Prospects of Colloidal Nanocrystals for Electronic - Computer Science

Colloidal Nanocrystals in Electronic Applications Chemical Reviews, 2010, Vol. 110, No. 1 401
Figure 14. Minibands in a silicon quantum dot crystal. (a) The
effect of dielectric barrier height on bandwidth and energy levels
in modeled quantum dot crystal. The dielectric effective mass is
0.4mo. The reference energy is taken from the conduction band edge
of silicon. The dot size, interdot distance, and anisotropic silicon
effective mass are the same as in Figure 13. (b) The effect of
interdot distance on bandwidth and energy levels. The calculation
parameters are the same as in Figure 13 except for the barrier height,
which was 0.5 eV (typical for SiC matrix). Reprinted with
permission from ref 238. Copyright 2006 American Institute of
Physics.
tures. Lazarenkova and Balandin calculated these parameters
for heavy hole minibands in a simple cubic array of Si
quantum dots in Ge matrix. 237,245 They observed that DOS
and the effective mass tensor in quantum dot crystals are
fundamentally different from those in bulk semiconductors
and in quantum well superlattices. The calculations showed
that the effective mass in quantum dot crystal is highly
anisotropic and strongly dependent on the miniband index.
The same authors solved elasticity equations and calculated
the phonon spectrum in Si/Ge quantum dot crystals. 245 Apart
from the fundamental scientific importance of the electron
and phonon spectra in ordered quantum dot arrays, there is
a practical interest in addressing this problem because these
parameters are very important for operation of photovoltaic 253
and thermoelectric 254,255 devices.
By changing the size of quantum dots, interdot distances,
barrier height, and regimentation, one can engineer
the 3D minibands in quantum dot crystals and fine-tune
electronic and optical properties of such nanostructures,
providing exciting possibilities for optimization of electronic,
photovoltaic, and thermoelectric devices. At the
same time, formation of the extended states requires high
materials quality in terms of (i) periodicity of the quantum
dots in an array; (ii) homogeneity of the dot size and
shape; (iii) strong interdot coupling; (iv) low concentrations
of surface defects, etc. 238,245 In real quantum dot
crystals, there is always some distribution of dot size and
fluctuations in the dot position. Extended states and
minibands can still be formed as long as the bandwidth
due to wave function overlap exceeds the total broadening,
which is mostly determined by the inhomogeneous broadening.
256 An important source of disorder, which is often
overlooked, originates from the fluctuations of local interdot
coupling strengths. This type of disorder should be very
common for arrays of colloidally synthesized NCs separated
by amorphous disordered layers of insulating organic ligands.
The interplay of the interparticle coupling and disorder will
be discussed in detail in section 5.
There is only limited information available on the
formation of extended states in superlattices of chemically
synthesized NCs. Formation of extended electron states
and minibands has been reported by Artemyev et al. 257-259
for a dense quantum dot ensemble consisting of monodisperse
small CdSe dots of average radius R ) 1.6-1.8
nm; extended electronic states have been observed in
arrays of metallic (Au and Ag) NCs. 260,261 On the basis of
the existing theoretical framework, these are all possible
reasons to expect miniband formation in NC solids and
BNSLs with properly designed interparticle communications.
In chemically synthesized NC solids, surface ligands form
dielectric interparticle barriers. The barrier height and width
play the key roles in the evolution of the band structure and
transport phenomena. Different approaches to the ligand
design are discussed in the next section.
4. Design of Surface Ligands
In section 2, we discussed the important role that surface
ligands play in the synthesis of colloidal nanomaterials;
they control nucleation, growth, chemical, and colloidal
stability. The surface ligands are also extremely important
for assembling individual particles into a NC solid. They
contribute to the interparticle interactions and determine
the spacing between neighboring NCs in short- and longrange
ordered NC assemblies. It was shown in section
3.4 that the inteparticle spacings have an extremely strong
impact on the electronic structure of NC solids. The
importance of surface ligands can hardly be overemphasized.
Because of high surface-to-volume ratio inherent
to the nanoscale objects, the surface has a strong influence
on physical properties of NCs including photophysics, 156,262
charge transport, 185,263 catalysis, 264 and magnetism. 4 Proper
surface chemistry is considered a key to make a good NCbased
photodetector, 265 solar cell, 168 transistor, 23 or lightemitting
device. 266 Table 1 summarizes the structural elements
of the ligand molecules considered and employed for
electronic applications of NC solids.
The most common ligand coatings described in the
literature are based on organic hydrocarbon molecules with
anchoring end groups. Such molecular structure offers the
highest chemical flexibility; however, it has a number of
serious drawbacks. Most organic ligands act as bulky
insulating barriers between NCs, hindering charge transport.
Numerous literature reports studied the effect of
length of ligand molecules on charge transport in arrays
of metallic NCs. Most common examples include Au and