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.
Make sure to be diligent in checking the terms for that LOC. Many banks reserve the right to cancel it if there's substantial change in your financial situation, e.g. if you were to lose your job.
Make sure your emergency fund remains accessible if you get into an emergency.
Lines of credit can be revoked immediately. I have family members who relied on a line of credit only to have the limit dropped and the interest rate hiked by 10%.
The low yield on the emergency cash laying in a checking account is to compensate for its liquidity.
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.