(CNN) When it comes to the big questions plaguing the world's scientists, they don't get much larger than this.

Where do you safely bury more than 28,000 cubic meters -- roughly six Big Ben clock towers -- of deadly radioactive waste for the next million years?

This is the "wicked problem" facing Germany as it closes all of its nuclear power plants in the coming years, according to Professor Miranda Schreurs, part of the team searching for a storage site.

Experts are now hunting for somewhere to bury almost 2,000 containers of high-level radioactive waste. The site must be beyond rock-solid, with no groundwater or earthquakes that could cause a leakage.

The technological challenges -- of transporting the lethal waste, finding a material to encase it, and even communicating its existence to future humans -- are huge.

But the most pressing challenge today might simply be finding a community willing to have a nuclear dumping ground in their backyard.

Searching for a nuclear graveyard

Germany decided to phase out all its nuclear power plants in the wake of the Fukushima disaster in 2011, amid increasing safety concerns.

The seven power stations still in operation today are due to close by 2022.

With their closure comes a new challenge -- finding a permanent nuclear graveyard by the government's 2031 deadline.

Germany's Ministry for Economic Affairs and Energy says it aims to find a final repository for highly radioactive waste "which offers the best possible safety and security for a period of a million years."

The country was a "blank map" of potential sites, it added.

Currently, high-level radioactive waste is stored in temporary facilities, usually near the power plant it came from.

But these facilities were "only designed to hold the waste for a few decades," said Schreurs, chair of environmental and climate policy at the Technical University of Munich, and part of the national committee assisting the search for a high-level radioactive waste site.

As the name suggests, high-level radioactive waste is the most lethal of its kind. It includes the spent fuel rods from nuclear power plants. "If you opened up a canister with those fuel rods in it, you would more or less instantly die," said Schreurs.

These rods are "so incredibly hot, it's very hard to transport them safely," said Schreurs. So for now they're being stored in containers where they can first cool down over several decades, she added.

There are dozens of these temporary storage sites dotted across Germany. The search is now on for a permanent home at least 1 kilometer underground.

Between a rock and a hard place

The location will need to be geologically "very very stable," said Schreurs. "It can't have earthquakes, it can't have any signs of water flow, it can't be very porous rock."

Finland, which has four nuclear power plants and plans to build more in the future, is a world leader in this field. Work is well underway on its own final repository for high-level waste -- buried deep in granite bedrock.

Germany's problem is "it doesn't have a whole lot of granite," said Schreurs. Instead, it has to work with the ground it's got -- burying the waste in things like rock salt, clay rock and crystalline granite.

Next year the team hope to have identified potential storage sites in Germany (there are no plans to export the waste). It's a mission that stretches beyond our lifetimes -- the storage facility will finally be sealed sometime between the years 2130 and 2170.

Communications experts are already working on how to tell future generations thousands of years from now -- when language will be completely different -- not to disturb the site.

Schreurs likened it to past explorers entering the pyramids of Egypt -- "we need to find a way to tell them 'curiosity is not good here.'"

People power

For now, nobody wants a nuclear dumping ground on their doorstep.

Schreurs admitted public mistrust was a challenge, given Germany's recent history of disastrous storage sites.

Former salt mines at Asse and Morsleben, eastern Germany, that were used for low- and medium-level nuclear waste in the 1960s and 1970s, must now be closed in multibillion-dollar operations after failing to meet today's safety standards.

The fears around high-level waste are even greater.

Protesters block railway tracks outside Gorleben in 2010.

For more than 40 years, residents in the village of Gorleben, Lower Saxony, have fought tooth-and-nail to keep a permanent high-level waste repository off their turf.

The site was first proposed in 1977 in what critics say was a political choice. Gorleben is situated in what was then a sparsely populated area of West Germany, close to the East German border, and with a high unemployment rate that politicians argued would benefit from a nuclear facility.

Over the decades, there have been countless demonstrations against the proposal. Protesters have blocked railway tracks to stop what they described as "Chernobyl on wheels" -- containers of radioactive waste headed for Gorleben's temporary storage facility.

An exploratory mine was eventually constructed in Gorleben, but it was never used for nuclear waste. And in the face of huge public opposition, the government in recent years decided to start afresh its national search for a dumping ground.

"If we did not build this big, strong and long-lasting resistance, I think the salt mine would already be used," said Kerstin Rudek, 51, who grew up in Gorleben and has been campaigning against a permanent nuclear repository for the last 35 years.

That doesn't mean she and other activists plan on quitting their campaign anytime soon. "They haven't canceled out Gorleben completely, so we are very suspicious it might still be chosen," said Rudek.

With more than 400 nuclear power plants around the world, many nearing the end of their operating lifetimes, the issue of waste storage will only become more urgent, said Schreurs.

Germany is in the unique position of knowing exactly how much waste it will be dealing with. Knowing where to put it is the challenge.