J. Phys. Chem. B 2006, 110, 25455-25461
25455
Time-Resolved Photoconductivity of PbSe Nanocrystal Arrays† James E. Murphy,‡,§ Matthew C. Beard,*,‡ and Arthur J. Nozik*,‡,§ Chemical and Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado, 80401, and Department of Chemistry and Biochemistry, UniVersity of Colorado at Boulder, Boulder, Colorado 80309 ReceiVed: July 20, 2006; In Final Form: September 25, 2006
We report the sub-picosecond photoconductivity dynamics of chemically treated PbSe nanocrystal arrays utilizing time-resolved terahertz spectroscopy (TRTS). TRTS allows both the degree of interdot electronic coupling and the carrier dynamics to be extracted simultaneously. The following capping ligands bonded to the quantum dot surface were studied: hydrazine, ethylenediamine, butlyamine, and aniline. In addition, the arrays were treated with NaOH. We find that the treatments affect both the degree of electronic coupling and the carrier dynamics.
Introduction New approaches to high efficiency solar energy conversion are required to meet the enormous need for inexpensive carbonfree energy.1-3 Three-dimensional arrays of semiconductor nanocrystals (NCs) (also called quantum dots) in p-i-n structures are a novel approach that offers the potential to control the microscopic charge generation, separation, and transport so as to maximize solar energy conversion efficiencies.3,4 Beneficial hot-carrier effects such as slowed hot-carrier cooling5-7 and multiple exciton generation8-10 may be engineered in these novel nanostructures. Nanocrystal (quantum dot) arrays also may be used to produce the intermediate bands in the proposed high efficiency intermediate band solar cells.11,12 A necessary characteristic of the NC arrays is that they exhibit very high mobility (viz. conductivity) for electrons and holes; this requires strong inter-NC electronic coupling and the subsequent formation of extended electronic states.13 This is a three-dimensional analogue to one-dimensional confined superlattices,7,14 where resonant coupling between quantum wells produces minibands. The average inter-NC spacing is a critical parameter that largely determines inter-NC coupling, but other factors such as site energy dispersion,15,16 NC size and shape, cross-linking via polydentate capping ligands,17 and Coulomb charging16 also contribute to efficient charge transport. Also, efficient carrier transport in NC solids requires minimization of carrier loss processes such as surface trapping. All of these factors are highly interdependent, and it is critical to investigate both the degree of coupling and carrier dynamics simultaneously. Time-resolved terahertz spectroscopy (TRTS) is a relatively new experimental tool that measures both inter-NC coupling, in a noncontact fashion, and carrier dynamics, with sub-picosecond temporal resolution.18-22 We report the first TRTS measurements for a series of chemically treated NC arrays where the inter-NC separation has been varied systematically. Our results indicate that the treatments have major effects on both the degree of inter-NC coupling and carrier dynamics. Inter-NC separations in NC solids are controlled, in large part, by the length of the surface capping ligand. Long-chained †
Part of the special issue “Arthur J. Nozik Festschrift”. * Authors to whom correspondence should be addressed. E-mail:
[email protected];
[email protected]. ‡ National Renewable Energy Laboratory. § University of Colorado.
organic capping ligands, such as oleic acid, play a vital role in synthesizing monodisperse, defect-free colloidal semiconductor NCs via moderately high temperature organometallic synthetic routes. Postsynthesis, capping ligands terminate the surface preventing agglomeration, allow the NCs to be suspended in a variety of solvents, and control the surface chemistry, for example, by reducing the rate of oxidation and passivating NC surface states. To achieve efficient inter-NC coupling the bulky, native capping ligand must be exchanged to allow for smaller inter-NC spacing. In 2003, the Guyot-Sionest group first showed that CdSe NC solids may be made more conductive by simply soaking the NC solid with its native bulky capping ligands in a dilute solution of short-chained amines.17 In subsequent studies,23,24 glancing angle X-ray scattering and atomic force microscopy techniques were used to show that this treatment works for many short-chained ligands and that the increase in conductivity of NC solids resulted from a large decrease in the average interdot distance. In a previous study utilizing TRTS Beard et al. studied disordered arrays of InP NCs and found that the photoconductivity increased dramatically when the average inter-NC spacing was reduced from 1.8 to 0.9 nm.18 Jarosz et al. studied the direct current (DC) photoconductivity of CdSe NC arrays24 that were chemically treated in a similar manner as we report here for PbSe NC arrays. They found a large increase in the photoconductivity that corresponds with a decrease in the average interNC separation as well as an increase in surface passivation. They attributed the increase in photoconductivity to an increase in the inter-NC coupling and improved surface passivation resulting in an increase in the photoionization of the NCs. In a TRTS measurement the photoconductivity is directly proportional to the inter-NC coupling, while in a DC measurement the photoconductivity is a product of the coupling and carrier lifetime. In this study we compare the transient photoconductivity using TRTS of several treated PbSe NC solids prepared in an identical manner with the following set of ligands: hydrazine (hy), H2NNH2; ethlyenediamine (en), H2NCH2CH2NH2; nbutylamine (ba), H2NCH2CH2CH2CH2; and aniline (an), H2NC6H5. Intimate contact was attempted by treating the NCs with NaOH. Figure 1a displays the absorbance spectrum of the as-synthesized, oleate-capped 5.7 nm diameter PbSe NCs with
10.1021/jp0646123 CCC: $33.50 © 2006 American Chemical Society Published on Web 11/02/2006
25456 J. Phys. Chem. B, Vol. 110, No. 50, 2006
Figure 1. (a) Absorbance spectrum of colloidal 5.7 nm diameter PbSe NCs used in this study. (b) TEM image of oleate-capped NCs forming a two-dimensional close-packed array. (c) After treatment with aniline, inter-NC spacing is reduced to 0.8 nm. (d) After treatment with ethylenediamine inter-NC spacing is less than 0.4 nm.
a size distribution of less than 4%. Figure 1b is a transmission electron microscopy (TEM) image of a two-dimensional array formed from these NCs having an average interdot distance of 1.8 nm, Figure 1c is a TEM image of the array after treatment with an, resulting in a decrease in the inter-NC distance to ∼0.8 nm, and Figure 1d is after treatment with en, with an inter-NC distance of 0.8 nm. We attribute this to the different electronic structures between the InP and the PbSe NCs. Only when the PbSe NCs begin to exhibit strong electronic coupling do we observe a measurable terahertz photoconductive response. Figure 3 displays the time-dependent photoconductivity, for long times (Figure 3a) and early times (Figure 3b), of the hy-, en-, NaOH-, and ba-treated PbSe NC solids photoexcited at 810 nm at an fluence of 560 µJ/cm2. The an-treated films did show a response; however it is ∼10 times lower than that from the ba-treated films shown here. The photoconductivity decay is dominated by a decrease in carrier density, N(τ), as carriers are trapped and/or recombine. The mobility, µ (Table 1), of the carriers may be estimated by assuming that all absorbed photons produce carriers at τ ) 0 and σ(τ) = eµN(τ). (The second assumption is strictly only true at zero frequency.) The mobility is a direct measure of the inter-NC coupling and decreases as the treatment is varied: en > NaOH > hy > ba > an > untreated films. The effective mobility is the value reported in Table 1 divided by the correction factor (approximately 20). The effective mobilities that we measure are in good agreement with those reported by Talapin and Murray.23 Both the dynamics and the inter-NC coupling depend on the exact treatment conditions, but films treated under identical conditions display the same dynamics and degree of inter-NC coupling. Current efforts to optimize the treatments are underway. Our results indicate that the length of the capping ligand may not completely determine inter-NC coupling. Ethylenediamine is longer than hy and only one bond length shorter than ba yet displays the highest inter-NC coupling. Ethylenediamine is a
TRTS of PbSe NC Arrays
J. Phys. Chem. B, Vol. 110, No. 50, 2006 25459
Figure 3. Photoconductivity dynamics for the ethylenediamine-, NaOH-, hydrazine-, and butlyamine-treated NC films: (a) long time dynamics; (b) fast dynamics.
bidentate ligand that is long enough to bind both of its amine groups to adjacent Pb2+ surface sites on one NC, thereby allowing the NCs to move closer than the en chain length. Alternatively, en may cross-link two adjacent NCs and allow for enhanced inter-NC coupling. While hy also has two anchoring amine groups, it may be too small to effectively bridge two NCs or bind to two lead cations at the surface of one NC. To understand the carrier dynamics, pump intensity measurements were made for the en-, hy-, and NaOH-treated films. The results are displayed in Figures 4a-c. All films studied display dynamics indicative of Auger recombination (AR). Recently, Barzykin et al.33 reported analytical solutions to the system of differential equations that describe AR.34,35 Two carrier loss rates are extracted from this model: an AR rate and a nonradiative loss rate most likely associated with carrier trapping at the surfaces of the NCs. We globally fit the AR model to all of our intensity-dependent data for a given NC solid. Within the global fitting routine, the AR and trapping rate are varied globally while the 〈Neh〉 is varied for each curve. The AR model fits the pumpfluence-dependent data for the hy- (Figure 4a) and en-treated (Figure 4b) PbSe NC solids quite well, with AR lifetimes determined to be 46.9 and 50 ps, respectively (black lines in Figures 4a and 4b). In comparison, optical pump/near IR probe transient absorption (bleach recovery) measurements of 5.7 nm colloidal PbSe NCs find an AR lifetime of 96 ps. The factor of 2 in the AR lifetime for the films relative to colloidal NCs may be due to strong inter-NC coupling. The trapping times for the hy and en treatments are 345 and 7.9 ps, respectively. The drastic changes in the observed dynamics are a result of the much faster trapping time found in the en-treated arrays relative to that of the hy-treated arrays. Measuring the ultrafast photoconductivity dynamics allows us to separate contributions from purely inter-
Figure 4. Intensity-dependent dynamics for (a) ethylenediamine-, (b) hydrazine-, and (c) NaOH-treated films. The thin black lines are global fits the AR model from ref 25. Only the en- and hy-treated films could be fit by this model.
NC coupling from those of fast carrier trapping. In contrast, the dynamics measured from NC films treated with NaOH could not be reproduced with this AR model. Solubility considerations resulted in using methanol in place of acetonitrile as the solvent for NaOH treatments. It is well-known that methanol and hydroxide ions undergo a proton transfer reaction, reaching equilibrium when the concentrations of hydroxide and methoxide anions are roughly equal. Having a mixture of two strongly basic exchanging ligands will lead to non-singleexponential trapping dynamics, making it more difficult to extract an AR lifetime. Further measurements are underway to understand the NaOH treatment chemistry. Preliminary measurements of treated PbTe NC films indicate that the decay dynamics are substantially faster than those in similarly treated PbSe films.
25460 J. Phys. Chem. B, Vol. 110, No. 50, 2006
Murphy et al.
TRTS experiments allow observation of both the degree of coupling and the carrier dynamics simultaneously. We find that the dynamics differ significantly depending on the chemical treatments. Arrays treated with hy do not have the largest interNC coupling; however, they do have longer carrier lifetimes and therefore are preferable for energy conversion applications. Understanding the specific interactions that result in longer lifetimes and stronger coupling will aid in the direct development of novel nanostructured materials for solar energy conversion, which may be in the form of electricity (photovoltaics) or fuels (photoelectrochemistry).3 Acknowledgment. This work is supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, Office of Science, U. S. Department of Energy. We thank Kelly Knustsen, Joseph Luther, Andrew Norman, and Randy Ellingson for helpful contributions to this work.
part of the conductivity is frequency-independent, while the imaginary part is linear in ω. Equation A.3 now becomes
∆E(t;τ) ) exp
[
]∫
-σr(τ)z 20c
∆E(t;τ) )
∫-∞∞ dω Ein(ω) exp(iωt){exp[ik˜/ph(ω;τ)z] -
exp[ik˜(ω)z]} (A.1)
where ∆E(t,τ) ) E/ph(t;τ) - E(t), E/ph(t;τ) is the transmitted electric field after photoexcitation with a pump-probe delay time of τ, E0(ω) is the electric field, in the frequency domain, impinging on the sample, k˜(ω) is the complex frequencydependent wavevector, k˜/ph(ω) is the wavevector of the photoexcited material, z is the photoexcited sample thickness, and ω is the radial frequency. For the nonphotoexcited material we assume that the permittivity is frequency-independent and that no absorption occurs. The nonphotoexcited wavevector is k(ω) ) ωn/c, where n is the index of refraction. Upon photoexcitation we assume that only free carriers are produced. The photoexcited wavevector is expressed in terms of a frequency-independent refractive index (the same as the nonphotoexcited refractive index) and a frequency-dependent complex photoconductivity, σ˜ (ω)
k˜/ph(ω)
(
x
ω ) c
iσ˜ (ω) ωn iσ˜ (ω) + ≈ 1+ ω0 c 2ω0
)
We then find
∆E(t;τ) )
( )
∫-∞∞ dω Ein(ω) exp(iωt) exp iωnz c
{ [ exp
×
] }
-iσ˜ (ω;τ)z -1 20cn
(A.3)
We now assume that the photoconductivity can be modeled with a Drude model, the real, σr, and imaginary, σi, parts are given by
σr(ω) )
0ωp2γ γ +ω 2
2
σi(ω) )
0ωp2ω γ +ω 2
2
{ [(
(A.4)
where ωp is the plasmon frequency and γ is the carrier scattering rate. When the scatter rate is large compared to the frequency γ . ω, then σr(ω) ) 0ωp2/γ ) eNµ and σi(ω) ) eNµω/γ, where N is the carrier density and µ is the mobility. The real
(
)]
nz × c
)] }
eN(τ)µz 2γ0cn
-1
(A.5)
Dividing by the nonphotoexcited transmitted field and recongnizing that FT[E(ω) exp(iωt0)] ) E(t - t0) and taking the natural log of both sides we find
ln
(
)
∆E(t,τ) ∆E(t,τ) +1 ≈ ) E(t) E(t) - σr(τ)z + ln 20nc
{
(
E0 0,t′ -
E0(0,t′)
}
)
eN(τ)µz 2γ0cn
(A.6)
The second term in eq A.6 represents the shifting of the terahertz pulse due to a change in the refractive index. The shift can be estimated by calculating eNµz/2γ0cn and is found to be less than 30 fs for these measurements. For these measurements the induced absorption dominates the signal. However, in theory, one can find a terahertz delay time, t′spec, where the second term in eq A.6 is zero
{
(
E0 0,t′spec -
ln
}
)
eN(τ)µz 2γ0cn
E0(0,t′spec)
)0
(A.7)
giving
∆E(t′spec,τ)
)
E(t′spec)
-σr(τ)z 20nc
(A.8)
In practice, it is impossible to know a priori the exact t′spec; therefore, to maximize the signal-to-noise ratio the time that corresponds to the largest difference is used
∆E(t′max,τ) (A.2)
[
dω Ein(ω) exp iω t + exp iω
Appendix A The change in the electric field transmission that occurs upon photoexcitation is given by
∞
-∞
E(t′max)
=
-σr(τ)z 20nc
(A.9)
We estimate that for these measurements neglecting eq A.11 results in an error that it is
