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Carrier mobilities in microcrystalline silicon films
Thin Solid Films 515 (2007) 7486 – 7489 www.elsevier.com/locate/tsf
Carrier mobilities in microcrystalline silicon films T. Bronger ⁎, R. Carius Forschungszentrum Jülich, IPV, 52425 Jülich, Germany Available online 25 January 2007
Abstract For a better understanding of electronic transport mechanisms in thin-film silicon solar cell quality films, we have investigated the Hall mobility for electrons in microcrystalline/amorphous silicon over a range of crystallinities and doping concentrations. We find that Hall mobility increases with increasing doping concentration in accordance with earlier measurements. With increasing amorphous fraction, the measured mobility decreases suggesting a negative influence of the additional disorder. The results suggest a differential mobility model in which mobility depends on the energy level of the carriers that contribute to the electrical current. © 2006 Elsevier B.V. All rights reserved. Keywords: Electrical properties; Mobility; Microcrystalline silicon; Thin-film silicon
1. Introduction For thin-film silicon solar cells, charge carrier mobility is one of the vital properties that could limit efficiency because low mobility may lead to higher carrier recombination. Recently, solar cell properties with absorber layers prepared at the transition from microcrystalline to amorphous growth have attracted much interest [1]. Although the electronic properties of μc-Si have been already investigated before [2–4] and models have been proposed [3,4], the influence of the microstructure on carrier mobility is still not well understood. The goal is to learn more about the dominating mechanisms of electronic transport in this material. In order to validate and improve the previous models, we need information about the density of states below the conduction band, in particular at the Fermi level, and information about the distribution of potential barriers which affect transport. Thus, in order to get more insight into the electronic structure of μc-Si, we have determined Hall mobilities of a sample series of thin silicon layers with different doping concentrations and crystallinities. In other words, we laid out a two-dimensional sample matrix with both parameters varied over a sensible range. This enabled us to determine the influence of these two parameters on conductivity, carrier mobility, and carrier density, ⁎ Corresponding author. E-mail address: [email protected] (T. Bronger). 0040-6090/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2006.11.091
as well as the influence of carrier density on mobility. Moreover, temperature-dependent measurements give additional clues to the underlying processes. 2. Experiments The samples are μc-Si:H layers with layer thicknesses from 3 to 5 μm. They were prepared on rough quartz substrate with VHF-PECVD (Very High Frequency Plasma Enhanced Chemical Vapour Deposition at 95 MHz) at TS = 200 °C. The pressure in the chamber was pdepo = 40 Pa and the plasma power density P = 0.07 W/cm2. The deposition feed gas for the undoped films was silane in hydrogen. Doping was achieved by gas admixture of PH3 for the deposition of n-type layers. All ppm values in this work refer to the gas phase concentration of the dopant gas with respect to silane. We structured and contacted the final Hall samples photolithographically in order to minimise offset voltages. The typical Hall bar geometry was 6 × 1.9 mm2, having two pairs of Hall contacts. The crystallinity of the samples ranges from 10% to 80%. So in particular, the transition between predominantly microcrystalline and predominantly amorphous silicon is included into the sample matrix. The crystallinities were determined by Raman scattering measurements at 647 nm excitation with the semi-quantitative estimate for the crystalline volume fraction ICRS = I520 / (I520 + I480) [5].
T. Bronger, R. Carius / Thin Solid Films 515 (2007) 7486–7489
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an activation energy, but slightly bended with a positive curvature. This observation is more pronounced for the investigated mobility but in a weaker form also valid for most carrier density curves. For the low crystallinity samples, there are two peculiarities worth mentioning: First, they show a maximum or a plateau of the Hall mobility slightly above room temperature. (Higher temperatures are impossible because they would be too close to the deposition temperature as stated above.) And secondly, the electron density seems to be singly-activated, with 52 meV and 12 meV for 1 ppm and 10 ppm, respectively. Fig. 3 shows room temperature mobility vs. electron density for two different crystallinities. One can clearly see that mobility increases with increasing carrier density for a given crystallinity. Finally, Fig. 4 shows that mobility increases with crystallinity for a fixed doping, an effect that is weaker for higher-doped samples. Fig. 1. Carrier concentration vs. doping concentration at room temperature of samples with various crystallinities. The solid line indicates a calculated upper limit further explained in the text.
The Hall setup used in the experiments holds the sample in a dark, evacuated cryostat, with a magnetic flux of 1.9 T through the sample, while the base voltage can be set between 10 V to 1000 V. The electrical power in the sample is kept low enough to avoid local heating so that Hall voltage is proportional to both base current and magnetic flux. Temperature was varied from 80 K to 430 K. The upper temperature limit was chosen well below the substrate temperature during deposition in order to avoid changes of the sample structure. During the measurement, the polarity of the magnetic field is switched, while the current through the sample is kept constant. For both directions of the magnetic field, the side voltages are determined. Their difference is twice the Hall voltage cleared from a constant offset voltage. The measurement of weakly doped and highly amorphous samples is difficult because of high sample resistances (up to 10 GΩ). Therefore, a sophisticated control and analysis program has been developed to distinguish between significant and insignificant measurements.
4. Discussion Fig. 1 shows that the samples exhibit the expected trend, namely that carrier density is proportional to gas dopant
3. Results Fig. 1 shows the dependence of carrier density on (nominal) doping concentration at room temperature. The solid straight line represents the case that both built-in factor and doping efficiency are unity, and that almost all donors are ionised, so that only the atomic density in silicon determines the carrier density. Fig. 2 visualises data derived from Hall measurements as a function of temperature of two crystallinities (35% and 70%) and with a nominal doping concentration of 1 and 10 ppm. In Fig. 2a the mobility and in Fig. 2b the carrier concentration is shown in an Arrhenius plot. Generally the behaviour is similar to the one described in [2,4] for highly crystalline material: Both mobility and carrier density decrease with decreasing temperature. Additionally, at least the mobility curves are not straight lines for which one could determine
Fig. 2. Electron mobility (a) and electron density (b) of samples with two crystallinities and two doping concentrations as a function of reciprocal temperature.
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T. Bronger, R. Carius / Thin Solid Films 515 (2007) 7486–7489
concentration. Quantitatively, all points lie below the solid lines which marks the carrier density if every dopant atom generates a free carrier. The measured carrier densities are a factor of two smaller. This shortage is similar to our earlier results and mostly can be attributed to a built-in coefficient of about 50% [4]. Moreover, the data suggests that the density of impurities and deep defects can be neglected here since there is no significant offset. Similarly, partial ionisation of donors is not an issue because at room temperature, more than 90% of all donors should be ionised, in line with the results in Fig. 2 for the less crystalline samples, where at 300 K donor depletion is reached. The temperature dependence of electron mobility in Fig. 2a clearly shows that it cannot be described by a single activation energy. Even very accurate temperature measurements (ΔT b 0.5 K) for one particular sample didn't straighten out the line. To describe the transport in μc-Si, we consider a combination of three effects: first, potential barriers limit transport; secondly, carriers can interact with traps; thirdly, transport occurs in the band tail below the conduction band, where, in analogy to amorphous silicon, mobility is energy-dependent [6]. Charged barriers at grain boundaries were used successfully in [7] to describe mobility effects in poly-crystalline silicon layers. However, such barriers have not been regarded as the major cause for highly doped μc-Si in [4] and [8], for various reasons. Other possible sources of barriers though, which may play a significant role in transport, such as thin amorphous regions between the crystallites, have been discussed [3,9]. Further candidates for barriers are stacking faults within the crystallites. The disorder in μc-Si causes a spatially and energetic distribution of barriers, which helps to understand the curves in Fig. 2a. With increasing temperature, the charge carriers are able
Fig. 3. Room temperature electron mobility vs. electron density for two different crystallinities.
Fig. 4. Room temperature electron mobility vs. crystallinity for two different doping concentrations.
to overcome higher barriers. This opens new paths with higher mobility (because they are less disordered and/or because they are shorter) through the microcrystalline material for the electrical current. Thus, the enhanced activation energy at high temperatures is the result of additional pathways over higher barriers leading to transport paths of enhanced mobility. There is a strong evidence for band tail states in μc-Si, for example through optical absorption experiments [10]. They have also been reported for poly-crystalline silicon in [11]. Electronic transport in this band tail was proposed [3]. The underlying idea is the concept of a differential mobility in the band tail similar to the one proposed by [6] for amorphous silicon. In this model, mobility is high for an energy level with a high density of states. The density of states is supposed to increase towards the conduction band, similarly to amorphous silicon. Since a raise in temperature means that electrons of increasingly high energy take part in the electrical transport, one expects an increasing effective mobility. Although this explains the qualitative dependence of mobility on temperature easily, more information is needed for explaining the curves quantitatively. First and foremost, knowledge of the density of states in the band tail is crucial for a viable model. This would be particularly interesting because it would help with the question whether or not barriers play a significant role in transport in μc-Si. As for the maximum of mobility at 300 K for less crystalline samples, we assume that the donor levels are depleted and the typical limiting factor of silicon, namely phonon scattering, becomes dominant above this temperature. The temperature dependence of the carrier density can be understood by the temperature-dependent shift of the Fermi level. Fig. 3 shows a clear trend for μc-Si films with low crystallinity (35%), namely that mobility increases with carrier density. In the differential mobility model, the increasing number of carriers results in a higher Fermi energy, so that carriers taking part in transport energetically lie in a region with a higher density of states, thus leading to an increased mobility [8].
T. Bronger, R. Carius / Thin Solid Films 515 (2007) 7486–7489
The dependence of mobility on crystallinity as visualised in Fig. 4 is explained best with the barrier model since the transition from a crystalline to an amorphous region is a high barrier due to the wider band gap. At high crystalline volume fraction, paths that are short and/or highly mobile are very probable for electrical transport. On the other hand, a decreasing crystalline volume fraction means an increasing necessity for the electrons to use paths with minor effective mobility (including the effect of increasing path length). Acknowledgements The authors wish to thank Thorsten Dylla for the preparation of the sample matrix, and Friedhelm Finger and Wolfhard Beyer for several discussions. References [1] O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Mück, B. Rech, H. Wagner, Sol. Energy Mater. Sol. Cells 62 (2000) 97.
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[2] G. Willeke, in: J. Kanicki (Ed.), Materials and Device Physics, Amorphous and Microcrystalline Semiconductor Devices, vol. 2, Artech House, Boston, 1992, p. 55, chap. 2. [3] R. Carius, J. Müller, F. Finger, N. Harder, P. Hapke, Thin Film Material and Devices — Developments in Science and Technology, World Scientific Co. Pte. Ltd., Singapore, 1999, p. 157. [4] U. Backhausen, R. Carius, F. Finger, P. Hapke, U. Zastrow, H. Wagner, Mater. Res. Soc. Symp. Proc. 452 (1997) 833. [5] L. Houben, M. Luysberg, P. Hapke, R. Carius, F. Finger, H. Wagner, Philos. Mag., A 77 (1998) 1447. [6] H. Overhof, P. Thomas, Electronic Transport in Hydrogenated Amorphous Semiconductors, Springer Tracts in Modern Physics, vol. 114, Springer, 1989. [7] J. Seto, J. Appl. Phys. 46 (1975) 5247. [8] N. Harder, Elektrischer Transport in dotierten und undotierten mikrokristallinen Siliziumschichten, Diploma thesis, Universität Leipzig, Germany (2000). [9] H. Overhof, M. Otte, M. Schmidtke, U. Backhausen, R. Carius, J. NonCryst. Solids 227 (1998) 992. [10] R. Carius, F. Finger, U. Backhausen, M. Luysberg, P. Hapke, L. Houben, M. Otte, H. Overhof, Mater. Res. Soc. Symp. Proc. 467 (1997) 283. 9. [11] J. Werner, M. Peisl, Phys. Rev., B, Condens. Matter Mater. Phys. 31 (1985) 6881.
Carrier mobilities in microcrystalline silicon films T. Bronger ⁎, R. Carius Forschungszentrum Jülich, IPV, 52425 Jülich, Germany Available online 25 January 2007
Abstract For a better understanding of electronic transport mechanisms in thin-film silicon solar cell quality films, we have investigated the Hall mobility for electrons in microcrystalline/amorphous silicon over a range of crystallinities and doping concentrations. We find that Hall mobility increases with increasing doping concentration in accordance with earlier measurements. With increasing amorphous fraction, the measured mobility decreases suggesting a negative influence of the additional disorder. The results suggest a differential mobility model in which mobility depends on the energy level of the carriers that contribute to the electrical current. © 2006 Elsevier B.V. All rights reserved. Keywords: Electrical properties; Mobility; Microcrystalline silicon; Thin-film silicon
1. Introduction For thin-film silicon solar cells, charge carrier mobility is one of the vital properties that could limit efficiency because low mobility may lead to higher carrier recombination. Recently, solar cell properties with absorber layers prepared at the transition from microcrystalline to amorphous growth have attracted much interest [1]. Although the electronic properties of μc-Si have been already investigated before [2–4] and models have been proposed [3,4], the influence of the microstructure on carrier mobility is still not well understood. The goal is to learn more about the dominating mechanisms of electronic transport in this material. In order to validate and improve the previous models, we need information about the density of states below the conduction band, in particular at the Fermi level, and information about the distribution of potential barriers which affect transport. Thus, in order to get more insight into the electronic structure of μc-Si, we have determined Hall mobilities of a sample series of thin silicon layers with different doping concentrations and crystallinities. In other words, we laid out a two-dimensional sample matrix with both parameters varied over a sensible range. This enabled us to determine the influence of these two parameters on conductivity, carrier mobility, and carrier density, ⁎ Corresponding author. E-mail address: [email protected] (T. Bronger). 0040-6090/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2006.11.091
as well as the influence of carrier density on mobility. Moreover, temperature-dependent measurements give additional clues to the underlying processes. 2. Experiments The samples are μc-Si:H layers with layer thicknesses from 3 to 5 μm. They were prepared on rough quartz substrate with VHF-PECVD (Very High Frequency Plasma Enhanced Chemical Vapour Deposition at 95 MHz) at TS = 200 °C. The pressure in the chamber was pdepo = 40 Pa and the plasma power density P = 0.07 W/cm2. The deposition feed gas for the undoped films was silane in hydrogen. Doping was achieved by gas admixture of PH3 for the deposition of n-type layers. All ppm values in this work refer to the gas phase concentration of the dopant gas with respect to silane. We structured and contacted the final Hall samples photolithographically in order to minimise offset voltages. The typical Hall bar geometry was 6 × 1.9 mm2, having two pairs of Hall contacts. The crystallinity of the samples ranges from 10% to 80%. So in particular, the transition between predominantly microcrystalline and predominantly amorphous silicon is included into the sample matrix. The crystallinities were determined by Raman scattering measurements at 647 nm excitation with the semi-quantitative estimate for the crystalline volume fraction ICRS = I520 / (I520 + I480) [5].
T. Bronger, R. Carius / Thin Solid Films 515 (2007) 7486–7489
7487
an activation energy, but slightly bended with a positive curvature. This observation is more pronounced for the investigated mobility but in a weaker form also valid for most carrier density curves. For the low crystallinity samples, there are two peculiarities worth mentioning: First, they show a maximum or a plateau of the Hall mobility slightly above room temperature. (Higher temperatures are impossible because they would be too close to the deposition temperature as stated above.) And secondly, the electron density seems to be singly-activated, with 52 meV and 12 meV for 1 ppm and 10 ppm, respectively. Fig. 3 shows room temperature mobility vs. electron density for two different crystallinities. One can clearly see that mobility increases with increasing carrier density for a given crystallinity. Finally, Fig. 4 shows that mobility increases with crystallinity for a fixed doping, an effect that is weaker for higher-doped samples. Fig. 1. Carrier concentration vs. doping concentration at room temperature of samples with various crystallinities. The solid line indicates a calculated upper limit further explained in the text.
The Hall setup used in the experiments holds the sample in a dark, evacuated cryostat, with a magnetic flux of 1.9 T through the sample, while the base voltage can be set between 10 V to 1000 V. The electrical power in the sample is kept low enough to avoid local heating so that Hall voltage is proportional to both base current and magnetic flux. Temperature was varied from 80 K to 430 K. The upper temperature limit was chosen well below the substrate temperature during deposition in order to avoid changes of the sample structure. During the measurement, the polarity of the magnetic field is switched, while the current through the sample is kept constant. For both directions of the magnetic field, the side voltages are determined. Their difference is twice the Hall voltage cleared from a constant offset voltage. The measurement of weakly doped and highly amorphous samples is difficult because of high sample resistances (up to 10 GΩ). Therefore, a sophisticated control and analysis program has been developed to distinguish between significant and insignificant measurements.
4. Discussion Fig. 1 shows that the samples exhibit the expected trend, namely that carrier density is proportional to gas dopant
3. Results Fig. 1 shows the dependence of carrier density on (nominal) doping concentration at room temperature. The solid straight line represents the case that both built-in factor and doping efficiency are unity, and that almost all donors are ionised, so that only the atomic density in silicon determines the carrier density. Fig. 2 visualises data derived from Hall measurements as a function of temperature of two crystallinities (35% and 70%) and with a nominal doping concentration of 1 and 10 ppm. In Fig. 2a the mobility and in Fig. 2b the carrier concentration is shown in an Arrhenius plot. Generally the behaviour is similar to the one described in [2,4] for highly crystalline material: Both mobility and carrier density decrease with decreasing temperature. Additionally, at least the mobility curves are not straight lines for which one could determine
Fig. 2. Electron mobility (a) and electron density (b) of samples with two crystallinities and two doping concentrations as a function of reciprocal temperature.
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T. Bronger, R. Carius / Thin Solid Films 515 (2007) 7486–7489
concentration. Quantitatively, all points lie below the solid lines which marks the carrier density if every dopant atom generates a free carrier. The measured carrier densities are a factor of two smaller. This shortage is similar to our earlier results and mostly can be attributed to a built-in coefficient of about 50% [4]. Moreover, the data suggests that the density of impurities and deep defects can be neglected here since there is no significant offset. Similarly, partial ionisation of donors is not an issue because at room temperature, more than 90% of all donors should be ionised, in line with the results in Fig. 2 for the less crystalline samples, where at 300 K donor depletion is reached. The temperature dependence of electron mobility in Fig. 2a clearly shows that it cannot be described by a single activation energy. Even very accurate temperature measurements (ΔT b 0.5 K) for one particular sample didn't straighten out the line. To describe the transport in μc-Si, we consider a combination of three effects: first, potential barriers limit transport; secondly, carriers can interact with traps; thirdly, transport occurs in the band tail below the conduction band, where, in analogy to amorphous silicon, mobility is energy-dependent [6]. Charged barriers at grain boundaries were used successfully in [7] to describe mobility effects in poly-crystalline silicon layers. However, such barriers have not been regarded as the major cause for highly doped μc-Si in [4] and [8], for various reasons. Other possible sources of barriers though, which may play a significant role in transport, such as thin amorphous regions between the crystallites, have been discussed [3,9]. Further candidates for barriers are stacking faults within the crystallites. The disorder in μc-Si causes a spatially and energetic distribution of barriers, which helps to understand the curves in Fig. 2a. With increasing temperature, the charge carriers are able
Fig. 3. Room temperature electron mobility vs. electron density for two different crystallinities.
Fig. 4. Room temperature electron mobility vs. crystallinity for two different doping concentrations.
to overcome higher barriers. This opens new paths with higher mobility (because they are less disordered and/or because they are shorter) through the microcrystalline material for the electrical current. Thus, the enhanced activation energy at high temperatures is the result of additional pathways over higher barriers leading to transport paths of enhanced mobility. There is a strong evidence for band tail states in μc-Si, for example through optical absorption experiments [10]. They have also been reported for poly-crystalline silicon in [11]. Electronic transport in this band tail was proposed [3]. The underlying idea is the concept of a differential mobility in the band tail similar to the one proposed by [6] for amorphous silicon. In this model, mobility is high for an energy level with a high density of states. The density of states is supposed to increase towards the conduction band, similarly to amorphous silicon. Since a raise in temperature means that electrons of increasingly high energy take part in the electrical transport, one expects an increasing effective mobility. Although this explains the qualitative dependence of mobility on temperature easily, more information is needed for explaining the curves quantitatively. First and foremost, knowledge of the density of states in the band tail is crucial for a viable model. This would be particularly interesting because it would help with the question whether or not barriers play a significant role in transport in μc-Si. As for the maximum of mobility at 300 K for less crystalline samples, we assume that the donor levels are depleted and the typical limiting factor of silicon, namely phonon scattering, becomes dominant above this temperature. The temperature dependence of the carrier density can be understood by the temperature-dependent shift of the Fermi level. Fig. 3 shows a clear trend for μc-Si films with low crystallinity (35%), namely that mobility increases with carrier density. In the differential mobility model, the increasing number of carriers results in a higher Fermi energy, so that carriers taking part in transport energetically lie in a region with a higher density of states, thus leading to an increased mobility [8].
T. Bronger, R. Carius / Thin Solid Films 515 (2007) 7486–7489
The dependence of mobility on crystallinity as visualised in Fig. 4 is explained best with the barrier model since the transition from a crystalline to an amorphous region is a high barrier due to the wider band gap. At high crystalline volume fraction, paths that are short and/or highly mobile are very probable for electrical transport. On the other hand, a decreasing crystalline volume fraction means an increasing necessity for the electrons to use paths with minor effective mobility (including the effect of increasing path length). Acknowledgements The authors wish to thank Thorsten Dylla for the preparation of the sample matrix, and Friedhelm Finger and Wolfhard Beyer for several discussions. References [1] O. Vetterl, F. Finger, R. Carius, P. Hapke, L. Houben, O. Kluth, A. Lambertz, A. Mück, B. Rech, H. Wagner, Sol. Energy Mater. Sol. Cells 62 (2000) 97.
7489
[2] G. Willeke, in: J. Kanicki (Ed.), Materials and Device Physics, Amorphous and Microcrystalline Semiconductor Devices, vol. 2, Artech House, Boston, 1992, p. 55, chap. 2. [3] R. Carius, J. Müller, F. Finger, N. Harder, P. Hapke, Thin Film Material and Devices — Developments in Science and Technology, World Scientific Co. Pte. Ltd., Singapore, 1999, p. 157. [4] U. Backhausen, R. Carius, F. Finger, P. Hapke, U. Zastrow, H. Wagner, Mater. Res. Soc. Symp. Proc. 452 (1997) 833. [5] L. Houben, M. Luysberg, P. Hapke, R. Carius, F. Finger, H. Wagner, Philos. Mag., A 77 (1998) 1447. [6] H. Overhof, P. Thomas, Electronic Transport in Hydrogenated Amorphous Semiconductors, Springer Tracts in Modern Physics, vol. 114, Springer, 1989. [7] J. Seto, J. Appl. Phys. 46 (1975) 5247. [8] N. Harder, Elektrischer Transport in dotierten und undotierten mikrokristallinen Siliziumschichten, Diploma thesis, Universität Leipzig, Germany (2000). [9] H. Overhof, M. Otte, M. Schmidtke, U. Backhausen, R. Carius, J. NonCryst. Solids 227 (1998) 992. [10] R. Carius, F. Finger, U. Backhausen, M. Luysberg, P. Hapke, L. Houben, M. Otte, H. Overhof, Mater. Res. Soc. Symp. Proc. 467 (1997) 283. 9. [11] J. Werner, M. Peisl, Phys. Rev., B, Condens. Matter Mater. Phys. 31 (1985) 6881.