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Recombination at high charge carrier concentrations in a-Si:H films
Thin Solid Films 383 Ž2001. 274᎐276
Recombination at high charge carrier concentrations in a-Si:H films M. Kunst U , F. Wunsch, S. von Aichberger ¨ Hahn Meitner Institut, Section SE, Glienicker Strasse 100, 14109 Berlin, Germany
Abstract The recombination at high excess charge concentrations Žhigher than 10 18 cmy3 . in a-Si:H has been studied by comparison of the excess electron concentration obtained by contactless transient photoconductivity measurements with numerical calculations. The first stage of the recombination process is described satisfactorily by a recombination between mobile excess electrons and all excess holes. In later stages this simple model predicts a too high recombination rate. A better description has been obtained if the recombination rate parameter depends on the energy of the hole. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Recombination; Amorphous semiconductors
1. Introduction Recombination at high excess charge carrier concentrations is important for several a-Si:H based Žopto-. electronic devices. Furthermore, it may be one of the reasons of the degradation of the material. From a theoretical point of view this process is interesting in view of kinetics and transport of charge carriers in amorphous semiconductors. In this work the recombination process is studied by contactless transient photoconductivity measurements in the microwave frequency range ŽTRMC measurements. as a function of the excitation density. 2. Experimental section TRMC measurements are performed by monitoring the change of the microwave power reflection coefficient upon pulsed Ž10 ns FWHM. illumination at 532 nm. The TRMC signal, ⌬ PrP, is proportional to the photoconductance ⌬ S w1x. In intrinsic a-Si:H films only
excess electrons at the bottom of the conduction band are assumed to contribute to ⌬ PrP: ⌬ PrPs An Ž t . n e
Ž1.
where nŽ t . refers to the excess number in cmy2 of electrons at time t after the start of the excitation and n to the electron mobility. The simulation of the experimental data was performed by numerical solution of the continuity equations for electrons and holes, where the interaction of the mobile excess charge carriers with the corresponding band tail Žmultiple trapping. has been taken into account, with the parameters given in the literature w2x ŽMT model.. The non-uniform generation of excess charge carriers Žthe absorption coefficient at 532 nm ␣ 532 s 10 5 cmy1 . is taken into account. The time profile of the generation is simulated using the time profile of the excitation pulse. The MT simulation model is used with various models for recombination. 3. Results and discussion
U
Corresponding author. Tel.: q49-30-80622923; fax: q49-3080622434. E-mail address: [email protected] ŽM. Kunst..
Under the present conditions TRMC signals in a-Si:H films are characterised by a risetime of approximately
0040-6090r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 0 . 0 1 6 0 2 - 3
M. Kunst et al. r Thin Solid Films 383 (2001) 274᎐276
275
excess number of electrons trapped in the tail. is constant. In this case: k⬚rec s rcbt k rec
Fig. 1. The number of mobile excess electrons at 10 ns Ž n ma x . and at 30 ns Ž n 30ns . after the maximum in cmy2 Žas calculated from the TRMC amplitude. as a function of the excitation density in electron᎐hole pairs cmy2 . The drawn line represents the best fit to the MT model for a recombination between the mobile electrons and all holes. The dotted line represents the best fit to the simple model
10 ns to a maximum followed by a fast decay until approximately 40 ns after the start of the excitation giving way to a more gradual decay w1x. The shape of the transients in intrinsic a-Si:H from 0 to 40 ns depends strongly on the shape of the excitation pulse. It was observed that the study of the signal maximum ŽTRMC amplitude. and the signal at 40 ns Ž30 ns after the maximum. is sufficient to determine the adequacy of a recombination model. In Fig. 1 n max Žcalculated from the TRMC amplitude. and n 30ns Ždetermined from the TRMC signal 30 ns after maximum. are plotted as a function of the excitation density. The results are exemplary as it was observed that intrinsic a-Si:H films with a concentration of deep traps smaller than 10 17 cmy3 are characterised by the same value of the TRMC amplitude within the accuracy of the measurements. Calculation of the drift mobility from the low excitation density range, where n max is proportional to the excitation density yields a value 0.5 cm2 Vy1 sy1 . In the higher excitation density range n max becomes sublinearly dependent on the excitation density ŽFig. 1.. This must be due to electron᎐hole recombination during the excitation without participation of dangling bonds. Recombination between mobile electrons Žat the bottom of the conduction band. and all holes Žmainly trapped in the valence band tail. for a rate parameter k rec s 10y8 cmy3 sy1 explains satisfactorily the dependence of n max Žas calculated from the TRMC amplitude. on the excitation density Žthe drawn line in Fig. 1.. Even a still simpler model which does not take multiple trapping into account and assumes only recombination between all electrons and all holes with the same rate parameter k⬚rec , explains n max perfectly Ždotted line in Fig. 1.. The two models are equivalent if rcbt Žthe ratio between the excess number of mobile electrons at the bottom of the conduction band to the
Ž2.
where rcbt s 0.1 for amorphous Si, which agrees very well with the results cited above. Both models overestimate the recombination between 10 and 40 ns after the start of the excitation ŽFig. 1.. Besides, the models do not yield the same results. In this context, it is important to note that MT calculations with parameters in the range given in the literature w2x show a decrease of rcbt in the first microseconds after excitation in contradiction to experimental data. A better fit of the experimental data will be obtained if the recombination rate decreases with time. This can be done by assuming that the recombination rate parameter depends on the energetic position of the hole Žthe energy E relative to the valence band.. This is very generally described by a stretched exponential dependence: k rec Ž E . s kUrec exp Ž y Ž ErEL .
B
.
Ž3.
with EL a reference energy and B a coefficient characterising the stretched exponential. It is clear from Fig. 2 that a better fit of the experimental data can be obtained. If other processes are taken into account Žnot considered in the present work., the recombination rate can decrease with time. Examples are: 䢇
䢇
the decrease of the excess charge concentration density by Želectron. diffusion; and the decrease of the concentration of holes available for recombination by hole trapping in deep defects.
Fig. 2. MT fits of the dependence of n ma x and n 30ns on the excitation density with a stretched exponential dependence of k rec on E wEq. Ž3.x: B s 1 Ž kUrec s 10y7 cm3 sy1 EL s 0.15 eV., B s 5.2 Ž kUrec s 10y7 cm3 sy1 ; EL s 0.32 eV., B s 6.9 Ž kUrec s 10y7 cm3 sy1 EL s 0.33 eV..
276
M. Kunst et al. r Thin Solid Films 383 (2001) 274᎐276
Fig. 3. The TRMC amplitude in an a-Si:H film Žfilled symbols. and in a c-Si film Žopen symbols. as a function of the excitation density. The excitation density unity corresponds to 40 mJ cmy2 .
Also in microcrystalline silicon Žc-Si. films the dependence of the TRMC amplitude on the excitation density shows a transition from a linear dependence at low excitation densities to a sublinear dependence at high excitation densities ŽFig. 3.. The linear range in c-Si extends to much higher excitation densities than in a-Si:H. This may be explained by the much lower absorption coefficient of 532 nm light Ž ␣ 532 s 10 4 cmy1 . c-Si. However, it may be a completely different kind of recombination process. In any case TRMC amplitudes of a-Si:H and c-Si have to be compared very carefully taking into account the dependence on the excitation density.
As a conclusion it can be pointed out that for high excitation densities Ž ⌬ n ) 10 18 cmy3 . pulse-induced charge carrier kinetics reveals an electron᎐hole recombination in a-Si:H, which is characterised by an effective rate parameter decreasing with time. The latter can be explained by the recombination probability on the energy of the holes trapped in the valence band tail. References w1x C. Swiatkowski, M. Kunst, Appl. Phys. A61 Ž1995. 623. w2x R. Bruggeman, Solid State Phenom. 44᎐46 Ž1995. 505. ¨
Recombination at high charge carrier concentrations in a-Si:H films M. Kunst U , F. Wunsch, S. von Aichberger ¨ Hahn Meitner Institut, Section SE, Glienicker Strasse 100, 14109 Berlin, Germany
Abstract The recombination at high excess charge concentrations Žhigher than 10 18 cmy3 . in a-Si:H has been studied by comparison of the excess electron concentration obtained by contactless transient photoconductivity measurements with numerical calculations. The first stage of the recombination process is described satisfactorily by a recombination between mobile excess electrons and all excess holes. In later stages this simple model predicts a too high recombination rate. A better description has been obtained if the recombination rate parameter depends on the energy of the hole. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Recombination; Amorphous semiconductors
1. Introduction Recombination at high excess charge carrier concentrations is important for several a-Si:H based Žopto-. electronic devices. Furthermore, it may be one of the reasons of the degradation of the material. From a theoretical point of view this process is interesting in view of kinetics and transport of charge carriers in amorphous semiconductors. In this work the recombination process is studied by contactless transient photoconductivity measurements in the microwave frequency range ŽTRMC measurements. as a function of the excitation density. 2. Experimental section TRMC measurements are performed by monitoring the change of the microwave power reflection coefficient upon pulsed Ž10 ns FWHM. illumination at 532 nm. The TRMC signal, ⌬ PrP, is proportional to the photoconductance ⌬ S w1x. In intrinsic a-Si:H films only
excess electrons at the bottom of the conduction band are assumed to contribute to ⌬ PrP: ⌬ PrPs An Ž t . n e
Ž1.
where nŽ t . refers to the excess number in cmy2 of electrons at time t after the start of the excitation and n to the electron mobility. The simulation of the experimental data was performed by numerical solution of the continuity equations for electrons and holes, where the interaction of the mobile excess charge carriers with the corresponding band tail Žmultiple trapping. has been taken into account, with the parameters given in the literature w2x ŽMT model.. The non-uniform generation of excess charge carriers Žthe absorption coefficient at 532 nm ␣ 532 s 10 5 cmy1 . is taken into account. The time profile of the generation is simulated using the time profile of the excitation pulse. The MT simulation model is used with various models for recombination. 3. Results and discussion
U
Corresponding author. Tel.: q49-30-80622923; fax: q49-3080622434. E-mail address: [email protected] ŽM. Kunst..
Under the present conditions TRMC signals in a-Si:H films are characterised by a risetime of approximately
0040-6090r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 0 . 0 1 6 0 2 - 3
M. Kunst et al. r Thin Solid Films 383 (2001) 274᎐276
275
excess number of electrons trapped in the tail. is constant. In this case: k⬚rec s rcbt k rec
Fig. 1. The number of mobile excess electrons at 10 ns Ž n ma x . and at 30 ns Ž n 30ns . after the maximum in cmy2 Žas calculated from the TRMC amplitude. as a function of the excitation density in electron᎐hole pairs cmy2 . The drawn line represents the best fit to the MT model for a recombination between the mobile electrons and all holes. The dotted line represents the best fit to the simple model
10 ns to a maximum followed by a fast decay until approximately 40 ns after the start of the excitation giving way to a more gradual decay w1x. The shape of the transients in intrinsic a-Si:H from 0 to 40 ns depends strongly on the shape of the excitation pulse. It was observed that the study of the signal maximum ŽTRMC amplitude. and the signal at 40 ns Ž30 ns after the maximum. is sufficient to determine the adequacy of a recombination model. In Fig. 1 n max Žcalculated from the TRMC amplitude. and n 30ns Ždetermined from the TRMC signal 30 ns after maximum. are plotted as a function of the excitation density. The results are exemplary as it was observed that intrinsic a-Si:H films with a concentration of deep traps smaller than 10 17 cmy3 are characterised by the same value of the TRMC amplitude within the accuracy of the measurements. Calculation of the drift mobility from the low excitation density range, where n max is proportional to the excitation density yields a value 0.5 cm2 Vy1 sy1 . In the higher excitation density range n max becomes sublinearly dependent on the excitation density ŽFig. 1.. This must be due to electron᎐hole recombination during the excitation without participation of dangling bonds. Recombination between mobile electrons Žat the bottom of the conduction band. and all holes Žmainly trapped in the valence band tail. for a rate parameter k rec s 10y8 cmy3 sy1 explains satisfactorily the dependence of n max Žas calculated from the TRMC amplitude. on the excitation density Žthe drawn line in Fig. 1.. Even a still simpler model which does not take multiple trapping into account and assumes only recombination between all electrons and all holes with the same rate parameter k⬚rec , explains n max perfectly Ždotted line in Fig. 1.. The two models are equivalent if rcbt Žthe ratio between the excess number of mobile electrons at the bottom of the conduction band to the
Ž2.
where rcbt s 0.1 for amorphous Si, which agrees very well with the results cited above. Both models overestimate the recombination between 10 and 40 ns after the start of the excitation ŽFig. 1.. Besides, the models do not yield the same results. In this context, it is important to note that MT calculations with parameters in the range given in the literature w2x show a decrease of rcbt in the first microseconds after excitation in contradiction to experimental data. A better fit of the experimental data will be obtained if the recombination rate decreases with time. This can be done by assuming that the recombination rate parameter depends on the energetic position of the hole Žthe energy E relative to the valence band.. This is very generally described by a stretched exponential dependence: k rec Ž E . s kUrec exp Ž y Ž ErEL .
B
.
Ž3.
with EL a reference energy and B a coefficient characterising the stretched exponential. It is clear from Fig. 2 that a better fit of the experimental data can be obtained. If other processes are taken into account Žnot considered in the present work., the recombination rate can decrease with time. Examples are: 䢇
䢇
the decrease of the excess charge concentration density by Želectron. diffusion; and the decrease of the concentration of holes available for recombination by hole trapping in deep defects.
Fig. 2. MT fits of the dependence of n ma x and n 30ns on the excitation density with a stretched exponential dependence of k rec on E wEq. Ž3.x: B s 1 Ž kUrec s 10y7 cm3 sy1 EL s 0.15 eV., B s 5.2 Ž kUrec s 10y7 cm3 sy1 ; EL s 0.32 eV., B s 6.9 Ž kUrec s 10y7 cm3 sy1 EL s 0.33 eV..
276
M. Kunst et al. r Thin Solid Films 383 (2001) 274᎐276
Fig. 3. The TRMC amplitude in an a-Si:H film Žfilled symbols. and in a c-Si film Žopen symbols. as a function of the excitation density. The excitation density unity corresponds to 40 mJ cmy2 .
Also in microcrystalline silicon Žc-Si. films the dependence of the TRMC amplitude on the excitation density shows a transition from a linear dependence at low excitation densities to a sublinear dependence at high excitation densities ŽFig. 3.. The linear range in c-Si extends to much higher excitation densities than in a-Si:H. This may be explained by the much lower absorption coefficient of 532 nm light Ž ␣ 532 s 10 4 cmy1 . c-Si. However, it may be a completely different kind of recombination process. In any case TRMC amplitudes of a-Si:H and c-Si have to be compared very carefully taking into account the dependence on the excitation density.
As a conclusion it can be pointed out that for high excitation densities Ž ⌬ n ) 10 18 cmy3 . pulse-induced charge carrier kinetics reveals an electron᎐hole recombination in a-Si:H, which is characterised by an effective rate parameter decreasing with time. The latter can be explained by the recombination probability on the energy of the holes trapped in the valence band tail. References w1x C. Swiatkowski, M. Kunst, Appl. Phys. A61 Ž1995. 623. w2x R. Bruggeman, Solid State Phenom. 44᎐46 Ž1995. 505. ¨