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Semiclassical model of electrically detected magnetic resonance in undoped a-Si:H
ELSETVIER
Journal of Non-Crystalline
Solids 19X-200 (1996) 267-270
Semiclassical model of electrically detected magnetic resonance in undoped a-Si:H K. Lips h Fachbereich
a, C. Lerner b, W. Fuhs b**
’ National Renewable Energy Laboratory, Golden, CO 80401, USA Physik und Wissenschqftliches Zentrum fir Materialwissenschafteften, Philipps Unicersitiit Marburg, D-35032 Marburg, Germany
Abstract A simple model for spin-dependent photoconductivity is presented based on rate equations for the density of spin pairs in singlet and triplet configuration. The pairs are formed by electrons localized in the conduction band tail and neutral dangling bonds (e-D”). We take into consideration thermally induced pair dissociation, spontaneous and microwave-induced spin flips and recombination by non-radiative tunneling from band tails into dangling bonds. Our model explains, satisfactorily. changes in line shape and the dependence of the signal intensity on defect density and microwave power. We conclude that tunneling dominates recombination even at 300 K. This recombination predominantly involves shallow band tail states.
1. Introduction Electrically detected magnetic resonance (EDMR) measures changes in the conductivity when the sample is brought into electron spin resonance (ESR). This conductivity requires that the spin selection rule determines the transition probability between localized states. In this case, the externally induced spin flip process enhances the transition rates, and hence decreases the recombination lifetime and therefore the photocurrent. The dominating signal in the photoconductivity of undoped a-Si:H (Fig. l(b)) is a superposition of the lines due to electrons localized in the conduction band tail (g = 2.0044) and neutral dangling bonds (g = 2.0055) [l-8]. Although it is widely accepted that this signal originates from non-
* Corresponding author. Tel.: + 49-6421-284246; 6421-287036; e-mail: [email protected]. 0022-3093/96/$15.00 Copyright SD1 0022-3093(95)00713-X
fax:
+ 49-
radiative tunneling of band tail electrons into defects [4-71, it is still unclear to what extent tunneling dominates recombination. Here, we present a semiclassical model to obtain a more quantitative interpretation of this effect. Different from preceding theories [9,10] we do not restrict the model to cases of infinite microwave power.
2. Theoretical approach Fig. l(a) shows a recombination scheme for the photoconductivity in a-Si:H based on EDMR experiments [4-71. The paths Q,, Q2 and Q, denote recombination steps that have been identified in EDMR spectra of undoped films [5,7]. The dominant spin-dependent process, Q,, requires the formation of localized spin pairs (e-D”) [8-101. The photoexcited electrons (generation rate G) which are trapped in the band tail (rate coefficient f) form spin pairs
0 1996 Elsevier Science B.V. All rights reserved
K. Lips et al./Joumal
268
of Non-Crystalline Solids 198-200
(1996) 267-270
perature range 150 K-300 K, LVsPis determined by the relaxation time of the band tail carriers since Tf < TP [12]. The second term in Eq. (2) represents the microwave induced spin flip rate in resonance. It decribes the behavior of a single spin packet. In this expression H, denotes the amplitude of the microwave field and y the gyromagnetic ratio. In case of microwave saturation (W,, > W\p> power broadening occurs which leads to
(4
1
W=Ws,+W;~t=W,,+;yH,.
(3)
Here, W,, no longer depends on T, and increases linearly with H,. The EDMR signal intensity is defined by Au _=2.015
2.010
2.005
2.000
u
1.995
g-value Fig. 1. (a) Recombination scheme for a-Si:H (details see text). (b) EDMR spectra (microwave modulation) of the Q, resonance.
with the nearest neutral dangling bond. Since we neglect all spin-spin interactions, equal concentrations of e-D” pairs with parallel (n,) and antiparallel (n,) spin orientation exist. The spin pairs dissociate thermally with rates d. ns and d. nT, flip their spin at a rate W. ns or W. nT or recombine with rates rs . n, and rT. nT, respectively. In the following, we assume that: (1) Q, is the rate limiting recombination step and (2) that there is no direct capture (DC) of free carriers into dangling bonds. For simplicity, we represent the tail states and the dangling bonds by a single energy level. This leads to the following set of rate equations for the concentrations of free majority carriers n and spin pairs ~1~ and n,.. k=G-fn+dn,+dn,,
(la)
ri,=$n-dn,+r,n,+Wn,--Wn,,
(lb)
tiT=ifn-dn,+r,n,+
Wn,-
Wn,.
n*-no .o
’
where n* and n” denote tions in the resonant and tively. With Eqs. (l)-(4) intensity as a function of rT and W.
(4) the free carrier concentranon-resonant case, respecwe can calculate the signal the rate coefficients d, r,,
3. Results In Fig. 2 the calculated signal intensity is depicted as a function of the dissociation rate coefficient, d, 100
IO-'
i
1
(ICI
The spin configuration of a pair is changed with the transfer rate, W, which is described by [I 11 w=
WSP+ w,,
= wsP + $Y~H:T,.
(2)
Wsp is the spontaneous spin flip rate which is determined by the spin-lattice relaxation times of the spins in resonance, Wsp = l/T,’ + l/Tp. In the tem-
Fig. 2. Calculated signal intensity for W,, =m as a function of the dissociation rate coefficient d. (a) rs = 1Oh s-‘, rT = 10’ s ’, parameter T,. (b) T; = I / bV"p = 3 X 10 * ’ s, parameter rs.
K. Lips et al./Journal
’ I*,*“,’
1o-2
j ‘111111’ “lllw 10"
IO-’
10'
’ ““l”’ 102
ofNon-Crystalline Solids 198-200 (1996) 267-270
tions is the microwave-induced spin flip rate coefficient, W,, , which is controlled by the microwave power, P. We find experimentally that Au/a increases linearly with P for low microwave power and a square root dependence at high power (Fig. 3). The saturation behavior of the ESR signal, also depicted in Fig. 3, is typical for a inhomogeneously broadened line. Saturation occurs at P,,, = 3 mW from which we calculate the spin lattice relaxation time of the dangling bond, TP = lo-’ s, in accordance with Ref. [12]. The observed change in the behavior of the EDMR signal on microwave power is predicted by relations (2) and (3).
103
P WV Fig. 3. ESR and EDMR signal crowave power, P.
intensities
269
as a function
of mi-
4. Discussion for infinite microwave power (W,, -+ ~1. The signal amplitude, Au/a, decreases with decreasing T,‘. The maximum signal is obtained when d = l/T:. It is evident that even in case of a thermalized spin system (wlp x=- r,> the signal amplitudes can be larger by orders of magnitude than what is expected from the polarization effect [ 131. If the recombination rate, rs, is enhanced by two orders of magnitude (Fig. 2(b)), As/a remains unchanged at small values of d. Therefore, an influence of the defect density, N,, on AU/U is to be expected for d > rs only. This implies that shallow states are involved predominantly. An important parameter for the model calculaN, (cm-3) 10’6 I
I 102 t
I(
10” I
10’8 3
A
T= 150K
I
10"
I
I
105
106
I
10'
rs(0 Fig. 4. EDMR signal intensity
versus defect density, No and rs. from Ref. [6]. The calculated by the solid line assuming d = 4 X
(0) taken from Ref. [4] and (0) signal intensity is represented IO7 s-’ (E, = 0.13 eV).
Our model predicts a shift of the Ql signal with increasing temperature which is confirmed experimentally (Fig. l(b)). At 150 K, the average g-value of the Ql signal, g = 2.0050, results from the superposition of the e- and the db-line which both equal amplitudes. With increasing temperature, however, Tp changes only little, whereas T;‘ decreases by about two orders of magnitude in the range 150 K to 300 K [12]. Therefore, the microwave-induced spin flip rate at room temperature decreases by the same amount and diminishes the contribution of the e-line strongly. Another parameter of the model which we changed in the EDMR experiment is the recombination rate. This is accomplished by varying the defect density, No, by light degradation, electron bombardment and successive annealing over more than two orders of magnitude. Fig. 4 shows data from several samples taken at 150 K [4,6]. The defect density of the samples was measured by PDS and CPM. In order to determine rs from the measured values of N,, we assume rs a ND and rs = 10’ s- ’ at low N, in agreement with response time measurements [ 141. We calculated the signal as a function of rs using T,D = lo-’ s, Tr = lo-’ s, and P = 200 mW. The only free parameter, the dissociation rate coefficient d, was used for the fit in Fig. 4. In our model, d is related to the depth of the discrete trapping level by the relation, d = v,. exp(-E,/kT) with v~,= 10’” s -I. The linear variation is best fitted assuming a trap depth Et = 0.13 eV. The above discussion demonstrates that all EDMR results are in accor-
270
K. Lips et al. / Journal
ofNon-Crystalline Solids lY8-200 (1996) 267-270
dance with the assumption that tunneling is the relevant recombination channel via defects in a-Si:H. This involves shallow band tail states predominately.
References [I] I. Solomon, [z] [3] [4]
5. Conclusions EDMR can be described in a simple rate equation system assuming that the dominating recombination step is tunneling of band tail electrons into neutral dangling bonds. The model accounts for most of our experimental results: (1) large A a/a although the spin system is thermalized; (2) dependence of A a/a on microwave power; (3) the linear dependence of A w/u on the defect density; and (4) shift of the g-value with increasing temperature. These results suggest that the tunneling process via shallow band tail states is the dominating recombination step even at 300 K.
[51 [6] [7] [81 [9] [lo]
[ 111
[12]
Acknowledgements The authors wish to thank the Bundesminister Forschung und Technologie (BMFT 0328327F) financial support.
[13] 1141
fur for
D.K. Biegelsen and J.C. Knights, Solid State Commun. 22 (1977) 505. E.A. Schiff, AIP Conf. Proc. 73 (1981) 233. R.A. Street, Phil. Mag. B 46 (1982) 273. H. Dersch, L. Schweitzer and J. Stuke, Phys. Rev. B 28 (1983) 4678. MS. Brandt and M. Stutzmann, Phys. Rev. B 43 (1991) 5184. W. Fuhs and K. Lips, J. Non-Cryst. Solids 137-138 (1991) 255. K. Lips, S. Schiitte and W. Fuhs, Phil. Mag. B 65 (1992) 945. W. Fuhs and K. Lips, .I. Non-Cryst. Solids 164-166 (1993) 541. D. Kaplan, I. Solomon and N.F. Mott, J. Phys. (Paris) 39 (1978) L51. B. Movaghar, B. Ries and L. Schweitzer, Phil. Mag. B 41 (1980) 159. K.J. Standley and R.A. Vaughan, in: Electron Spin Relaxation Phenomena in Solids (Adam Hilger, London, 1969) p. 89. M. Stutzmann and D.K. Biegelsen, Phys. Rev. B 28 (1983) 6256. D.J. Lepine, Phys. Rev. B 6 (1972) 436. M. Hoheisel and W. Fuhs, Phil. Mag. B 57 (1988) 411.
Journal of Non-Crystalline
Solids 19X-200 (1996) 267-270
Semiclassical model of electrically detected magnetic resonance in undoped a-Si:H K. Lips h Fachbereich
a, C. Lerner b, W. Fuhs b**
’ National Renewable Energy Laboratory, Golden, CO 80401, USA Physik und Wissenschqftliches Zentrum fir Materialwissenschafteften, Philipps Unicersitiit Marburg, D-35032 Marburg, Germany
Abstract A simple model for spin-dependent photoconductivity is presented based on rate equations for the density of spin pairs in singlet and triplet configuration. The pairs are formed by electrons localized in the conduction band tail and neutral dangling bonds (e-D”). We take into consideration thermally induced pair dissociation, spontaneous and microwave-induced spin flips and recombination by non-radiative tunneling from band tails into dangling bonds. Our model explains, satisfactorily. changes in line shape and the dependence of the signal intensity on defect density and microwave power. We conclude that tunneling dominates recombination even at 300 K. This recombination predominantly involves shallow band tail states.
1. Introduction Electrically detected magnetic resonance (EDMR) measures changes in the conductivity when the sample is brought into electron spin resonance (ESR). This conductivity requires that the spin selection rule determines the transition probability between localized states. In this case, the externally induced spin flip process enhances the transition rates, and hence decreases the recombination lifetime and therefore the photocurrent. The dominating signal in the photoconductivity of undoped a-Si:H (Fig. l(b)) is a superposition of the lines due to electrons localized in the conduction band tail (g = 2.0044) and neutral dangling bonds (g = 2.0055) [l-8]. Although it is widely accepted that this signal originates from non-
* Corresponding author. Tel.: + 49-6421-284246; 6421-287036; e-mail: [email protected]. 0022-3093/96/$15.00 Copyright SD1 0022-3093(95)00713-X
fax:
+ 49-
radiative tunneling of band tail electrons into defects [4-71, it is still unclear to what extent tunneling dominates recombination. Here, we present a semiclassical model to obtain a more quantitative interpretation of this effect. Different from preceding theories [9,10] we do not restrict the model to cases of infinite microwave power.
2. Theoretical approach Fig. l(a) shows a recombination scheme for the photoconductivity in a-Si:H based on EDMR experiments [4-71. The paths Q,, Q2 and Q, denote recombination steps that have been identified in EDMR spectra of undoped films [5,7]. The dominant spin-dependent process, Q,, requires the formation of localized spin pairs (e-D”) [8-101. The photoexcited electrons (generation rate G) which are trapped in the band tail (rate coefficient f) form spin pairs
0 1996 Elsevier Science B.V. All rights reserved
K. Lips et al./Joumal
268
of Non-Crystalline Solids 198-200
(1996) 267-270
perature range 150 K-300 K, LVsPis determined by the relaxation time of the band tail carriers since Tf < TP [12]. The second term in Eq. (2) represents the microwave induced spin flip rate in resonance. It decribes the behavior of a single spin packet. In this expression H, denotes the amplitude of the microwave field and y the gyromagnetic ratio. In case of microwave saturation (W,, > W\p> power broadening occurs which leads to
(4
1
W=Ws,+W;~t=W,,+;yH,.
(3)
Here, W,, no longer depends on T, and increases linearly with H,. The EDMR signal intensity is defined by Au _=2.015
2.010
2.005
2.000
u
1.995
g-value Fig. 1. (a) Recombination scheme for a-Si:H (details see text). (b) EDMR spectra (microwave modulation) of the Q, resonance.
with the nearest neutral dangling bond. Since we neglect all spin-spin interactions, equal concentrations of e-D” pairs with parallel (n,) and antiparallel (n,) spin orientation exist. The spin pairs dissociate thermally with rates d. ns and d. nT, flip their spin at a rate W. ns or W. nT or recombine with rates rs . n, and rT. nT, respectively. In the following, we assume that: (1) Q, is the rate limiting recombination step and (2) that there is no direct capture (DC) of free carriers into dangling bonds. For simplicity, we represent the tail states and the dangling bonds by a single energy level. This leads to the following set of rate equations for the concentrations of free majority carriers n and spin pairs ~1~ and n,.. k=G-fn+dn,+dn,,
(la)
ri,=$n-dn,+r,n,+Wn,--Wn,,
(lb)
tiT=ifn-dn,+r,n,+
Wn,-
Wn,.
n*-no .o
’
where n* and n” denote tions in the resonant and tively. With Eqs. (l)-(4) intensity as a function of rT and W.
(4) the free carrier concentranon-resonant case, respecwe can calculate the signal the rate coefficients d, r,,
3. Results In Fig. 2 the calculated signal intensity is depicted as a function of the dissociation rate coefficient, d, 100
IO-'
i
1
(ICI
The spin configuration of a pair is changed with the transfer rate, W, which is described by [I 11 w=
WSP+ w,,
= wsP + $Y~H:T,.
(2)
Wsp is the spontaneous spin flip rate which is determined by the spin-lattice relaxation times of the spins in resonance, Wsp = l/T,’ + l/Tp. In the tem-
Fig. 2. Calculated signal intensity for W,, =m as a function of the dissociation rate coefficient d. (a) rs = 1Oh s-‘, rT = 10’ s ’, parameter T,. (b) T; = I / bV"p = 3 X 10 * ’ s, parameter rs.
K. Lips et al./Journal
’ I*,*“,’
1o-2
j ‘111111’ “lllw 10"
IO-’
10'
’ ““l”’ 102
ofNon-Crystalline Solids 198-200 (1996) 267-270
tions is the microwave-induced spin flip rate coefficient, W,, , which is controlled by the microwave power, P. We find experimentally that Au/a increases linearly with P for low microwave power and a square root dependence at high power (Fig. 3). The saturation behavior of the ESR signal, also depicted in Fig. 3, is typical for a inhomogeneously broadened line. Saturation occurs at P,,, = 3 mW from which we calculate the spin lattice relaxation time of the dangling bond, TP = lo-’ s, in accordance with Ref. [12]. The observed change in the behavior of the EDMR signal on microwave power is predicted by relations (2) and (3).
103
P WV Fig. 3. ESR and EDMR signal crowave power, P.
intensities
269
as a function
of mi-
4. Discussion for infinite microwave power (W,, -+ ~1. The signal amplitude, Au/a, decreases with decreasing T,‘. The maximum signal is obtained when d = l/T:. It is evident that even in case of a thermalized spin system (wlp x=- r,> the signal amplitudes can be larger by orders of magnitude than what is expected from the polarization effect [ 131. If the recombination rate, rs, is enhanced by two orders of magnitude (Fig. 2(b)), As/a remains unchanged at small values of d. Therefore, an influence of the defect density, N,, on AU/U is to be expected for d > rs only. This implies that shallow states are involved predominantly. An important parameter for the model calculaN, (cm-3) 10’6 I
I 102 t
I(
10” I
10’8 3
A
T= 150K
I
10"
I
I
105
106
I
10'
rs(0 Fig. 4. EDMR signal intensity
versus defect density, No and rs. from Ref. [6]. The calculated by the solid line assuming d = 4 X
(0) taken from Ref. [4] and (0) signal intensity is represented IO7 s-’ (E, = 0.13 eV).
Our model predicts a shift of the Ql signal with increasing temperature which is confirmed experimentally (Fig. l(b)). At 150 K, the average g-value of the Ql signal, g = 2.0050, results from the superposition of the e- and the db-line which both equal amplitudes. With increasing temperature, however, Tp changes only little, whereas T;‘ decreases by about two orders of magnitude in the range 150 K to 300 K [12]. Therefore, the microwave-induced spin flip rate at room temperature decreases by the same amount and diminishes the contribution of the e-line strongly. Another parameter of the model which we changed in the EDMR experiment is the recombination rate. This is accomplished by varying the defect density, No, by light degradation, electron bombardment and successive annealing over more than two orders of magnitude. Fig. 4 shows data from several samples taken at 150 K [4,6]. The defect density of the samples was measured by PDS and CPM. In order to determine rs from the measured values of N,, we assume rs a ND and rs = 10’ s- ’ at low N, in agreement with response time measurements [ 141. We calculated the signal as a function of rs using T,D = lo-’ s, Tr = lo-’ s, and P = 200 mW. The only free parameter, the dissociation rate coefficient d, was used for the fit in Fig. 4. In our model, d is related to the depth of the discrete trapping level by the relation, d = v,. exp(-E,/kT) with v~,= 10’” s -I. The linear variation is best fitted assuming a trap depth Et = 0.13 eV. The above discussion demonstrates that all EDMR results are in accor-
270
K. Lips et al. / Journal
ofNon-Crystalline Solids lY8-200 (1996) 267-270
dance with the assumption that tunneling is the relevant recombination channel via defects in a-Si:H. This involves shallow band tail states predominately.
References [I] I. Solomon, [z] [3] [4]
5. Conclusions EDMR can be described in a simple rate equation system assuming that the dominating recombination step is tunneling of band tail electrons into neutral dangling bonds. The model accounts for most of our experimental results: (1) large A a/a although the spin system is thermalized; (2) dependence of A a/a on microwave power; (3) the linear dependence of A w/u on the defect density; and (4) shift of the g-value with increasing temperature. These results suggest that the tunneling process via shallow band tail states is the dominating recombination step even at 300 K.
[51 [6] [7] [81 [9] [lo]
[ 111
[12]
Acknowledgements The authors wish to thank the Bundesminister Forschung und Technologie (BMFT 0328327F) financial support.
[13] 1141
fur for
D.K. Biegelsen and J.C. Knights, Solid State Commun. 22 (1977) 505. E.A. Schiff, AIP Conf. Proc. 73 (1981) 233. R.A. Street, Phil. Mag. B 46 (1982) 273. H. Dersch, L. Schweitzer and J. Stuke, Phys. Rev. B 28 (1983) 4678. MS. Brandt and M. Stutzmann, Phys. Rev. B 43 (1991) 5184. W. Fuhs and K. Lips, J. Non-Cryst. Solids 137-138 (1991) 255. K. Lips, S. Schiitte and W. Fuhs, Phil. Mag. B 65 (1992) 945. W. Fuhs and K. Lips, .I. Non-Cryst. Solids 164-166 (1993) 541. D. Kaplan, I. Solomon and N.F. Mott, J. Phys. (Paris) 39 (1978) L51. B. Movaghar, B. Ries and L. Schweitzer, Phil. Mag. B 41 (1980) 159. K.J. Standley and R.A. Vaughan, in: Electron Spin Relaxation Phenomena in Solids (Adam Hilger, London, 1969) p. 89. M. Stutzmann and D.K. Biegelsen, Phys. Rev. B 28 (1983) 6256. D.J. Lepine, Phys. Rev. B 6 (1972) 436. M. Hoheisel and W. Fuhs, Phil. Mag. B 57 (1988) 411.