A true emergency fund is not there to earn money. It's a solid chunk of cash meant to be available with less than 24 hour notice to take care of emergencies. You can't think of it as doing nothing. It's purpose is to remain complete and liquid, which is impossible to guarantee if you invest it in any way due to short term volatility.
The only good way to ensure both quick availability and that the entire amount is going to be there when you need it is to place it in something like a savings account or CDs or other similar no-loss/easy access types of situations.
That being said, an E fund should not be so large as to be a significant portion of your portfolio, as that would be taking a large percentage out of your growth potential. Again, it's there for emergencies, so shoot for having 3-6 months worth of expenses in cash - not years of expenses - since you likely could come up with other, better alternatives given more time.