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Time-domain measurement of spin-dependent recombination in microcrystalline silicon
Journal of Non-Crystalline Solids 299–302 (2002) 566–570 www.elsevier.com/locate/jnoncrysol
Time-domain measurement of spin-dependent recombination in microcrystalline silicon Christoph Boehme *, Peter Kanschat, Klaus Lips Hahn-Meitner-Institut, Kekul estr. 5, D-12489 Berlin, Germany
Abstract Time-domain measurement of spin-dependent recombination (TSR) is based on the transient measurement of spindependent recombination after an intensive, short microwave pulse. The method allows an accurate measurement of the recombination and dissociation probabilities of recombining charge carrier pairs and gives quantitative insight into the recombination dynamics in semiconductors. A first application of TSR on the tunneling recombination between bandtail states and dangling bonds (db) in microcrystalline silicon are presented. We will discuss the TSR method in detail and show that we can determine the temperature dependence of the hopping rate of photo-excited charge carriers among bandtail states. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 72.20.Jv; 72.20.Ee; 76.30.)v; 76.90.+d
1. Introduction Defect characterization methods such as electrically detected magnetic resonance (EDMR) and optically detected magnetic resonance (ODMR) have proven to be highly versatile methods for the characterization of spin-dependent recombination mechanisms in semiconductors and thus, for the investigation of many types of recombination active defects. Various systems of semiconductor structures and devices have been investigated [1–5], with these methods such as dangling bond (db) recombination paths in hydrogenated amorphous and microcrystalline silicon, a-Si:H and
*
Corresponding author. Tel.: +49-30 67053 314; fax: +49-30 67053 333. E-mail address: [email protected] (C. Boehme).
lc-Si:H, respectively. While the db has been discovered by conventional electron spin resonance (ESR) [6,7], most of the recombination paths involving db states have been investigated by EDMR and ODMR methods [1]. Fig. 1 illustrates one of these mechanisms as described by Kanschat et al. [4] in undoped lc-Si:H. At low temperatures, photogenerated charge carrier transport takes place mostly by electron hopping through shallow tail states (CE-centers) close to the conduction band edge. A tunneling recombination of charge carriers from trap states can take place through dbs. Providing that both states, CE and db, are paramagnetic, this recombination is only possible when the CE and db centers are in a spin state with singlet character (anti-parallel spin orientation), the recombination channel is therefore spin dependent. Since the recombination of triplets are forbidden, under steady state condition a surplus
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 1 0 2 3 - 7
C. Boehme et al. / Journal of Non-Crystalline Solids 299–302 (2002) 566–570
of triplets will exist. The idea of EDMR is to take advantage of the spin selection rule by applying a resonant ESR microwave that changes the spin orientation and enhances the singlet state density and hence increases the recombination rate. This is monitored by detecting the photocurrent as a function of the external magnetic field. EDMR therefore is simply the combination of an ESR and a transport measurement and is superior to ESR in many aspects. The sensitivity of EDMR can be orders of magnitude better than ESR due to its independence from the sample volume [1]. Due to the selectiveness of ESR one can identify the states that belong to specific recombination paths. EDMR has been proven to be a method which can provide much information about the type, density and even the local structure of defects. In spite of these advantages, EDMR fails to give sufficient quantitative information about the dynamics of the recombination processes. Spindependent recombination in the picture of Kaplan et al. (KSM model [9]), takes place through the formation of intermediate pairs (KSM-pairs) of electrons and holes which can either recombine with a probability r or dissociate with probability d. For the CE–db process mentioned above, the recombination corresponds to a transition of a trapped electron into the dbs and the dissociation due to the tunneling of a trapped electron into a
Fig. 1. Illustration of trap-dangling bond (CE–db) recombination in lc-Si:H at low temperatures. Hopping conduction of photogenerated excess charge carriers takes place between shallow tail states close to the conduction band edge. Spin pairs can form between such electrons and neutral dbs as indicated by the shaded ellipse. If the pair has singlet character recombination is allowed with a probability r. If the pair has triplet character recombination is forbidden. Therefore the photocurrent in both cases will be different. Dissociation of the pair can take place out of any spin state with probability d.
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different CE state (Fig. 1) or, at elevated temperature, a thermal emission into the conduction band. Previous efforts to study the recombination dynamics were carried out by Eickelcamp et al. [2] who described the line shape dependence of continuous wave (cw) EDMR signals from recombination and dissociation probabilities and Hiromitsu et al. [8] who took a first approach to the extraction of information about recombination dynamics from the time domain of chopped EDMR. The drawback of these previous methods have always been the bad extractability of the wanted information from the given experimental data leading only to crude estimates for the recombination and dissociation probabilities.
2. The time-domain measurement of spin-dependent recombination The time-domain measurement of spin-dependent recombination (TSR) is based on a setup as illustrated in Fig. 2. Similar to EDMR, the sample is exposed to an external homogeneous magnetic field B0 , such that the spin states are split due to the Zeeman interaction. The sample is cooled by a helium cryostat. Excess charge carriers are created by a 3W cw-Ar-ion laser. The photocurrent is amplified by a high speed current amplifier, which is connected to a transient recorder. The most important difference of the TSR setup to the conventional EDMR experiment is the use of strong (kW instead of mW intensities) and short
Fig. 2. The experimental setup of the TSR experiment. Details see text.
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C. Boehme et al. / Journal of Non-Crystalline Solids 299–302 (2002) 566–570
(ns range) microwave pulses. The short pulses are generated by a Gunn diode and amplified by a traveling wave tube microwave amplifier. The experiment is carried out by measuring the transient photocurrent after a short ESR microwave pulse is irradiated onto the sample. With this technique the microwave radiation and the relaxation of the photocurrent are separated in time and all physical information is obtained from the photocurrent transient. During and after the resonant microwave pulse of length sP the population of the triplets and singlets are quickly altered thereby changing the steady state recombination rate R by a difference DR following a double exponential decay function [10] " rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# r r2 þ w2 DRðtÞ ¼ DR1 ðt0 Þ exp d þ þ w þ 2 4 ! " r ½t t0 þ DR2 ðt0 Þ exp d þ þ w 2 ! rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# r2 þ w2 ½t t0 ; ð1Þ 4 where DR1 ðt0 Þ and DR2 ðt0 Þ are initial conditions at time t0 , and w ¼ ðcB1 þ 1=T1 Þ is the spin flip rate due to the microwave field B1 (c is the gyromagnetic ratio) and due to the spin-lattice relaxation time T1 . The variables d and r are the unknown characteristic parameters of the recombination process. When the sample is sufficiently cooled so that T1 becomes long and the radiation is turned off, the condition w d r holds and the general solution of Eq. (1) becomes DRoff ðtÞ DR1 ðsP Þ expðr½t sP Þ þ DR2 ðsP Þ expðd½t sP Þ:
ð2Þ
The initial conditions DR1 ðsP Þ and DR2 ðsP Þ dependent on the pulse length sP . Thus, the relaxation of the recombination rate after the pulse reveals both the recombination as well as the dissociation probability. The recombination rate change can be measured by the transient photocurrent since the relative recombination rate change is small ðDr=r 1Þ and therefore the relationship Dr=r ¼ DI=I applies. The limitation of
such a real time measurement is the time constant of the setup. The relative current (recombination) change induced by ESR hardly exceeds values of 104 –103 . Because of noise limitations and the low conductivity of semiconductors at low temperatures, even the best state of the art high speed current amplifiers can hardly exceed frequencies in the MHz range. Nevertheless, a much higher time resolution can be obtained by recording the transient amplitude at any given time as a function of the pulse length. Since sP can be changed in 2 ns steps, our setup provides a 2 ns resolution. When the microwave is sufficiently strong, the spin flip rate w becomes large ðw r dÞ and Eq. (1) becomes r DRon ðtÞ DR1 ð0Þ expð2wtÞ þ DR2 ð0Þ exp t : 2 ð3Þ The factors DR1 ð0Þ and DR2 ð0Þ are dependent on the steady state of the system without microwave that exist at the beginning of the pulse ðt ¼ 0Þ. Since the recombination rate change DRon ðsP Þ at the end of the pulse at time sP is the initial condition of Eq. (2), the variation of the pulse length leads to a projection of Eq. (3) on the transient of the much slower decay with time constant d [10].
3. First experimental results with TSR We have utilized TSR for the investigation of nominally undoped lc-Si:H, deposited with electron cyclotron resonance chemical vapor deposition (ECRCVD) on a 1737 corning glass substrate. The sample has a thickness of 2:7 lm and a dark conductivity of rd ¼ 3:8 104 X1 cm1 at room temperature. As mentioned above, the time resolution of the experimental setup is the limiting variable for the TSR experiment. Therefore, a special sample geometry had to be used in order to keep the sample’s RC time low. A 300 nm thick meander shaped lateral Al-contact grid system was deposited on the 4 mm 8 mm sample such that an effective contact length of about 400 mm was accommodated with an average contact distance of 50 lm. Unwanted non-resonant effects like magnetoresistance and microwave-induced current
C. Boehme et al. / Journal of Non-Crystalline Solids 299–302 (2002) 566–570
changes have always been subtracted from the transient. Before the transient measurement was carried out, a verification of the resonant character was made at T ¼ 5 K by recording the transient amplitude at time t ¼ 20 ls after the pulse as a function of the external field B0 (Fig. 3(a)). The sweep reveals two peaks at g ¼ 2:0058ð2Þ and g ¼ 2:001ð2Þ which correspond to the observations made with conventional EDMR in lc-Si:H by Kanschat et al. [4] identifying these lines as the db and CE resonances, respectively. Fig. 3(b) shows the signal transient recorded at the peak of the
Fig. 3. (a) The magnetic field dependence of the transient amplitude taken 20 ls after the microwave pulse ðsP ¼ 320 nsÞ. The solid line is the result of a fit with two Lorentzians (dashed lines) with their respective g values, (b) the real time transient measured at the peak of the resonance at g ¼ 2:0055. The data (solid gray line) is fitted by a single exponential with given time constant sd (dashed line).
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resonance (g ¼ 2:0055). Since the other exponential decay with time constant r from Eq. (2) was swallowed by the time resolution of the current amplifier, a single exponential fit of this graph is made (hardly distinguishable from the data) that reveals a time constant sd ¼ ð32:6 0:1Þ ls. Here, the inverse of sd can be identified with the pair dissociation rate d ¼ 1=sd ¼ 3:1ð1Þ 104 s1 since the temperature is sufficiently low such that the assumption w d holds. As illustrated in Fig. 3, the exponential fit of the decay function is excellent; the error of the measured time constant is therefore not determined by the fit correlation but the fluctuation of the laser intensity as well as the sample temperature. The error margins of all displayed data points are therefore within the diameter of the circles and crosses which indicate the respective points. With increasing temperature 1=sd remains constant up to about T ¼ 70 K (Fig. 4). Beyond this temperature, 1=sd increases strongly. As shown by Zhou et al. [11], the spin-lattice relaxation probability T11 in lc-Si:H exceeds at this temperature 3 104 s1 , and therefore the dissociation
Fig. 4. The temperature dependence of s1 versus sample d temperature. Below T ¼ 70 K, spin-lattice relaxation is negligible so that the decay time is determined by the dissociation probability d. The temperature independence confirms the tunneling picture of the KSM-pair dissociation process. At higher temperatures, the spin-lattice relaxation time becomes relevant and the decay time is not dissociation related anymore. The solid line is a guide to the eye. The error margins are within the radii of the circles that indicate the data points.
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C. Boehme et al. / Journal of Non-Crystalline Solids 299–302 (2002) 566–570
Fig. 5. The dependence of the transient amplitude versus the pulse length sP . The solid line represents the double exponential fit with fast and slow time constants sw and sr , respectively. The inset shows the linear dependence of s1 as a function of w the microwave field B1 . The error margins are within the radii of the circles and the crosses that indicate the data points.
probability d. Above T ¼ 70 K, 1=sd is determined by the spin-lattice relaxation probability 1=T1 . This behavior is well known from the transients of conventional EDMR [1]. For the evaluation of the recombination probability r, the transient amplitude versus the pulse length was recorded at T ¼ 5 K according to Eq. (3) (Fig. 5). A double exponential fit to our data reveals time constants of sw ¼ ð28 3Þ ns for the fast decay and sr ¼ ð580 60Þ ns for the slow decay. The fast decay can be identified with the spin flip rate 2w, since it turns out to be proportional to the microwave radiation field B1 (Fig. 5, inset). Hence, the necessary conditions outlined above ðd r wÞ are met at T ¼ 5 K and the time constant sr can be identified with 2=r yielding a value for r ¼ ð3:4 0:3Þ 106 s1 .
4. Discussion TSR provides a useful tool for the quantitative investigation of the CE–db recombination dynamics in lc-Si:H. The dissociation probability of
KSM-pairs has a value of d ¼ ð3:1 0:1Þ 104 s1 which is temperature independent up to T ¼ 70 K, the end of the measurable range. Since a thermal dissociation of spin pairs should reveal a strong temperature dependence of 1=d our observation can only be interpreted with the assumption that pair dissociation is a tunneling process of a trapped electron into another trap. The measured dissociation probability can therefore be identified with the tunneling probability between traps. This result strongly supports the picture of low temperature hopping transport and tunneling recombination in lc-Si:H as shown in Fig. 1. The use of very short and intensive resonant microwave pulses allows the reconstruction of the recombination transient during the pulse in the ns range. Therefore, the recombination probability r can be measured. The above results show that TSR is a very powerful method that will enable future access to the dynamics of hopping and recombination process with a resolution unheard of before.
References [1] M. Stutzmann, M.S. Brandt, M.W. Bayerl, J. Non-Cryst. Solids 266–269 (2000) 1. [2] T. Eickelkamp, S. Roth, M. Mehring, Mol. Phys. 95 (1998) 967. [3] H. Dersch, L. Schweitzer, J. Stuke, Phys. Rev. B 28 (8) (1983) 4678. [4] P. Kanschat, K. Lips, W. Fuhs, J. Non-Cryst. Solids 266– 269 (2000) 524. [5] F.C. Rong, W.R. Buchwald, E.H. Pointdexter, W.L. Warren, D.J. Keeble, Solid State Electron. 34 (8) (1991) 835. [6] Z.Z. Ditina, L.P. Strakov, H.H. Helms, Sov. Phys. Semicond. 2 (1969) 1006. [7] M. Brodsky, R.S. Title, Phys. Rev. Lett. 23 (1969) 581. [8] I. Hiromitsu, Y. Kaimori, M. Kitano, T. Ito, Phys. Rev. B 59 (3) (1999) 2151. [9] D. Kaplan, I. Solomon, N.F. Mott, J. Phys. Lett. 39 (1978) L51. [10] C. Boehme, K. Lips, Nucl. Instrum. Methods B 186 (4) (2002) 30. [11] J.-H. Zhou, S. Yamasaki, J. Isoya, K. Ikuta, M. Kondo, A. Matsuda, K. Tanaka, Mater. Res. Soc. Symp. Proc. 452 (1997) 821.
Time-domain measurement of spin-dependent recombination in microcrystalline silicon Christoph Boehme *, Peter Kanschat, Klaus Lips Hahn-Meitner-Institut, Kekul estr. 5, D-12489 Berlin, Germany
Abstract Time-domain measurement of spin-dependent recombination (TSR) is based on the transient measurement of spindependent recombination after an intensive, short microwave pulse. The method allows an accurate measurement of the recombination and dissociation probabilities of recombining charge carrier pairs and gives quantitative insight into the recombination dynamics in semiconductors. A first application of TSR on the tunneling recombination between bandtail states and dangling bonds (db) in microcrystalline silicon are presented. We will discuss the TSR method in detail and show that we can determine the temperature dependence of the hopping rate of photo-excited charge carriers among bandtail states. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 72.20.Jv; 72.20.Ee; 76.30.)v; 76.90.+d
1. Introduction Defect characterization methods such as electrically detected magnetic resonance (EDMR) and optically detected magnetic resonance (ODMR) have proven to be highly versatile methods for the characterization of spin-dependent recombination mechanisms in semiconductors and thus, for the investigation of many types of recombination active defects. Various systems of semiconductor structures and devices have been investigated [1–5], with these methods such as dangling bond (db) recombination paths in hydrogenated amorphous and microcrystalline silicon, a-Si:H and
*
Corresponding author. Tel.: +49-30 67053 314; fax: +49-30 67053 333. E-mail address: [email protected] (C. Boehme).
lc-Si:H, respectively. While the db has been discovered by conventional electron spin resonance (ESR) [6,7], most of the recombination paths involving db states have been investigated by EDMR and ODMR methods [1]. Fig. 1 illustrates one of these mechanisms as described by Kanschat et al. [4] in undoped lc-Si:H. At low temperatures, photogenerated charge carrier transport takes place mostly by electron hopping through shallow tail states (CE-centers) close to the conduction band edge. A tunneling recombination of charge carriers from trap states can take place through dbs. Providing that both states, CE and db, are paramagnetic, this recombination is only possible when the CE and db centers are in a spin state with singlet character (anti-parallel spin orientation), the recombination channel is therefore spin dependent. Since the recombination of triplets are forbidden, under steady state condition a surplus
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 1 0 2 3 - 7
C. Boehme et al. / Journal of Non-Crystalline Solids 299–302 (2002) 566–570
of triplets will exist. The idea of EDMR is to take advantage of the spin selection rule by applying a resonant ESR microwave that changes the spin orientation and enhances the singlet state density and hence increases the recombination rate. This is monitored by detecting the photocurrent as a function of the external magnetic field. EDMR therefore is simply the combination of an ESR and a transport measurement and is superior to ESR in many aspects. The sensitivity of EDMR can be orders of magnitude better than ESR due to its independence from the sample volume [1]. Due to the selectiveness of ESR one can identify the states that belong to specific recombination paths. EDMR has been proven to be a method which can provide much information about the type, density and even the local structure of defects. In spite of these advantages, EDMR fails to give sufficient quantitative information about the dynamics of the recombination processes. Spindependent recombination in the picture of Kaplan et al. (KSM model [9]), takes place through the formation of intermediate pairs (KSM-pairs) of electrons and holes which can either recombine with a probability r or dissociate with probability d. For the CE–db process mentioned above, the recombination corresponds to a transition of a trapped electron into the dbs and the dissociation due to the tunneling of a trapped electron into a
Fig. 1. Illustration of trap-dangling bond (CE–db) recombination in lc-Si:H at low temperatures. Hopping conduction of photogenerated excess charge carriers takes place between shallow tail states close to the conduction band edge. Spin pairs can form between such electrons and neutral dbs as indicated by the shaded ellipse. If the pair has singlet character recombination is allowed with a probability r. If the pair has triplet character recombination is forbidden. Therefore the photocurrent in both cases will be different. Dissociation of the pair can take place out of any spin state with probability d.
567
different CE state (Fig. 1) or, at elevated temperature, a thermal emission into the conduction band. Previous efforts to study the recombination dynamics were carried out by Eickelcamp et al. [2] who described the line shape dependence of continuous wave (cw) EDMR signals from recombination and dissociation probabilities and Hiromitsu et al. [8] who took a first approach to the extraction of information about recombination dynamics from the time domain of chopped EDMR. The drawback of these previous methods have always been the bad extractability of the wanted information from the given experimental data leading only to crude estimates for the recombination and dissociation probabilities.
2. The time-domain measurement of spin-dependent recombination The time-domain measurement of spin-dependent recombination (TSR) is based on a setup as illustrated in Fig. 2. Similar to EDMR, the sample is exposed to an external homogeneous magnetic field B0 , such that the spin states are split due to the Zeeman interaction. The sample is cooled by a helium cryostat. Excess charge carriers are created by a 3W cw-Ar-ion laser. The photocurrent is amplified by a high speed current amplifier, which is connected to a transient recorder. The most important difference of the TSR setup to the conventional EDMR experiment is the use of strong (kW instead of mW intensities) and short
Fig. 2. The experimental setup of the TSR experiment. Details see text.
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C. Boehme et al. / Journal of Non-Crystalline Solids 299–302 (2002) 566–570
(ns range) microwave pulses. The short pulses are generated by a Gunn diode and amplified by a traveling wave tube microwave amplifier. The experiment is carried out by measuring the transient photocurrent after a short ESR microwave pulse is irradiated onto the sample. With this technique the microwave radiation and the relaxation of the photocurrent are separated in time and all physical information is obtained from the photocurrent transient. During and after the resonant microwave pulse of length sP the population of the triplets and singlets are quickly altered thereby changing the steady state recombination rate R by a difference DR following a double exponential decay function [10] " rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# r r2 þ w2 DRðtÞ ¼ DR1 ðt0 Þ exp d þ þ w þ 2 4 ! " r ½t t0 þ DR2 ðt0 Þ exp d þ þ w 2 ! rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# r2 þ w2 ½t t0 ; ð1Þ 4 where DR1 ðt0 Þ and DR2 ðt0 Þ are initial conditions at time t0 , and w ¼ ðcB1 þ 1=T1 Þ is the spin flip rate due to the microwave field B1 (c is the gyromagnetic ratio) and due to the spin-lattice relaxation time T1 . The variables d and r are the unknown characteristic parameters of the recombination process. When the sample is sufficiently cooled so that T1 becomes long and the radiation is turned off, the condition w d r holds and the general solution of Eq. (1) becomes DRoff ðtÞ DR1 ðsP Þ expðr½t sP Þ þ DR2 ðsP Þ expðd½t sP Þ:
ð2Þ
The initial conditions DR1 ðsP Þ and DR2 ðsP Þ dependent on the pulse length sP . Thus, the relaxation of the recombination rate after the pulse reveals both the recombination as well as the dissociation probability. The recombination rate change can be measured by the transient photocurrent since the relative recombination rate change is small ðDr=r 1Þ and therefore the relationship Dr=r ¼ DI=I applies. The limitation of
such a real time measurement is the time constant of the setup. The relative current (recombination) change induced by ESR hardly exceeds values of 104 –103 . Because of noise limitations and the low conductivity of semiconductors at low temperatures, even the best state of the art high speed current amplifiers can hardly exceed frequencies in the MHz range. Nevertheless, a much higher time resolution can be obtained by recording the transient amplitude at any given time as a function of the pulse length. Since sP can be changed in 2 ns steps, our setup provides a 2 ns resolution. When the microwave is sufficiently strong, the spin flip rate w becomes large ðw r dÞ and Eq. (1) becomes r DRon ðtÞ DR1 ð0Þ expð2wtÞ þ DR2 ð0Þ exp t : 2 ð3Þ The factors DR1 ð0Þ and DR2 ð0Þ are dependent on the steady state of the system without microwave that exist at the beginning of the pulse ðt ¼ 0Þ. Since the recombination rate change DRon ðsP Þ at the end of the pulse at time sP is the initial condition of Eq. (2), the variation of the pulse length leads to a projection of Eq. (3) on the transient of the much slower decay with time constant d [10].
3. First experimental results with TSR We have utilized TSR for the investigation of nominally undoped lc-Si:H, deposited with electron cyclotron resonance chemical vapor deposition (ECRCVD) on a 1737 corning glass substrate. The sample has a thickness of 2:7 lm and a dark conductivity of rd ¼ 3:8 104 X1 cm1 at room temperature. As mentioned above, the time resolution of the experimental setup is the limiting variable for the TSR experiment. Therefore, a special sample geometry had to be used in order to keep the sample’s RC time low. A 300 nm thick meander shaped lateral Al-contact grid system was deposited on the 4 mm 8 mm sample such that an effective contact length of about 400 mm was accommodated with an average contact distance of 50 lm. Unwanted non-resonant effects like magnetoresistance and microwave-induced current
C. Boehme et al. / Journal of Non-Crystalline Solids 299–302 (2002) 566–570
changes have always been subtracted from the transient. Before the transient measurement was carried out, a verification of the resonant character was made at T ¼ 5 K by recording the transient amplitude at time t ¼ 20 ls after the pulse as a function of the external field B0 (Fig. 3(a)). The sweep reveals two peaks at g ¼ 2:0058ð2Þ and g ¼ 2:001ð2Þ which correspond to the observations made with conventional EDMR in lc-Si:H by Kanschat et al. [4] identifying these lines as the db and CE resonances, respectively. Fig. 3(b) shows the signal transient recorded at the peak of the
Fig. 3. (a) The magnetic field dependence of the transient amplitude taken 20 ls after the microwave pulse ðsP ¼ 320 nsÞ. The solid line is the result of a fit with two Lorentzians (dashed lines) with their respective g values, (b) the real time transient measured at the peak of the resonance at g ¼ 2:0055. The data (solid gray line) is fitted by a single exponential with given time constant sd (dashed line).
569
resonance (g ¼ 2:0055). Since the other exponential decay with time constant r from Eq. (2) was swallowed by the time resolution of the current amplifier, a single exponential fit of this graph is made (hardly distinguishable from the data) that reveals a time constant sd ¼ ð32:6 0:1Þ ls. Here, the inverse of sd can be identified with the pair dissociation rate d ¼ 1=sd ¼ 3:1ð1Þ 104 s1 since the temperature is sufficiently low such that the assumption w d holds. As illustrated in Fig. 3, the exponential fit of the decay function is excellent; the error of the measured time constant is therefore not determined by the fit correlation but the fluctuation of the laser intensity as well as the sample temperature. The error margins of all displayed data points are therefore within the diameter of the circles and crosses which indicate the respective points. With increasing temperature 1=sd remains constant up to about T ¼ 70 K (Fig. 4). Beyond this temperature, 1=sd increases strongly. As shown by Zhou et al. [11], the spin-lattice relaxation probability T11 in lc-Si:H exceeds at this temperature 3 104 s1 , and therefore the dissociation
Fig. 4. The temperature dependence of s1 versus sample d temperature. Below T ¼ 70 K, spin-lattice relaxation is negligible so that the decay time is determined by the dissociation probability d. The temperature independence confirms the tunneling picture of the KSM-pair dissociation process. At higher temperatures, the spin-lattice relaxation time becomes relevant and the decay time is not dissociation related anymore. The solid line is a guide to the eye. The error margins are within the radii of the circles that indicate the data points.
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C. Boehme et al. / Journal of Non-Crystalline Solids 299–302 (2002) 566–570
Fig. 5. The dependence of the transient amplitude versus the pulse length sP . The solid line represents the double exponential fit with fast and slow time constants sw and sr , respectively. The inset shows the linear dependence of s1 as a function of w the microwave field B1 . The error margins are within the radii of the circles and the crosses that indicate the data points.
probability d. Above T ¼ 70 K, 1=sd is determined by the spin-lattice relaxation probability 1=T1 . This behavior is well known from the transients of conventional EDMR [1]. For the evaluation of the recombination probability r, the transient amplitude versus the pulse length was recorded at T ¼ 5 K according to Eq. (3) (Fig. 5). A double exponential fit to our data reveals time constants of sw ¼ ð28 3Þ ns for the fast decay and sr ¼ ð580 60Þ ns for the slow decay. The fast decay can be identified with the spin flip rate 2w, since it turns out to be proportional to the microwave radiation field B1 (Fig. 5, inset). Hence, the necessary conditions outlined above ðd r wÞ are met at T ¼ 5 K and the time constant sr can be identified with 2=r yielding a value for r ¼ ð3:4 0:3Þ 106 s1 .
4. Discussion TSR provides a useful tool for the quantitative investigation of the CE–db recombination dynamics in lc-Si:H. The dissociation probability of
KSM-pairs has a value of d ¼ ð3:1 0:1Þ 104 s1 which is temperature independent up to T ¼ 70 K, the end of the measurable range. Since a thermal dissociation of spin pairs should reveal a strong temperature dependence of 1=d our observation can only be interpreted with the assumption that pair dissociation is a tunneling process of a trapped electron into another trap. The measured dissociation probability can therefore be identified with the tunneling probability between traps. This result strongly supports the picture of low temperature hopping transport and tunneling recombination in lc-Si:H as shown in Fig. 1. The use of very short and intensive resonant microwave pulses allows the reconstruction of the recombination transient during the pulse in the ns range. Therefore, the recombination probability r can be measured. The above results show that TSR is a very powerful method that will enable future access to the dynamics of hopping and recombination process with a resolution unheard of before.
References [1] M. Stutzmann, M.S. Brandt, M.W. Bayerl, J. Non-Cryst. Solids 266–269 (2000) 1. [2] T. Eickelkamp, S. Roth, M. Mehring, Mol. Phys. 95 (1998) 967. [3] H. Dersch, L. Schweitzer, J. Stuke, Phys. Rev. B 28 (8) (1983) 4678. [4] P. Kanschat, K. Lips, W. Fuhs, J. Non-Cryst. Solids 266– 269 (2000) 524. [5] F.C. Rong, W.R. Buchwald, E.H. Pointdexter, W.L. Warren, D.J. Keeble, Solid State Electron. 34 (8) (1991) 835. [6] Z.Z. Ditina, L.P. Strakov, H.H. Helms, Sov. Phys. Semicond. 2 (1969) 1006. [7] M. Brodsky, R.S. Title, Phys. Rev. Lett. 23 (1969) 581. [8] I. Hiromitsu, Y. Kaimori, M. Kitano, T. Ito, Phys. Rev. B 59 (3) (1999) 2151. [9] D. Kaplan, I. Solomon, N.F. Mott, J. Phys. Lett. 39 (1978) L51. [10] C. Boehme, K. Lips, Nucl. Instrum. Methods B 186 (4) (2002) 30. [11] J.-H. Zhou, S. Yamasaki, J. Isoya, K. Ikuta, M. Kondo, A. Matsuda, K. Tanaka, Mater. Res. Soc. Symp. Proc. 452 (1997) 821.