The first modern people who lived in Siberia were the Tatars. They were not criminals and didn't even know that their land is such a nice place for the criminals - they just happened to be born there and I guess, they loved the place a lot. Later, Siber ia was conquered by Cossacks who were not more (probably less) criminals than were the conquistadors.
After that...well, after that the government did send a lot of convicted people to Siberia. I am not using the term "criminals" because at that time, the punishment traditionally served all the purposes it serves now (to keep dangerous people away from the capital cities, etc.) plus one - development of huge and potentially rich territories. Majority of these "criminals" were not professional criminals but rather peasants who were convicted because of the political or religious reasons or just for being at the wrong place on the wrong time (the development thing needed a lot of people because the waste of this resource was high). After serving their term, survivors would often settle down in Siberia where it was still possible to get a free piece of land and return to their farmers' business. Few land reforms, when the government gave away free land and paid for the transportation of peasants, willing to move to Siberia from European part of Russia and Ukraine even more lessened the percentage of real criminals there.
The next few big waves of migration hit Siberia after the Great October Socialist Revolution (1917). First wave consisted of enthusiasts who wanted to built "garden-cities" and develop those vast, rich and empty lands - they came voluntarily. (Parents of my high school teacher were British, who asked for Soviet citizenship and came in Siberia in the 20-th to participate in creation of the "society of tomorrow " .) The second wave arrived in locked railroad cars - farmers that did not want to join collective farms, people of other nations who did not want to join Soviet Union or say farewell to their arms, Cossacks who were little bit of both an d so on. Then came people arrested during purges of the armed forces, industry, Communist party and the police itself. When the World War II crossed the borders of the Soviet Union, a lot of plants and factories from industrially developed Ukraine and Eur o pean part of Russia were relocated to Siberia together with the workers, then there were entire nations, that Stalin did not want to have close to the front line, then there were military establishments that began at a great pace convert huge crowds of citizens into soldiers and hospitals, for those soldiers who were not killed immediately.
After the war there were few more partly successful campaigns whose purpose was to make people, especially professionals and highly qualified workers move from Moscow and other "boring" places to more "romantic" environment.
I'm not saying that real criminals ("socially-close elements" according to official police terminology of Stalin's time) were not brought into Siberia. The conveyer belt of East-Siberian Railway never stopped and neither the court system - criminals were convicted, sent to Siberia, served their terms, went back to their hometowns, celebrated homecoming, were convicted and so on. However, the number of real criminals was relatively small because (a) for variety of reasons real criminals prefer developed central regions, (b) criminal rates were quite low in the "country of victorious socialism" and (c) by that time Siberia was only one of quite a few possible regions where process of "correction of socially unacceptable behavior " went especially well. Kazakhstan, Far East, Northern European regions of Russian Europe - all had their share of correctional institutions. During the periods with normal migration patterns criminals probably could accumulate in Siberia and that would bring their number up but that just could not happen during mass movements of people, like the migration waves described above. All these movements and developments made Siberia what it is now - cities with million plus population and subways, hundreds of miles of barely populated land between them, science centers and, well, correctional facilities.
So, not the number of criminals in Siberia provided this place with the reputation it has. What did? I don't know. It's probably just a tradition.
Another stereotype states that if a foreigner gets in troubles
in Russia he is sent to Siberia "to clean all the snow"
. (BTW, I like that expression a lot. Why? Look here.) The reality is that such a trip is
very unlikely - all foreigners are kept in a special facility
which is located in the Urals region. I'm not saying it's any
better but just to be precise. :)
I guess, the parents of this stereotype are two other stereotypes: