Is there a minimum percentage that will produce herd immunity?
Answer from the WHO (mirror):
The percentage of people who need to have antibodies in order to achieve herd immunity against a particular disease varies with each disease. For example, herd immunity against measles requires about 95% of a population to be vaccinated. The remaining 5% will be protected by the fact that measles will not spread among those who are vaccinated. For polio, the threshold is about 80%.
The estimation of the threshold for COVID-19 herd immunity is 70% according to the Mayo Clinic (mirror):
Even if infection with the COVID-19 virus creates long-lasting immunity, a large number of people would have to become infected to reach the herd immunity threshold. Experts estimate that in the U.S., 70% of the population — more than 200 million people — would have to recover from COVID-19 to halt the epidemic.