Comparison of Techniques for Measuring Recombination Lifetime in Photovoltaic Materials: Trapping Effects
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Comparison of Techniques for Measuring Recombination Lifetime in Photovoltaic Materials: Trapping Effects Richard K. Ahrenkiel1,2, Steven W. Johnston1, and Wyatt K. Metzger1 1 Measurements and Characterization Division, National Renewable Energy Laboratory, 1617 Cole Blvd., Golden, CO, 80401 2 Department of Physics and Astronomy, University of Denver, 2112 E. Wesley Ave., Denver, CO, 80208 INTRODUCTION Minority-carrier or recombination lifetime is a critical photovoltaic parameter and is directly related to performance and efficiency. Here, we will analyze techniques that are currently used for the lifetime characterization of photovoltaic materials at NREL and elsewhere. These are: (A) time-resolved photoluminescence (TRPL); (B) microwave reflection (µPCD); (C) quasi-steady-state photoconductance (QSSPC); and (D) resonantcoupled photoconductive decay (RCPCD). The first three techniques are commercially available, whereas RCPCD, which was developed at the National Renewable Energy Laboratory (NREL), has been extensively used there to support the national photovoltaic program [1]. The NREL TRPL technique has been described elsewhere [2,3]. Here, we present data and compare results on a variety of semiconductor materials measured by the four techniques. The samples range from direct-bandgap GaAs to indirect-bandgap silicon. Techniques A, B, and D are currently suitable for direct-bandgap semiconductors such as GaAs and InGaAs. Techniques B, C, and D are applied to single-crystal and multicrystalline silicon. When shallow traps are present, the data acquisition must be properly interpreted in order to extract the recombination lifetimes. A. The effect of shallow traps on carrier transport: theory A trap is usually defined as a shallow defect that temporarily captures an electron or hole and then releases the carrier prior to any significant recombination. We will describe the trap with a capture cross section, σt, and a trap density, Nt. The trap capture lifetime is then given by: 1 = Vthσ t N t , (1)
τt
where Vth is the thermal velocity. The trap will re-emit the carrier at a rate en with an emission time τe. Using the optical excitation function G(t), one can write the rate equation for excess electrons as: d∆n ∆n ∆n = G(t) − − Vthσ t (N t − ∆n t )∆n + t . (2) dt τR τe Here ∆n is the density of free electrons, ∆nt is the density of trapped electrons, and τR is the recombination lifetime. We can write the companion rate equation for trap occupation as: d∆n t ∆n = Vthσ t (N t − ∆n t )∆n − t . (3) dt τe The optical pulse also generates an equal number of holes, ∆p. The holes are assumed to not interact with the trap, and therefore the rate equation for hole recombination is:
d∆p ∆p = G(t) − . (4) dt τR Charge neutrality requires that: ∆n + ∆n t = ∆p . (5) At steady-state equilibrium, the trap capture and emission rates are equal (Eq. 3), and therefore, the steady-state excess free-electron,∆ns, and trapped electron, ∆nt0, densities are: ∆n s = Gτ R ; ∆n s (6) ∆n t 0 = ∆n s τ t + Nt τ e In the steady st
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