Center for Basic Sciences, National Renewable Energy Laboratory
Golden, CO 80401, USA
The maximum thermodynamic efficiency for the conversion of unconcentrated
solar irradiance into electrical free energy in the radiative limit assuming detailed balance, a
single threshold absorber, and electron-phonon equilibrium was calculated by Shockley and
Queissar in 1961 to be about 31%; this analysis is also valid for the conversion to chemical free
energy. This efficiency is attainable in semiconductors with band gaps ranging from about 1.25
to 1.45 eV. Since conversion efficiency is one of the most important parameters to optimize for
implementing photovoltaic and photochemical cells on a truly large scale several schemes for
exceeding the Shockley-Queissar (S-Q) limit have been proposed and are under active
investigation. These include tandem cells, hot carrier solar cell, solar cells producing multiple
electron-hole pairs per photon through impact ionization, multiband and impurity band solar
cells, and thermophotovoltaic/thermophotonic cells. Here, we will only discuss hot carrier and
impact ionization solar cells, and the effects of size quantizaton on the carrier dynamics that
control the probability of these processes.
The solar spectrum contains photons with energies ranging from about 0.5 to 3.5 eV. Photons with energies below the semiconductor bandgap are not absorbed, while those with energies above the bandgap create electrons and holes with a total excess kinetic energy equal to the difference between the photon energy and the bandgap. This excess kinetic energy creates an effective temperature for the charge carriers that is much higher than the lattice temperature; such carriers are called “hot electrons and hot holes”, and their initial temperature upon photon absorption can be as high as 3000 K, with the lattice temperature at 300 K. The division of this kinetic energy between electrons and holes is determined by their effective masses, with the carrier having the lower effective mass receiving more of the excess energy.
A major factor limiting the thermodynamic conversion efficiency to 31% is that the absorbed photon energy above the semiconductor bandgap is lost as heat through electron-phonon scattering and subsequent phonon emission, as the carriers relax to their respective band edges. The main approach to reduce this loss in efficiency has been to use a stack of cascaded multiple p-n junctions in the absorber with band gaps better matched to the solar spectrum; in the limit of an infinite stack of band gaps perfectly matched to the solar spectrum, the ultimate conversion efficiency at one sun intensity can increase to about 66%.
Another approach to increasing the conversion efficiency of photovoltaic cells to above 65% by reducing the loss caused by the thermal relaxation of photogenerated hot electrons and holes is to utilize the hot carriers before they relax to the band edge via phonon emission. There are two fundamental ways to utilize the hot carriers for enhancing the efficiency of photon conversion. One way produces an enhanced photovoltage, and the other way produces an enhanced photocurrent. The former requires that the carriers be extracted from the photoconverter before they cool, while the latter requires the energetic hot carriers to produce a second (or more) electron-hole pair through impact ionization, - a process that is the inverse of an Auger process whereby two electron-hole pairs recombine to produce a single highly energetic electron-hole pair. In order to achieve the former, the rates of photogenerated carrier separation, transport, and interfacial transfer across the semiconductor interface must all be fast compared to the rate of carrier cooling. The latter requires that the rate of impact ionization (i.e. inverse Auger effect) is greater than the rate of carrier cooling and other relaxation processes for hot carriers.
In recent years it has been proposed, and experimentally verified in some cases, that the relaxation dynamics of photogenerated carriers may be markedly affected by quantization effects in the semiconductor (i.e., in semiconductor quantum wells, quantum wires, quantum dots, superlattices, and nanostructures). That is, when the carriers in the semiconductor are confined by potential barriers to regions of space that are smaller than or comparable to their deBroglie wavelength or to the Bohr radius of excitons in the semiconductor bulk, the relaxation dynamics can be dramatically altered; specifically the hot carrier cooling rates may be dramatically reduced, and the rate of impact ionization could become competitive with the rate of carrier cooling .
We have recently demonstrated greatly slowed hot electron cooling in InP QDs. For QDs one mechanism for breaking the phonon bottleneck that is predicted to slow carrier cooling in QDs, and hence allow fast cooling, is the Auger process. Here, a hot electron can give its excess kinetic energy to a thermalized hole via an Auger process, and then the hole can then cool quickly because of its higher effective mass and more closely-spaced quantized states. However, if the hole is removed from the QD core by a fast hole trap at the surface, then the Auger process is blocked and the phonon bottleneck effect can occur, thus leading to slow electron cooling. This effect was first shown for CdSe QDs. We have also shown the effect for InP QDs, where fast hole trapping species were found to slow the electron cooling to above 7 ps. This is to be compared to the electron cooling time of 0.3 ps for passivated InP QDs without a hole trap present and where the holes are in the QD core and able to undergo an Auger process with the electrons.
To utilize these effects shown by quantum dots for photovoltaic devices, three quantum dot solar cell configurations are described: (1) photoelectrodes comprising QD arrays, (2) QD-sensitized nanocrystalline TiO2, and (3) QDs dispersed in a blend of electron- and hole-conducting polymers. All of these potenitally high efficiency configurations require slow hot carrier cooling times, and we discuss our initial results on slowed hot electron cooling and enhanced impact ionization in InP QDs.