Article pubs.acs.org/JPCC
Frequency-Modulated Gigahertz Complex Conductivity of TiO2 Nanoparticles: Interplay of Free and Shallowly Trapped Electrons Akinori Saeki,*,†,‡ Yoshihiro Yasutani,† Hikaru Oga,† and Shu Seki† †
Department of Applied Chemistry, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan Japan Science and Technology Agency (JST)-PRESTO, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan
‡
ABSTRACT: In a quest to explore the prominent electronic properties of titanium dioxide (TiO2), precise knowledge on the electron mobility and trapping process is an immensely important part of organic photovoltaic applications. We have investigated the frequency dispersion of complex photoconductivity of TiO2 nanoparticles by laser-flash frequency-modulated time-resolved microwave conductivity (FM-TRMC) in the 9−34 GHz region. The absolute ratio of imaginary to real transient conductivities was analyzed by the combination of Drude−Smith and Drude−Zener models, which allows for determining the trap depth (ET) and population of trapped electrons (f trap). We have identified that the shallowly trapped electrons (ET = 70−110 meV, f trap > 0.8) have a large impact on the negative imaginary conductivity, while the free electron confined in TiO2 nanoparticle significantly contributes to the positive real part in spite of its small population (99.5%) were purchased from Aldrich and Frontier Carbon Inc., respectively. They were dissolved in o-dichlorobenzene at 1:1 weight ratio and drop cast on a quartz substrate. 2.2. Flash-Photolysis TRMC. The third harmonic generation (THG; 355 nm) of a Nd:YAG laser (Continuum Inc., Surelite II, 5−8 ns pulse duration, 10 Hz) was used as an excitation source, which is capable of direct excitation of the bandgap of anatase TiO2 (3.2 eV).53 The laser power was attenuated by neutral density filters and monitored by a photodiode power meter. A resonant cavity of X-band (ca. 9.1 GHz) and the details of the system and analysis have been reported previously.54,55 Similar types of microwave conductivity measurement systems with the resonant cavity were designed for Ku-band (ca. 15.4 GHz), K-band (ca. 22.9 GHz), and Q- (or Ka-) band (ca. 33.2 GHz). In all cases, the power of probing continuous microwave at the cavity was set at 3 mW, which is sufficiently small not to heat the sample. The resonant cavity was tuned at the overcoupling condition, so that the increase of reflected microwave power means the increase of dielectric loss (vide infra) and accordingly positive real conductivity. 2.3. Separation of Real and Imaginary Components of Transient Photoconductivity. Slater developed the cavity perturbation theory56 which relates the resonant angular frequency, ω0 (=2πf 0), and the change of cavity quality factor (Q = f 0/Δf1/2, Δf1/2 is the full bandwidth at half-maximum of the reflected microwave power near the f 0) to the complex conductivity, as given by
Δσ′ = ε0 ωΔε ′′
(4)
Δσ ′′ = −ε0 ωΔε′
(5)
The combination of eqs 2 through 5 together with the approximation, Δ(Δf1/2) ≈ f 0Δ(1/Q),52 yields the same expression as eq 1 by equating the geometry factor through 2F′ = F. In our experiments, the sample geometry factor F was calculated by the handmade software incorporating the results of electrostatic simulation in the cavity performed by MWstudio.55 The real photoconductivity transient Δσ′ is converted to the product of the quantum efficiency, ϕ, and the sum of charge carrier mobilities, ∑μ (= μ+ + μ−), by ϕ∑μ =
1 Δσ′ eI0FLight
(6)
where e, I0, and FLight are the unit charge of a single electron, the excitation photon density of the laser (photons cm−2), and a correction factor (m−1). The FLight was calculated in the same manner with F, but the depth profile of the exciting laser is convoluted.55 When the Δσ′ is small (this is usually true for photoinduced transient conductivity of organic electronics) and the Δω0 (i.e., Δσ′′) is negligible, Δσ′ can be approximated by
Δσ′ =
A=
1 ΔPr A Pr
(7)
∓Q (1/ R 0 ± 1) πf0 ε0εr
(8)
where A, and ΔPr/Pr are the sensitivity factor and the change in the fractional microwave power observed in the reflection from the cavity at the resonant frequency, respectively.57,58 The R0 is the ratio of reflected (Pr) and incident (Pi) microwave power (R0 = Pr/Pi), and the εr is the real part of the relative dielectric constant inside the cavity. Since the right term of eq 7 is experimentally determined, transient decays of Δσ′ and ϕ∑μ are readily evaluated at each sample by precise measurements of I0, excitation wavelength, Q value, and microwave frequency and power. 22562
dx.doi.org/10.1021/jp505214d | J. Phys. Chem. C 2014, 118, 22561−22572
The Journal of Physical Chemistry C
Article
In the presence of imaginary conductivity, the change of the reflected microwave power, ΔPr, at the resonant frequency involves contributions from both Δσ′ and Δσ′′. In this case, they appear as the change of the reflected microwave power level between “light” and “dark” at the resonant frequencies and the shift of the resonant frequency, respectively (see eq 1). Therefore, Δσ′ and Δσ′′ can be separated by analyzing the kinetics at multiple frequencies near the resonant frequency. Figure 1 shows the Q curves in the dark and just after the light Figure 2. Positive real (Δσ′) and negative imaginary (Δσ′′) transient photoconductivities of (a) TiO2−NP and (b) P3HT:PCBM probed at 9.1 GHz. The ratio of |Δσ′/Δσ′′| is indicated.
dielectric constant ε′ (eq 5) and the negative shift of the resonant frequency (eq 1). For a comparison, we examined a P3HT:PCBM blend film (1:1 in wt % fraction),62 a representative of bulk heterojunction OPV. It exhibited a positive Δσ′ and negative Δσ′′ as well; however, |Δσ′max/ Δσ′′max| was further increased to 15.3 (Figure 2b), indicating that the imaginary part is somewhat regarded as negligible, in accordance with the situation of pentacene polycrystalline film.59 Noteworthy is that the decay speed of Δσ′′ in TiO2−NP is always faster than Δσ′ at 9.1−33.2 GHz (Figure 3a−d), while
Figure 1. Transient Q curve of TiO2−NP under dark (black circles) and light (peak-top, gray squares) exposure to the laser pulse. The solid lines are the least mean square curves of the second order function. The vertical and horizontal shifts of the minimum point are proportional to the real (Δσ′) and imaginary (Δσ′′) conductivities, respectively. The kinetics at the frequencies of A, B, and C are shown in the inset.
pulse irradiation, which are evaluated from the frequency dependence of the reflected microwave power near the dark resonant frequency (ca. 0.1 MHz). The least mean square fit by the second or third order function indicated a good approximation for the dip of the transient Q curve. This analysis was performed for all the time delays, and consequently Δσ′(t) was evaluated by eq 7 and ΔPr(t), enabling us to remove the contribution from the shift of the resonant frequency.59 Then Δσ′′(t) was obtained from the extracted Δω0(t) and eq 1. The frequency dependence of ΔPr for a wide frequency area (ca. 10 MHz) can be fitted by a Lorentzian function, which also allows for the separation between the frequency shift and change of the reflected power.50,60,61 However, we scanned this off-resonant frequency by only ca. 0.1 MHz, where the Q curve dip is well-reproduced by the above-mentioned simple low-order function. Such a small scanning area of frequency has a merit for almost unchanged time resolution, a fast measurement, and a high sensitivity. Figure 3. Normalized real (Δσ′) and imaginary (Δσ′′) photoconductivity transients of (a−d) TiO2−NP and (e−h) P3HT:PCBM. The probed microwave frequency is shown in the inset.
3. RESULTS AND DISCUSSION 3.1. Kinetic Analysis of Complex Conductivity. Figure 2a shows the kinetic traces of Δσ′(t) and Δσ′′(t) of TiO2−NP at 9.1 GHz. The observed positive real and negative imaginary components along with the ratio of their maxima (|Δσ′max/ Δσ′′max| = 5.8) are in good agreement with the previous 8.7 GHz TRMC results of 9 nm sized anatase nanocrystals (|ΔG′max/ΔG′′max| = 7.2, where G is the conductance) and polycrystalline anatase TiO2 film (|ΔG′max/ΔG′′max| = 6.0).50 The positive Δσ′ corresponds to the increase of the dielectric loss ε′′ (eq 4) and decrease of Q value (eq 1), while the negative Δσ′′ represent the increase in the real part of the
P3HT:PCBM displays identical profiles of Δσ′ and Δσ′′, irrespective of the probed microwave frequency (Figure 3e−h). The half-lifetimes (τ1/2) of transient complex conductivity are given in Table 1 together with their ratios. The ratio of imaginary to real parts, τ1/2′′/τ1/2′, were found as small as 0.2− 0.4, which provides a simple indicator to discern the kinetic difference in real and imaginary photoconductivities. The mismatch of decays is suggestive of the presence of at least two kinds of transient species in TiO2−NP having different 22563
dx.doi.org/10.1021/jp505214d | J. Phys. Chem. C 2014, 118, 22561−22572
The Journal of Physical Chemistry C
Article
Table 1. Summary of Kinetic Analysis of Transient Photoconductivity in TiO2−NP Δσ′(t) or Δσ′′(t)a
Δσ′′(t)/Δσ′(t)b
f (GHz)
τ1/2′ (μs)
τ1/2′′ (μs)
τ1/2′′/τ1/2′
k (10 s−1)
β
α
9.1 15.4 22.9 33.2
2.7 2.3 1.4 0.52
1.1 0.44 0.36 0.11
0.41 0.19 0.26 0.22
1.4 2.9 4.1 6.5
0.65 0.65 0.50 0.55
0.67 0.52 0.55 0.42
a
6
Half-lifetime of Δσ′(t) or Δσ′′(t). bFitting parameters of eq 9.
contributions to the real and imaginary conductivities. Peter et al. have reported the roles of free and trapped electrons in DSSC by photoinduced microwave reflectance measurements at 33 GHz, where the change of reflectance was detected in working solar cells including metal electrodes and liquid electrolyte.63 The similar difference of the real and imaginary photoconductive decays was also observed in polycrystalline CdSe,61 where Cocivera et al. explained the 10 GHz microwave conductivity by the time evolution of the free and trapped electrons densities. In both DSSC and CdSe studies, trapped electrons rather than free electrons are claimed relevant to the imaginary conductivity. On the contrary in P3HT:PCBM, the charge carrier trapping process on the measurement time scale (later than nanosecond) does not take place at room temperature, as is evident from the excellent coincidence between TRMC and transient absorption spectroscopy (TAS) transients.64,65 Therefore, it is reasonable to speculate that the time-dependent change in the population of free and trapped electrons in TiO2−NP is responsible for the temporal stark deviation in Δσ′ and Δσ′′. To quantitatively analyze the difference between Δσ′ and Δσ′′ and to compensate for the variation of the time resolution at the respective microwave frequency, we plotted normalized decays of Δσ′′(t)/Δσ′(t) and analyzed them by a stretched exponential function (Figure 4a), expressed by Δσ ′′(t )/Δσ′′max = exp( −(kt )β ) + α Δσ′(t )/Δσ′max
Figure 4. Normalized kinetic decays of Δσ′′/Δσ′ observed in (a) TiO2−NP at I0 = 9.1 × 1014 photons cm−2, (b) TiO2−NP at I0 = 1.1 × 1014 photons cm−2, and (c) TiO2−NP/Dye at I0 = 9.1 × 1014 photons cm−2. The decays are colorized by the probing microwave frequencies. The black lines are the fitting curves given by eq 9. (d) The histogram of the decay rate, k, for respective frequency and sample.
A sharp contrast in the decays of real and imaginary conductivities has been observed in thin films of polycrystalline CdSe.61 From the dependences of light intensity and temperature, Cocivera et al. have clarified three time regions: (1)
