Quantum Photocell: Using Quantum Coherence to Reduce Radiative Recombination and Increase Efficiency

The fundamental limit to photovoltaic efficiency is widely thought to be radiative recombination which balances radiative absorption. We here show that it is possible to break detailed balance via quantum coherence, as in the case of lasing without inversion and the photo-Carnot quantum heat engine. This yields, in principle, a quantum limit to photovoltaic operation which can exceed the classical one. The present work is in complete accord with the laws of thermodynamics.

Figure 1

(a) Schematic of photocell consisting of quantum dots sandwiched between $p$ and $n$ doped semiconductors. Monochromatic solar radiation excites electrons from the $|v⟩$ to $|c⟩$ states in the quantum dots. (b) Chemical potentials ${\mu }_v$ and ${\mu }_c$ are indicated by dashed lines. The ”built-in” field in the depletion layer separates electrons and holes; however, they can radiatively recombine before being separated. Absorption in the bulk semiconductor is avoided by ensuring that $\hslash \nu <{ϵ}_g$; e.g., in the figure we choose $\hslash \nu =1.80\mathrm{eV}$ and ${ϵ}_g=1.81\mathrm{eV}$. (c) The energy loss by phonon emission from electrons excited well above the band edge can be essentially eliminated by dividing the photon flux into frequency components, each of which is directed to a cell with its band gap matched to the incident light. For example frequency sensitive beam splitters are here depicted as dividing the solar radiation into red, green, and blue beams which are tuned to the three cells with $\hslash {\nu }_i\approx {ϵ}_g^i$ where $i=R$, $G$, and $B$.

Figure 2

(a) Atoms in coherent superposition of ground states $b$, $c$ which are driven by microwaves. The radiation indicated by the lighter (red) line draws equally from levels $b$ and $c$. The probability of exciting the level $a$ goes as the square sum of the sum of the probability amplitudes, i.e., $P_{\mathrm{absorb}}=|A_a+A_b{|}^2$, and can be zero. The probability of emission goes as $P_{\mathrm{emission}}=|A_a{|}^2+|A_b{|}^2$ and does not vanish. This is the basis for lasing without inversion. (b) The use of quantum coherence in the excited state doublet $a$, $b$ makes possible the opposite behavior, i.e., cancellation of emission but not absorption.

Figure 3

(a) Quantum dots having upper level conduction band states, $|c_1⟩$ and $|c_2⟩$, are coherently driven by a field such that $\hslash {\nu }_0=\frac{1}{2}({ϵ}_{c_1}-{ϵ}_{c_2})$. The monochromatic solar photons having energy $\hslash \nu$ are tuned to the midpoint between the upper levels. The host semiconductor system, in which the quantum dots are embedded, has effective Fermi energies ${\mu }_c$ and ${\mu }_v$ for the conduction and valence bands. (b) A single mode photo-Carnot engine in which the working photon “fluid” is heated by quantum fuel consisting of atoms having quantum coherence induced between the lower levels.