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Determination of the density of states in amorphous silicon from thermostimulated conductivity measurements
Journal of Non-Crystalline Solids 97&98 (1987) 711-714 North-Holland, Amsterdam
711
DETERMINATION OF THE DENSITY OF STATES IN AMORPHOUSSILICON FROM THERMOSTIMULATED CONDUCTIVITY MEASUREMENTS G. LANDWEER, R. SCHREUTELKAMP, H. SIMONS, J. BEZEMER and W.F. van der WEG Department of Atomic and I n t e r f a c e Physics, U n i v e r s i t y of Utrecht, P.O. Box 80.000, 3508 TA Utrecht, The Netherlands The density of states between the Fermi l e v e l and the conduction band in glow-discharge a-Si:H has been determined by measuring thermostimulated currents and photo-currents simultaneously. During the TSC measurements the sample is exposed to l i g h t pulses of low i n t e n s i t y . From the measurements both g(E) and the ~ product can be c a l c u l a t e d . Results are shown from samples grown at d i f f e r e n t glow-discharge powers. Minimum values of g(E) at 0.3 eV below Ec range from 1016 to 1017 eV- l cm-~.
i.
INTRODUCTION The increase in c o n d u c t i v i t y by c a r r i e r s released from traps can be used t o
determine the d e n s i t y of gap states. I f gap states are f i l l e d
at a low tempera-
t u r e , the thermostimulated c o n d u c t i v i t y (TSC) during the heating of the sample is a measure f o r the d i s t r i b u t i o n of traps in the gap. A thorough d e s c r i p t i o n of TSC measurements has been given by Simmons et a l . l ) . T o determine the number of released c a r r i e r s from TSC, the ~z product of the c a r r i e r s has to be known. Zhu and Fritzsche 2) showed how t h i s product can be found from p h o t o c o n d u c t i v i t y measurements. These measurements are r a t h e r e x t e n s i v e , since the ~T product depends on the temperature as well as on the trapped c a r r i e r d i s t r i b u t i o n
in
the bandgap. We suggest here a technique to combine thermostimulated and photoinduced current measurements. Although both electrons and holes c o n t r i b u t e to the TSC, we suppose t h a t the influence of the hole t r a n s p o r t in i n t r i n s i c
amorphous s i l i c o n can be neglected.
In t h a t case, TSC y i e l d s the d e n s i t y of states in the bandgap between the conduction band and the Fermi l e v e l . 2.
DESCRIPTION OF THE METHOD 1.1. P r i n c i p l e In our experiments we used samples with coplanar electrodes which were 0.50
mm apart. Before a TSC measurement, the samples are kept at a low temperature and exposed to l i g h t to f i l l
the gap states. The i n t e n s i t y and the duration of
the i l l u m i n a t i o n may vary in a wide range to o b t a i n , a f t e r a c e r t a i n r e l a x a t i o n time, an occupation of t r a p states which is l a r g e l y independent of the t o t a l photon f l u x . The energy range of f i l l e d
traps is characterized by quasi-Fermi
0022-3093/87/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
712
G. Landweer et al. / Determination of the density of states
l e v e l s which l i e close to the m o b i l i t y edges. By increasing the temperature at a constant r a t e of about 5 K/min, trapped electrons are released continuously u n t i l the quasi-Fermi l e v e l s reach the Fermi l e v e l . To determine the number of released electrons from a measured TSC curve, Zhu and Fritzsche 2) used steady state photocurrent measurements at various temperatures.
In our method, low i n t e n s i t y l i g h t pulses are appJied at r e g u l a r time
i n t e r v a l s during the measurement o f a TSC curve. The d u r a t i o n of a l i g h t pulse is between 0.01 and i second. The induced current pulse, which is superimposed on the thermostimulated c u r r e n t , has a length of 30 s or less, depending on the sample p r o p e r t i e s . Tests have shown t h a t these l i g h t pulses do not d i s t u r b the l e v e l of the TSC curve between the photocurrent pulses. I f the number of the absorbed photons is known, the number of released c a r r i e r s can be found r a t h e r e a s i l y by comparing the i n t e g r a t e d thermostimulated current during a small time i n t e r v a l with the area of the photocurrent pulse. Figure 1 shows schematically a part of a TSC curve and a photocurrent pulse. I f we assume t h a t the i n i t i a l
occupation function of the traps equals u n i t y ,
the d e n s i t y of states f o l l o w s from the number of released c a r r i e r s w i t h i n a small energy i n t e r v a l AE scanned in a time i n t e r v a l At:
g(E)AE = (N/v)(A1/A2). (I) Here N is the number of absorbed photons and v is the volume of the sample. The areas AI and A2 are defined in f i g u r e 1. From the p h o t o - c o n d u c t i v i t y also a ~T product can be found: 2 A2 = pTeNV/I ,
(2)
with 1 the distance between the electrodes and V the applied v o l t a g e . A d e f i n i t i o n o f ~ and T is given in section 1.3.
I
T
'
'
'
'
I
'
'
'
'
I
'
-0.2 EM,
eV
-0.4 o =o
-0.6
ou) F-
-0.8
<- At ->
Time - - > FIGURE 1 TSC-curve with a photo-current peak o f area A2. The integrated TSC current in At is denoted by AI .
Temperature, K
FIGURE 2 Energy o f maximum TSC, EM, versus the temperature T. The s~arting temperature is 80 K and B is 5 K/min.
G. Landweer et al. / Determination of the density of states
713
1.2. The energy of maximum TSC, EM Simmons et a l . 1) have shown t h a t during a TSC experiment only trapped carr i e r s are released from a small energy range around EM, determined by a s t r o n g l y peaked function P(E,T) with a width of 2kT.
The maximum of t h i s
function is found at the energy EM = -0.967 kT In(5ZVe/B ) +0.017,
(3)
with B the heating rate in K/s and Ue an e f f e c t i v e attempt to escape frequency expressed in s " I . The numbers in (3) depend somewhat upon the s t a r t i n g temperat u r e , which was 80 K in our experiments. With ~EM/Bt = B~EM/3T formula (1) y i e l d s : g(E) = AIN/{A2~tvBK(O.967) In (52re/B)}.
(4)
1.3. Attempt-to-escape frequency To determine g(E), the non-retrapping model o f Simmons et a l . I) was used, in which the release o f c a r r i e r s is described by an attempt-to-escape frequency ~0' The c o n d u c t i v i t y however is considered to be governed by a m u l t i p l e trapping process. For t h a t reason a c o r r e c t i o n f a c t o r has to be introduced to account f o r the mean number of retrapping events m before recombination.
This
y i e l d s the e f f e c t i v e attempt-to-escape frequency ~e = vo/m" The value of v e is e x p e r i m e n t a l l y found by assuming t h a t EM = EF at the temperature where the thermostimulated current becomes small compared to the dark c o n d u c t i v i t y , lhe a c t i v a t i o n energy of the dark c o n d u c t i v i t y at t h a t temperature gives EF. The f a c t o r m can also be defined as the r a t i o of the recombination l i f e t i m e and the mean l i f e t i m e in the conduction band between t r a p p i n g , m = T/T t . The m o b i l i t y ~, mentioned before, is the microscopic m o b i l i t y . Misra et a l . 3) made c a l c u l a t i o n s f o r the TSC based on a m u l t i p l e trapping model in which the r a t i o of the number of electrons in the conduction band and the number of electrons in the trap states is given by nc/n : {Nc/g(E )} exp(-E/kT).
(5)
Their r e s u l t y i e l d s the TSC as a function o f g(E), ~, T and Nc. This Nc is the d e n s i t y of states in the lower part of the conduction band. They derived t h a t ve(E ) = Ncl~g(E ) must hold to bring the non-trapping model in agreement with t h e i r m u l t i p l e
(6)
trapping model. In our experiment we used a constant value f o r re, determined at EF. l his seems to be a reasonable approximation, moreover since g (E) in f o r mula (4) is r a t h e r i n s e n s i t i v e to changes in v e. From the energy o f the Fermi l e v e l , s u b s t i t u t e d f o r EM in formula (3) we found v e to be of the order of I07/s. 2.
EXPERIMENTSAND DISCUSSION To i l l u s t r a t e
of i n t r i n s i c
the method, r e s u l t s are shown of measurements on four samples
a-Si l a y e r s , l he layers were deposited at four d i f f e r e n t glow-
714
G. Landweer et aL / Determination of the density of states
discharge powers, 5, 10, 20 and 40 W. The growth rates amounted to 0.58, 0.86, 1.08 and 1.52 nm/s, respectively. Figure 3 shows the density of states in the energy range of 0.15 to 0.65 eV below the conduction band as calculated from our TSC measurementswith formula (4). The sample grown at 5 W has the lowest number of gap states. This may indicate that at a higher power more damage in the layer is caused by the ion bombardement from the glow-discharge. The samples are supposed to be of a rather good quality. An oxygen content of less than 0.1% was found from ERD measurements. In layers with more contamination a higher density of states was found. Figure 4 shows the ~T product of the same layers as a function of the temperature. As d i s t i n c t from the results of Zhu and Fritzsche2), our values of uT decrease continuously with lower temperature. We do not observe the increase in ~T below 250 K which is associated with thermal quenching of photoconductivity. We conclude that TSC measurement is a relatively easy way to determine the density of states, which is an important aspect of the quality of a-Si:H mat e r i a l . The method is limited to a part of the bandgap. Starting at lower temperatures, values closer to the conduction band can be found. The Fermi level can not be reached however within about 0.1 eV or several kT, which is the temperature r e s o l u t i o n of the method. 19
|
'
r
,
I
I
I
I
r
|
'
W2owow
T>
%-5 x
W
i
®~®
/ AAAA /
15
,~ 4 0 W
L i l i l i l ~ ' l i l l
-0.6
-0.4 -0.2 E, eV
FIGURE 3 Density of states of four samples grown at different powers which are indicated in fig. 4. The straight line symbolizes the conduction band t a i l . In the figure EC' is 0 eV.
X®
-7 [
®
~'
ll x
® i. ® •
l 4
6 I 0 ( 0 ) ~ , K- I
8
)ll
10
FIGURE 4 Product of microscopic mobility and recombination lifetime of four samples. The ~T product concerns samples with p a r t i a l l y f i l l e d traps up to quasi-Fermi levels.
REFERENCES 1) J.G. Simmons, G.W. Taylor and M.C. Tam, Phys. Rev. B 7 (1973) 3714. 2) M. Zhu and H. Fritzsche, Phil. Mag. B, 53 (1986) 41. 3) D.S. Misra, Vijay A. Singh and S.C. Agarwal, Solid St. Commun, 55 (1985) 147.
711
DETERMINATION OF THE DENSITY OF STATES IN AMORPHOUSSILICON FROM THERMOSTIMULATED CONDUCTIVITY MEASUREMENTS G. LANDWEER, R. SCHREUTELKAMP, H. SIMONS, J. BEZEMER and W.F. van der WEG Department of Atomic and I n t e r f a c e Physics, U n i v e r s i t y of Utrecht, P.O. Box 80.000, 3508 TA Utrecht, The Netherlands The density of states between the Fermi l e v e l and the conduction band in glow-discharge a-Si:H has been determined by measuring thermostimulated currents and photo-currents simultaneously. During the TSC measurements the sample is exposed to l i g h t pulses of low i n t e n s i t y . From the measurements both g(E) and the ~ product can be c a l c u l a t e d . Results are shown from samples grown at d i f f e r e n t glow-discharge powers. Minimum values of g(E) at 0.3 eV below Ec range from 1016 to 1017 eV- l cm-~.
i.
INTRODUCTION The increase in c o n d u c t i v i t y by c a r r i e r s released from traps can be used t o
determine the d e n s i t y of gap states. I f gap states are f i l l e d
at a low tempera-
t u r e , the thermostimulated c o n d u c t i v i t y (TSC) during the heating of the sample is a measure f o r the d i s t r i b u t i o n of traps in the gap. A thorough d e s c r i p t i o n of TSC measurements has been given by Simmons et a l . l ) . T o determine the number of released c a r r i e r s from TSC, the ~z product of the c a r r i e r s has to be known. Zhu and Fritzsche 2) showed how t h i s product can be found from p h o t o c o n d u c t i v i t y measurements. These measurements are r a t h e r e x t e n s i v e , since the ~T product depends on the temperature as well as on the trapped c a r r i e r d i s t r i b u t i o n
in
the bandgap. We suggest here a technique to combine thermostimulated and photoinduced current measurements. Although both electrons and holes c o n t r i b u t e to the TSC, we suppose t h a t the influence of the hole t r a n s p o r t in i n t r i n s i c
amorphous s i l i c o n can be neglected.
In t h a t case, TSC y i e l d s the d e n s i t y of states in the bandgap between the conduction band and the Fermi l e v e l . 2.
DESCRIPTION OF THE METHOD 1.1. P r i n c i p l e In our experiments we used samples with coplanar electrodes which were 0.50
mm apart. Before a TSC measurement, the samples are kept at a low temperature and exposed to l i g h t to f i l l
the gap states. The i n t e n s i t y and the duration of
the i l l u m i n a t i o n may vary in a wide range to o b t a i n , a f t e r a c e r t a i n r e l a x a t i o n time, an occupation of t r a p states which is l a r g e l y independent of the t o t a l photon f l u x . The energy range of f i l l e d
traps is characterized by quasi-Fermi
0022-3093/87/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
712
G. Landweer et al. / Determination of the density of states
l e v e l s which l i e close to the m o b i l i t y edges. By increasing the temperature at a constant r a t e of about 5 K/min, trapped electrons are released continuously u n t i l the quasi-Fermi l e v e l s reach the Fermi l e v e l . To determine the number of released electrons from a measured TSC curve, Zhu and Fritzsche 2) used steady state photocurrent measurements at various temperatures.
In our method, low i n t e n s i t y l i g h t pulses are appJied at r e g u l a r time
i n t e r v a l s during the measurement o f a TSC curve. The d u r a t i o n of a l i g h t pulse is between 0.01 and i second. The induced current pulse, which is superimposed on the thermostimulated c u r r e n t , has a length of 30 s or less, depending on the sample p r o p e r t i e s . Tests have shown t h a t these l i g h t pulses do not d i s t u r b the l e v e l of the TSC curve between the photocurrent pulses. I f the number of the absorbed photons is known, the number of released c a r r i e r s can be found r a t h e r e a s i l y by comparing the i n t e g r a t e d thermostimulated current during a small time i n t e r v a l with the area of the photocurrent pulse. Figure 1 shows schematically a part of a TSC curve and a photocurrent pulse. I f we assume t h a t the i n i t i a l
occupation function of the traps equals u n i t y ,
the d e n s i t y of states f o l l o w s from the number of released c a r r i e r s w i t h i n a small energy i n t e r v a l AE scanned in a time i n t e r v a l At:
g(E)AE = (N/v)(A1/A2). (I) Here N is the number of absorbed photons and v is the volume of the sample. The areas AI and A2 are defined in f i g u r e 1. From the p h o t o - c o n d u c t i v i t y also a ~T product can be found: 2 A2 = pTeNV/I ,
(2)
with 1 the distance between the electrodes and V the applied v o l t a g e . A d e f i n i t i o n o f ~ and T is given in section 1.3.
I
T
'
'
'
'
I
'
'
'
'
I
'
-0.2 EM,
eV
-0.4 o =o
-0.6
ou) F-
-0.8
<- At ->
Time - - > FIGURE 1 TSC-curve with a photo-current peak o f area A2. The integrated TSC current in At is denoted by AI .
Temperature, K
FIGURE 2 Energy o f maximum TSC, EM, versus the temperature T. The s~arting temperature is 80 K and B is 5 K/min.
G. Landweer et al. / Determination of the density of states
713
1.2. The energy of maximum TSC, EM Simmons et a l . 1) have shown t h a t during a TSC experiment only trapped carr i e r s are released from a small energy range around EM, determined by a s t r o n g l y peaked function P(E,T) with a width of 2kT.
The maximum of t h i s
function is found at the energy EM = -0.967 kT In(5ZVe/B ) +0.017,
(3)
with B the heating rate in K/s and Ue an e f f e c t i v e attempt to escape frequency expressed in s " I . The numbers in (3) depend somewhat upon the s t a r t i n g temperat u r e , which was 80 K in our experiments. With ~EM/Bt = B~EM/3T formula (1) y i e l d s : g(E) = AIN/{A2~tvBK(O.967) In (52re/B)}.
(4)
1.3. Attempt-to-escape frequency To determine g(E), the non-retrapping model o f Simmons et a l . I) was used, in which the release o f c a r r i e r s is described by an attempt-to-escape frequency ~0' The c o n d u c t i v i t y however is considered to be governed by a m u l t i p l e trapping process. For t h a t reason a c o r r e c t i o n f a c t o r has to be introduced to account f o r the mean number of retrapping events m before recombination.
This
y i e l d s the e f f e c t i v e attempt-to-escape frequency ~e = vo/m" The value of v e is e x p e r i m e n t a l l y found by assuming t h a t EM = EF at the temperature where the thermostimulated current becomes small compared to the dark c o n d u c t i v i t y , lhe a c t i v a t i o n energy of the dark c o n d u c t i v i t y at t h a t temperature gives EF. The f a c t o r m can also be defined as the r a t i o of the recombination l i f e t i m e and the mean l i f e t i m e in the conduction band between t r a p p i n g , m = T/T t . The m o b i l i t y ~, mentioned before, is the microscopic m o b i l i t y . Misra et a l . 3) made c a l c u l a t i o n s f o r the TSC based on a m u l t i p l e trapping model in which the r a t i o of the number of electrons in the conduction band and the number of electrons in the trap states is given by nc/n : {Nc/g(E )} exp(-E/kT).
(5)
Their r e s u l t y i e l d s the TSC as a function o f g(E), ~, T and Nc. This Nc is the d e n s i t y of states in the lower part of the conduction band. They derived t h a t ve(E ) = Ncl~g(E ) must hold to bring the non-trapping model in agreement with t h e i r m u l t i p l e
(6)
trapping model. In our experiment we used a constant value f o r re, determined at EF. l his seems to be a reasonable approximation, moreover since g (E) in f o r mula (4) is r a t h e r i n s e n s i t i v e to changes in v e. From the energy o f the Fermi l e v e l , s u b s t i t u t e d f o r EM in formula (3) we found v e to be of the order of I07/s. 2.
EXPERIMENTSAND DISCUSSION To i l l u s t r a t e
of i n t r i n s i c
the method, r e s u l t s are shown of measurements on four samples
a-Si l a y e r s , l he layers were deposited at four d i f f e r e n t glow-
714
G. Landweer et aL / Determination of the density of states
discharge powers, 5, 10, 20 and 40 W. The growth rates amounted to 0.58, 0.86, 1.08 and 1.52 nm/s, respectively. Figure 3 shows the density of states in the energy range of 0.15 to 0.65 eV below the conduction band as calculated from our TSC measurementswith formula (4). The sample grown at 5 W has the lowest number of gap states. This may indicate that at a higher power more damage in the layer is caused by the ion bombardement from the glow-discharge. The samples are supposed to be of a rather good quality. An oxygen content of less than 0.1% was found from ERD measurements. In layers with more contamination a higher density of states was found. Figure 4 shows the ~T product of the same layers as a function of the temperature. As d i s t i n c t from the results of Zhu and Fritzsche2), our values of uT decrease continuously with lower temperature. We do not observe the increase in ~T below 250 K which is associated with thermal quenching of photoconductivity. We conclude that TSC measurement is a relatively easy way to determine the density of states, which is an important aspect of the quality of a-Si:H mat e r i a l . The method is limited to a part of the bandgap. Starting at lower temperatures, values closer to the conduction band can be found. The Fermi level can not be reached however within about 0.1 eV or several kT, which is the temperature r e s o l u t i o n of the method. 19
|
'
r
,
I
I
I
I
r
|
'
W2owow
T>
%-5 x
W
i
®~®
/ AAAA /
15
,~ 4 0 W
L i l i l i l ~ ' l i l l
-0.6
-0.4 -0.2 E, eV
FIGURE 3 Density of states of four samples grown at different powers which are indicated in fig. 4. The straight line symbolizes the conduction band t a i l . In the figure EC' is 0 eV.
X®
-7 [
®
~'
ll x
® i. ® •
l 4
6 I 0 ( 0 ) ~ , K- I
8
)ll
10
FIGURE 4 Product of microscopic mobility and recombination lifetime of four samples. The ~T product concerns samples with p a r t i a l l y f i l l e d traps up to quasi-Fermi levels.
REFERENCES 1) J.G. Simmons, G.W. Taylor and M.C. Tam, Phys. Rev. B 7 (1973) 3714. 2) M. Zhu and H. Fritzsche, Phil. Mag. B, 53 (1986) 41. 3) D.S. Misra, Vijay A. Singh and S.C. Agarwal, Solid St. Commun, 55 (1985) 147.