It's not that borrowing money is free, zero interest rates means the government pays zero interest for its loans, not companies. It does put downward pressure on interest rates companies pay but they're still going to have to pay a couple percent apy.

The reason zero interest rates are good for tech is because it forces capital to seek more long-term and risky investments. If I have a lot of money and can get 6% apy from loaning it to the US government, the safest bet on the market, why would I invest in something else? If i can't get any money from loaning to the government (zero interest rates), and i cant get much from loaning it to other institutions because of that downward pressure, then maybe I'll buy some more risky tech stocks because it's possible for that company to grow more then the 1-2% id get from just lending my money. Most of techs financing is done through selling stock, not loans.