Maura Pomoni, Athina Giannopoulou and Panagiotis Kounavis

1. Univ. of Patras 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

2. Univ. of Patras 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

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

4. The analysis have shown that Univ. of Patras or

5. Y signal is related to the gap states with which the electrons and holes interact and contribute to Yn , Yp Electrons the majority carriers n>>p Univ. of Patras The states contributing Yn High Frequency (HF) regime Low Frequency (LF) regime holes holes electrons Trapping & detrapping electrons Deep trapping In some cases Y2n + Y3n=0 and so Yn=Y1n Y1n>>Y2n + Y3n and so Yn=Y1n

6. The states contributing Yp Univ. of Patras Holes the minority carriers High Frequency (HF) regime Low Frequency (LF) regime holes holes Y1p>>Y2p+Y3p and so Yp=Y1p

7. n>>p Effective trapping rate of electrons =1/τωn Univ. of Patras Effective trapping rate of holes =1/τωp HF regime LF regime The so-called H function Yn=1/τωn Reflects the DOS of the CB side Yp=1/τωp Reflects the DOS of the VB side do not reflect the DOS Yn, Yp

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

9. Majority carriers (electrons) dominate Y signal n>>p Univ. of Patras at ωtΗ=ωtc=ncnc Bias light dependence Y signal drops by a factor of 2 This can be used to determine the capture coefficient Two bias light levels Y follows 1/τωn Normalized Y/Y0 spectrum Y moderate bias Y0 weak bias near dark equilibrium For If the majority carriers dominate and Y signal follows 1/τωn thenormalized Y/Y0 ratio follows the universal H function …providing that the capture coefficient cnvof the states below EF for the majority carriers is much lower than that cncof the states above EF

10. For Majority carriers (electrons) dominate Y signal, but Y<1/τωn Univ. of Patras μpτωp<< μnτωn because Recombination through the states below EF increases electrons holes The normalized Y/Y0 spectrum is below the universal spectrum of H function for Ce=cnv/cnc≥1 The decay of Y signal in the LF regime is steeper than 1/τωn if Y differs from the 1/τωn the normalized Y/Y0 ratio does not follow the universal H function In general,

11. Majority carriers (electrons) do not dominate Y signal Univ. of Patras μpτωp>> μnτωn Bias light dependence Y does not follow 1/τωn μpτωp= μnτωn For Mixed contributions from electrons and holes μpτωp= μnτωn Minority carriers (holes) dominate the normalized Y/Y0 ratio is above the universal H function for μpτωp>> μnτωn

12. DOS spectroscopy Univ. of Patras If thenormalized Y/Y0 ratio follows H function The majority carriers (electrons) dominate & Y follows 1/τωn the capture coefficient is obtained coefficient from This formula can be used for a DOS spectroscopy at ωtΗ=ωtc=ncnc and Y signal drops by a factor of 2 Alternatively ωtc can be obtained from the DOS in the frequency regime at ωtL/4 =ωtc/4 is the onset of LF regime (plateau)

13. Experimental spectra of a-As2Se3 The majority carriers (holes) dominate and Y signal follows 1/τωp Univ. of Patras DOS spectroscopy at ωtΗ=ωtc=ncnc and Y signal drops by a factor of 2 Capture radius 2.8 Ǻ Neutral centers Exponential dependence (valence band-tail) thenormalized Y/Y0 ratio follows the universal H function

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

15. Various species of states DOS spectroscopy Provides the DOS of both species of states Univ. of Patras model a-Si:H LF Vertical line the signature of various species of states Normal db’s HF Dc(Eωn) LF db’s with a Si-H back bond or a three center Si-H-Si bond Dhc(Eωn) HF From at ωtL/4 =ωtc/4 is the onset of LF (plateau) The states with the lowest capture coefficient

16. Experimental spectra from the literature where the majority carriers do not dominate U. of Patras μc-Si:H a-Si:H lightly p-type doped from MPC measurements of Bruggemann J Mat. Sc.14, 629 (2003) from the MPC measurements of Kleider & Longeaud Sol. St. Phen.44&46 596 (1995) Y signal exponential dependence Y does not follow 1/τωn Y does not follow1/τωn at lowest ω Bias light dependence The normalized Y/Y0 ratio does not follow the universal H function Mixed contributions from electrons and holes Mixed contributions from electrons and holes The normalized Y/Y0 ratio at lowest ω does not follow the universal H function reasonable for the the lightly p-type doped material A DOS spectroscopy is impossible

17. Conclusions U. of Patras the transport of the majority carriers dominates giving the highest mobility effective trapping time If Y signal follows the universal H function around each ωti. Y signal follows the effective trapping rate of the majority carriers into the probed states. HF The states with the highest capture coefficient A DOS spectroscopy using a general formula gives The states with the lowest capture coefficient LF If the Y signal deviates from the universal frequency dependence of H function, then there are possible contributions from both carriers. The applicability of our analysis was demonstrated in a-As2Se3, undoped and lightly p-doped a-Si:H samples and μc-Si:H.