Who can borrow from the ECB? 

Monetary science behind low central rates according to Euro is that with such a large population base having adopted Euro and such a small supply compared to dollars, these negative rates keep people from saving too much cash in the bank and driving up the euro exchange rate which would make exports less competitive. It is a trick to balancing conservativism in the financial system. If they would follow America's lead they would get the shaft, they could raise rates and people would save more, the euro would appreciate and governments would compensate by increasing spending, then the euro system would be hooked on a export defecit like the USA.