Relationship between Phase Shift, Square-Wave Response and Density of States in Modulated Photocurrent Spectroscopy
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0910-A09-01
Relationship between Phase Shift, Square-Wave Response and Density of States in Modulated Photocurrent Spectroscopy Steve Reynolds1, and Charlie Main2 1 Institute of Photovoltaics, Forschungszentrum Juelich, Leo Brandt Str., Juelich, NRW, D52425, Germany 2 Division of Electronic Engineering and Physics, University of Dundee, Nethergate, Dundee, Angus, DD1 4HN, United Kingdom
ABSTRACT Low- and high-frequency modulated photoconductivity measurements (LF and HF MPC) have been made on amorphous silicon films prepared by the expanding thermal plasma (ETP) and RF PECVD techniques. Time constants have been measured by decay of square wave excitation and behavior of complex frequency response. The influence of quasi-Fermi level position has been examined. Band tail slopes of 32 meV (ETP) and 37 meV (PECVD), and defect densities of order 1018 and 1017 cm-3 eV-1 respectively are found. Tail state capture coefficients of order 3×10-8 cm3 s-1 are calculated from overlapping LF and HF regimes. Defect state values for ETP (≤ 10-8 cm3 s-1) are smaller than for PECVD silicon films (≥ 10-7 cm3 s-1). INTRODUCTION Modulated Photocurrent Spectroscopy (MPC) [1] may be used to determine transport parameters such as the distribution of localized states (DOS) and capture coefficients in semiconductors. It consists in measuring the amplitude |I (ω)| and phase φ(ω) of the photocurrent in a biased coplanar sample, generated by a source of light of photon energy greater than the band gap modulated at angular frequency ω. Two limiting regimes of interaction of free carriers with gap states may be identified (we assume the response is dominated by electrons): (i) HF regime. At higher modulation frequencies and low carrier generation rates, the photocurrent response is determined mainly by emission of carriers from states above the quasi-Fermi level. By varying ω the DOS distribution may be probed [2]: N HF ( Eω ) =
2Gω qFA sin(ϕ (ω )) , Eω = EC − kT ln(ν 0 / ω ) × (C n / µ )πkT I (ω )
(1)
Gω is the ac carrier generation rate per unit volume, q the elementary charge, F the electric field, A the conduction cross-section, ν0 the attempt-to-escape frequency, k is Boltzmann’s constant, EC the conduction band reference energy and T the absolute temperature. Note that the DOS contains a factor (Cn / µ) where Cn is the capture coefficient and µ the free carrier mobility.
(ii) LF regime. At higher generation rates, when the photocarrier density is much greater than the thermal carrier density, the phase response becomes linear at sufficiently low frequencies. Under these conditions, carrier capture and subsequent recombination in states at an energy Et close to the quasi-Fermi level EFn controls the ac response, and the DOS [3] N LF ( Et ) =
2G dc tan(ϕ ) , Et ≈ E Fn × ω kT
(2)
Gdc is the steady photocarrier generation rate per unit volume. This expression contains only experimentally measurable quantities and in principle enables the DOS distribution to be probed by varying ∆E Fn = kT ln( I dc / I 0 ) , where Idc and I0 are respect
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