This thesis explores ways to create highly efficient, thin-film solar cells. Both high short circuit current density and high open circuit voltage are required for high efficiency in photovoltaics. High current is achieved by absorbing most of the above bandgap photons, and then extracting the resulting electrons and holes. To achieve high absorption in thin films, surface texturing is necessary. Surface texturing allows for absorption enhancement due to total internal reflection, known as light trapping. However, in subwavelength-thick solar cells (~100 nm thick), the theory of light trapping is not understood, and both the maximum achievable absorption and the optimal surface texture are open questions. Computational electromagnetic optimization is used to find surface textures yielding an absorption enhancement of 40 times the absorption in a flat solar cell, the highest enhancement achieved in a subwavelength-thick solar cell with a realistic index of refraction. The optimization makes use of adjoint gradient methods, which allow the problem of designing a 3D surface to be computationally tractable.

However, while high current requires high absorption, high voltage requires re-emission of the absorbed photons out of the front surface of the photovoltaic cell. This re-emission out the front of the solar cell is required by the detailed balance formulism outlined by Shockley and Quiesser in 1961. At the open circuit voltage condition, where no current is collected, ideally all absorbed photons are eventually re-emitted out the front surface of the solar cell. The small escape cone for a semiconductor/air interface, as described by Snell's law, makes it difficult for the photon to escape out of the front surface; it is much more likely for the luminescent photon to be lost to an absorbing back substrate. Thus, a back reflector on a solar cell is crucial to obtaining high voltage, as it helps the internally emitted photons in the cell escape out of the front surface. The open circuit voltage difference between a solar cell with a back mirror and a solar cell with an absorbing substrate is quantified, and it is found that the benefit of using a back mirror depends on the absorptivity of the solar cell material. The back mirror concept is extended to the sub-cells of a multijunction cell, and an air gap as an "intermediate" reflector is proposed and analyzed. In a dual junction solar cell, it is shown that proper mirror design with air gaps and antireflection coatings leads to an increase in open circuit voltage, resulting in a ~5% absolute efficiency increase in the solar cell.

Finally, it is shown that these concepts in high efficiency solar cells can be extended to thermophotovoltaics. In solar photovoltaics, radiation from the sun is converted to electricity with photovoltaic cells. In thermophotovoltaics, radiation from a local heat source is converted to electricity with photovoltaic cells. This method of converting heat to electricity can be extremely efficient if sub-bandgap photons are reflected back and re-absorbed by the hot source (which is usually around 1200 C). Greater than 50% efficient heat to electricity conversion with thermophotovoltaics is possible if the photovoltaic cells have good back mirrors.