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J. Phys. Chem. C 2009, 113, 15992–15996
Temperature Dependence of Electron Transport in CdSe Quantum Dot Films Ruben Loef,*,† Arjan J. Houtepen,† Elise Talgorn,† Joop Schoonman,‡ and Albert Goossens† Opto-Electronic Materials, Delft UniVersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands, and Materials for Energy ConVersion and Storage, Delft UniVersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands ReceiVed: February 26, 2009; ReVised Manuscript ReceiVed: July 14, 2009
To elucidate minority carrier transport in CdSe quantum dot films, a detailed DLTS study on TiO2/CdSe quantum dot heterojunctions is performed. Long transient times are found, which are related to tunneling instead of the thermal emission of electrons. Surprisingly, the transient times increase with increasing temperature, which is possibly related to thermal expansion of the tunnel barrier width between quantum dots. This effect can give rise to unexpected behavior of quantum dot devices. C(t) ) C∞ + ∆Ce-t/τ
1. Introduction Because of their unique electrical and optical properties, quantum dots are promising candidates for use in optoelectrical devices. However, the transport of holes and electrons in quantum dot layers is relatively slow. In contrast to bulk semiconductors, charge carriers have to migrate from dot to dot. The position of the energy levels in quantum dots is sizedependent. Because of the size distribution in the quantum dot layer, the energy levels are disordered. Charge carrier transport in quantum dot layers is, therefore, generally accepted to follow a nonresonant tunneling process.1–5 Deep-level transient spectroscopy, DLTS, is a powerful tool to study the dynamics of trapping and the emission of charge carriers in bulk and in thinfilm semiconductor junctions6 and can also be applied on quantum dot layers. However, because of the slow charge carrier transport, the obtained capacitance transients can be related to the nonresonant tunneling rate, instead of emission of the charge carriers. Here, we use DLTS to study charge carrier transport in quantum dot CdSe/TiO2 heterojunctions. As expected, we find increasing currents with increasing temperatures in current-voltage studies. Surprisingly, with detailed capacitance studies, we also find decreasing electron tunneling rates with increasing temperatures, most likely due to the thermal expansion of the tunnel barrier. This phenomenon can give rise to unexpected thermal behavior of quantum-dot-based devices. With DLTS, the thermal emission rate and energy positions of trapped charge carriers are determined from capacity transients after applying a potential step toward reverse potentials. Subsequently, trapped electrons and/or holes are slowly released to the conduction and valence band, respectively, and move out of the depletion layer under the influence of the electric field, causing a small change in depletion layer capacitance. Transient times and activation energies are determined from the capacitances at two fixed time intervals (double boxcar method) or from the complete capacitance transient. In this paper, the latter is used. The complete capacitance transient C(t) is measured and fitted to * To whom correspondence should be addressed. Fax: +31-182787421. E-mail:
[email protected]. † Opto-Electronic Materials, Delft University of Technology. ‡ Materials for Energy Conversion and Storage, Delft University of Technology.
(1)
Here, C∞ is the capacitance at t ) ∞, ∆C the total capacitance change (i.e., C(0) - C∞), and τ the transient time. In some cases, more exponents are needed to fit the data accurately, for instance, when the decays of two trap states are interfering. The emission rate er of the charge carriers then follows6
er )
1 ) γT2σe-Et/kBT τ
(2)
The value of prefactor γ is unknown for our system. Its value, however, is not involved in our further analysis. σ is the capture cross section, Et the thermal activation energy of the trap, kB the Boltzmann constant, and T the temperature in Kelvin. DLTS measurements are performed at different temperatures. From eq 2, it follows that the slope of a ln(τT2) versus 1/T plot is equal to Et/kB. In bulk semiconductors, emitted charge carriers will be swept from the depletion region almost instantaneously by the electric field. In this case, the emission of a charge carrier from the trap state to an energy band is rate-determining. However, in quantum dot films, this can be different. In fact, charge carrier transport is expected to be slower than charge carrier emission in most quantum dot systems.7–12 Especially, in quantum dots with large capping molecules, such as TOPO and HDA, charge transport is expected to be slow. Transport of charge carriers in quantum dot layers typically occurs via a nonresonant tunneling process, which is slightly different from traditional resonant tunneling. In a resonant tunneling process, a charge carrier tunnels between neighboring sites with exactly the same energy level. The energy barrier is described as a finite potential barrier with width L and height (φ0 - E). The tunnel rate, Γ, through an energy barrier is described by13
Γ ≈ Γ0e-2k1L
10.1021/jp9017713 CCC: $40.75 2009 American Chemical Society Published on Web 08/18/2009
(3)
Electron Transport in CdSe Quantum Dot Films
k1 )
2meff(φ0 - E)
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(4)
p2
In these expressions, Γ0 is the rate at vanishing tunnel barrier width and height, p the reduced Planck’s constant, meff the effective mass, and E the energy of the tunneling particle. It can be seen that resonant tunneling is a temperature-independent process. However, in disordered quantum dot films, it is unlikely to find two energy levels at exactly the same energy position within tunneling distance due to the distribution in quantum dot sizes and related distribution in energy levels. To overcome the energy mismatch, additional thermal energy is needed to compensate for the energy gap between neighboring sites. In this case, the tunneling process is now nonresonant. Miller and Abrahams introduced an approach by adding a Boltzmann term to eq 3, resulting in3
Γ ) Γ0e-(2k1L+(∆E/kBT))
(5)
In this equation, ∆E is the energy mismatch between tunneling sites. In most nonresonant tunneling processes, the Boltzmann term is dominant, which allows 2k1L to be neglected. Nevertheless, neglecting 2k1L is not allowed in this work, as will be described in Results and Discussion. More complex relationships to describe nonresonant tunneling have been derived,1,2,14 but we follow the Miller-Abrahams approach here because it explains our findings adequately. To date, DLTS is applied on a limited number of quantum dot devices. DLTS on quantum dot CdSe/ZnSe systems has been studied by Sadofyev and co-workers.15,16 On alternating molecular beam epitaxy (MBE) deposited CdSe quantum dots and ZnSe layers, they found activation energies between 130 and 290 meV, depending on the configuration of the samples. The observed activation energies are assigned to the emission of electrons in the CdSe QDs to the ZnSe buffer layer. Most other DLTS studies on quantum dots are performed on samples containing InAs and InAs/GaAs QDs. In these studies, it is concluded that both thermally activated emission and resonant tunneling contribute to the DLTS signal of quantum dot devices.10–12,17,18 For the InAs and InAs/GaAs samples, it is found that, at low temperatures, tunneling dominates over thermal emission. This can be explained by the fact that resonant tunneling is a temperature-independent process, whereas the thermal emission rate decreases with decreasing temperature. Furthermore, it is reported that, because of inhomogeneity in the system, migration of charge carriers should be described as a disordered random-walk process. For this process, capacitance transients do not follow a single exponential decay. Instead, the capacitance decay has to be described with a multiexponential function with a broad distribution of transient times, which is well approximated with a stretched exponential10,19,20
( )
C(t) ) C0 + ∆Ce-
t τ*
β
(6)
Here, β is the stretching parameter and τ* the average time constant. Here, we present a detailed DLTS study on TOPO/HDA-capped quantum dot CdSe/TiO2 heterojunctions at different temperatures and with different quantum dot sizes. 2. Experimental Aspects 2.1. Quantum Dot Synthesis. A one-pot “Greener” synthesis, as described by Mekis et al.,21 is followed to obtain the
CdSe quantum dots using the Schlenk technique. Tri-noctylphosphine oxide (TOPO, 99%, Aldrich) is degassed under vacuum at 180 °C for about 1 h. After the TOPO is cooled to 120 °C, 5 g of hexadecylamine (HDA, 95%, Alfa Aesar) and 0.15 g of n-tetradecylphosphonic acid (TDPA, 98%, Alfa Aesar) are added. Degassing is continued for at least 20 min at 120 °C. Subsequently, a solution of 0.158 g of selenium (powder, 99.99+, Chempur) in 2 mL of tri-n-octylphosphine (TOP, 97%, ABCR) is injected. After the mixture is heated to 300 °C, a solution of 0.12 g of cadmium acetate (Cd(Ac)2, anhydrous, 99.999%, Strem Chemicals) in 3 mL of TOP is injected rapidly under vigorous stirring. The mixture is kept at 260 °C during further particle growth. At different time intervals, samples are taken from the solution to obtain quantum dots with different sizes. After the synthesis, the quantum dots are washed three times by successively dissolving them in toluene (anhydrous, 99.8%, Aldrich), precipitating them with methanol (anhydrous, 99.8%, Aldrich), and removing the liquid after centrifugation. Finally, the quantum dots are dissolved in a 9:1 (v/v) n-hexane (anhydrous, Alfa Aesar)/octane (99.5%, Fluka) mixture. Precursor solutions and quantum dots are prepared and stored in a glovebox under nitrogen atmosphere. The quantum dot sizes are characterized with absorbance spectroscopy using a PerkinElmer Lambda 40 UV/vis spectrometer. 2.2. Sample Preparation. Flat films of TiO2 on transparent conductive oxide (TCO) glass (SnO2/F) are produced by Everest Coatings in Delft, The Netherlands. The samples are made with chemical vapor deposition at elevated temperatures with titanium tetraisopropoxide (TTIP) as a titanium precursor. After deposition, the samples are annealed at 450 °C for 6 h in air to improve the anatase crystal structure of the layers. Quantum dot films with different particle sizes are deposited on the TiO2 films by drop-casting from the different quantum dot solutions. After drying the samples at room temperature, the samples are heated to 70 °C for about 1 h. Circular gold contacts (3 mm diameter) are deposited by physical vapor deposition (PVD). Wires are glued on these contacts with silver epoxy. The samples are mounted in a cryostat. During transportation of the samples from and to the PVD setup and the cryostat, the quantum dot films are exposed to air for a few minutes. 2.3. Electrical Measurements. DLTS measurements on the TiO2/CdSe QD samples are performed under vacuum in a twoelectrode setup. The working electrode is connected to the gold spot on the quantum dot layer, while the counter electrode is connected to the TCO back contact. Constant dc potentials and dc potential steps are applied with a Princeton Applied Research potentiostat (PAR283). First, a potential of 0.3 V is applied on the working electrode for 30 s. Subsequently, the potential is stepped to the trap-filling potential of 0.6 V for 500 s. Finally, the potential is stepped back to the emission potential of 0.3 V for 800 s. The capacitance of the samples is monitored using a frequency response analyzer (Schlumberger FRA 1255). An ac voltage of 30 mV with a 300 kHz frequency is applied in addition to the dc potential. The resolution of the measurements is 2 points/s. DLTS spectra are taken in the dark at temperatures from room temperature to 350 K. 3. Results and Discussion In a previous study,22 we presented a detailed investigation of the capacitance-voltage behavior of the same samples. It is found that the quantum dot layers show p-type behavior, although the currents are very low because of the insulating
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TABLE 1: Overview of the Samples. The Peak Position and Full Width at Half-Maximum (fwhm) are Related to the First Peak in the Absorption Spectrum. The Quantum Dot Diameter, DQD, is Determined from the Absorption Peak. Acceptor Densities per cm3 and the Estimated Number of Acceptors per QD are Taken from the C-2-O Investigations in Our Previous Work22 peak position (eV)
fwhm (eV)
DQD (nm)
NA,QD (cm-3)
estimated acceptors per QD
2.49 2.44 2.41 2.40 2.32
0.17 0.11 0.17 0.17 0.18
2.4 2.6 2.7 2.7 3.1
1.5 × 1018 6.4 × 1017 1.2 × 1017 5.5 × 1016 4.8 × 1016
2 × 10-1 7 × 10-2 2 × 10-2 7 × 10-3 7 × 10-3
nature of the quantum dot layers. The quantum dot sizes and acceptor densities NQD are shown in Table 1. Furthermore, the Bode plots of the samples (Figure 1) show that, at a frequency of 300 kHz, the capacitance of all samples can be determined directly from the imaginary part of the impedance. Moreover, current-voltage (J-φ) measurements (Figure 2) show good diode behavior. At higher temperatures, higher currents are observed. This confirms that hole transport in the quantum dot layer, indeed, follows a thermally activated process, although TiO2 may also play a role in this thermal behavior. Figure 3 shows the band bending in the TiO2 film and quantum dot layers, as obtained from the capacitance-voltage studies. A two-electrode setup is used for DLTS measurements. At all potentials, both the TiO2 and the CdSe quantum dot films are not fully depleted (Figure 3B). Figure 4 shows typical DLTS transients at the final emission potential of 3.1 nm quantum dot CdSe/TiO2 samples. Similar transients are found for samples
Figure 3. Band diagrams for the CdSe quantum dot/TiO2 heterojunction for the case where the CdSe quantum dot layer is fully depleted (A), both layers are not fully depleted (B), and the flat-band situation (C). Vbi is the built-in potential. The figure depicts band bending over a layer of quantum dots, rather than band bending in a single quantum dot.
Figure 4. Typical DLTS transients of TiO2/CdSe QD (3.1 nm) heterojunctions after a potential step from 0.6 to 0.3 V at different temperatures.
Figure 5. Transient times obtained from fitting DLTS spectra to a stretched exponential for 2.4 nm (squares), 2.6 nm (circles), and 2.7 nm (triangles) diameter CdSe quantum dots.
Figure 1. Bode plots of 2.7 nm quantum dot CdSe/TiO2 devices at φ ) 0 V at 310 K (squares), 330 K (circles), and 350 K (triangles). Z' is represented by filled symbols, Z'' by open symbols. The inset shows the equivalent circuit for these samples. R1 is the series resistance, R2 the shunt resistance, and C1 the space-charge capacitance. The lowfrequency R3-CPE1 (constant phase element) branch represents trapping of charge carriers.
Figure 2. Typical J-φ curves for 3.1 nm quantum dot CdSe/TiO2 heterojunctions at temperatures ranging from 297 to 350 K. This graph is taken from our previous paper.22
with different quantum dot sizes. For all temperatures and quantum dot sizes, the transients show an exponential decrease, which indicates that, at these time scales, trapped minority carriers are observed. In the case of p-type quantum dot films, this means that electrons are trapped. Trapped holes are not observed on these time scales. Because the observed DLTS signals are most likely determined by tunneling of the charge carriers instead of the actual detrapping (as will be explained below), signals related to majority carriers (i.e., holes) are expected to be observed at shorter time scales. The capacitance transients are fitted to a stretched exponential decay function. Figure 5 shows the temperature dependence of τ* for different quantum dot sizes. It can be seen that, in general, 0.2 < β < 0.45. These values can be related to the R3-CPE branch in the inset of Figure 1, representing trapping of charge carriers. In Figure 1 and previous work, we show Bode plots of the samples.22 Those spectra are fitted to the equivalent circuit mentioned above. The CPE represents a distributed capacitor of which the impedance ZCPE is described as ZCPE ) A(jω)-R. The deviation of the CPE from a capacitance is related to a 1-R .23 Comparing this to the distribution in RC-time ∝ τR-CPE
Electron Transport in CdSe Quantum Dot Films
J. Phys. Chem. C, Vol. 113, No. 36, 2009 15995
Figure 6. Schematic representation of potential energy over the TOPO/ HDA-capped CdSe QD layer. The TOPO/HDA molecules create an energy barrier between the different quantum dots. Electrons in the conduction band (CB) can move between the quantum dots by tunneling. The difference in HOMO and LUMO (∆E) due to size distribution in the quantum dots is neglected in this figure.
stretched exponential gives R ) 1 - β. Fitting the impedance spectra resulted in 0.6 < R < 0.8, which is indeed close to 1 β. Therefore, we postulate that the R3-CPE branch in the equivalent circuit is related to the capacitance change due to the electron transport observed here. When we focus again on the transient times, it is remarkable that these are relatively long. However, it has to be noted that the transient times are related to tunneling of electrons through wide tunnel barriers (i.e., TOPO/HDA capping). The transient times reported here are comparable to those reported by Ginger and Greenham for current decays of ITO/CdSe QD samples.24 J-φ measurements at scan rates of 100 mV/s, as shown in Figure 2, indicate that majority carrier (i.e., hole) transport is much faster. The faster hole transport indicates that hole tunneling apparently experiences a lower tunnel barrier. No clear correlation between quantum dot size and transient times is observed. The relationship between the temperature and the transient time is discussed here. Figure 5 shows that, for T > 335 K, the transient time decreases with temperature, as expected. A thermally activated process is dominant at these temperatures. As mentioned above, two processes play a role in the capacitance decay, that is, emission of trapped electrons and nonresonant tunneling of the electrons to the depletion layer edge. Emission of electrons is expected to be faster at T > 335 K. Therefore, nonresonant tunneling is the rate-limiting process at these temperatures. For T < 335 K, we surprisingly find increasing transient times with increasing temperatures, which is not expected for thermally activated processes. Again, electron emission and nonresonant tunneling are considered. Both options are expected to show thermally activated behavior and, thus, to give decreasing transient times with increasing temperatures. This indicates that there is another process that, surprisingly, dominates the thermally activated processes. On the basis of eq 5, one can imagine two causes for this unexpected temperature dependence: a temperature dependence of the tunnel barrier height or of the tunnel barrier width. These possibilities are explored below. The tunnel barrier in our devices is determined by the TOPO and HDA molecules that are bound to the surfaces of the quantum dots. Figure 6 shows the potential energy over the quantum dots and the barriers schematically. The width of the energy barrier is between 1 (complete intertwining) and 2 (no intertwining) times the length of an HDA molecule (≈2-4 nm). The energy mismatch ∆E of the energy levels is related to the difference in quantum dot diameters and the potential drop over
Figure 7. Change in tunnel barrier height (φ0 - E) (top) and width L (bottom) for a 70× longer transient time. Because the exact values of the electron energy E and barrier height are not known, ∆φ0 and ∆L are given at different (φ0 - E) values. ∆φ0 is dependent on the tunnel barrier width and is given for a barrier width of 2 and 4 nm.
the quantum dot film. The widths of the first peaks in the absorption spectra provide an indication of the spread in band gap energies. Table 1 shows the full width at half-maximum (fwhm) of these peaks. The fwhm is used as an indication for ∆E, which is found to be less than 0.2 eV. Compared to the expected barrier height (φ0 - E) of a few eV, this spread in energy is small. To explain the increasing transient time with increasing temperature, it is postulated that either the barrier height (φ0 E) or the barrier width L is temperature-dependent. The nature of this effect may be found in the thermal expansion of the barrier width and shifts of the energy bands, respectively. Both possibilities are considered below. From Figure 5, it can be seen that, between T ) 297 and 335 K, the transient times decrease with approximately a factor of 70, that is
Γ335 τ*297 ) ) e-2(k1,335L335-k1,297L297) ≈ 0.014 Γ297 τ*335
(7)
In this expression, the temperature is indicated with a subscript. First, we consider the case where L is fixed and (φ0 - E) is temperature-dependent. Rewriting eq 7 leads to
( )
ln
τ*297 2meff ) -2 L(√(φ0,335 - E) - √(φ0,297 - E)) τ*335 p2 ) -4.2 (8)
∆φ0 is plotted against (φ0 - E) in Figure 7 (top), according to eq 8. In this case, Γ335/Γ297 is also dependent on L. Therefore, the limiting cases where L ) 2 nm and L ) 4 nm are plotted. For CdSe, meff ) 0.13 × me and me is the mass of an electron. It can be seen that a change in barrier height of at least 600 meV is needed to explain the differences in observed transient times. A change of barrier height can be caused by a shift of conduction bands of TOPO, HDA, and CdSe with temperature. It is known for groups II-VI materials that the band gap Ebg changes with temperature and -dEbg/dT ≈ -0.5 meV/K.25 For
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TOPO and HDA, dEbg/dT is not expected to be much larger. Therefore, in the applied temperature range of 53 K, the influence of energy band shifts is much too small to explain the slower tunneling at higher temperatures. For the case where the barrier height (φ0 - E) is fixed and L is temperature-dependent, eq 7 can be rewritten to
( )
ln
τ*297 ) -2 τ*335
2m(φ0 - E) p2
-2
(L335 - L297) )
2m(φ0 - E) p2
∆L ) -4.2 (9)
Figure 7 (bottom) shows ∆L plotted against (φ0 - E), according to eq 9. It can be seen that a change of barrier width of 5-10 Å explains the change of a factor of 10 in transient times. Linear thermal expansion is assumed to describe a change of the tunnel barrier width. The thermal expansion in one direction is described as
∆L ) R∆T L0
(10)
Here, L0 is the initial width and R the thermal expansion coefficient. Combining eqs 9 and 10 gives
ln
τ*297 ∝ ∆T τ*335
(11)
It can be seen from Figure 5 that the relationship between ln(τ*) and T is close to linear for T < 335 K. Assuming ∆L ) 0.6 nm and L0 ) 3 nm leads to R ≈ 5 × 10-3 K-1. In this example, the thermal expansion is 20% over a temperature range of only 38 K, which appears, on first sight, unreasonably large. The thermal expansion of TOPO and HDA on CdSe quantum dot surfaces is not known, but most organic compounds have much lower thermal expansion coefficients, of the order of 10-6-10-4 K-1. On the other hand, for polymer melts, thermal expansion coefficients up to 10-3 K-1 have been reported.26 It should be noted that the measurements described here are performed around the melting point of TOPO (≈51 °C, 324 K) and HDA (≈44 °C, 317 K) and phase transitions may be involved. Wuister et al. showed that such phase transitions may be accompanied with structural rearrangements of the quantum dots.27 Thus, although the thermal expansion of the tunnel barrier that is required to explain our results appears too large to be reasonable, we cannot fully exclude this possibility. 4. Conclusions The temperature has a marked influence on DLTS transient times of TiO2/CdSe QD heterojunctions. Transient times in the order of seconds to minutes are found. These relatively slow
capacitance transients are related to tunneling of electrons between quantum dots. For T < 335 K, the transient times increase with increasing temperature. Thermal expansion of the tunnel barrier is the only process we can think of that explains this behavior, although the required thermal expansion of the TOPO/HDA capping, 5-10 Å, is very large. When we compare this expansion with that of polymer melts and keep phase transitions in mind, we conclude that we cannot exclude this possibility. Above 335 K, a thermal-activated tunnel process is dominant, that is, faster transport at higher temperatures. Acknowledgment. Everest Coatings (Delft, The Netherlands) is acknowledged for supplying the TiO2 samples. References and Notes (1) Efros, A. L.; Shklovskii, B. I. J. Phys. C: Solid State Phys. 1975, 8, L49–L51. (2) Mott, N. F. Philos. Mag. 1969, 19, 835–852. (3) Miller, A.; Abrahams, E. Phys. ReV. 1960, 120, 745–755. (4) Yu, D.; Wang, C. J.; Wehrenberg, B. L.; Guyot-Sionnest, P. Phys. ReV. Lett. 2004, 92, 216802. (5) Houtepen, A. J.; Kockmann, D.; Vanmaekelbergh, D. Nano Lett. 2008, 8, 3516–3520. (6) Lang, D. V. J. Appl. Phys. 1974, 45, 3023–3032. (7) Kruszewski, P.; Dobaczewski, L.; Markevich, V. P.; Mitchell, C.; Missous, M.; Peaker, A. R. Phys. B 2007, 401-402, 580–583. (8) Lin, S. W.; Song, A. M.; Missous, M.; Hawkins, I. D.; Hamilton, B.; Engstro¨m, O.; Peaker, A. R. Mater. Sci. Eng., C 2006, 26, 760–765. (9) Schulz, S.; Schramm, A.; Heyn, C.; Hansen, W. Phys. ReV. B: Condens. Matter Mater. Phys. 2006, 74, 033311–033314. (10) Geller, M.; Stock, E.; Kapteyn, C.; Sellin, R. L.; Bimberg, D. Phys. ReV. B: Condens. Matter Mater. Phys. 2006, 73, 205331–205338. (11) Chang, W.-H.; Chen, W. Y.; Hsu, T. M.; Yeh, N.-T.; Chyi, J.-I. Phys. ReV. B 2002, 66, 195337. (12) Engstro¨m, O.; Kaniewska, M.; Kaczmarczyk, M.; Jung, W. Appl. Phys. Lett. 2007, 91, 133117. (13) Atkins, P. W. Physical Chemistry, 5th ed.; Oxford University Press: Oxford, 1997. (14) Chandler, R. E.; Houtepen, A. J.; Nelson, J.; Vanmaekelbergh, D. Phys. ReV. B 2007, 75, 085325–085334. (15) Kozlovsky, V. I.; Litvinov, V. G.; Sadofyev, Y. G. J. Phys.: Condens. Matter 2004, 16, S133–S140. (16) Litvinov, V. G.; Kozlovsky, V. I.; Sadofyev, Y. Phys. Status Solidi B 2002, 229, 513–517. (17) Ibanez, J.; Leon, R.; Vu, D. T.; Chaparro, S.; Johnson, S. R.; Navarro, C.; Zhang, Y. H. Appl. Phys. Lett. 2001, 79, 2013–2015. (18) Schulz, S.; Schnu¨ll, S.; Heyn, Ch.; Hansen, W. Phys. ReV. B 2004, 69, 195317. (19) Schramm, A.; Schulz, S.; Heyn, C.; Hansen, W. Phys. ReV. B 2008, 77, 153308. (20) Scher, H.; Shlesinger, M. F.; Bendler, J. T. Phys. Today 1991, 44, 26. (21) Mekis, I.; Talapin, D. V.; Kornowski, A.; Haase, M.; Weller, H. J. Phys. Chem. B 2003, 107, 7454–7462. (22) Loef, R.; Houtepen, A. J.; Talgorn, E.; Schoonman, J.; Goossens, A. Nano Lett. 2009, 9, 856–859. (23) Macdonald, J. R. Impedance Spectroscopy, Emphasizing Solid Materials and Systems; John Wiley and Sons: New York, 1987. (24) Ginger, D. S.; Greenham, N. C. J. Appl. Phys. 2000, 87, 1361– 1368. (25) Ravindra, N. M.; Bhardwaj, R. P.; Kumar, K. S.; Srivastava, V. K. Infrared Phys. 1981, 21, 369–381. (26) Lide, D. R., Ed. CRC Handbook of Chemistry and Physics (Internet Version), 88th ed.; Taylor and Francis Group, LLC: Boca Raton, FL, 2008. (27) Wuister, S. F.; van Houselt, A.; Donega, C. D. M.; Vanmaekelbergh, D.; Meijerink, A. Angew. Chem., Int. Ed. 2004, 43, 3029–3033.
JP9017713
