Hi Phil, you ask a great question! Being powered exclusively by solar cells is a dream for the aviation industry and has been achieved on a very specialized aircraft that was able to fly around the world on solar power alone . However, what you have to consider is that the plane used in that test was HIGHLY adapted and was by no means a commercial flight like the ones that transport people around the world today. There are a number of challenges to actually being to fly exclusively with solar cells:

You need a lot of power to make your plane take off. Remember that power is energy/time. While you can benefit from the wonders of lift when the plane is flying high and consistently, you need to expend a lot of energy very quickly to generate enough acceleration to take off. Solar power, assuming no changes in the cloud cover or outside factors, provides a constant stream of energy. In fossil fuel powered planes, you can just burn more fuel during your take-off but if you rely exclusively on solar power, you will need some means of storing energy that will give you that extra boost at the start of your flight. This can be done with batteries, but many battery cells are not very well adapted to high power requirements.

Batteries and solar cells, together, are heavy. There's a reason we use fossil fuels: they're really energy dense. Combustion of a small amount of fossil fuels generates a lot of energy. Now if we consider the batteries we would need (energy storage) and the solar cells (energy generation), that can quickly become very heavy without necessarily producing more energy. Current lithium ion batteries can have energy densities of about 110-200 Wh/kg, meaning that for 1 kg of battery, we can store 110-200 Watt-hours (Wh) density of storage devices . Many fossil fuels have energy densities that are about 100x greater than that . Even if we can only harness 10% of the heat from burning the fossil fuels, that means that fossil fuels give us 10x more usable energy per kg, and in aviation, where the weight of your aircraft is extremely important, that makes a lot of difference.

So far though, we have only considered the batteries; you still need to consider all of the extra weight of the solar cells in your final equation.

Obviously, solar-powered flight is not impossible. Energy density, however, is one of the most difficult things still to overcome in pursuit of powering commercial flights only with solar cells, especially over long distances. Cleaner alternatives to fossil fuel power exist though and hydrogen may prove an important fuel source for powering the flights of tomorrow. Thanks again for the question!

Some people are trying, but the huge challenge with airplanes (larger than the very small and lightweight solar airplanes for single passengers that exist today) powered by renewable energy is the density of Li-ion batteries.

Energy storage is necessary for any intermittent source of energy like solar and wind. It is unclear whether batteries will ever be lightweight enough for us to make battery powered passenger/commercial airplanes. The other difficulty is the amount of power required on takeoff - right now, I don't think we have batteries that can discharge fast enough to support the necessary acceleration on a runway.

I wouldn't get my hopes up for electric planes, but instead focus on funding high-speed rail replacing all domestic flights! Trains can be extremely energy efficient.

. "In the wee hours of July 26, 2016, Solar Impulse 2 landed in Abu Dhabi to eager crowds and cameras. After 14 months of travel and 550 hours in the air, the plane had accomplished what many had deemed impossible: traveling 25,000 miles around the world—over four continents, two oceans and three seas—without a drop of liquid fuel. The sun's vibrant rays supplied the craft's only power."

This is the link to the Solar Impulse 2 flight.