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Modulated photocurrent as a powerful method to reveal transport by the majority carriers of disordered semiconductors and to resolve all the kinds of probed states Maura Pomoni, Athina Giannopoulou and Panagiotis Kounavis Department of Engineering Sciences, University of Patras, 26504 Patra, Greece Univ. of Patras

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Possible contribution from both carriers complicates interpretation of photoconductivity measurements This limitation is overcome in the modulated photocurrent (MPC) Specific features in the MPC spectra can be used to reveal whether the transport of the majority carriers dominates In this case, a DOS spectroscopy based on a general formula can be used to evaluate the DOS parameters of the various species of states with which the majority carriers interact Univ. of Patras

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The essential parameter of the MPC is the out of phase Y signal Phase shift Modulated photoconductivity Modulated light Generation rate Mobility of the majority carriers Out of phase MPC Y signal Experimental setup Measured Univ. of Patras DOS

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The analysis have shown that Univ. of Patras or

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Y signal is related to the gap states with which the electrons and holes interact and contribute to Y n, Y p High Frequency (HF) regimeLow Frequency (LF) regime Electrons the majority carriers n>>p The states contributing Y n In some cases Y 2n + Y 3n =0 and so Y n =Y 1n Y 1n >>Y 2n + Y 3n and so Y n =Y 1n Univ. of Patras Trapping & detrapping Deep trapping electrons holes electrons holes

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High Frequency (HF) regimeLow Frequency (LF) regime Holes the minority carriers The states contributing Y p Y 1p >> Y 2p +Y 3p and so Y p =Y 1p Univ. of Patras holes

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HF regime LF regime n>>p =1/τ ωn Effective trapping rate of holes Effective trapping rate of electrons =1/τ ωp Univ. of Patras Y n =1/τ ωn Reflects the DOS of the CB side Y p =1/τ ωp Reflects the DOS of the VB side Y n, Y p do not reflect the DOS The so-called H function

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n>>p Majority carriers (electrons) dominate μ p τ ωp << μ n τ ωn μ p τ ωp >> μ n τ ωn μ p τ ωp = μ n τ ωn Minority carriers (holes) dominate Mixed contributions From both carriers How can we know whether the majority carriers dominate A DOS spectroscopy is impossible A DOS spectroscopy can be achieved ? DOS model Comparable densities below and above E F E F is abοve midgap so that electrons the majority carriers μp=μnμp=μn μ p <<μ n μ p >>μ n Univ. of Patras

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n>>p Majority carriers (electrons) dominate Y signal If the majority carriers dominate and Y signal follows 1/τ ωn at ω t Η =ω t c =nc n c This can be used to determine the capture coefficient Bias light dependence Y moderate bias Y 0 weak bias near dark equilibrium Y follows 1/τ ωn Two bias light levels Normalized Y/Y 0 spectrum the normalized Y/Y 0 ratio follows the universal H function Univ. of Patras Y signal drops by a factor of 2 …providing that the capture coefficient c n v of the states below E F for the majority carriers is much lower than that c n c of the states above E F For

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Univ. of Patras For The decay of Y signal in the LF regime is steeper than 1/τ ωn The normalized Y/Y 0 spectrum is below the universal spectrum of H function for C e =c n v /c n c ≥1 In general, electrons holes Recombination through the states below E F increases Majority carriers (electrons) dominate Y signal, but Y<1/τ ωn if Y differs from the 1/τ ωn the normalized Y/Y 0 ratio does not follow the universal H function because μ p τ ωp << μ n τ ωn

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Minority carriers (holes) dominate Mixed contributions from electrons and holes the normalized Y/Y 0 ratio is above the universal H function for Bias light dependence μ p τ ωp >> μ n τ ωn μ p τ ωp = μ n τ ωn Majority carriers (electrons) do not dominate Y signal Y does not follow 1/τ ωn Univ. of Patras μ p τ ωp = μ n τ ωn μ p τ ωp >> μ n τ ωn For

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Univ. of Patras DOS spectroscopy This formula can be used for a DOS spectroscopy & Y follows 1/τ ωn The majority carriers (electrons) dominate If the normalized Y/Y 0 ratio follows H function at ω t Η =ω t c =nc n c the capture coefficient is obtained coefficient from and Y signal drops by a factor of 2 Alternatively ω t c can be obtained from the DOS in the frequency regime at ω t L /4 = ω t c /4 is the onset of LF regime (plateau)

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Univ. of Patras Experimental spectra of a-As 2 Se 3 the normalized Y/Y 0 ratio follows the universal H function The majority carriers (holes) dominate and Y signal follows 1/τ ωp at ω t Η =ω t c =nc n c and Y signal drops by a factor of 2 2.8 Ǻ Neutral centers Exponential dependence (valence band-tail) DOS spectroscopy Capture radius

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Univ. of Patras Various species of states DOS model Experimental spectra of a-Si:H Additional states having a 100 times higher capture coefficient From the decay of Y signal by the factor of 2 ω t H is determined From The highest capture coefficient the experimental Y signal follows 1/τ ωn

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at ω t L /4 = ω t c /4 is the onset of LF (plateau) From Normal db’s db’s with a Si-H back bond or a three center Si-H-Si bond LF HF Provides the DOS of both species of states DOS spectroscopy model D c (E ωn ) D hc (E ωn ) Univ. of Patras a-Si:H HF LF The states with the lowest capture coefficient Vertical line the signature of various species of states Various species of states

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Mixed contributions from electrons and holes reasonable for the the lightly p-type doped material U. of Patras Experimental spectra from the literature where the majority carriers do not dominate from the MPC measurements of Kleider & Longeaud Sol. St. Phen.44&46 596 (1995) The normalized Y/Y 0 ratio does not follow the universal H function a-Si:H lightly p-type doped from MPC measurements of Bruggemann J Mat. Sc.14, 629 (2003) μc-Si:H Y does not follow 1/τ ωn The normalized Y/Y 0 ratio at lowest ω does not follow the universal H function Y does not follow 1/τ ωn at lowest ω Mixed contributions from electrons and holes A DOS spectroscopy is impossible Y signal exponential dependence Bias light dependence

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U. of Patras Conclusions the transport of the majority carriers dominates giving the highest mobility effective trapping time Y signal follows the effective trapping rate of the majority carriers into the probed states. A DOS spectroscopy using a general formula gives If the Y signal deviates from the universal frequency dependence of H function, The applicability of our analysis was demonstrated in a-As 2 Se 3, undoped and lightly p-doped a-Si:H samples and μc-Si:H. If Y signal follows the universal H function around each ω t i. The states with the highest capture coefficient The states with the lowest capture coefficient then there are possible contributions from both carriers. HF LF

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