples obtained from DOS d i s t r i b u t i o n g(E) f o r samples of SiH 4 at 500°C in d i f f e r e n t runs. The v a l u - d i f f e r e n t thicknesses obtained from es of d are determined by a t a l y s t e p . SiH 4 at 500°C. d e v i a t i o n from c o r r e c t behaviour seems to increase with decreasing thickness. In our view, since other e l e c t r i c a l
p r o p e r t i e s have been checked to be thickness
independent ( e.g. m o b i l i t y ), t h i s f a c t could be explained by taking i n t o account t h a t v o l t a g e drop at the cathode is estimated to be 0.4 V and i t extends up to 0.2 ~m : t h e r e f o r e ,
samples t h i n n e r than 0.6 ~m s t a r t to be non-homogeneous
with respect to Fermi l e v e l p o s i t i o n in the m o b i l i t y gap. 4. RESULTS AND DISCUSSION The most typical results obtained for films deposited at 500°C from SiH4 are reported in Fig. 2. Three facts seem to be clear : l) DOS distribution for thicker samples resemble very much to FE data6 for GD films deposited at 300°C. The peak increases of importance for thinner samples as the mean g(E) value. FE data show a peak at 0.4 eV: the deviation from this value, i f not a physical one, may be related to Eq. (1) which is used to calculate EF. I f ~ is lower, na increases and consequently EF gets nearer to Ec. Hall mobility 2 in our samples is relatively thickness-independent and i t ranges from O.l to l cm2V-Is- l . The lowest value
350
C. Manfredotti et al. /Analysis o f SCLC curves
3.0 Si2H6
,+~ 2.0
°°oOooo
,?,
~
g~eak(E (c•" eV-l )
Td= 460°C d = 2000 ,~
SiH4
• gpeak(E) fro• SCLC • Spin density N • s normalized to gpea
Ns(C•-3
101
°°°o•
0.5 0.4 0.3
••
1018
\~'--..
°°OOoo/
0.2
I 0.5
l 0.55
I
l
0.6
E(eV)
Fig. 3 Typical DOS d i s t r i b u t i o n for Si2H6 samples
]017
I
thickness
while the peak of g(E) ' becomes more evident. The same p e a k
•
1016
has been used in the present work; 2) g(EF) increases with decreasing
,
o.5
I
i.
d(,•)
Fig. 4 g as derived from Fig 2 and N. eak . " . n~rmallzed to g . as a functlon of thickness d. peak
seem to be less evident in Si2H6 samples ( Fig. 3 ). This r e l a t i v e behaviour is in good agreement with ESR results on the same samples as a function of thickness ( see Fig. 4 ). Constant values are reached above 0.6 ~m. These results can be acconuted for only assuming a non-homogeneoussample, with different dangling bonds densities at the surface and in the bulk. Therefore, thinner samples are more defective; 3) values of g(EF) are very low, while spin densities as deduced from ESR measurements are larger than lO19 cm-3. Therefore, g(EF) value cannot be always used as a key parameter in order to get an idea of f i l m q u a l i t y . In our samples, D states at the midgap are l i k e l y contributing to ESR signal. Finally, band t a i l s in the 0.4-0.7 eV region show kT values of 30 - 60 meV. C
REFERENCES I) C. Manfredotti, C.DeBlasi and S.Galassini, Phys. St. Sol. (a)36 (1976) 569 2) C. Manfredotti, "LPCVD amorphous s i l i c o n " , 6th Int. Conf. on Thin Films, Stockolm, August ]984. 3) B. C. Cook, Nucl. Instr. Methods 24 (1963) 256. 4) K.D.Mackenzie, P.G. LeComber and W.E.Spear, Phil.Mag. B46 (1982) 377. 5) W. den Bo~r, J. Phys. Paris 42, C4 (1982) 451. 6) A. Madan, P.G. Le Comber and W.E. Spear, J. Non Cryst. Solids 20 (1976) 239.