Electrical Transport in Colloidal Quantum Dot Films - The Journal of

Apr 12, 2012 - Biography. Philippe Guyot-Sionnest is a professor of chemistry and physics at the University of Chicago since 1991. His group (http://p...
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Electrical Transport in Colloidal Quantum Dot Films Philippe Guyot-Sionnest James Franck Institute, The University of Chicago, 929 East 57th Street, Chicago, IL60637 ABSTRACT: In nanocrystal solids, the small density of states of quantum dots makes it difficult to achieve metallic conductivity without band-like transport. However, to achieve band-like transport, the energy scale of the disorder should be smaller than the coupling energy. This is unlikely with the present systems due to the size polydispersivity. Transport by hopping may nevertheless lead to an increased mobility with decreasing temperature for some temperature range, and such behavior at finite temperature is not proof of band-like conduction. To date, at low temperature, variable range hopping in semiconductor or weakly coupled metal nanocrystal solids dominates transport, as in disordered semiconductors.

effective ligand exchange procedure,16 ohmic conductivity was finally observed in the rather monodispersed CdSe QDS with mobilities up to 10−2 cm2/V/s.17 However, the conductivity decreased with decreasing temperature,17,18 indicating insulating behavior unlike with MNS, even with very short ligands.19 The ligand exchange in preformed films16 has been developed further and is widely used,5−7,20 while new chemical strategies have also been devised21 to improve the coupling between the nanocrystals. For completeness, some conductivity in ZnO nanocrystalline systems built by sol−gel deposition of ZnO colloids was early on established by Hoyer and Weller.22 Supporting conducting electrodes of other oxides based on the assembly of nanocrystalline particles also have important applications,23,24 but the spectroscopy of these systems is not that of QDS. Conductivity in QDS should follow two simple rules. (1) There must be stable and partial occupation of the sparse and identifiable quantum dot state. (2) The charges must be able to hop between these states on separate particles on a reasonable time scale. In addition, one needs to appreciate that there is much disorder in the present systems. Figure 1 shows a plausible cartoon of the current paths in a nanocrystal array. Electrochemistry allowed the first steps with conductive QDS, and it has the advantage of allowing high charge density in a volume that can be monitored by optical spectroscopy.14,15,17,25 This is important to ascertain the nature of the states involved in the transport. However, effective electrochemistry also requires a porous material and the introduction of counterions, and this limits the extent of the material processing that can be explored. At present, most transport measurements are done using FET5 without any spectroscopic identification of the quantum state occupation. The main figure of merit is the mobility, and the mobility has increased dramatically as a result of bolder

T

he precise engineering of the electronic interactions and wave functions with nanomaterials is promising improved and novel functions. This promise has been fulfilled with thin epitaxial layers such as semiconductor quantum wells, with giant magnetoresistance metal films, and effectively with the layered high Tc superconductors. To achieve three-dimensional nanoenginneered solids, the colloidal synthesis of monodispersed nanocrystals and self-assembly1,2 is a promising approach, but a challenge is to control the electronic coupling between the separate building blocks. In the past decade, photodetectors,3,4 FETs,5 and solar cells6,7 made from colloidal nanocrystal solids have been investigated. There is rapid progress, and several excellent reviews exist already,8,9 and this Perspective addresses the topic of electrical transport in nanoparticle solids when carriers must travel via the nanocrystal states.

The precise engineering of the electronic interactions and wave functions with nanomaterials is promising improved and novel functions. Metals and insulators are different phases of the electronic system. A metal is a material for which the carrier mobility increases with decreasing temperature down to the lowest temperatures, with delocalized wave functions. An insulator is a material where ohmic transport arises by thermal activation. In principle, nanocrystal solids should allow one to tune through the transition by adjusting the coupling between the particles. With metal nanoparticle solids (MNS),10 4 nm silver MNS separated by 0.5 nm have been reported to be metallic,11 and 5 nm gold MNS are separated by butane dithiol ligands or shorter.12 In contrast, semiconductor quantum dot solids (QDS) with similar or better monodispersivity initially did not even display ohmic transport.3,4 By controlling the Fermi level with charge-transfer doping13−15 and with a simple but © 2012 American Chemical Society

Received: January 12, 2012 Accepted: April 12, 2012 Published: April 12, 2012 1169

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A unity transmission with a finite barrier requires states with a detuning negligible compared to the line width and a line width smaller than the coupling.30 The optical analogue is the Fabry− Pérot etalon, where 100% transmission can be achieved for nearly monochromatic light even though the transmission of each mirror can be extremely low. If, on the other hand, the states are not in resonance or their line widths are broader than the coupling, then the transmission coefficient is reduced to a 2 1/2

small value that can be approximated as ; = e−2(2mVB/ℏ ) l = e−βl, where β is the attenuation of the wave function probability in the barrier with height VB and width l.30 With metal dots of a few nanometer diameter, the density of states is high, and there are many channels, on the order of the number of surface atoms. Therefore, the conductance in eq 1 may reach the quantum conductance even though the transmission per channel can remain small. This is why MNS with short thiol chains can exhibit metallic conductivity. In contrast, for lightly doped quantum dots (QDs), the number of channels must remain small by definition. For example, a CdSe QD has only one channel, while a PbSe QD may have 16 channels because the lowest conduction or valence states are four-fold degenerate. The small number of channels in QDS requires therefore high transmission, on the order of unity, for metallic conduction. However, such high transmission is most unlikely with the present synthetic control of the colloidal nanomaterials. Therefore, while metallic conductivity can take place with MNS despite much disorder, the requirement is a lot more stringent with QDS. Dif f iculty of Band Conduction in QDS Due to Disorder. With precise superlattices of quantum wells of epitaxial materials, bands have been observed since the 1970s,31,32 and lead to new effects such as a negative differential resistance when the voltage drop between the wells is equivalent to the width of the band. Band formation requires a coupling larger than the energy detuning and larger than the natural line widths of the states, the same requirement as that for unity transmission through a finite barrier. Even in ordered systems, sufficient electron−electron repulsion can split the band, leading to the Mott insulator,33 but more commonly, disorder localizes the electrons, as in Anderson localization.34 Low transmission due to variations in confinement energy, electron−electron repulsion, and variations in coupling and thermal broadening lead to hopping conductivity instead. For the QDS of CdSe or PbSe colloidal nanocrystals that are typically investigated, the confinement energy of the electrons is 0.2−0.5 eV, and the disorder is a sizable fraction. The confinement energy scales as rα, where r is the radius and α is −2 at low energy and closer to −1 at high energies, where the bulk band dispersion becomes nonparabolic. With a size variation of 5%, the inhomogeneous energy standard deviation is δE/E = αδr/r ≈ 10−5%. This leads to a contribution to the activation energy Ea of ∼0.02−0.05 eV, which is larger than the expected thermal broadening at temperatures below room temperature. If two particles are very close and properly oriented, they are furthermore likely to sinter along their common face and lose nearly one-third of the confinement energy, leading to even greater disorder of 0.03− 0.15 eV. Such disorder will cause a broadening and red shift of the spectra. Broadening and red shifts are often seen in closepacked QDS, but they are often optimistically attributed to electronic delocalization between nanoparticles.35 While this may be partially true, as discussed below, the energy scale required for efficient electronic coupling is much smaller than

Figure 1. Composite cartoon picture of a TEM of relatively well ordered PbSe nanocrystals overlaid with the breakdown pattern of a macroscopic plasma disk. It aims to convey the notion that in classical hopping, the flow of electrons is not wave-like but diffusive and likely favoring easy paths.

surface chemical modifications and annealing procedures. The risk is to achieve high-mobility nanocrystalline thin films,26 but the retention of some of the original exciton features in the absorption spectra is often considered sufficient evidence for QDS. PbS and PbSe QDS first exhibited high mobilities of order 1 cm2/V/s,5 but more recently, CdSe QDS have shown a mobility in excess of 10 cm2/V/s and increasing with decreasing temperatures.27 There is also a report of PbSe QDS under very strong optical excitation showing similar behavior.28 Both reports proposed that the increased mobility with lowering temperature arises because of band transport and reduced scattering as the temperature is lowered.27,28 The next paragraphs discuss an alternative explanation. Dif f iculty of Metallic Conduction in QDS. Since MNS were reported to display metallic behavior, metallic behavior in QDS might be expected to be easily achievable as well. However, an essential difference is the much smaller density of states in QDS. As a benchmark, it is proposed that MNS and QDS should become metallic when the interdot resistance drops below the quantum resistance h/e2, which is also the sheet resistance of a two-dimensional sample. The qualitative argument for R ≈ h/e2 is based on considering two dots with an electron shuttling in between.29 The energy barrier associated with shuttling the electron between the dots is called Ea, such that Ea = e2/C, where C is the capacitance. The time taken to shuttle the electron is on the order of RC, and if the electron is in a coherent state, one should have Ea = e2/C ≈ h/τ ≈ h/RC, which implies R ≈ h/e2. The conductivity, σ, of a dot solid is then obtained in relation to the interdot resistance, R, by σ = 1/Rd, where d is the center to center distance for a cubic network. For a homogeneous nanocrystal solid, this leads to σMI ≈ e2/hd as the target conductivity, where d is the dot center to center distance. σMI ≈ 55 S·cm−1 for d = 7 nm. This is a very high value of the conductivity that has not yet been approached with QDS and is in the upper range of values reported for metallic MNS.10 Possibly, a system may still exhibit metallic behavior if only a fraction of the material is metallic throughout. Using the Landauer formula,30 the conductance between two nanocrystals at low temperature is G=

1 2e 2 = R h

∑ ;i ,j i,j

(1)

where; i,j is the transmission of the conductance channel between states i and j of the left and right dots, respectively. 1170

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where τhop−1 is the effective hopping rate. If hopping is an exponentially activated process, τhop−1 = τo−1e−Ea/kT, where τo−1 is the attempt frequency; then, the mobility increases with decreasing temperatures up to T = Ea/k. Drawing conclusions from the temperature-dependent mobility about the existence of band-like conduction requires, therefore, lower-temperature investigations. To obtain an approximate but explicit value for τo, one can use τ0 = RC, which gives τo−1 = (2Ea/h); for a QDS with only one channel. ; depends on the degree of coherence between the initial and final states. If the width or detuning of the states is broader than the coupling, the coherence is lost and ; = e−βl. The mobility in three dimensions with one conductance channel is then obtained as

the red shifts often reported. Furthermore, it is not obvious that the broadening is a necessary outcome of electronic coupling, and it is certainly not seen in quantum superlattices. When the nanocrystals will be atomically precise, such as in the platelets recently introduced by Ithurria et al.,36 the confinement energy disorder will be greatly reduced, and one may one day approach the order realized with the epitaxial materials. In addition to disorder of the energy levels, there is electron−electron repulsion in small dots, and this applies to QDS and MNS as well. An upper estimate of the energy is the charging energy Ec0 = e2/4πεr valid for an isolated sphere in a uniform medium of optical dielectric constant ε. For a particle of 7 nm diameter in an alkane matrix (ε ≈ 2), this is 0.1 eV. A better estimate is the capacitance of a metal sphere embedded in a metallic shell, with an insulating gap of thickness l and dielectric constant ε, Ec = l/(r + l)Ec0. With a dot separation of l = 1 nm, the charging energy contributes then ∼0.025 eV to the activation energy Ea. This is similar to the disorder in confinement, but it gets smaller as the dot separation decreases or as the matrix dielectric constant increases. There is also disorder in the coupling between the particles because the coupling is exponential in distance. For example, with an alkane barrier, the coupling between dots varies by an order of magnitude for ∼2 Å variation in dot separation. Such variation in the separation is very likely in a nanoparticle assembly. In many studies, the nanoparticles are first capped with long alkane chain ligands for good solubility and film formation, and the ligands are then removed/exchanged with shorter ligands after the films are formed.16 This leads to a rearrangement that is likely not uniform either locally or across the samples. For example, particles on the substrate surface may be affected differently than those in the bulk. More recently, charged-stabilized colloids have been used to make the films directly.21 The resulting short particle distance helps increase the coupling and reduce the charging energy. However, as the particle distance is reduced, it also becomes more likely that sintering/necking arises between similarly oriented crystalline particles, greatly increasing disorder, as discussed above. Many separate sources of disorder make it extremely unlikely that QDS based on colloidal assemblies are anywhere close to exhibiting band-like transport behavior.

μ=

For electron transfer though an alkane, β ≈ 0.9−1.2 Å from various measurements,37 and a separation of 1 nm gives a transmission of ; = 10−4−6.10−6. A study of the length effect with alkane ligands for PbSe QDS showed the exponential dependence with β ≈ 1.1 Å−1.38 Alkanes are very insulating, and most materials offer lower barriers. For example, phenyl ligands for which β ≈ 0.5−0.7 Å−137 readily increase mobility in CdSe QDS by orders of magnitude.17 For dots with a d = 7 nm center to center distance and at T = Ea/k, eq 3 gives the maximum mobility as μ = 14e−βl cm2/V/s . This is in fair agreement with extrapolated values from weakly coupled CdSe17 and PbSe38 QDS at moderate temperature. It is noted again that PbSe QDS should allow more conductance channels than CdSe, possibly 16 because the lowest quantum state is four-fold degenerate. With FET, the diffusion is in the 2D regime because hopping takes place mainly in the layer of dots closest to the gate, and this gives μmax = 21e−βl cm2/V/s. The temperature dependence of the mobility is shown in Figure 2 with d = 7 nm, e−βl = 10−3, and varying values of Ea.

Figure 2. Mobility as a function of temperature using eq 3 for a value of e−βl = 10−3, d = 7 nm, and the indicated activation energy.

Expression for the Mobility in the Hopping Regime. The evidence for band-like conductivity in QDS has so far been only the increasing mobility with decreasing temperature.27,28 However, in hopping transport, the preexponential factor may have such a temperature dependence. For example, Marcus theory gives the microscopic rate of electron transfer with a preexponential factor ∼1/√T. More generally, Einstein’s relations between mobility and diffusion in three dimensions give ed 2 6τhopkT

(3) −1

Many separate sources of disorder make it extremely unlikely that QDS based on colloidal assemblies are anywhere close to exhibiting band-like transport behavior.

μ=

ed 2Ea −βl − Ea / kT e 3hkT

Advances in inorganic ligand exchange21 have led to high FET mobilities around ∼10 cm2/V/s with CdSe QDS,27 and this is already close to the upper limit of eq 3. It will be important to quantify the degree of confinement remaining in these systems. Specifically, one could investigate the gap between the 1Se and 1Pe states and the role of interfacial states. If these systems are in the QDS regime, where tunneling occurs only via the 1Se state, ∼10 cm2/V/s is a very high mobility that might invalidate eq 3. Recently, Chu et al. applied microscopic calculations based on Marcus theory on this system39 and found that the calculated electronic coupling energy was much

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For photovoltaic applications of QDS in the near-infrared, striving to achieve higher mobility than 10−2 cm2/V/s will not necessarily pay off because the exciton dissociation is already quite efficient. The recombination rate on defects or defective nanocrystals is proportional to the mobility; therefore, increasing the mobility brings no advantage from that point of view as well. The real improvement is obviously to eliminate the recombination centers, and this typically means a better surface control of the nanocrystals. In a more subtle point, it is also noted that in current PV devices using QDSs, the opencircuit voltage,Voc, is typically less than half of the energy gap.6,7,41 Bulk crystalline semiconductors such as Si or CdTe have very sharp absorption edges, but with QDS, the disorder will lead to a tail of absorbing states. This can dramatically reduce the cell efficiency even if all recombination is radiative. To emphasize this point, Figure 3 shows Voc assuming an

weaker than the reorganization energy. As a result, phononassisted hopping is the transport mechanism and not band-like conductivity, in agreement with the discussion above. In summary of this section, at temperatures above T ≈ Ea/k, hoping transport can lead to mobility increasing with decreasing temperature, and some evidence other than the temperaturedependent mobility is required to claim band-like transport.

At temperatures above T ≈ Ea/k, hoping transport can lead to mobility increase with decreasing temperature, and some evidence other than the temperaturedependent mobility is required to claim band-like transport. Practical Relevance for Optoelectronic Applications. The discussion above relates several properties of QDS to the transmission ; of a QDS. The maximum mobility μmax and the effective hopping time τhop are shown for a few values in Table 1. Table 1. Mobility, Hopping Time, and Coupling Energy As a Function of the Transmission Coefficient between Dots with One Channel of Conductance ;

mobility μmax (cm2/V/s)

τhop

coupling energy

1 10−3 10−6

14 1.4 × 10−2 1.4 × 10−5

230 fs 230 ps 230 ns

8 meV 8 μeV 8 neV

Figure 3. Calculated Voc at 300 K for a solar cell material with 100% absorption above the gap and an exponentially decaying absorption below the gap with the indicated Urbach energies. The calculation is in the Shockley−Queisser limit. The inset shows a 50 meV tail on the absorption for a 1 eV gap.

For this table, d = 7 nm. The coupling energy between dots is taken as ℏτ0−1 = Ea; /π, and Ea is taken as 25 meV. As ; ≈ 1, the coupling energy is on order of the activation energy, and it is noted that as ; approaches unity, eq 3 is not meaningful. The table highlights the fact that only very small coupling energies are required for high mobility and that they are much smaller than the red shift/broadening often observed experimentally in QDS. Again, these are instead likely attributable to partial ripening/sintering/necking of particles. The hopping time, which is directly obtained from the mobility in eq 2, is relevant for optical applications where the exciton needs to be ionized, such as for photodetectors or photovoltaics. This is because if the exciton binding energy is small compared to the thermal energy, its ionization time is simply the hopping time. The quantum efficiency for photoionization is then η = τr/(τhop + τr), where τr is the competing exciton recombination rate that includes radiative and nonradiative processes inside of the dot. Equation 2 gives τhop ≈ 0.3 ns for a mobility of 10−2 cm2/(V s) at room temperature, and d = 7 nm. In the visible and near-infrared, the radiative recombinations in colloidal dots are typically in the 30 ns regime for CdSe dots and in the microsecond regime for near-infrared PbSe. Therefore, a mobility of 10−2 cm2/(V s) should already give ionization efficiencies larger than 99%. For applications in the mid-infrared,40 energy transfer to the ligands or matrix phonons may be more rapid than 1 ns, and mobility closer to 10−1 cm2/(V s) will be required. Only if faster nonradiative processes need to considered, such as Auger recombination or exciton cooling, would a even higher mobility be required.

Urbach tail42 below the absorption edge. Voc is given by the Schockley−Queisser value43 ⎛ ⎛ ∞ ⎞ ⎞ ⎟ kT ⎜ ⎜ ∫0 α E ϕS E , T dE ⎟ Voc = ln + 1⎟ e ⎜⎜ ⎜⎜ ∫ ∞ α E ϕ E , T dE ⎟⎟ ⎟ T ⎝ ⎝ 0 ⎠ ⎠

() ( ) () ( )

where the absorption α(E) is 100% above the gap and decreases exponentially below the gap. ϕS(E,T) is the AM1.5 solar irradiation, and ϕT(E,T) is the blackbody radiation at temperature T. Figure 3 shows that an exponential tail with a 50 meV decay constant, which is not large by the standards of QDS, already accounts for a 50% reduction of Voc. It is suggested that the sharpness of the absorption edge of the QDS is a major limitation for solar cell applications, calling therefore for improved monodispersivity and order.

It is suggested that the sharpness of the absorption edge of the QDS is a major limitation for solar cell applications, calling therefore for improved monodispersivity and order. Hopping at Low Temperatures. This last section discusses the conductivity properties of QDS at low enough temperatures. 1172

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threshold as shown in Figure 5.18 Furthermore, a proposed scaling argument I ≈ (V − Vt)n 53 is never observed over more than one or two decades of current.53 Recent experiments on weakly coupled MNS have now reported agreement with ESVRH,48 with results very similar to CdSe QDS. For completeness, one report on PbSe QDS used alternatively a Coulomb blockade nearest-neighbor hopping and the ES-VRH to explain separate data, but it did not control the Fermi level.54 Experiments on PbSe QDS with a controlled Fermi level confirmed the applicability of the ES-VRH model.55 Experiments with the CdSe QDS indicated that an electron could tunnel through as many as four nanocrystals at the lowest temperature and bias used.18 The physical reality of such long tunneling distances associated with VRH is often disbelieved. The answer is simply that the current also drops by many orders of magnitude exactly as it should. A sticking point in the first comparison of the QDS results with the VRH theory was that the relative values of T* and E*, which should be related by E* = kB/2eξT*, disagreed by a factor of 4.18 The disagreement originated from the assumption that the localization length would be on the order of the nanocrystal radius, while in fact ξ = 2d/βl, and it depends obviously on the coupling between particles. Further experiments resolved the discrepancy.56 With β ≈ 1.1 Å−1 for the alkane and l ≈ 9 Å for CdSe dots cross-linked with heptanediamine, d = 7 nm gives ξ = 1.4 nm, which is larger than the experimental value of 1.1 nm56 but in fair agreement given the simplicity of the expressions. VRH in QDS also predicts that as the density of states is lowered and above a crossover temperature, the conductance follows a T1/4 exponent, which is Mott-VRH in 3D. The predicted crossover temperature is Tcross = 5.9e4g0ξ/κ2kB,where g0 is the density of state at the Fermi level and κ is the dielectric constant.49 Highly monodispersed CdSe QDS have shown the expected crossover56 and have thus provided a very successful verification of the applicability of VRH theories to the QDS. For completeness, there are reports of deviation from the 1/2 or 1/4 exponents. A 2/3 exponent was reported with ZnO nanocrystalline films57 and also for MNS.12 This result, intermediate between Arrhenius and ES-VRH, might arise from large-scale inhomogeneity that skews the measured I(T) because different parts of the sample in series or parallel contribute differently to the overall conductance as the temperature is changed. With weakly coupled monodispersed gold MNS, ES-VRH accounts very well for the transport data, similar to the CdSe QDS.48 Metal dots based on Au or Ag will however not show Mott-VRH because the density of states is large and not adjustable. In summary, this Perspective provides a qualitative discussion of charge transport in nanocrystal solids. It is first argued that metallic conductivity can “easily” take place with metal nanoparticle solids simply because of the large number of conductance channels between the metallic nanocrystals. In contrast, it is suggested that the small density of states of quantum dot solids will require resonant transport between particles with high transmission coefficients to achieve metallic conductivity. This will require a stronger coupling than the disorder in energy, but the disorder is too large with the present systems. Instead, it is argued that, to date, transport in QDS arises by hopping. An expression for the mobility is given. It is noted that the preexponential factor in the hopping mobility may lead to increased mobility with decreasing temperature at finite temperatures. Such behavior may be mistakenly attributed

As the temperature is sufficiently low, hopping transport is so far always observed with the QDS, but it deviates from the Arrhenius behavior in eq 3 because of variable range hopping (VRH).44 If the probability of an electron tunneling to the nearest neighbor is ; with ; ≪ 1, then the probability for tunneling through n-dot is ; n. This was named “superexchange” in the 1960s45 but it is called tunneling in nanocrystals solids46 or “cotunneling” in the context of MDS.47,48 Expressing the transmission as ; = exp(−2d/ξ), the tunneling probability through n-dot is ; n = exp(−2nd/ξ) = exp(−2r/ξ), where r = nd is the center to center distance of an n-dot hop (see Figure 4).

Figure 4. In VRH, the conductance to a more distant state is favored because of the smaller activation energy, but the tunneling probability is exponentially smaller.

It is therefore as if the wave function had an exponential decay of length ξ, which is called the “localization length” in VRH. In terms of the barrier material and thickness, ξ = 2d/βl, which is obtained by identifying with ; = exp(−βl). Monodispersed CdSe QDS follow the Arrhenius behavior G ≈ exp − Ea/T at moderate temperature,17 but at sufficiently low temperature, G ≈ exp − (T*/T)1/2,18 in agreement with the Efros−Shklovskii VRH (ES-VRH),49 where the dominant energy barrier is electron−electron repulsion.50 In the nonOhmic regime, at high bias, the conductivity also approaches asymptotically the VRH-predicted G ≈ exp − (E*/E)1/2 with the applied field E, as shown in Figure.5. Agreement between

Figure 5. Conductivity of CdSe QDS from ref 18. The figure on the left shows the current versus the bias across a 10 μm electrode gap. The figure on the right is the same data graphed as conductance versus the inverse root of the electric field, becoming asymptotically linear and temperature-independent at high fields.

ES-VRH and the experimental conductivity as a function of temperature and field extends over many orders of magnitude.18 Other models for the non-Ohmic regime are not as successful. The Poole−Frenkel mechanism for field extraction of trapped charges is widely used for insulating materials,51 but it does not account for the full range of transport data in the conductive CdSe QDS. A “Coulomb blockade” nearest-neighbor hopping model52 has also been applied to MNS.53 This model supposes the existence of a welldefined Coulomb blockade energy that leads to a threshold Vt and nonlinear I(V) curves at low temperatures. The more sensitive experiments in QDS indicate that there is no such 1173

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to band-like conductivity. As a function of the transmission between dots, the mobility, hopping time, and coupling energy are discussed. Transport by hopping is good enough for many low current applications at ambient temperatures, and it is argued that there is not a clear need for mobilities in excess of 0.1 cm2/V/s for photodetection or photovoltaics. For photovoltaic applications, it is pointed out that the poor spectral definition of the band edge in QDS might result in too low open-circuit voltages. Finally, at low temperatures, variable range hopping in semiconductor or weakly coupled metal nanocrystal solids dominates transport, as in disordered semiconductors.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest. Biography Philippe Guyot-Sionnest is a professor of chemistry and physics at the University of Chicago since 1991. His group (http://pgslab.uchicago. edu/grouppage/index.html) introduced single dot microscopy, the CdSe/ZnS core/shell, intraband spectroscopy, n- and p-type quantum dots, and conductivity in QDS. His Ph.D. (1987, physics, Berkeley) with Y. R. Shen introduced surface SFG and led to time-resolved adsorbate vibrational spectroscopy.

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ACKNOWLEDGMENTS

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REFERENCES

The work is supported by the DOE under Grant No. DEFG02-06ER46326. I acknowledge many helpful discussions within the James Franck Institute, including those with Profs. D. K. Morr, H. M. Jaeger, K. F. Freed, T. F. Rosenbaum, and D. V. Talapin. The work derives from the contributions of former and current graduate students, starting with Prof. M. Shim who succeeded in injecting electrons in colloidal dots, Dr. C. Wang who introduced the spectroelectrochemistry of colloidal dots, Prof. D. Yu who achieved ohmic conductivity in CdSe QDS and pointed out the applicability of VRH, Dr. B. Wehrenberg who extended these observations to the PbSe dots, and H. Liu who observed the crossover between Mott and ES-VRH.

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