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Charge Carrier Lifetime Shift Induced by Temperature Variation during a MWPCD Measurement
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 38 (2013) 153 – 160
SiliconPV: March 25-27, 2013, Hamelin, Germany
Charge carrier lifetime shift induced by temperature variation during a MWPCD measurement Christian Möllera,b * and Kevin Lauera a
CiS Forschungsinstitut für Mikrosensorik und Photovoltaik GmbH, Konrad-Zuse-Str. 14, 99099 Erfurt, Germany b TU Ilmenau, Institut für Physik, Weimarer Str. 32, 98693 Ilmenau, Germany
Abstract In this work the temperature of a silicon sample excited by a laser during a time dependent microwave-detected photoconductance decay (MWPCD) measurement was logged. 2 °C temperature increase on the backside of the wafer was observed. Temperature dependent charge carrier lifetime calculations using the determined temperature characteristic are compared to time dependent MWPCD measurements of a boron-doped wafer with high oxygen content. The time duration to reach the final temperature fits well with the time scale of the fast forming recombination center of the boron-oxygen related defect. Charge carrier lifetime variation due to temperature increase is discussed in view of different defect parameters.
© 2013 The Authors. Published by Elsevier Ltd. © 2013 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the scientific committee of the SiliconPV 2013 Selection and/or peer-review under responsibility of the scientific committee of the SiliconPV 2013 conference conference Keywords: charge carrier lifetime, temperature variation, boron-oxygen related defect, MWPCD
1. Motivation The most frequent lifetime limiting recombination center in current solar grade boron-doped Czochralski (CZ) silicon solar cells is caused by a boron-oxygen related defect [1]. This recombination active defect is activated under illumination or electron injection in the dark. Bothe and Schmidt [2] detected a fast and a slowly forming recombination center in time dependent V oc measurements. However, despite intensive research, the origin of the boron oxygen recombination center is still unclear [3]. In temperature corrected Voc measurements the fast forming recombination center is not visible [4]. That leads to the assumption, that the physical effects occurring during the illumination for defect formation are overlaid by temperature induced lifetime variations. For every charge carrier lifetime
* Corresponding author. Tel.: +49 361 663 1211; fax: +49 361 663 1413. E-mail address: [email protected]
1876-6102 © 2013 The Authors. Published by Elsevier Ltd.
Selection and/or peer-review under responsibility of the scientific committee of the SiliconPV 2013 conference doi:10.1016/j.egypro.2013.07.262
154
Christian Möller and Kevin Lauer / Energy Procedia 38 (2013) 153 – 160
measurement, excess carriers have to be generated by laser or flash lamp. Due to the illumination a temperature increase in the sample occurs. During time dependent studies with permanent charge carrier lifetime measurement this temperature increase is not negligible. In this study, the charge carrier lifetime change during defect formation was measured with a microwave-detected photoconductance decay (MWPCD) setup in which the laser was also used to activate the boron-oxygen defect. In this work, temperature increase induced by long time MWPCD measurements is recorded for the first time. Temperature dependent calculations are compared with MWPCD measurements of the formation of the boron-oxygen complex. The observed temperature induced lifetime effects are discussed in view of the boron-oxygen recombination center activation. 2. Experimental details The photoconductance decay was measured with the Semilab WT-2000 MWPCD device. A description of the setup is given in Refs. [5] and [6]. Excess charge carrier generation and light soaking of the sample was done with the laser of the setup. The laser works at 904 nm with 200 ns pulse length and a maximum average intensity of 8500 Wm-2. Charge carrier lifetime was calculated form the MWPCD signal and compared with a quasi-steady-state photoconductance decay (QSSPC) measurement to calibrate the excess charge carrier density [7]. To deactivate the boron-oxygen related defect the sample is annealed at 200°C for 10 min [1] before each measurement. The temperature of the sample was measured with a Peltier element on the backside of a test wafer with a thickness of 120 μm directly below the MWPCD excitation laser. For temperature- and time dependent charge carrier lifetime measurement the same measuring procedure is used: First, a lifetime measurement at a time range of some milliseconds is done. The laser pulse generates excess charge carriers and the microwave reflection decay is logged. The mean deposited laser intensity in this time sequence induces only a very low temperature increase. Afterwards the maximum laser power is deposited into the sample. This is achieved by a shortened time range between the laser pulses. Microwave reflection decay is not logged. This intense illumination is done for about 70 s. Now the microwave reflection decay is measured again (longer time between the single laser pulses), followed by intense illumination and so on. All presented charge carrier lifetime calculations take band to band recombination, Auger recombination [8] and Shockley-Read-Hall (SRH) recombination [9,10] into account. The temperature dependences of the parameters are considered after Green [11]. 3. Results 3.1. Temperature change during the measurement The time dependent temperature characteristic is shown in Fig. 1. Temperature was normalised to the final temperature at the Celsius scale. As fitting function y
A1 exp
t
b1
A2 exp
t
b2
1
was chosen. A temperature difference up to 2 °C occurs during the first three hours of the measurement, independent of the common expected starting temperature (this was observed with different starting temperatures up to 28 °C).
Christian Möller and Kevin Lauer / Energy Procedia 38 (2013) 153 – 160
normalised temperature
1.00
0.98
0.96
measured temperature exponential fit
0.94
0
3000
6000
9000
12000
15000
time (s) Fig. 1. Temperature change during the first four hours of the measurement. The temperature is normalised to the final temperature at the Celsius scale. Temperature steady state is reached after about 12000 s.
The time to reach the temperature steady state in Fig. 1 is influenced by the lateral thermal conduction and the heat radiation of the silicon sample. A fast (the first 200 s) and a slow (3 hours) temperature increase is observed. The fast temperature increase is caused by the thermal conduction in vertical dimension. A COMSOL Multiphysics [12] simulation is used to establish this assumption. Thermal diffusion from the laser light excitation to the sensor at the rear side of the sample was simulated. Further, surface to ambient radiation was supposed. Model size was 0.12 x 0.4 mm2. Fig. 2 displays the result of the simulation for a 120 μm thick sample with different heat fluxes. The time to reach the temperature steady state is independent of the inserted heat flux. The sample thickness influences the time to reach the steady state (insert of Fig. 2). Temperature increase stops after about 120 s in the 120 μm sample and after about 150 s in the 200 μm sample (dashed vertical lines in Fig. 2). This time scale fits well with the experimental observed time scale of about 180 s for the fast temperature increase at the beginning. The second, slower temperature increase is caused by the thermal diffusion in horizontal direction. With increasing thermal warming the surface to ambient radiation increase due to the larger warmed-up area and the temperature rise decelerate. 27.0
26.5 27
temperature (°C)
temperature (°C)
2
570 W/m 2 400 W/m
26.0
25.5
25.0
0
26
200μm, 570 W/m 25
0
100
100
time (s) 200
2
200
300
time (s) Fig. 2. Simulated temperature increase at the backside of a silicon sample due to a constant heat flux at the top. The inset shows the result of the simulation for a 200 μm thick sample. The time to reach the steady state is dependent on the sample thickness.
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Christian Möller and Kevin Lauer / Energy Procedia 38 (2013) 153 – 160
3.2. Temperature influence on lifetime
8.0%
b) 1.0
1.0
0.8
0.8
5.4%
Et (eV)
Et(eV)
a)
0.6
0.6
0.4
0.4
2.4%
0.2
0.2
0.0
0.0 1E-18
1E-16
1E-18
1E-14
n
1E-16
1E-14
-0.6%
2
2
(cm ) n
(cm )
relative lifetime change due to temperature increase of 2°C
Fig. 3 shows the relative change in lifetime due to a temperature increase of 2 °C (from 26 °C to 28 °C) and the impact of the defect density Nt. Constant electron capture cross section n and variable hole cross section p looks similar (not shown here). Dependent on the capture cross sections, charge carrier lifetime increase or decrease during temperature rising. A strong lifetime increase (positive percent values, filled area) up to 8 % is possible. The trap energies of the corresponding defects are located near valence and conduction band. Lifetime decrease up to 0.6 % after temperature rising is possible by defects located in the middle of the band gap. The area of constant charge carrier lifetime (white area in Fig. 3) after temperature shifting decrease with increasing trap density Nt.
Fig. 3. Calculated charge carrier lifetime change due to a temperature increase of 2 °C for different trap energies Et and electron capture cross sections n. Positive values characterize a lifetime increase. The transition from decreasing (shaded areas) to increasing lifetime is accentuated by the white area. Constant parameters of the calculation were hole capture cross section p = 2·10-15 cm2, excess carrier density = 1·1015 cm-3 and background doping p0 = 3·1015 cm-3. The trap density Nt has an impact on the dimension of the lifetime change: a) Nt = 1·1011 cm-3 b) Nt = 1·1013 cm-3. The scale in b) is valid for both diagrams.
b) 444.4 n
444.2
p
=1 10
-16
cm
2
=2 10
-15
cm
2
Et=Ec-0.27 eV
444.0
12
-3
Nt=2 10 cm
443.8 443.6 0
3000
6000
9000
time (s)
12000 15000
calculated lifetime (μs)
calculated lifetime (μs)
a)
180 177
n p
174
=1 10
-14
cm
2
=2 10
-15
cm
2
Et=Ec-0.22 eV 11
-3
Nt=5 10 cm
171 0
3000
6000
9000
12000 15000
time (s)
Fig. 4. Charge carrier lifetime calculation for different SRH defect parameters during the logged temperature change. Lifetime a) decrease and b) increase induced by temperature rising is possible.
157
Christian Möller and Kevin Lauer / Energy Procedia 38 (2013) 153 – 160
3.3. Charge carrier lifetime simulation The simulated charge carrier lifetime change due to the fitted temperature characteristic from Fig. 1 is displayed in Fig. 4. Note that the only lifetime changing effect is the temperature increase of 2 °C over the whole simulation time. Dependent on the chosen defect parameter, slight increase (Fig. 4a) and weaker decrease (Fig. 4b) of the lifetime is possible. Defect parameters were arbitrarily chosen in respect to the visible lifetime change. The different defect densities Nt are used to shift the calculated charge carrier lifetime to a reasonable absolute value. 3.4. MWPCD measurements In Fig. 5 the lifetime change during illumination of one sample before (a) and after (b) thermal donor annealing is shown. The well known fast- and slowly forming components of the boron-oxygen related defect are visible [2]. To deactivate the influence of thermal donors the sample was annealed at 600 °C for 20 min. The lower lifetime after thermal donor annealing is caused by surface passivation degradation and activation of defects in the silicon bulk. Note that the lifetime decrease during formation of the fast recombination center is significantly lower than before heat treatment. b) MWPCD
MWPCD
270
270 240
260 10
2
10
3
10
4
250 240
before annealing 0
3000
6000 9000 12000 15000 time (s)
effective lifetime (μs)
effective lifetime (μs)
a)
102
99
102
96 after 20 min
93
@600°C annealing 0
3000
99 96 2
10
6000
3
10
9000
4
10
12000
15000
time (s)
Fig. 5. Lifetime change in the first four hours in a p-type CZ silicon sample with interstitial oxygen content of [Oi] = 10.5·1017cm-3. a) Measurement before thermal donator annealing treatment, b) after thermal donator annealing treatment. The insets show a larger time scale and the point in time where the measurement induced temperature increase stops (red vertical line).
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Christian Möller and Kevin Lauer / Energy Procedia 38 (2013) 153 – 160
4. Discussion 4.1. Physical reasons for the time scale to reach the steady state The short time scale behaviour, visible in Fig. 1, was simulated with COMSOL Multiphysics. The calculated time scale to reach the temperature steady state in vertical dimension fits well with the experimental value. The second, slower temperature increase is caused by the thermal diffusion in horizontal direction. With increasing thermal warming the surface to ambient radiation increase due to the larger warmed-up area and the temperature rise decelerate. This was not simulated due to the increasing solving time for a realistic model: The inserted heat flux is caused by a 200 ns laser pulse followed by a time without laser illumination (illumination time laps during one second: altogether 0.6 ms laser illumination, 999.4 ms without illumination). During the measurement interval (after 70 s intense illumination) the time between the laser pulses is increased. Furthermore the horizontal dimensions increase (up to 5 cm) what leads to an increasing number of mesh elements. These points influence although the simulation of the fast temperature increase what explain the slightly higher experimental determined time to reach the vertical steady state. The denoted average laser intensity of the MWPCD setup is one magnitude higher than the heat flux in the COMSOL Multiphysics simulation (Fig. 2). This is caused by the different energy distribution in the experiment and the simulation: The major amount of the MWPCD laser power is used to generate excess charge carriers. Only a small fraction of the laser power warms up the sample. The inserted heat flux in the simulation is only used to warm up the sample. An excess charge carrier generation is not considered. This leads to an underestimated inserted heat flux in the simulation. Note that the penetration depth of the microwaves influences the sampled temperature range in vertical dimension. The logged lifetime is the average out of the mean value of the temperature gradient. The penetration depth for the used sample conductibility is in the range of 500 μm. Therefore the received lifetime value is averaged over the whole sample thickness and the existent temperature gradient. 4.2. Influence of temperature increase on the lifetime limiting defect The transition from fast- to slowly forming component of the boron-oxygen related defect correlates well with the experimentally determined time to reach the steady state temperature. By using appropriate Shockley-Read-Hall (SRH) parameters charge carrier lifetime change is observed. Both lifetime decrease and increase due to temperature rising is possible. The lifetime decrease due to the fast forming recombination center can not be explained with a temperature increase. The calculated possible lifetime decrease is to low (0.6 % relative). The lifetime limiting defect before light soaking and thermal donor annealing causes only a small lifetime increase (or decrease) with increasing temperature. This change is negligible compared with the lifetime decrease caused by formation of the fast recombination center. In contrast the change in defect formation kinetic after thermal donor annealing (Fig. 5b) can be explained with a measurement induced temperature increase. Due to thermal donor annealing the lifetime limiting defect changes. The boron-oxygen related defect is not influenced of this transformation. The SRH parameters of the lifetime limiting defect (before illumination) causes a lifetime increase due to temperature rising. With starting illumination the lifetime increases due to the temperature rinsing, simultaneously the lifetime decreases due to formation of the boron-oxygen related defect. Result is a constant lifetime (or slightly increase/decrease dependent on the strength of the two components). Such behaviour is visible in Fig. 5b. Note that the lifetime decrease after annealing is only 2 μs (Fig 5b) in contrast to 25 μs before annealing (Fig 5a).
Christian Möller and Kevin Lauer / Energy Procedia 38 (2013) 153 – 160
The decrease in lifetime caused by the formation of the fast recombination center can not be explained by using only the temperature increase during the measurement. But with changed SRH parameters, for example after thermal donor annealing, the temperature influence on lifetime is more pronounced and the lifetime change due to defect formation of the boron-oxygen related defect is compensated by the temperature influence on lifetime. The temperature change during time dependent lifetime measurements have to be taken into account especially for the so called boron-oxygen related defect. Due to the subsequent light soaking temperature change and charge carrier lifetime varies dependent on defect parameters. The fast forming recombination center is not explainable only with temperature increase during the measurement. Nonetheless temperature variations during charge carrier lifetime measurements influence the lifetime dependent on defect parameters. 5. Summary Temperature variation during a time dependent microwave-detected photoconductance decay (MWPCD) measurement was logged. 2 °C temperature increase during the first 3 hours of the measurement takes place. Temperature dependent charge carrier lifetime calculations with different Shockley-Read-Hall (SRH) parameters show lifetime increase (up to 8 % relative) and decrease (up to 0.6 % relative) dependent on the used SRH parameters by a temperature increase of 2 °C. Charge carrier lifetime degradation was measured during formation of the so called boron-oxygen complex induced by illumination with the MWPCD laser. The formation of the fast forming recombination center takes place at the same time scale like the observed temperature increase. Dependent on thermal treatment the defect formation kinetic of the boron-oxygen related defect varies. This can be explained by a change in SRH parameters due to annealing. The modified defect parameters cause an increase of charge carrier lifetime by temperature rising and overlie the lifetime decrease of the boron-oxygen related defect. However, the charge carrier lifetime decrease during formation of the so called fast forming recombination center is not explainable with a temperature increase. Acknowledgements The authors gratefully acknowledge the financial support by the German Federal Ministry of Education and Research within the framework of the Leading-Edge Cluster Competition and the research cluster Solarvalley Central Germany under contract No. 03SF0398A.
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References [1] H. Fischer and W. Pschunder, Proceedings of the tenth IEEE Photovoltaic Specialists Conference (IEEE, New York, 1973), p. 404 [2] K. Bothe and J. Schmidt, J. Appl Phys. 99 (2006) 013701 [3] V. Markevich, T. Peaker, B. Hamilton, L. Murin, Y. H. Yoon, and G. Rozgonyi, 22nd Workshop on Crystalline Silicon Solar Cells & Modules: Materials and Processes 103 (2012) [4] T.U. N rland, B.R. Olaisen, L. Arnberg, Solid State Phenomena 178-179 (2011) 435 [5] M. Kunst and G. Beck, J. Appl. Phys. 60 (1986) 3558 [6] M. Kunst and G. Beck, J. Appl. Phys. 63 (1988) 1093 [7] K. Lauer, A. Laades, H. Übensee, H. Metzner, and A. Lawerenz, J. Appl. Phys. 104 (2008) 104503 [8] M. J. Kerr and A. Cuevas, J. Appl. Phys. 91 (2002) 2473 [9] W. Shockley and W. Read, Phys. Rev. 87 (1952) 835 [10] R. N. Hall, Phys. Rev. 87 (1952) 387 [11] M. A. Green, J. Appl. Phys. 67 (1990) 2944 [12] http://www.comsol.com/
ScienceDirect Energy Procedia 38 (2013) 153 – 160
SiliconPV: March 25-27, 2013, Hamelin, Germany
Charge carrier lifetime shift induced by temperature variation during a MWPCD measurement Christian Möllera,b * and Kevin Lauera a
CiS Forschungsinstitut für Mikrosensorik und Photovoltaik GmbH, Konrad-Zuse-Str. 14, 99099 Erfurt, Germany b TU Ilmenau, Institut für Physik, Weimarer Str. 32, 98693 Ilmenau, Germany
Abstract In this work the temperature of a silicon sample excited by a laser during a time dependent microwave-detected photoconductance decay (MWPCD) measurement was logged. 2 °C temperature increase on the backside of the wafer was observed. Temperature dependent charge carrier lifetime calculations using the determined temperature characteristic are compared to time dependent MWPCD measurements of a boron-doped wafer with high oxygen content. The time duration to reach the final temperature fits well with the time scale of the fast forming recombination center of the boron-oxygen related defect. Charge carrier lifetime variation due to temperature increase is discussed in view of different defect parameters.
© 2013 The Authors. Published by Elsevier Ltd. © 2013 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the scientific committee of the SiliconPV 2013 Selection and/or peer-review under responsibility of the scientific committee of the SiliconPV 2013 conference conference Keywords: charge carrier lifetime, temperature variation, boron-oxygen related defect, MWPCD
1. Motivation The most frequent lifetime limiting recombination center in current solar grade boron-doped Czochralski (CZ) silicon solar cells is caused by a boron-oxygen related defect [1]. This recombination active defect is activated under illumination or electron injection in the dark. Bothe and Schmidt [2] detected a fast and a slowly forming recombination center in time dependent V oc measurements. However, despite intensive research, the origin of the boron oxygen recombination center is still unclear [3]. In temperature corrected Voc measurements the fast forming recombination center is not visible [4]. That leads to the assumption, that the physical effects occurring during the illumination for defect formation are overlaid by temperature induced lifetime variations. For every charge carrier lifetime
* Corresponding author. Tel.: +49 361 663 1211; fax: +49 361 663 1413. E-mail address: [email protected]
1876-6102 © 2013 The Authors. Published by Elsevier Ltd.
Selection and/or peer-review under responsibility of the scientific committee of the SiliconPV 2013 conference doi:10.1016/j.egypro.2013.07.262
154
Christian Möller and Kevin Lauer / Energy Procedia 38 (2013) 153 – 160
measurement, excess carriers have to be generated by laser or flash lamp. Due to the illumination a temperature increase in the sample occurs. During time dependent studies with permanent charge carrier lifetime measurement this temperature increase is not negligible. In this study, the charge carrier lifetime change during defect formation was measured with a microwave-detected photoconductance decay (MWPCD) setup in which the laser was also used to activate the boron-oxygen defect. In this work, temperature increase induced by long time MWPCD measurements is recorded for the first time. Temperature dependent calculations are compared with MWPCD measurements of the formation of the boron-oxygen complex. The observed temperature induced lifetime effects are discussed in view of the boron-oxygen recombination center activation. 2. Experimental details The photoconductance decay was measured with the Semilab WT-2000 MWPCD device. A description of the setup is given in Refs. [5] and [6]. Excess charge carrier generation and light soaking of the sample was done with the laser of the setup. The laser works at 904 nm with 200 ns pulse length and a maximum average intensity of 8500 Wm-2. Charge carrier lifetime was calculated form the MWPCD signal and compared with a quasi-steady-state photoconductance decay (QSSPC) measurement to calibrate the excess charge carrier density [7]. To deactivate the boron-oxygen related defect the sample is annealed at 200°C for 10 min [1] before each measurement. The temperature of the sample was measured with a Peltier element on the backside of a test wafer with a thickness of 120 μm directly below the MWPCD excitation laser. For temperature- and time dependent charge carrier lifetime measurement the same measuring procedure is used: First, a lifetime measurement at a time range of some milliseconds is done. The laser pulse generates excess charge carriers and the microwave reflection decay is logged. The mean deposited laser intensity in this time sequence induces only a very low temperature increase. Afterwards the maximum laser power is deposited into the sample. This is achieved by a shortened time range between the laser pulses. Microwave reflection decay is not logged. This intense illumination is done for about 70 s. Now the microwave reflection decay is measured again (longer time between the single laser pulses), followed by intense illumination and so on. All presented charge carrier lifetime calculations take band to band recombination, Auger recombination [8] and Shockley-Read-Hall (SRH) recombination [9,10] into account. The temperature dependences of the parameters are considered after Green [11]. 3. Results 3.1. Temperature change during the measurement The time dependent temperature characteristic is shown in Fig. 1. Temperature was normalised to the final temperature at the Celsius scale. As fitting function y
A1 exp
t
b1
A2 exp
t
b2
1
was chosen. A temperature difference up to 2 °C occurs during the first three hours of the measurement, independent of the common expected starting temperature (this was observed with different starting temperatures up to 28 °C).
Christian Möller and Kevin Lauer / Energy Procedia 38 (2013) 153 – 160
normalised temperature
1.00
0.98
0.96
measured temperature exponential fit
0.94
0
3000
6000
9000
12000
15000
time (s) Fig. 1. Temperature change during the first four hours of the measurement. The temperature is normalised to the final temperature at the Celsius scale. Temperature steady state is reached after about 12000 s.
The time to reach the temperature steady state in Fig. 1 is influenced by the lateral thermal conduction and the heat radiation of the silicon sample. A fast (the first 200 s) and a slow (3 hours) temperature increase is observed. The fast temperature increase is caused by the thermal conduction in vertical dimension. A COMSOL Multiphysics [12] simulation is used to establish this assumption. Thermal diffusion from the laser light excitation to the sensor at the rear side of the sample was simulated. Further, surface to ambient radiation was supposed. Model size was 0.12 x 0.4 mm2. Fig. 2 displays the result of the simulation for a 120 μm thick sample with different heat fluxes. The time to reach the temperature steady state is independent of the inserted heat flux. The sample thickness influences the time to reach the steady state (insert of Fig. 2). Temperature increase stops after about 120 s in the 120 μm sample and after about 150 s in the 200 μm sample (dashed vertical lines in Fig. 2). This time scale fits well with the experimental observed time scale of about 180 s for the fast temperature increase at the beginning. The second, slower temperature increase is caused by the thermal diffusion in horizontal direction. With increasing thermal warming the surface to ambient radiation increase due to the larger warmed-up area and the temperature rise decelerate. 27.0
26.5 27
temperature (°C)
temperature (°C)
2
570 W/m 2 400 W/m
26.0
25.5
25.0
0
26
200μm, 570 W/m 25
0
100
100
time (s) 200
2
200
300
time (s) Fig. 2. Simulated temperature increase at the backside of a silicon sample due to a constant heat flux at the top. The inset shows the result of the simulation for a 200 μm thick sample. The time to reach the steady state is dependent on the sample thickness.
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Christian Möller and Kevin Lauer / Energy Procedia 38 (2013) 153 – 160
3.2. Temperature influence on lifetime
8.0%
b) 1.0
1.0
0.8
0.8
5.4%
Et (eV)
Et(eV)
a)
0.6
0.6
0.4
0.4
2.4%
0.2
0.2
0.0
0.0 1E-18
1E-16
1E-18
1E-14
n
1E-16
1E-14
-0.6%
2
2
(cm ) n
(cm )
relative lifetime change due to temperature increase of 2°C
Fig. 3 shows the relative change in lifetime due to a temperature increase of 2 °C (from 26 °C to 28 °C) and the impact of the defect density Nt. Constant electron capture cross section n and variable hole cross section p looks similar (not shown here). Dependent on the capture cross sections, charge carrier lifetime increase or decrease during temperature rising. A strong lifetime increase (positive percent values, filled area) up to 8 % is possible. The trap energies of the corresponding defects are located near valence and conduction band. Lifetime decrease up to 0.6 % after temperature rising is possible by defects located in the middle of the band gap. The area of constant charge carrier lifetime (white area in Fig. 3) after temperature shifting decrease with increasing trap density Nt.
Fig. 3. Calculated charge carrier lifetime change due to a temperature increase of 2 °C for different trap energies Et and electron capture cross sections n. Positive values characterize a lifetime increase. The transition from decreasing (shaded areas) to increasing lifetime is accentuated by the white area. Constant parameters of the calculation were hole capture cross section p = 2·10-15 cm2, excess carrier density = 1·1015 cm-3 and background doping p0 = 3·1015 cm-3. The trap density Nt has an impact on the dimension of the lifetime change: a) Nt = 1·1011 cm-3 b) Nt = 1·1013 cm-3. The scale in b) is valid for both diagrams.
b) 444.4 n
444.2
p
=1 10
-16
cm
2
=2 10
-15
cm
2
Et=Ec-0.27 eV
444.0
12
-3
Nt=2 10 cm
443.8 443.6 0
3000
6000
9000
time (s)
12000 15000
calculated lifetime (μs)
calculated lifetime (μs)
a)
180 177
n p
174
=1 10
-14
cm
2
=2 10
-15
cm
2
Et=Ec-0.22 eV 11
-3
Nt=5 10 cm
171 0
3000
6000
9000
12000 15000
time (s)
Fig. 4. Charge carrier lifetime calculation for different SRH defect parameters during the logged temperature change. Lifetime a) decrease and b) increase induced by temperature rising is possible.
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Christian Möller and Kevin Lauer / Energy Procedia 38 (2013) 153 – 160
3.3. Charge carrier lifetime simulation The simulated charge carrier lifetime change due to the fitted temperature characteristic from Fig. 1 is displayed in Fig. 4. Note that the only lifetime changing effect is the temperature increase of 2 °C over the whole simulation time. Dependent on the chosen defect parameter, slight increase (Fig. 4a) and weaker decrease (Fig. 4b) of the lifetime is possible. Defect parameters were arbitrarily chosen in respect to the visible lifetime change. The different defect densities Nt are used to shift the calculated charge carrier lifetime to a reasonable absolute value. 3.4. MWPCD measurements In Fig. 5 the lifetime change during illumination of one sample before (a) and after (b) thermal donor annealing is shown. The well known fast- and slowly forming components of the boron-oxygen related defect are visible [2]. To deactivate the influence of thermal donors the sample was annealed at 600 °C for 20 min. The lower lifetime after thermal donor annealing is caused by surface passivation degradation and activation of defects in the silicon bulk. Note that the lifetime decrease during formation of the fast recombination center is significantly lower than before heat treatment. b) MWPCD
MWPCD
270
270 240
260 10
2
10
3
10
4
250 240
before annealing 0
3000
6000 9000 12000 15000 time (s)
effective lifetime (μs)
effective lifetime (μs)
a)
102
99
102
96 after 20 min
93
@600°C annealing 0
3000
99 96 2
10
6000
3
10
9000
4
10
12000
15000
time (s)
Fig. 5. Lifetime change in the first four hours in a p-type CZ silicon sample with interstitial oxygen content of [Oi] = 10.5·1017cm-3. a) Measurement before thermal donator annealing treatment, b) after thermal donator annealing treatment. The insets show a larger time scale and the point in time where the measurement induced temperature increase stops (red vertical line).
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4. Discussion 4.1. Physical reasons for the time scale to reach the steady state The short time scale behaviour, visible in Fig. 1, was simulated with COMSOL Multiphysics. The calculated time scale to reach the temperature steady state in vertical dimension fits well with the experimental value. The second, slower temperature increase is caused by the thermal diffusion in horizontal direction. With increasing thermal warming the surface to ambient radiation increase due to the larger warmed-up area and the temperature rise decelerate. This was not simulated due to the increasing solving time for a realistic model: The inserted heat flux is caused by a 200 ns laser pulse followed by a time without laser illumination (illumination time laps during one second: altogether 0.6 ms laser illumination, 999.4 ms without illumination). During the measurement interval (after 70 s intense illumination) the time between the laser pulses is increased. Furthermore the horizontal dimensions increase (up to 5 cm) what leads to an increasing number of mesh elements. These points influence although the simulation of the fast temperature increase what explain the slightly higher experimental determined time to reach the vertical steady state. The denoted average laser intensity of the MWPCD setup is one magnitude higher than the heat flux in the COMSOL Multiphysics simulation (Fig. 2). This is caused by the different energy distribution in the experiment and the simulation: The major amount of the MWPCD laser power is used to generate excess charge carriers. Only a small fraction of the laser power warms up the sample. The inserted heat flux in the simulation is only used to warm up the sample. An excess charge carrier generation is not considered. This leads to an underestimated inserted heat flux in the simulation. Note that the penetration depth of the microwaves influences the sampled temperature range in vertical dimension. The logged lifetime is the average out of the mean value of the temperature gradient. The penetration depth for the used sample conductibility is in the range of 500 μm. Therefore the received lifetime value is averaged over the whole sample thickness and the existent temperature gradient. 4.2. Influence of temperature increase on the lifetime limiting defect The transition from fast- to slowly forming component of the boron-oxygen related defect correlates well with the experimentally determined time to reach the steady state temperature. By using appropriate Shockley-Read-Hall (SRH) parameters charge carrier lifetime change is observed. Both lifetime decrease and increase due to temperature rising is possible. The lifetime decrease due to the fast forming recombination center can not be explained with a temperature increase. The calculated possible lifetime decrease is to low (0.6 % relative). The lifetime limiting defect before light soaking and thermal donor annealing causes only a small lifetime increase (or decrease) with increasing temperature. This change is negligible compared with the lifetime decrease caused by formation of the fast recombination center. In contrast the change in defect formation kinetic after thermal donor annealing (Fig. 5b) can be explained with a measurement induced temperature increase. Due to thermal donor annealing the lifetime limiting defect changes. The boron-oxygen related defect is not influenced of this transformation. The SRH parameters of the lifetime limiting defect (before illumination) causes a lifetime increase due to temperature rising. With starting illumination the lifetime increases due to the temperature rinsing, simultaneously the lifetime decreases due to formation of the boron-oxygen related defect. Result is a constant lifetime (or slightly increase/decrease dependent on the strength of the two components). Such behaviour is visible in Fig. 5b. Note that the lifetime decrease after annealing is only 2 μs (Fig 5b) in contrast to 25 μs before annealing (Fig 5a).
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The decrease in lifetime caused by the formation of the fast recombination center can not be explained by using only the temperature increase during the measurement. But with changed SRH parameters, for example after thermal donor annealing, the temperature influence on lifetime is more pronounced and the lifetime change due to defect formation of the boron-oxygen related defect is compensated by the temperature influence on lifetime. The temperature change during time dependent lifetime measurements have to be taken into account especially for the so called boron-oxygen related defect. Due to the subsequent light soaking temperature change and charge carrier lifetime varies dependent on defect parameters. The fast forming recombination center is not explainable only with temperature increase during the measurement. Nonetheless temperature variations during charge carrier lifetime measurements influence the lifetime dependent on defect parameters. 5. Summary Temperature variation during a time dependent microwave-detected photoconductance decay (MWPCD) measurement was logged. 2 °C temperature increase during the first 3 hours of the measurement takes place. Temperature dependent charge carrier lifetime calculations with different Shockley-Read-Hall (SRH) parameters show lifetime increase (up to 8 % relative) and decrease (up to 0.6 % relative) dependent on the used SRH parameters by a temperature increase of 2 °C. Charge carrier lifetime degradation was measured during formation of the so called boron-oxygen complex induced by illumination with the MWPCD laser. The formation of the fast forming recombination center takes place at the same time scale like the observed temperature increase. Dependent on thermal treatment the defect formation kinetic of the boron-oxygen related defect varies. This can be explained by a change in SRH parameters due to annealing. The modified defect parameters cause an increase of charge carrier lifetime by temperature rising and overlie the lifetime decrease of the boron-oxygen related defect. However, the charge carrier lifetime decrease during formation of the so called fast forming recombination center is not explainable with a temperature increase. Acknowledgements The authors gratefully acknowledge the financial support by the German Federal Ministry of Education and Research within the framework of the Leading-Edge Cluster Competition and the research cluster Solarvalley Central Germany under contract No. 03SF0398A.
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