Depending on how often you expect to need an emergency fund and what the relevant interest rates are for illiquid saving (eg: paying down student loan debt) and unsecured borrowing, it may make more sense to have your emergency fund in an unsecured line of credit or credit cards.
Example with made-up numbers: Suppose you spend $2000/mo, you have an unused line of credit of $10000 @ 10%, your student loans are at 5%, and you are taking home $4000/mo. If you have an emergency that costs $2000 that hits your line of credit, that ends up roughly being an extra month servicing $2000 of debt at 10% instead of 5%. If you keep $2000 in cash instead of paying down student loan debt, that ends up meaning you service $2000 of debt at 5% instead of paying it down. These are roughly the same thing, so you wind up ahead if the LoC is sitting empty ~50% of the time.
Granted, these are much more favorable numbers than typical use of credit card debt, but the point remains - if you have access to credit on good terms, and you won't need it often, and you have good illiquid returns on excess cash, you ought to take a look at using credit to handle emergencies instead of cash.