·Table of Contents ·General | Temperature dependence of 1/F noise and transport characteristics as a non-destructive testing of monocrystalline silicon solar cellsA.Ibrahim and Z.ChobolaTechnical University of Brno, Faculty of Civil Engineering, Physics department, Zizkova 17, 602 00 Brno, CZ., Fax: +420541147666, Tel:+420541147659. E-Mail: ali@dp.fce.vutbr.cz Contact |
Fig 1: Block diagram of the noise voltage measurements under temperature | Fig 2: I-V-T characteristics of a Si solar cell of structure n^{+}pp^{++} of area 100 cm^{2} |
(A) TEMPERATURE DEPENDENCE OF THE DARK I-V CHARACTERISTICS
The temperature dependence of the dark I-V characteristics is often useful indicator of the principal mechanism responsible for current conduction in a device. Over the range of bias, where the Si solar cells operate in the photovoltaic modes, the mechanism of the I-V characteristics should be diffusion, the same process as in a Shockley p-n junctions. Measurements on a monocrystalline Si solar cell of n^{+}pp^{++} structure using a 0.7 W.cm p-type silicon wafer over the 300K to 400Kare shown in Fig.2. The experimental data can be described to a high degree of precision by an equations of the form[5]:
(1) |
(2) |
where D_{p} and D_{n} are the diffusion coefficients for the holes and electrons, respectively. W is the width of the depletion layer and t_{d} is the diffusion lifetime of the charge carriers in the junction and finally, L_{n} and L_{p} are the diffusion lengths for electrons and holes respectively. For logarithmic segments at high voltage end of each characteristics prior to the series resistance region, the n_{1} close values are close to be 1 indicating a diffusion process. The low voltage portions have n_{2} close to 2 indicating recombination in the depletion layer of the junction, as given by the second term in Eq.(1).
The most striking feature of these curves is that they are parallel straight lines over nearly three decades of the current, with a positive temperature coefficient over the whole range of bias voltage.
(B) 1/F NOISE MEASUREMENTS WITH TEMPERATURE
Hooge and Hoppenbrouwers[6] have measured the 1/f noise voltage generated in continuous gold films (with physical properties close to bulk values) in the presence of a steady current. They found that the noise power spectrum S_{V}(f) for samples at room temperature could be expressed by the empirical formula:
(3) |
where N is the number of the charge carriers in the sample, f is the frequency, and V is the voltage across the sample. And the 1/f noise is often considered as arising from resistance fluctuations that generate a fluctuation voltage in the presence of a steady current. Equation(3) is valid also for semiconductors, where 1/f noise in semiconductors is a bulk and surface effects[7].
The 1/f noise in metal films could be caused by temperature fluctuations that modulate sample resistance R and generate voltage fluctuations in the presence of a steady current I [8]. Thus:
(4) |
<(DT)^{2}> is the mean-square temperature fluctuation. At thermal equilibrium where C_{v} is the heat capacity of the sample. At room temperature, C_{v}=3NK, and S_{v}(f)aV^{2}b^{2}T^{2}/3N. The temperature fluctuation DT in the sample of a resistance R and temperature coefficient of resistivity will be observed as a voltage fluctuation DV = IRbDT in the presence of a constant current I. The voltage fluctuation spectrum S_{V}(f) is then related to the temperature fluctuation spectrum S_{T}(f) by S_{v}(f) = V^{2}b^{2}S_{T}(f). If the temperature fluctuations are due to equilibrium exchange of energy between the sample and its environment, then in this case Dependencies of the S_{V}(f) with frequency for a Si solar cell of a n^{+}pp^{++} structure at a temperatures ranges from 300K to 400K are shown in Fig.3.
The sample is under a forward bias voltages of values 200 mV, 150 mV and 100 mV for 300K, 350K and 400K, respectively. As the temperature increases S_{V}(f) decreases and S_{V}(f) is proportional to f^{-1}. The equilibrium temperature fluctuations modulating the resistance of the sample and this is the physical origin of the 1/f noise under temperature effect or at thermal equilibrium. [9]
The dependence of the noise voltage with 1/T at 10^{3} Hz of the UNIPAN measuring unit and the current through the sample is fixed at 8 mA is shown in Fig.4. The temperature fluctuations obey the diffusion equation. The activation energy from this Arrhenius plot in forward direction is 0.44 eV for the Si solar cell.
Fig 3: The S_{V}(f) vs frequency for a Si solar cell at of structure n^{+}pp^{++} in a temperature range of 300-400K. | Fig 4: Noise voltage as a function of 1/T for the Si solar cell of structure n^{+}pp^{++}. |
The results of the voltage noise for the Si solar cells of a structure n^{+}pp^{++} in the temperature range from 25-125 ^{0}C are useful for calculating the activation energy of the sample under test and also can be used as a tool for evaluating the quality of the product of technology.
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