Liquidity is the speed at which you can convert an asset into spendable cash without material price impact. Restrictions — holding periods, transaction caps, early withdrawal penalties — correlate with yield. Resist trading the emergency fund’s liquidity for yield; the entire premise is access in the week you need it, not the year after.
Rolling investing in US Treasury bills or CDs buys a modest yield improvement without giving up usable liquidity. The standard structure for the stochastic-buffer tier: take a target balance (say $40,000) and buy weekly tranches of 4-week T-bills ($10,000 each, four weeks running) with auto-roll on. In a slow-burn emergency, switch off auto-roll and harvest $10,000 per week. In a fast emergency, sell the lot in the secondary market and absorb a few basis points of bid-ask. Mechanics and CD variants are detailed at section “Laddering and Rolling Strategies”.