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The circuit point of view of the temperature dependent open circuit voltage decay of the solar cell
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Solar Energy 83 (2009) 1446–1453 www.elsevier.com/locate/solener
The circuit point of view of the temperature dependent open circuit voltage decay of the solar cell A. Sertap Kavasoglu *, Nese Kavasoglu, Sener Oktik Mugla University, Clean Energy Research & Development Centre, 48170 Kotekli/Mugla, Turkey Mugla University, Faculty of Arts and Sciences, Physics Department, 48170 Kotekli/Mugla, Turkey Received 2 November 2008; received in revised form 5 March 2009; accepted 9 March 2009 Available online 7 April 2009 Communicated by: Associate Editor Takhir Razykov
Abstract The open circuit voltage decay (OCVD) technique has been used to determine the minority carrier lifetime. In this study, an experimental and analytical method is described for determination of minority carrier lifetime at porous Si based solar cell by photo induced OCVD technique. The cell is illuminated by a monochromatic light source (k = 658 nm) in the open circuit configuration, and the decay of voltage is measured after abruptly terminating the excitation. For the analysis of the OCVD characteristic of solar cell device, equivalent electrical circuit has been proposed in which the diffusion capacitance is connected in series with the contribution of the solar cell interface. Exact minority carrier lifetimes at low (50–170 K) and high (190–330 K) temperature regions have been obtained as 28.9 and 2.65 ls from the temperature dependent OCVD measurements by using an alternative extraction technique. Ó 2009 Elsevier Ltd. All rights reserved. Keywords: Minority carrier lifetime; Porous Si based solar cell; Open circuit voltage decay technique; Circuit level simulation
1. Introduction In some works, photovoltaic properties (such as wavelength depended photosensitivity, internal quantum efficiency, illuminated and dark I–V measurements) of porous Si based solar cell structures have been extensively studied and reported in the literature (Rabha et al., 2008; Badawy, 2008). Porous silicon is increasingly applied to the fabrication of photovoltaic devices as a low-cost material (Smestad et al., 1992). Porous Si based solar cells are influenced by the electronic properties of interface. Various reports have been made to correlate these properties with the solar cell performance (Badawy, 2008; Bisi et al., 2000). The most important advantage of using porous Si in solar cells is its band gap and large minority carrier lifetime. In addition, this device is attractive because of the *
Corresponding author. Tel.: +90 252 211 1674; fax: +90 252 223 8656. E-mail address: [email protected] (A.S. Kavasoglu).
0038-092X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2009.03.009
feasibility for fabricating low cost–low temperature fabrication process for fast photo diodes having response times of 650 ls. The minority carrier lifetime, eminent parameter influencing the performance of a solar cell, is often measured with the transient methods. The minority carrier lifetime in Si based device was obtained by OCVD and short-circuit decay techniques have been noted by several groups (Deshmukh and Nagaraju, 2005; Stutenbaeumer and Lewetegn 2000). OCVD technique, relatively facile, is frequently used for estimation effective minority carrier lifetime in the solar cells. In particular, evaluation of open circuit voltage versus temperature data provides valuable information about the main recombination route in the devices (Rau and Schock, 1999). Until now, there could not be found any theoretical model about the temperature depended effective minority carrier lifetime extraction technique by using equivalent circuit approximation. The observed temperature depended effective minority carrier lifetime behavior
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in this study, cannot be explained by existence model in literature (Hsieh and Card, 1984). It thus became necessary to construct alternative theoretical approximation. We proposed a procedure to extract effective carrier lifetime of the devices. The presented theoretical results explain the role of equivalent circuits in time dependent open circuit transient characteristic of the investigated solar cell. OCVD characteristics of solar cells are customarily described by an equivalent circuit model, which includes series resistance, diode dynamic resistance and capacitance. Dynamic resistance and capacitance values are modulated by temperature. This effect significantly alters the device transient characteristics (Moore, 1980) with respect to ideal behavior and makes the measured OCVD characteristics strongly temperature dependent, especially below room temperature under monochromatic illumination level (Castanier et al., 1981). In this study, the theoretical method suggests that minority carrier lifetime is not directly accessible parameter. It can be measured as an effective minority carrier lifetime, which is strongly temperature depended. According to our model, effective minority carrier lifetime decreases exponentially with temperature. This behavior cannot be explained by ordinary OCVD theory (Lederhandler and Giacoletto, 1955). This denotes that our proposed analyzing method is valid otherwise; the expected OCVD curve is going to be consisting of stretch exponential form (see Eq. (1)). The OCVD characteristic can be significantly influenced by the capacitive effect, which can be considered as consisting of both depletion layer capacitance (Cd) and diffusion capacitance (Cdiff) under sufficient monochromatic illumination level. The diffusion capacitance of the injected carriers dominates over the depletion layer capacitance (Schroder, 1990; Sinton and Swanson, 1987). The OCVD time introduced by a junction capacitance causes that the minority carrier lifetime can be overestimated (Green, 1983). It is necessary that the minority carrier lifetime is much larger than the time constant for diffusion to calculate an effective minority carrier lifetime from the OCVD (Schroder, 1990; Sinton and Swanson, 1987). In addition, there may arise some uncertainty in minority carrier lifetime due to fact that our porous Si solar cell-type is ‘‘back surface field” (BSF) solar cell (Sze, 1981) generally contains two interfaces (p+/p and p/n+ contact intercept region) in the junction formation, forasmuch as OCVD method measures the recombination lifetime. At that point, a reconstruction technique/model is required to extract the effective minority carrier lifetime from the measured non-traditional OCVD data in the presence of an interface effect. OCVD technique was one of the earliest methods for minority carrier lifetime determination. However, very little attention has been paid to the temperature depended OCVD at monochromatic illumination of solar cells in the literature, especially at low temperature. In this study, effective minority carrier lifetime has been calculated from the temperature dependent OCVD measurements by using an alternative extraction technique.
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2. Theory The time variation of OCVD (DV oc ðtÞ) is given elsewhere (Lederhandler and Giacoletto, 1955), qV i i kBT h t In 1 þ ese ekB T DV oc ðtÞ ¼ ð1Þ q where t is the time (for collecting data during the transient response), V i the junction voltage at t = 0, se the effective minority carrier lifetime, T temperature and q, k B are the well known constants. qV ð i t Þ Let z ¼ e kB T se . For tii kqVB Ti se , z value approximates to zero. However, if this condition can be met, it can be shown using the approximation Inð1 þ zÞ z, k B T kqV Ti t ð2Þ e B e se DV oc ðtÞ ¼ q where DV oc ðtÞ ¼ V oc ðtÞ V bias . V bias is the final value of the open circuit voltage which depends on the intensity of the bias light. The voltage decay is constituted of a sum of exponentially decaying modes (Joardar and Schroder, 1992). It is obvious from Eq. (2) that the OCVD curve is represented by single exponential function. The voltage decay curve can be approximated as a pure exponential. That is; t
DV oc ðtÞ ¼ DV oc ð0Þese
ð3Þ
Several equivalent circuits have been proposed for determining solar cell ac parameters using different electrical characterization technique (Deshmukh and Nagaraju, 2005; Deshmukh et al., 2004; Kumar et al., 2000; Suresh, 1996; Sharma et al., 1992). Especially, the study (Deshmukh et al., 2004) is of great practical interests. In this paper, we propose an alternative technique for this measurement and show how the equivalent circuit can be further improved. Equivalent circuit model, useful in a transient analysis, should include the diffusion capacitance, dynamic resistance Rd , series resistance Rs and interface elements (Rint) and (Cint). Under low frequency (high excitation period) excitation condition the diode capacitance arises from two distinct regions of charges (Jasprit, 1995). (i) Under reverse biased conditions, there are fundamentally no injected carriers to the depletion region and the junction capacitance dominates. A dipole of fixed positive and negative charge in the depletion region of the junction constitutes the junction capacitance. (ii) Under forward bias condition, there are minority carrier injections to the depletion region. The diffusion capacitance arises from minority carrier injection from the region outside the depletion region. For the analysis of the OCVD characteristic of simulated solar cell, equivalent electrical circuit has been proposed corresponding to solar cell structure. For the OCVD measurement, one should use a light source,
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which’s rise and fall times must be much smaller than the minority carrier lifetime of the sample. It will be helpful if light of shorter wavelengths are filtered out and the intensity of longer wavelengths is kept sufficient to keep the injection level large enough to ignore the space charge capacitance effects and low enough to work in the low injection limit (Dhariwal and Vasu, 1981). Long wavelength monochromatic light is advisable due to ability of long penetration depth. The applying monochromatic square light pulse through a solar cell under test is defined as, V ; ½0; t1 ð4Þ V apl ðtÞ ¼ 0; ½t1 ; t2 where t2 is the period and t1 light on time, V the amplitude in square light pulse. We interpret the total charge (Q) of the solar cell in terms of equivalent circuit model (Fig. 1). The diffusion capacitance is connected in series with Rint and C int which mimic the contribution of the solar cell interface. The electrical behavior of a solar cell is described in terms of charge control model. Having taken connection configuration of the circuit components in the device’s equivalent circuit into consideration, one obtains Eq. (5) when the switch is at I position, Q Rs dQ Rint ð5Þ þ1 þ Rs þ Rs þ Rint V ¼ C Rd dt Rd The term C includes diffusion capacitance and unwanted portion of interface capacitance in series connected form. C int strongly influences to OCVD characteristic. C is obtained by simply calculating the total capacity of two capacities connected in series, C ¼
C int C diff C int þ C diff
ð6Þ
The purpose is to solve Eq. (5) using transient conditions. Charging equation (Eq. (7)) is written from the solving the differential Eq. (5),
sc ¼
h i C Rs þ Rint 1 þ RRds 1 þ RRds
ð9Þ
Discharging equations is written from the solving the differential Eq. (5) for condition V = 0, t
QðtÞ ¼ Qmax esc ; discharging equation
ð10Þ
When the switch is at position II, Rs becomes larger then Rd (Rs Rd ), because Rs almost equals to series contribution of voltage follower input impedance. Under this condition, it is convenient to simplify Eq. (9) as, Rint ð11Þ sc ¼ C R d 1 þ Rd We can approximate to Eq. (11) to take into account Rd Rint , then sc ¼ C R d
ð12Þ
The V d ðtÞ (absolute value of voltage across the dynamic resistance) is described as dQ V d ðtÞ ¼ Rd ð13Þ dt V d ðtÞ can be expressed in terms of Rd and C such as t Rd e Rd C ð14Þ V d ðtÞ ¼ V R d þ Rs It is obviously seen that the calculated function is a good agreement with Eq. (3). From the diffusion limited current theory, forward voltqV d age depended current is given by I 0 ðe kB 1Þ, where I o is the saturation current. Rd and C diff are influenced by temperature. The temperature dependence of Rd is described by (Kavasoglu et al., 2008); Rd ðT Þ ¼
1 ðk B T =qÞ ¼ qV d dI=dV I o ek B T
ð15Þ
ð8Þ
For relatively low excitation frequencies by light pulse, the diffusion capacitances may be given as (Friesen and Ossenbrink, 1997) qV c qsp I o ekB T ð16Þ C diff ðT Þ ¼ kBT
and the time constant (sc ) of the proposed RC network is,
where V c the voltage across the diffusion capacitance, sp the exact minority carrier lifetime for C diff C int . For the
t sc
QðtÞ ¼ Qmax ð1 e Þ; charging equation
ð7Þ
where Qmax ¼
Rd CV R d þ Rs
Fig. 1. Schematic structure and proposed equivalent circuit of the porous Si based solar cell.
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maximum illumination level, the created electron–hole pair density is quite large and can dominate the capacitance like forward bias condition. That is why we neglected the depletion region capacitance. If interface capacitance contribution is much larger then the diffusion capacitance (C diff C int ) then C equals C diff . Under this assumption, Eq. (12) is rewritten as sc ¼ C diff Rd . For the long-base diode, sc se , so a reasonable estimate of the effective lifetime can be taken as se without much error. q
se ðT Þ ¼ sp ekB T
ðV c V d Þ
ð17Þ
For the obtained effective minority carrier lifetime to be almost equal to the exact minority carrier lifetime, it is compulsory that V d V c . The V d V c prerequisite is not perpetually satisfied. This means that interface effect may alter effective minority carrier lifetime. For that reason, in practice, it may be difficult to measure effective minority carrier lifetime directly with sufficiently high accuracy. It is therefore of great practical interest to investigate effective minority carrier lifetime as a function of temperature. It is worth noting that, since the ðV c V d Þ potential difference corresponds to barrier energy difference DE ¼ qðV c V d Þ, it must be positive. At this point, it is convenient to generalize Eq. (17); DE 1 ð18Þ In se ðT Þ ¼ In sp þ kB T The effective carrier lifetime now can be defined as an Arrhenius plot of inverse temperature. In consequence, plotting Inse ðT Þ T1 allows determination of the barrier energy difference and exact minority carrier lifetime from the slope of this curve and intercept with Inse ðT Þ axis, respectively. 3. Experimental details The OCVD measurements were performed on highly efficient porous Si solar cell. The fabrication of the devices was given in detail at (Tuzun et al., 2006). A diagram of the measurement setup is shown in Fig. 2. It consists of a pulse generator, a MOSFET pulse driver and one 4-bit duty cycle control-multiplexing unit that control the ladder network resistors. OCVD measurements were performed with a TDS 220 digital oscilloscope and an IBM compatible PC. The control of the various experimental parameters and data acquisition was carried out with a computer. Measurement was performed inside evacuated close-cycle OXFORD He cryostats with ITC 502 intelligent temperature controller. A delay of a few seconds between subsequent measuring steps was built into the program to assure steady–state conditions for the measurement of the temperature. The ITC 502 temperature controller has auto PID mode with RS-232 computer interface. So, cooling and heating rate and other parameters systematically controlled by PC. We have also independently measured temperature on the sample by K-type thermocouple with a
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suitable connected extension cable through the feedthrough. The device was connected to voltage follower unit for dc measurement via the equipped suitable coaxial cable. In addition, for each measurement step the average of up to thirty-two measurements was taken to increase the signal-to-noise ratio by TDS 220 digital oscilloscope. The light source is a group of LEDs of 658 nm wavelength. This excitation wavelength is enough to create electron–hole pair in device depletion region. The LED group was driven by a MOSFET current pump driver that could be operated between 2 and 50 mA. A clock generator generates low frequency and high accuracy sharp transient pulses. The duty cycle value of the pulse can be controlled by the ladder network circuits. The control of the various resistor values and data acquisition was carried out with a personal computer. The open circuit transient time of the samples was recorded using a Tektronix model TDS220 digitizing oscilloscope equipped voltage follower (LF351). To ensure that the solar cell under test was not being loaded down by the measuring circuit, a high input impedance, low output-impedance buffer, consisting of a LF351 operational amplifier in the unity gain configuration, was placed between the solar cell and the input terminals of the oscilloscope. The LED was a commercial one with average emission wavelength k = 658 nm and average power 1 mW. Typical photon fluxes that we obtain could be varied between 106 and 1018 photons cm2 s1. The setup provides current pulses to the LED with fall times faster than 200 ns. A rather fast silicon pin photodiode BPW34, with rise and fall times of 100 ns, was used to test the measurement setup and LEDs before any particular set of OCVD measurements on devices. Measurements were carried out in the temperature range 50–330 K and current outputs of level 2 (36 mA LED current). The pulse repetition frequency and the pulse width was always adjusted to allow OCVD curve to fall to the bias light level before the appearance of the next forward biasing pulse. 4. Results and discussion We can obtain repetitive charging and discharging by using a fast light source (LED). Output of the light source is the ‘‘square wave” sequence as illustrated in Fig. 3. Both the intensity and frequency of the light output can be adjusted. As long as the period of the square light pulse is much longer than the effective minority carrier lifetime of the solar cell, the electron–hole pair will be created and annihilated. The voltage is shown by the solid curve in Fig. 3. As it is seen in Fig. 3, there are two significant regions, indicating rising and falling edge of the photo voltage between the notable steady state regions. As can be seen from Fig. 3, the steady state regions systematically change with temperature. We have seen that one can extract two V oc values independently by choosing peak and bias light level of the excitation pulse. The OCVD spectra consist of an ideal exponential transient, which sim-
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Fig. 2. Experimental setup for OCVD measurement.
Fig. 3. Photo voltage response of solar cell to chopped excitation at 658 nm, showing ideal exponential decay after light off.
ply gives the time constant. The exponentially transient curve is mostly determined by the time constant of the solar cell. It is convenient to generalize Eq. (3) by introducing the DV oc ðtÞ ¼ V oc ðtÞ V bias and assuming V o ¼ DV oc ; V oc ðtÞ t
V oc ðtÞ ¼ V bias þ V o ese
ð19Þ
Applicability of the Eq. (19) on the OCVD curve of the device is illustrated in Fig. 3 by means of the curve fitting using Eq. (19). It is seen that the transient region of the curve is well fitted with Eq. (19). Any surface recombination in the device is not taken into account because of the served temperature dependency of V oc t spectrum (Fig. 3) can not be explained by surface recombination (Schroder, 1990; Deshmukh and Nagaraju, 2005; Sharma et al., 1992; Mahan et al., 1979). The influence of effective
capacitance (C ) on the time constant, however causes a shift of the solar cell OCVD curve along the time axis, because, other possibilities are disregarded. The proposed technique for the determination of effective minority carrier lifetime is based on time depended In½V oc ðtÞ V bias plot at fixed temperatures. In½V oc ðtÞ V bias ¼ In V o
t se
ð20Þ
In order to determine effective minority carrier lifetime in a device, the Eq. (19) is used. Fig. 4 shows the suggested plots of the measured OCVD curves for device. The InV o peak value is obtained at the intersection of the curve and the vertical axis, while the inverse effective minority
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carrier lifetime is obtained from the slope of the curve. As can be seen in Fig. 4, the inverse effective minority carrier lifetime value increases with increasing temperature. Analysis of V oc ðtÞ V bias data by In½V oc ðtÞ V bias –t plot exhibits excellent one linear curve (see Fig. 4). This behavior cannot be explained by ordinary OCVD theory (Lederhandler and Giacoletto, 1955). This denotes that analyzing method is valid. Fig. 5 shows ln se values as a function of the inverse temperature. The main errors in this analysis probably arise from the error in the curve fitting process of the In½V oc ðtÞ V bias - t plot. We have made a completely independent series of twenty-two measurements of the transient characteristic on a investigated device for each temperature then we have calculated mean time constant (sc ). For instance, the mean values and standard deviations are sc ¼ 4:13 105 1:06 107 s at 50 K. As the temperature increases, the magnitude of the effective minority carrier lifetime decreases. For the case of V c ¼ V d , Eq. (18) simplifies to DE 0. This clearly shows that the measured effective minority carrier lifetime value reaches exact minority carrier lifetime value. However, the observed se versus temperature behavior is differ from that. The extracted se versus temperature plot for a proposed technique (Eq. (18) and Fig. 5) should be an exponential curve (in a linear scale). The graphical solution of sp is illustrated in Fig. 5 for investigated device values of DE. The curve consists of two linear regions (in semi-log scale) in spite of the same excitation wavelength. The calculated slope values of the curves are positive number. It is displayed that a plot of Inse against 1=T gave good straight lines at two distinct regions (50–170 K and 190–330 K) for investigated device, as shown in Fig. 5. It is concluded
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Fig. 5. Variation of Inse with the inverse temperature in the 50–330 K.
DE
that se may be expressed as se ðT Þ ¼ sp ekB T . The estimated values of DE are given in Fig. 5. It is difficult to attach DE to any specific mechanism as the temperature dependence of se is a combined effect of any physical parameters such as trap density, capture cross section of the trap state and thermal velocity. Nevertheless, the observed DE is directly linked to the barrier difference between the porous Si n+-type+n inversion layer/p type crystalline Si interface and p type crystalline Si/porous Si of p+-type interface. Probably this energy difference stems from negligible energy difference but not small enough to escape it to being temperature dependency of se . At low (50–170 K) and high (190–330 K) temperature region exact minority carrier lifetime has been obtained as 28.9 and 2.65 ls, respectively. In
Fig. 4. In½V oc ðtÞ V bias versus time plot of the measured OCVD data.
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our studies, we have found lower values of sp for higher DE. To get more photovoltaic power and efficiency from the solar cell, high value of minority carrier lifetime is appropriate. Having an indirect band gap, silicon has relatively weak light absorption and requires about 1–20 lm of material to absorb near-infrared and red light. The weak absorption in porous Si means that a significant fraction of the above-band-gap photons will generate carriers in the neutral region where the minority carrier lifetime must be very long to allow for long diffusion lengths. At that point, one may say that at lower temperature with red light excitation, indirect transition takes prominent role. On the contrary, at higher temperature excitation energy is not enough to perform significant absorption. Using Fig. 3, we have obtained V oc values from the steady state regions. The obtained V oc values were plotted as a function of temperature. Fig. 6 compares the temperature dependency of the open circuit voltage values at two different intensity levels, one with a maximum illumination level and one with a bias light level. It was observed that two characteristics displayed very different behavior to each other. Especially, potential difference between twoillumination levels increases towards to lower temperatures. As can be seen from the curve in the Fig. 6, V oc values at peak injection level and bias light level are directed into different directions at region I (50–190 K). We think that the different directions in region I are stem from trapped charge between the p+ porous silicon and the p type crystalline silicon. The resulting trapped charge behaves as an additional capacitance in equivalent circuit. However, they converge with increasing temperature in region II (190–330 K). It is apparent that V oc (at bias light level) almost saturates with decreasing temperature. Dotted lines display the extrapolation of the open circuit voltages to a temperature 0 K. The extrapolation yields activation energy, Ea . Activation energy determines the transport of holes to buffer/absorber interface, in case of interface
Fig. 6. Temperature dependence of the open circuit voltages V oc under different illumination intensities.
recombination without tunneling (Nadenau et al., 2000). The open circuit voltage of the porous Si based device extrapolates to values of approximately 0.95 eV as seen in Fig. 6. We think that the dominant recombination process occurs at the interface between the p+ porous silicon and the p type crystalline silicon. Fig. 7 shows extracted sp values as a function of temperature. As the temperature increases the magnitude of the exact minority carrier lifetime, stay stable until threshold temperature. If the temperature increases above this threshold temperature, exact minority carrier lifetime exhibits very big and abrupt chance. We thought that this abrupt change stems from critical discrete trap excitation energy. The temperature behaviour of the exact minority carrier lifetime is a good agreement with below equation. sp ðT Þ ¼
ðsmax smin p p Þ 1þe
k B T Et Ec
þ smin p
ð21Þ
This equation explains that there is a critical trap energy level referenced to thermal energy level. 5. Conclusion In this study, the OCVD technique is used to determine effective minority carrier lifetime in porous Si based solar cell. We interpret the total charge of the solar cell in terms of equivalent circuit model, which includes interface effects. A new analytical method is proposed for determination of exact minority carrier lifetime in case of the effective minority carrier lifetime is temperature dependent. We observed two linear regions in the In½V oc ðtÞ V bias t plot, this denotes that interface effect does not stable with temperature in porous Si based solar cell. The exact minority carrier lifetimes are determined as 2.65 and 28.9 ls for region I (50–190 K) and region II (190–330 K), respectively.
Fig. 7. Exact minority carrier lifetime as a function of temperature.
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Acknowledgements The authors acknowledge the supports given by NATO (project no. SfP 971829), TUBITAK-Marmara Research Centre (Turkey), Institute of Fundamental Problems for High Technology, Ukrainian Academy of Sciences. References Badawy, W.A., 2008. Effect of porous silicon layer on the performance of Si/oxide photovoltaic and photoelectrochemical cells. J. Alloy. Comp. 347, 464. Bisi, O., Ossicini, S., Pavesi, L., 2000. Porous silicon: a quantum sponge structure for silicon based optoelectronics. Surf. Sci. Rep. 38, 1. Castanier, L., Vilamajo, E., Llaberia, J., Garrido, J., 1981. Investigations of the OCVD transients in solar cells. J. Phys. D: Appl. Phys. 14, 1867. Deshmukh, M.P., Kumar, R.A., Nagaraju, J., 2004. Measurement of solar cell ac parameters using the time domain technique. Rev. Sci. Instrum. 75, 2732. Deshmukh, M.P., Nagaraju, J., 2005. Measurement of silicon and GaAs/Ge solar cell device parameters. Sol. Energ. Mat. Sol. C. 89, 403. Dhariwal, S.R., Vasu, N.K., 1981. Mathematical formulation for the photo-induced open circuit voltage decay method for measurement of minority carrier lifetime in solar cells. IEEE Electron Dev. 2, 53. Green, M.A., 1983. Minority carrier lifetimes using compensated differental open circuit voltage decay. Solid State Electron. 26, 1117. Friesen, G., Ossenbrink, H.A., 1997. Capacitance effects in high-efficiency cells. Sol. Energ. Mat. Sol. C. 48, 77. Hsieh, Y.K., Card, H.C., 1984. Recombination in germanium: Voltagedecay experiments on induced-junction devices and validity of the SRH model. Solid State Electron. 27, 1061. Jasprit, S., 1995. Semiconductor Optoelectronics: Physics and Technology. McGraw-Hill, International Editions, pp. 313. Joardar, K., Schroder, D.K., 1992. Analysis of the small-signal voltage decay technique in the characterization of Si concentrator solar cells. IEEE T. Electron Dev. 39, 1622. Kavasoglu, A.S., Kavasoglu, N., Oktik, S., 2008. Simulation for capacitance correction from Nyquist plot of complex impedance–voltage characteristics. Solid State Electron. 52, 990.
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Kumar, R.A., Suresh, M.S., Nagaraju, J., 2000. Measurement and comparison of AC parameters of silicon (BSR and BSFR) and gallium arsenide (GaAs/Ge) solar cells used in space applications. Sol. Energ. Mat. Sol. C. 60, 155. Lederhandler, S.R., Giacoletto, J. 1955. Measurement of minority carrier lifetime and surface effects in junction devices. In: Proceedings of IRE. p. 477. Mahan, J.E., Ekstedt, T.W., Frank, R.I., Kaplow, R., 1979. Measurement of minority carrier lifetime in solar cells from photo-induced opencircuit voltage decay. IEEE T. Electron Dev. 26, 733. Moore, A.R., 1980. Carrier lifetime in photovoltaic solar concentrator cells by the small signal open-circuit decay. RCA Rev. 40, 549. Nadenau, V., Rau, U., Jasenek, A., Shock, H.W., 2000. Electronic properties of CuGaSe2-based heterojunction solar cells. Part I. Transport analysis. J. Appl. Phys. 87, 584. Rabha, B., Dimassi, M., Bouaı¨cha, W., Ezzaouia, M., Bessais, H. 2008. Laser-beam-induced current mapping evaluation of porous siliconbased passivation in polycrystalline silicon solar cells. doi:10.1016/ j.solener.2008.11.002. Rau, U., Schock, H.W., 1999. Electronic properties of Cu(In,Ga)Se2 heterojunction solar cells–recent achievements, current understanding, and future challenges. Appl. Phys. A 69, 131. Schroder, D.K., 1990. Semiconductor Meterial and Device Characterization. Wiley, New York. Sharma, S.K., Pavithra, D., Sivakumar, G., Srinivasamurthy, N., Agrawal, B.L., 1992. Determination of solar cell diffusion capacitance and its dependence on temperature and 1 MeV electron influence level. Sol. Energ. Mat. Sol. C. 26, 169. Sinton, R.A., Swanson, R.M., 1987. Recombination in highly injected silicon. IEEE T. Electron Dev. 34, 1380. Smestad, G., Kunst, M., Vial, C., 1992. Photovoltaic response in electrochemically prepared photoluminescent porous silicon. Sol. Energ. Mat. Sol. C 26, 277. Stutenbaeumer, U., Lewetegn, E., 2000. Comparison of minority carrier diffusion length measurements in silicon solar cells by the photoinduced open-circuit voltage decay (OCVD) with different excitation sources. Renew. Energ. 20, 65. Suresh, M.S., 1996. Measurement of solar cell parameters using impedance spectroscopy. Sol. Energ. Mat. Sol. C 43, 21. Sze, S.M., 1981. Physics of Semiconductor Devices, second ed. Wiley, New York. Tuzun, O., Oktik, S., Altindal, S., Mammadov, T.S., 2006. Electrical characterization of novel Si solar cells. Thin Solid Films 511, 258.
Solar Energy 83 (2009) 1446–1453 www.elsevier.com/locate/solener
The circuit point of view of the temperature dependent open circuit voltage decay of the solar cell A. Sertap Kavasoglu *, Nese Kavasoglu, Sener Oktik Mugla University, Clean Energy Research & Development Centre, 48170 Kotekli/Mugla, Turkey Mugla University, Faculty of Arts and Sciences, Physics Department, 48170 Kotekli/Mugla, Turkey Received 2 November 2008; received in revised form 5 March 2009; accepted 9 March 2009 Available online 7 April 2009 Communicated by: Associate Editor Takhir Razykov
Abstract The open circuit voltage decay (OCVD) technique has been used to determine the minority carrier lifetime. In this study, an experimental and analytical method is described for determination of minority carrier lifetime at porous Si based solar cell by photo induced OCVD technique. The cell is illuminated by a monochromatic light source (k = 658 nm) in the open circuit configuration, and the decay of voltage is measured after abruptly terminating the excitation. For the analysis of the OCVD characteristic of solar cell device, equivalent electrical circuit has been proposed in which the diffusion capacitance is connected in series with the contribution of the solar cell interface. Exact minority carrier lifetimes at low (50–170 K) and high (190–330 K) temperature regions have been obtained as 28.9 and 2.65 ls from the temperature dependent OCVD measurements by using an alternative extraction technique. Ó 2009 Elsevier Ltd. All rights reserved. Keywords: Minority carrier lifetime; Porous Si based solar cell; Open circuit voltage decay technique; Circuit level simulation
1. Introduction In some works, photovoltaic properties (such as wavelength depended photosensitivity, internal quantum efficiency, illuminated and dark I–V measurements) of porous Si based solar cell structures have been extensively studied and reported in the literature (Rabha et al., 2008; Badawy, 2008). Porous silicon is increasingly applied to the fabrication of photovoltaic devices as a low-cost material (Smestad et al., 1992). Porous Si based solar cells are influenced by the electronic properties of interface. Various reports have been made to correlate these properties with the solar cell performance (Badawy, 2008; Bisi et al., 2000). The most important advantage of using porous Si in solar cells is its band gap and large minority carrier lifetime. In addition, this device is attractive because of the *
Corresponding author. Tel.: +90 252 211 1674; fax: +90 252 223 8656. E-mail address: [email protected] (A.S. Kavasoglu).
0038-092X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2009.03.009
feasibility for fabricating low cost–low temperature fabrication process for fast photo diodes having response times of 650 ls. The minority carrier lifetime, eminent parameter influencing the performance of a solar cell, is often measured with the transient methods. The minority carrier lifetime in Si based device was obtained by OCVD and short-circuit decay techniques have been noted by several groups (Deshmukh and Nagaraju, 2005; Stutenbaeumer and Lewetegn 2000). OCVD technique, relatively facile, is frequently used for estimation effective minority carrier lifetime in the solar cells. In particular, evaluation of open circuit voltage versus temperature data provides valuable information about the main recombination route in the devices (Rau and Schock, 1999). Until now, there could not be found any theoretical model about the temperature depended effective minority carrier lifetime extraction technique by using equivalent circuit approximation. The observed temperature depended effective minority carrier lifetime behavior
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in this study, cannot be explained by existence model in literature (Hsieh and Card, 1984). It thus became necessary to construct alternative theoretical approximation. We proposed a procedure to extract effective carrier lifetime of the devices. The presented theoretical results explain the role of equivalent circuits in time dependent open circuit transient characteristic of the investigated solar cell. OCVD characteristics of solar cells are customarily described by an equivalent circuit model, which includes series resistance, diode dynamic resistance and capacitance. Dynamic resistance and capacitance values are modulated by temperature. This effect significantly alters the device transient characteristics (Moore, 1980) with respect to ideal behavior and makes the measured OCVD characteristics strongly temperature dependent, especially below room temperature under monochromatic illumination level (Castanier et al., 1981). In this study, the theoretical method suggests that minority carrier lifetime is not directly accessible parameter. It can be measured as an effective minority carrier lifetime, which is strongly temperature depended. According to our model, effective minority carrier lifetime decreases exponentially with temperature. This behavior cannot be explained by ordinary OCVD theory (Lederhandler and Giacoletto, 1955). This denotes that our proposed analyzing method is valid otherwise; the expected OCVD curve is going to be consisting of stretch exponential form (see Eq. (1)). The OCVD characteristic can be significantly influenced by the capacitive effect, which can be considered as consisting of both depletion layer capacitance (Cd) and diffusion capacitance (Cdiff) under sufficient monochromatic illumination level. The diffusion capacitance of the injected carriers dominates over the depletion layer capacitance (Schroder, 1990; Sinton and Swanson, 1987). The OCVD time introduced by a junction capacitance causes that the minority carrier lifetime can be overestimated (Green, 1983). It is necessary that the minority carrier lifetime is much larger than the time constant for diffusion to calculate an effective minority carrier lifetime from the OCVD (Schroder, 1990; Sinton and Swanson, 1987). In addition, there may arise some uncertainty in minority carrier lifetime due to fact that our porous Si solar cell-type is ‘‘back surface field” (BSF) solar cell (Sze, 1981) generally contains two interfaces (p+/p and p/n+ contact intercept region) in the junction formation, forasmuch as OCVD method measures the recombination lifetime. At that point, a reconstruction technique/model is required to extract the effective minority carrier lifetime from the measured non-traditional OCVD data in the presence of an interface effect. OCVD technique was one of the earliest methods for minority carrier lifetime determination. However, very little attention has been paid to the temperature depended OCVD at monochromatic illumination of solar cells in the literature, especially at low temperature. In this study, effective minority carrier lifetime has been calculated from the temperature dependent OCVD measurements by using an alternative extraction technique.
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2. Theory The time variation of OCVD (DV oc ðtÞ) is given elsewhere (Lederhandler and Giacoletto, 1955), qV i i kBT h t In 1 þ ese ekB T DV oc ðtÞ ¼ ð1Þ q where t is the time (for collecting data during the transient response), V i the junction voltage at t = 0, se the effective minority carrier lifetime, T temperature and q, k B are the well known constants. qV ð i t Þ Let z ¼ e kB T se . For tii kqVB Ti se , z value approximates to zero. However, if this condition can be met, it can be shown using the approximation Inð1 þ zÞ z, k B T kqV Ti t ð2Þ e B e se DV oc ðtÞ ¼ q where DV oc ðtÞ ¼ V oc ðtÞ V bias . V bias is the final value of the open circuit voltage which depends on the intensity of the bias light. The voltage decay is constituted of a sum of exponentially decaying modes (Joardar and Schroder, 1992). It is obvious from Eq. (2) that the OCVD curve is represented by single exponential function. The voltage decay curve can be approximated as a pure exponential. That is; t
DV oc ðtÞ ¼ DV oc ð0Þese
ð3Þ
Several equivalent circuits have been proposed for determining solar cell ac parameters using different electrical characterization technique (Deshmukh and Nagaraju, 2005; Deshmukh et al., 2004; Kumar et al., 2000; Suresh, 1996; Sharma et al., 1992). Especially, the study (Deshmukh et al., 2004) is of great practical interests. In this paper, we propose an alternative technique for this measurement and show how the equivalent circuit can be further improved. Equivalent circuit model, useful in a transient analysis, should include the diffusion capacitance, dynamic resistance Rd , series resistance Rs and interface elements (Rint) and (Cint). Under low frequency (high excitation period) excitation condition the diode capacitance arises from two distinct regions of charges (Jasprit, 1995). (i) Under reverse biased conditions, there are fundamentally no injected carriers to the depletion region and the junction capacitance dominates. A dipole of fixed positive and negative charge in the depletion region of the junction constitutes the junction capacitance. (ii) Under forward bias condition, there are minority carrier injections to the depletion region. The diffusion capacitance arises from minority carrier injection from the region outside the depletion region. For the analysis of the OCVD characteristic of simulated solar cell, equivalent electrical circuit has been proposed corresponding to solar cell structure. For the OCVD measurement, one should use a light source,
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which’s rise and fall times must be much smaller than the minority carrier lifetime of the sample. It will be helpful if light of shorter wavelengths are filtered out and the intensity of longer wavelengths is kept sufficient to keep the injection level large enough to ignore the space charge capacitance effects and low enough to work in the low injection limit (Dhariwal and Vasu, 1981). Long wavelength monochromatic light is advisable due to ability of long penetration depth. The applying monochromatic square light pulse through a solar cell under test is defined as, V ; ½0; t1 ð4Þ V apl ðtÞ ¼ 0; ½t1 ; t2 where t2 is the period and t1 light on time, V the amplitude in square light pulse. We interpret the total charge (Q) of the solar cell in terms of equivalent circuit model (Fig. 1). The diffusion capacitance is connected in series with Rint and C int which mimic the contribution of the solar cell interface. The electrical behavior of a solar cell is described in terms of charge control model. Having taken connection configuration of the circuit components in the device’s equivalent circuit into consideration, one obtains Eq. (5) when the switch is at I position, Q Rs dQ Rint ð5Þ þ1 þ Rs þ Rs þ Rint V ¼ C Rd dt Rd The term C includes diffusion capacitance and unwanted portion of interface capacitance in series connected form. C int strongly influences to OCVD characteristic. C is obtained by simply calculating the total capacity of two capacities connected in series, C ¼
C int C diff C int þ C diff
ð6Þ
The purpose is to solve Eq. (5) using transient conditions. Charging equation (Eq. (7)) is written from the solving the differential Eq. (5),
sc ¼
h i C Rs þ Rint 1 þ RRds 1 þ RRds
ð9Þ
Discharging equations is written from the solving the differential Eq. (5) for condition V = 0, t
QðtÞ ¼ Qmax esc ; discharging equation
ð10Þ
When the switch is at position II, Rs becomes larger then Rd (Rs Rd ), because Rs almost equals to series contribution of voltage follower input impedance. Under this condition, it is convenient to simplify Eq. (9) as, Rint ð11Þ sc ¼ C R d 1 þ Rd We can approximate to Eq. (11) to take into account Rd Rint , then sc ¼ C R d
ð12Þ
The V d ðtÞ (absolute value of voltage across the dynamic resistance) is described as dQ V d ðtÞ ¼ Rd ð13Þ dt V d ðtÞ can be expressed in terms of Rd and C such as t Rd e Rd C ð14Þ V d ðtÞ ¼ V R d þ Rs It is obviously seen that the calculated function is a good agreement with Eq. (3). From the diffusion limited current theory, forward voltqV d age depended current is given by I 0 ðe kB 1Þ, where I o is the saturation current. Rd and C diff are influenced by temperature. The temperature dependence of Rd is described by (Kavasoglu et al., 2008); Rd ðT Þ ¼
1 ðk B T =qÞ ¼ qV d dI=dV I o ek B T
ð15Þ
ð8Þ
For relatively low excitation frequencies by light pulse, the diffusion capacitances may be given as (Friesen and Ossenbrink, 1997) qV c qsp I o ekB T ð16Þ C diff ðT Þ ¼ kBT
and the time constant (sc ) of the proposed RC network is,
where V c the voltage across the diffusion capacitance, sp the exact minority carrier lifetime for C diff C int . For the
t sc
QðtÞ ¼ Qmax ð1 e Þ; charging equation
ð7Þ
where Qmax ¼
Rd CV R d þ Rs
Fig. 1. Schematic structure and proposed equivalent circuit of the porous Si based solar cell.
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maximum illumination level, the created electron–hole pair density is quite large and can dominate the capacitance like forward bias condition. That is why we neglected the depletion region capacitance. If interface capacitance contribution is much larger then the diffusion capacitance (C diff C int ) then C equals C diff . Under this assumption, Eq. (12) is rewritten as sc ¼ C diff Rd . For the long-base diode, sc se , so a reasonable estimate of the effective lifetime can be taken as se without much error. q
se ðT Þ ¼ sp ekB T
ðV c V d Þ
ð17Þ
For the obtained effective minority carrier lifetime to be almost equal to the exact minority carrier lifetime, it is compulsory that V d V c . The V d V c prerequisite is not perpetually satisfied. This means that interface effect may alter effective minority carrier lifetime. For that reason, in practice, it may be difficult to measure effective minority carrier lifetime directly with sufficiently high accuracy. It is therefore of great practical interest to investigate effective minority carrier lifetime as a function of temperature. It is worth noting that, since the ðV c V d Þ potential difference corresponds to barrier energy difference DE ¼ qðV c V d Þ, it must be positive. At this point, it is convenient to generalize Eq. (17); DE 1 ð18Þ In se ðT Þ ¼ In sp þ kB T The effective carrier lifetime now can be defined as an Arrhenius plot of inverse temperature. In consequence, plotting Inse ðT Þ T1 allows determination of the barrier energy difference and exact minority carrier lifetime from the slope of this curve and intercept with Inse ðT Þ axis, respectively. 3. Experimental details The OCVD measurements were performed on highly efficient porous Si solar cell. The fabrication of the devices was given in detail at (Tuzun et al., 2006). A diagram of the measurement setup is shown in Fig. 2. It consists of a pulse generator, a MOSFET pulse driver and one 4-bit duty cycle control-multiplexing unit that control the ladder network resistors. OCVD measurements were performed with a TDS 220 digital oscilloscope and an IBM compatible PC. The control of the various experimental parameters and data acquisition was carried out with a computer. Measurement was performed inside evacuated close-cycle OXFORD He cryostats with ITC 502 intelligent temperature controller. A delay of a few seconds between subsequent measuring steps was built into the program to assure steady–state conditions for the measurement of the temperature. The ITC 502 temperature controller has auto PID mode with RS-232 computer interface. So, cooling and heating rate and other parameters systematically controlled by PC. We have also independently measured temperature on the sample by K-type thermocouple with a
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suitable connected extension cable through the feedthrough. The device was connected to voltage follower unit for dc measurement via the equipped suitable coaxial cable. In addition, for each measurement step the average of up to thirty-two measurements was taken to increase the signal-to-noise ratio by TDS 220 digital oscilloscope. The light source is a group of LEDs of 658 nm wavelength. This excitation wavelength is enough to create electron–hole pair in device depletion region. The LED group was driven by a MOSFET current pump driver that could be operated between 2 and 50 mA. A clock generator generates low frequency and high accuracy sharp transient pulses. The duty cycle value of the pulse can be controlled by the ladder network circuits. The control of the various resistor values and data acquisition was carried out with a personal computer. The open circuit transient time of the samples was recorded using a Tektronix model TDS220 digitizing oscilloscope equipped voltage follower (LF351). To ensure that the solar cell under test was not being loaded down by the measuring circuit, a high input impedance, low output-impedance buffer, consisting of a LF351 operational amplifier in the unity gain configuration, was placed between the solar cell and the input terminals of the oscilloscope. The LED was a commercial one with average emission wavelength k = 658 nm and average power 1 mW. Typical photon fluxes that we obtain could be varied between 106 and 1018 photons cm2 s1. The setup provides current pulses to the LED with fall times faster than 200 ns. A rather fast silicon pin photodiode BPW34, with rise and fall times of 100 ns, was used to test the measurement setup and LEDs before any particular set of OCVD measurements on devices. Measurements were carried out in the temperature range 50–330 K and current outputs of level 2 (36 mA LED current). The pulse repetition frequency and the pulse width was always adjusted to allow OCVD curve to fall to the bias light level before the appearance of the next forward biasing pulse. 4. Results and discussion We can obtain repetitive charging and discharging by using a fast light source (LED). Output of the light source is the ‘‘square wave” sequence as illustrated in Fig. 3. Both the intensity and frequency of the light output can be adjusted. As long as the period of the square light pulse is much longer than the effective minority carrier lifetime of the solar cell, the electron–hole pair will be created and annihilated. The voltage is shown by the solid curve in Fig. 3. As it is seen in Fig. 3, there are two significant regions, indicating rising and falling edge of the photo voltage between the notable steady state regions. As can be seen from Fig. 3, the steady state regions systematically change with temperature. We have seen that one can extract two V oc values independently by choosing peak and bias light level of the excitation pulse. The OCVD spectra consist of an ideal exponential transient, which sim-
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Fig. 2. Experimental setup for OCVD measurement.
Fig. 3. Photo voltage response of solar cell to chopped excitation at 658 nm, showing ideal exponential decay after light off.
ply gives the time constant. The exponentially transient curve is mostly determined by the time constant of the solar cell. It is convenient to generalize Eq. (3) by introducing the DV oc ðtÞ ¼ V oc ðtÞ V bias and assuming V o ¼ DV oc ; V oc ðtÞ t
V oc ðtÞ ¼ V bias þ V o ese
ð19Þ
Applicability of the Eq. (19) on the OCVD curve of the device is illustrated in Fig. 3 by means of the curve fitting using Eq. (19). It is seen that the transient region of the curve is well fitted with Eq. (19). Any surface recombination in the device is not taken into account because of the served temperature dependency of V oc t spectrum (Fig. 3) can not be explained by surface recombination (Schroder, 1990; Deshmukh and Nagaraju, 2005; Sharma et al., 1992; Mahan et al., 1979). The influence of effective
capacitance (C ) on the time constant, however causes a shift of the solar cell OCVD curve along the time axis, because, other possibilities are disregarded. The proposed technique for the determination of effective minority carrier lifetime is based on time depended In½V oc ðtÞ V bias plot at fixed temperatures. In½V oc ðtÞ V bias ¼ In V o
t se
ð20Þ
In order to determine effective minority carrier lifetime in a device, the Eq. (19) is used. Fig. 4 shows the suggested plots of the measured OCVD curves for device. The InV o peak value is obtained at the intersection of the curve and the vertical axis, while the inverse effective minority
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carrier lifetime is obtained from the slope of the curve. As can be seen in Fig. 4, the inverse effective minority carrier lifetime value increases with increasing temperature. Analysis of V oc ðtÞ V bias data by In½V oc ðtÞ V bias –t plot exhibits excellent one linear curve (see Fig. 4). This behavior cannot be explained by ordinary OCVD theory (Lederhandler and Giacoletto, 1955). This denotes that analyzing method is valid. Fig. 5 shows ln se values as a function of the inverse temperature. The main errors in this analysis probably arise from the error in the curve fitting process of the In½V oc ðtÞ V bias - t plot. We have made a completely independent series of twenty-two measurements of the transient characteristic on a investigated device for each temperature then we have calculated mean time constant (sc ). For instance, the mean values and standard deviations are sc ¼ 4:13 105 1:06 107 s at 50 K. As the temperature increases, the magnitude of the effective minority carrier lifetime decreases. For the case of V c ¼ V d , Eq. (18) simplifies to DE 0. This clearly shows that the measured effective minority carrier lifetime value reaches exact minority carrier lifetime value. However, the observed se versus temperature behavior is differ from that. The extracted se versus temperature plot for a proposed technique (Eq. (18) and Fig. 5) should be an exponential curve (in a linear scale). The graphical solution of sp is illustrated in Fig. 5 for investigated device values of DE. The curve consists of two linear regions (in semi-log scale) in spite of the same excitation wavelength. The calculated slope values of the curves are positive number. It is displayed that a plot of Inse against 1=T gave good straight lines at two distinct regions (50–170 K and 190–330 K) for investigated device, as shown in Fig. 5. It is concluded
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Fig. 5. Variation of Inse with the inverse temperature in the 50–330 K.
DE
that se may be expressed as se ðT Þ ¼ sp ekB T . The estimated values of DE are given in Fig. 5. It is difficult to attach DE to any specific mechanism as the temperature dependence of se is a combined effect of any physical parameters such as trap density, capture cross section of the trap state and thermal velocity. Nevertheless, the observed DE is directly linked to the barrier difference between the porous Si n+-type+n inversion layer/p type crystalline Si interface and p type crystalline Si/porous Si of p+-type interface. Probably this energy difference stems from negligible energy difference but not small enough to escape it to being temperature dependency of se . At low (50–170 K) and high (190–330 K) temperature region exact minority carrier lifetime has been obtained as 28.9 and 2.65 ls, respectively. In
Fig. 4. In½V oc ðtÞ V bias versus time plot of the measured OCVD data.
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our studies, we have found lower values of sp for higher DE. To get more photovoltaic power and efficiency from the solar cell, high value of minority carrier lifetime is appropriate. Having an indirect band gap, silicon has relatively weak light absorption and requires about 1–20 lm of material to absorb near-infrared and red light. The weak absorption in porous Si means that a significant fraction of the above-band-gap photons will generate carriers in the neutral region where the minority carrier lifetime must be very long to allow for long diffusion lengths. At that point, one may say that at lower temperature with red light excitation, indirect transition takes prominent role. On the contrary, at higher temperature excitation energy is not enough to perform significant absorption. Using Fig. 3, we have obtained V oc values from the steady state regions. The obtained V oc values were plotted as a function of temperature. Fig. 6 compares the temperature dependency of the open circuit voltage values at two different intensity levels, one with a maximum illumination level and one with a bias light level. It was observed that two characteristics displayed very different behavior to each other. Especially, potential difference between twoillumination levels increases towards to lower temperatures. As can be seen from the curve in the Fig. 6, V oc values at peak injection level and bias light level are directed into different directions at region I (50–190 K). We think that the different directions in region I are stem from trapped charge between the p+ porous silicon and the p type crystalline silicon. The resulting trapped charge behaves as an additional capacitance in equivalent circuit. However, they converge with increasing temperature in region II (190–330 K). It is apparent that V oc (at bias light level) almost saturates with decreasing temperature. Dotted lines display the extrapolation of the open circuit voltages to a temperature 0 K. The extrapolation yields activation energy, Ea . Activation energy determines the transport of holes to buffer/absorber interface, in case of interface
Fig. 6. Temperature dependence of the open circuit voltages V oc under different illumination intensities.
recombination without tunneling (Nadenau et al., 2000). The open circuit voltage of the porous Si based device extrapolates to values of approximately 0.95 eV as seen in Fig. 6. We think that the dominant recombination process occurs at the interface between the p+ porous silicon and the p type crystalline silicon. Fig. 7 shows extracted sp values as a function of temperature. As the temperature increases the magnitude of the exact minority carrier lifetime, stay stable until threshold temperature. If the temperature increases above this threshold temperature, exact minority carrier lifetime exhibits very big and abrupt chance. We thought that this abrupt change stems from critical discrete trap excitation energy. The temperature behaviour of the exact minority carrier lifetime is a good agreement with below equation. sp ðT Þ ¼
ðsmax smin p p Þ 1þe
k B T Et Ec
þ smin p
ð21Þ
This equation explains that there is a critical trap energy level referenced to thermal energy level. 5. Conclusion In this study, the OCVD technique is used to determine effective minority carrier lifetime in porous Si based solar cell. We interpret the total charge of the solar cell in terms of equivalent circuit model, which includes interface effects. A new analytical method is proposed for determination of exact minority carrier lifetime in case of the effective minority carrier lifetime is temperature dependent. We observed two linear regions in the In½V oc ðtÞ V bias t plot, this denotes that interface effect does not stable with temperature in porous Si based solar cell. The exact minority carrier lifetimes are determined as 2.65 and 28.9 ls for region I (50–190 K) and region II (190–330 K), respectively.
Fig. 7. Exact minority carrier lifetime as a function of temperature.
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