Commercially available solar panels now routinely convert 20% of the energy contained in sunlight into electricity, a truly remarkable feat of science and engineering, considering that it is theoretically impossible for silicon-based solar cells to be more than 32% efficient. This upper bound, known as the Shockley-Queisser Limit, was first calculated by the eponymous scientists (who actually gave 30% as their original limit) in the Journal of Applied Physics in 1961  (see also updates by Rühle ).
Now, if we can answer why solar panels are thus limited, we can understand the essentials of photovoltaics (PV), which have their basis in the photoelectric effect, and p-n semiconductor junctions. While many have never heard of it, the photoelectric effect is of monumental importance, and when Albert Einstein received the 1921 Nobel Prize in physics, it was “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect,” while p-n junctions lie at the foundations of modern electronics, including transistors and LEDs. Indeed, a solar cell is essentially an LED in reverse: Instead of an electric current generating light, light generates electric current!
Part the First: Brief Background on Emissions Factors
Electricity generation accounts for almost one-third of US territorial greenhouse gas emissions, and the average US residence consumes just under 11,000 kilowatt-hours (kWh) electricity per year (in addition to other fuels, such as natural gas). Thus, it is essential to understand the impact of electricity use, and especially how changes in use at the household level will affect emissions.
I wrote several hundred pages of a book that amounted to exhorting people to alter their own habits of residential energy consumption (turn down the heat, you rogues!), as well as upgrade their built environment (e.g. insulate the attic) and appliances, or even, *gasp*, add solar to their roofs. All this because the numbers, at least in the abstract, showed that such banal acts of conservation (not counting solar) can reduce the carbon footprint of residential energy use by at least 30-50%, from a baseline average of about 12 metric tonnes (1 tonne = 1 metric ton) of CO$_2$-equivalent (CO$_2$e). But a demonstration of how, over the course of roughly 5 years, the net energy use in my house actually fell progressively from around 17,000 kWh of electricity per year down to less than zero (net) seems in order.