Nanomaterials for Photovoltaics (v11) 14. Intermediate-Band Solar Cells

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1 1 14. Intermediate-Band Solar Cells Intermediate (impurity) band solar cells (IBSCs) (I) Concept first proposed by A. Luque and A. Martí in Establish an additional electronic band within the band gap of a semiconductor. Usual optical absorption between conduction band (CB) and valence band (VB) augmented by additional transitions between intermediate band (IB) and CB or VB. Preserve output voltage of a single-junction device, while increasing photocurrent by carrier generation via subbandgap absorption. Maximum theoretical efficiency ~63%, (higher than two-junction tandem) IBSCs (II) The equilibrium band diagram for an IBSC is shown below We use a generic labeling scheme, with ECV EIV ECI The IB provides pathways for current generation via sub-bandgap light. The equilibrium Fermi level should reside near the center of the IB to enable it to both accept electrons from the VB and donate electrons to the CB. IBSCs (III) Luque and Marti calculated the maximum efficiency as shown below

2 2 The optimal efficiency occurs when the IB is not near the center of the gap. Ideally, the conventional bandgap is E 1.9 ev and the IB is positioned within the gap at 0.7 ev from either edge. CV IBSCs (IV) Under illumination, the carrier population in the IB must remain independent of n in the CB and p in the VB. Otherwise the IB would provide an undesirable recombination path. Therefore, a quasi-fermi level EFi must be established that is separate from EFc for the CB and EFv for the VB. Current should be collected only as electrons from the CB and holes from the VB. No current should be collected directly from the IB, as this will reduce the output voltage. The IB must be electrically isolated from the external contacts. IBSCs (V) A possible implementation of the IBSC is a p/i/n structure IBSCs (VI) The analysis is simplified if we assume light can only be absorbed by the highest available transition, which is called photon selectivity. We assume h EL not absorbed EL h EH absorbed by EL EH h EG absorbed by EH EG h absorbed by EG These conditions are ensured by finite widths of the CB, VB, and IB [Green, 2006]. To find the photocurrents, let's assume full concentration JG, photo q N EG,, Ts,0 JH, photo q N EH, EG, Ts,0 JL, photo q N EL, EH, Ts,0 IBSCs (VII) We have a separate quasi-fermi level for each band. The chemical potentials are

3 3 CV EFc EFv IV EFi EFv CI EFc EFi These satisfy qv CV CI IV. Detailed balance dictates that radiative emission also occurs between these bands. If radiation is the only current-loss mechanism, and emission is also selective, the diode currents are approximately qv kt,,,,0 1 q H kt,,,,0 1 q L kt,,,,0 1 JG qn EG Tc G JG e JH qn EH EG Tc H JH e J qn E E T J e L L H c L L IBSCs (VIII) The net result with these assumptions can be described by an equivalent circuit containing three solar cells We can see the immediate advantage is that the current-matching condition for a tandem is removed. IBSCs (IX) Based on the diagram above, we can describe the IBSC using a series combination of IV and CI (tandem) cells in parallel with the CV cell. For the CV cell, say ph 0 qv n1kt J 1 V J1 J1 e 1 For the IV and CI cells, we can use the tandem result J V J net J 2 J 2 Define 2 net e J J J net ph 0 IV IV IV net ph 0 CI CI CI net net net JIV JCI 2 J J J J 2 J J J net net net 2 IV CI 2 qv nkt

4 4 J J J The net current is A B J V J V J V 1 2 IBSCs (X) The IB should be decoupled from the CB and VB via phonon scattering, therefore is must be narrow. It should be half-filled with carriers (i.e., metallic). It should also have comparable density of states to the CB and VB edges to accommodate interband transitions. Some structures that may satisfy these conditions are discussed below. Deep-level impurities are essentially randomly distributed foreign atoms (dopants), which are easily introduced. But such impurities do not typically have a periodic arrangement, so coupling among them does give rise to a well-defined band. The resulting impurity band can enhance recombination losses. Self-assembled quantum dots are periodic arrangement of closely spaced nanostructures that can provide narrow, mid-gap band. The Fermi level within this band can be adjusted by doping. But it is difficult to control their size, shape, and spacing and actual epitaxial QD structures synthesized by S-K growth more closely resemble periodic islands. IBSCs (XI) Experimental approaches used doping to introduce dopants only within the QD layers. Say number of dots/unit volume. The number of levels introduced is then 2 N QD N QD is the, due to spin degeneracy.

5 5 Incorporating one dopant atom per QD causes the IB to be half full, placing the Fermi level in the center of the IB. IBSCs (XII) Epitaxial growth of quantum-dot (QD) arrays is most often performed in Stranski-Krastanov (S-K) mode. Nucleation of the QDs is driven by strain. leading to approximately truncated pyramid shape. To acheive the necessary optical density, multiple layers of QDs are needed. The strain field extend across adjacent QD layers, allowing them to align vertically and form a band.

6 6 IBSCs (XIII) Epitaxial QDs can often be aligned laterally [Mano et al. J. Appl. Phys., (2005)]. An idealized QD superlattice band structure is depicted below. Though simple analysis is often based on bulk band offsets, it has been shown that the actual band alignment is affected by coherency strain [Dahal et al. Prog. in PV., (2010)].

7 7 IBSCs (XIV) Ideal electronic structure has no VB offsets, and no CB offsets between WL and barrier. IBSCs (XV) The impurity-band implementation has been studied with ZnTe:O. Spectroscope and electrical measurements show evidence of the impurity band [W. Wang et al., APL 95, (2009)].

8 8 The device implementation is depicted below. IBSCs: conclusion IB solar cells provide three distinct band gaps for the collection of light, allowing higher quantum efficiency, in principle. Idealized operation gives same output voltage as a single-gap device. Periodic QD arrays, particularly in III-Vs, are prime candidates for IB formation. Rapid improvements in the synthesis of epitaxial QD arrays complement the development of 3rd - generation PV devices. Photocurrent generation from sub-bandgap light is observed in experiment. No significant efficiency improvements

9 9 have been demonstrated. Skepticism remains whether IB can exist without enhancing recombination and/or limiting photovoltage.