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C: Energy Conversion and Storage; Energy and Charge Transport

Understanding Thermal Admittance Spectroscopy in Low-Mobility Semiconductors Shuo Wang, Pascal Kaienburg, Benjamin Klingebiel, Diana Schillings, and Thomas Kirchartz J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01921 • Publication Date (Web): 23 Apr 2018 Downloaded from http://pubs.acs.org on April 23, 2018

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The Journal of Physical Chemistry

Understanding Thermal Admittance Spectroscopy in Low-mobility Semiconductors Shuo Wang1,2,*, Pascal Kaienburg1, Benjamin Klingebiel1, Diana Schillings1 and Thomas Kirchartz1,3 1

IEK5-Photovoltaik, Forschungszentrum Jülich, 52425 Jülich, Germany 2

3

School of Physics, Nankai University, 300071 Tianjin, P.R. China

Faculty of Engineering and CENIDE, University Duisburg-Essen, Germany

*corresponding author: E-mail: [email protected]

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ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Thermal admittance spectroscopy (TAS) is frequently used to analyze the properties of trap states in semiconductor devices. We perform detailed simulations in combination with experiments to understand the effect of low carrier mobility on the analysis of trap states by TAS. We show that the apparent characteristic peak in the differential capacitance spectra is strongly dominated by the dielectric relaxation (DR) peak caused by low carrier mobilities for the case of shallow traps and low trap densities. The model for the DR dominated case is successfully applied to interpret the experimental results from poly(3-hexylthiophene-2,5-diyl) (P3HT) based diodes. In contrast, for deep states with high density of states, we are able to properly estimate the energetic position but the low carrier mobility affects the correct determination of the attempt-to-escape frequency as well as the capture cross section. Our results reveal that low carrier mobilities cause inherent obstacles in accurately determining the trap properties and thereby affect the analysis of the origin and nature of the trap states by admittance spectroscopy.

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I. Introduction Thermal admittance spectroscopy (TAS) is a powerful tool to access charge carrier kinetics in semiconducting devices such as solar cells. In the past TAS has been predominantly used to characterize the properties of localized states within the band gap of the semiconductor.1-5 Measuring the capacitance of a diode as a function of frequency and temperature allows in many cases to measure the depth of a defect and its capture cross section which defines how strongly the localized state or defect interacts with the extended states in the conduction or valence band of the semiconductor. Admittance spectroscopy was originally proposed by Walter et al.

6

and

has been applied to inorganic solar cells such as Cu(In,Ga)Se2 (CIGS),6-10 CdTe,11,

12

Cu2ZnSnSe4 (CZTSe),13-15 and amorphous silicon (a-Si)16 solar cells, and nanoparticle materials.17-19 In recent years, with the emergence of new solution process based solar cells, admittance spectroscopy was also used to characterize the defect distribution in organic20-25 and perovskite photovoltaic materials.26-29 However, one of the most important prerequisites for the proper defect evaluation by admittance spectroscopy is that emission of carriers from a defect is actually the slowest step in carrier generation that is dominating the frequency and temperature dependence of the capacitance. In low mobility or low conductivity semiconductors, the transport of electrons and holes from the contact into the bulk of the semiconductor might have a similar time constant as carrier emission from traps. In other words, the determination of the properties of defects is only possible if the characteristic frequency of dielectric relaxation is substantially higher than the frequency at which a defect level stops reacting to the applied ac signal. This issue has been debated regarding fictitious trap features of high-mobility inorganic solar cells at low temperatures. For example, Reislöhner et al. attributed the so-called N1 defect in CIGS solar cells to the freeze-out of carrier mobility,30 while Li et al. interpreted the so-called 3



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H1 trap signature in CdTe solar cells by the freeze-out of carrier concentration.31 For lowmobility organic materials, this issue becomes problematic even at room temperatures.32 Although the possibility of carrier freeze-out effects is well-known, various recent publications disregarded the possible effect of the finite mobilities of charge carriers on the interpretation of TAS data.21, 23, 33-38 Recently Xu et al. discussed this issue in P3HT:PC61BM system by assuming a constant attempt-to-escape frequency and proposed a ‘safe’ mobility for trap depth evaluation depending on the active layer thickness.39 However, a comprehensive study on this issue where the determination of the attempt-to-escape frequency from TAS is also considered is still missing. In this work, we perform detailed simulations using the drift-diffusion simulator SCAPS

40, 41

combined with experimental results, to show that in low-mobility devices, the applicability of admittance spectroscopy analysis for defect characterization depends on the energy position and density of states (DOS) of the defect, even in a fully depleted device. However even in the case where the activation energy of the defect can be identified, the attempt-to-escape frequency as well as the cross section of the defect level will be strongly underestimated because of the low carrier mobility.

II. Basic Theory of Admittance Spectroscopy For an ideally defect-free diode-like device working under zero or moderate reverse bias conditions, the space charge region behaves like a capacitor, and the width of it changes with the applied bias voltage. Thus the differential capacitance = ⁄ originates from the shift of the depletion edge modulated by the ac perturbation. When defect states exist in the band gap, their contributions to the capacitance have to be taken into account. The schematic band diagram of a Schottky junction with p-type active layer is 4


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illustrated in Fig.1 for explanation. A discrete defect at the energy ET crosses the Fermi-level EF at xT because of band bending. Localized states in the vicinity of position xT can change their occupation in response to the variation of band bending caused by the ac voltage and then contribute to the junction capacitance. The defect states can only respond to the ac voltage if the emission rate of the state ep is higher than the angular frequency ω of the ac voltage, ep ≥ ω. The emission rate of the state can be expressed by = ⁄ = ⁄ = ⁄

(1),

where is the attempt-to-escape frequency, k the Boltzmann’s constant, T the temperature, the activation energy of the trap states with respect to the valence band in this case, the thermal velocity, the capture cross section, and the effective density of states of the valence band. Here we assume the temperature dependence of ∝ ⁄ and ∝ ⁄ , thus is the so-called reduced attempt-to-escape frequency which is temperature independent. For a specific trap state, we define a demarcation frequency ω0 = 2πf0 = ep (full theoretical expression of this frequency is shown as Eq. (S1) in the Supporting Information). For lower frequencies, ωω0, the trap states will not contribute to the capacitance.

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EC

energy E [eV]

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1

Eω (T,ω) EF

ET

0 EV

-1

xT

20

40

60

80

position x [nm] Figure 1. Band diagram for a typical Schottky junction with a p-type doped active layer. ET is the position of the trap state. Eω is the deepest limit to be detected with certain combination of frequency ω and temperature T. Correspondingly, the demarcation energy Eω (when ep=ω0) can be derived from Eq. (1) as = ln #

$%& '( )* +,

-

(2).

The demarcation energy defines the deepest energy level that responds to the ac modulation at a certain combination of frequency ω and temperature T. Thus, by gradually decreasing ω or increasing T, one can sweep Eω from near the valence band to mid-gap. Assuming an energetic distribution of trap states NT(E), the total increase of capacitance resulting from the trap states will be the integral over the contributions from the states at discrete energies within the responsible energetic range. Then the density of state at Eω can be estimated by the derivative of the capacitance as 6 = −

/0 d4

12 5

where Vbi is the built-in potential and d the layer thickness. 6


(3),

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Thus, in admittance spectroscopy measurement, the complex admittance of the solar cell is measured as a function of applied ac frequency and temperature under zero or reverse-bias voltages. Then the junction capacitance is derived from the imaginary part of the admittance. The first order derivative of the capacitance with respect to the logarithm of frequency is directly proportional to the trap density (see Eq. (3)) and is referred to as the differential capacitance d4

spectrum (−6 d7 vs. f). A temperature dependent measurement has to be performed to get the activation energy ET and the attempt-to-escape frequency ν0 of the trap states.

III.

Simulation Methods

In order to investigate the applicability of the admittance spectroscopy analysis in low mobility photovoltaic devices, simulations were performed using the drift-diffusion solver SCAPS (the validity of drift-diffusion simulations for organic solar cells is to be discussed in Section 2 in Supporting Information) developed by M. Burgelman at University of Gent. For the sake of simplicity, we assume a single p-type active layer with the basic parameters shown in Table 1. The band gap Eg and relative permittivity εr are borrowed from poly(3-hexylthiophene-2,5-diyl) (P3HT), which is one of the best-studied polymeric semiconductors. The shallow acceptor doping NA was assumed to be always active in the simulations. A single acceptor-like defect level NT was set in the band gap with the energy ET being defined with respect to the edge of the valence band. The values of NA, NT, ET, and µ were initially set as given in the table and then varied and discussed in the following sections. The work function of the anode was assumed to be aligned with the Fermi level of the active layer, which ensures a flat band at this side; whereas the work function of the cathode was set to be fixed at 4.2eV to form a Schottky junction with Vbi around 0.8V at 300K (band diagram as illustrated in Fig.1).

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Table 1. Parameters used for the simulations if not stated otherwise. Parameters Effective density of states in conduction band NC [cm-3] Effective density of states in valence band NV [cm-3] Electron affinity χ [eV] Band gap Eg [eV] Relative permittivity εr Anode work function [eV]

Values Reference 20 10 39 1020 39 3.2 42 2.0 43 3.1 a aligned with EF in active layer 4.2 107 2 16 10 44 5×1016 (varied)

Cathode work function [eV] Thermal velocity at 300K υth [cm/s] Shallow acceptor density NA [cm-3] Total density of states of acceptor-like defect level NT [cm-3] Energy level of acceptor-like defect level with respect to 0.26 (varied) valence band ET [eV] Hole capture cross section σp[cm2] 10-17 39 2 Carrier mobility µe= µh [cm /Vs] 10 (varied) Attempt-to-escape frequency at 300K ν0= σp υth NV [s-1] 1010 a The relative permittivity εr is derived by 89 = : ; ⁄8 , where d=200 nm, ε0 is the vacuum permittivity, and Cg=1.37×10-8 F/cm2 is obtained from C-V measurement of the P3HT device as described in Section 4 in the Supporting Information at a reverse bias of -4V.

IV.

Results

4.1 Identification of the Trap Peak and Dielectric Relaxation Peak As a starting point, we calculated the influence of carrier mobility on the C-f spectra and differential capacitance spectra based on the parameters in Table 1 and with the results of the simulations being shown in Fig.2. When assuming a high mobility of 10 cm2/Vs, we observe two distinct capacitance steps in Fig.2 (a) (dark yellow line). From the input parameters, one can estimate the characteristic frequencies of steps from trap states (ωT) and dielectric relaxation (ωD) from Eq. S1 and Eq. S2 as 1.4×105 Hz and 7.5×109 Hz respectively. Thus, we assign the capacitance step at lower frequencies to trap states while the capacitance step at higher frequencies originates from the finite mobility of the free carriers which are at some frequency not able to follow the ac voltage anymore. In the latter situation, the active layer behaves as a 8


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dielectric and the geometric capacitance defined by the thickness and permittivity (assumed to be temperature and frequency independent in simulations for simplicity) of the active layer is

Capacitance C [nF/cm2]

measured.

40

(a)

trap step

32 24

16

dielectric relaxation 10-1 10 step

10-3

10-4 mobility [cm2/Vs]

overlapping peak

-f dC/df [nF/cm2]

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(b) dielectric relaxation peak ID

12 8

trap peak IT

4 0 104

106

108

1010

Frequency f [Hz]

Figure 2. (a) Simulated capacitance as a function of frequency and (b) the derived differential capacitance spectra. The transitions of the trap peak and dielectric relaxation peak as a function of carrier mobility. The characteristic peaks in the differential capacitance spectra in (b) correspond to the capacitance steps in (a). ID and IT represent the magnitudes of the dielectric relaxation peaks and trap peaks respectively.

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Corresponding to the capacitance steps in Fig.2 (a), we observe two characteristic peaks in the differential capacitance spectra in Fig.2 (b). The frequencies of the two peaks correspond to the calculated characteristic frequencies of steps. With decreasing carrier mobility, the trap peak remains at a frequency of around 100 kHz while the dielectric relaxation (DR) peak shifts to lower frequencies. When the carrier mobility is lower than 10-3 cm2/Vs, the dielectric relaxation peak shifts into the same range as the trap peak and the two peaks overlap with each other. In this case, discriminating between the two effects (emission from a defect, free carrier transport) becomes difficult. In the situation that the overlap happens, the dominant contribution determines the temperature dependence of the apparent characteristic peak. Thus it is necessary to figure out at first which peak is dominant and the factors that affect the relative ratio of the intensities of trap peak IT and dielectric relaxation peak ID, which is defined as R = IT/ID. The larger this ratio, the easier to distinguish the trap peak from the dielectric relaxation peak. As the capacitance of the junction basically reflects the charge concentration in the device that can follow the ac modulation signal, we consider three factors that are likely to affect this ratio: the shallow acceptor concentration NA, total density NT of acceptor-like defects and the energetic position ET of the acceptor-like defect level with respect to the valence band. From the simulation results shown in Fig. 3 (a), the IT/ID ratio is controlled by the NT/NA ratio instead of by the absolute value of NA. The IT/ID ratio increases with increasing the NT/NA ratio. Note that in the case of NA ≤5×1016cm-3 the active layer is fully depleted and therefore different capacitance features will emerge (to be discussed in Section 5.2). The effect of the energy level of trap states ET on the IT/ID ratio is shown in Fig.3 (b). We observe a similar effect of NT/NA ratio, but the ET

10


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has a pronounced influence on the IT/ID ratio which increases when the defect position is moved deeper into the band gap.

IT / ID ratio

100

(a)

ET= 0.26 eV

10-1

NA [cm-3] 5×1015 5×1016 1018 1019

10-2

101

IT / ID ratio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(b)

NA=5×1016 cm-3

100 10-1 10-2

ET [eV]

10-3

0.1 0.2 0.3

10-4 10-2

10-1

100

101

102

0.4 0.6

103

NT/NA ratio Figure 3. The simulated ratio of the magnitudes between the trap peak and the dielectric relaxation peak (IT/ID) as shown in Fig. 2 as a function of the NT/NA ratio with (a) different NA concentration and (b) different energy position of defect ET. In panel (a), the value of ET is fixed at 0.26 eV and in panel (b) the doping density is fixed at NA at 5×1016 cm-3. The two cases in red circles are selected for the following discussion shown in Fig.4 and Fig.5. 4.2 Case Dominated by Dielectric Relaxation Peak In the case where IT /ID

Understanding Thermal Admittance Spectroscopy ... - ACS Publications

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