Intel manufactured its 1-kilobit 1103 RAM on an 8 μm P-MOS process.
Through most of the 1970s, DRAM was made from NMOS. The first successful CMOS memory was the Hitachi HM6147 SRAM, a 4-kilobit chip which used a 3 μm CMOS process. This was not the first 4-kb chip on the market (it was preceded by, among others, the Intel 2114 SRAM), but it’s more comparable to the CMOS DRAMs that followed it.
The first 16K RAM chip was the Intel 2116, circa 1976, and the market leader was the MOSTEK 4116, introduced circa 1977. Unfortunately, I don’t have a reference for their feature size at hand, but NMOS memories of the sizes you’re asking about would have used a process somewhere in the neighborhood of 6 micron, between the 8 micron process of the 1K RAM and the 5 micron process of the 64K RAM. There were other innovations in process technology beyond shrinking the feature size, particularly in the 4116.
MOSTEK’s 1979 databook said,
At MOSTEK, all new products are being designed to work on either current process technology (5 microns) or new generation SCALED POLY 5. To accomplish this goal all new products are designed to operate on a single 5 volt power supply. All products use advanced state-of-the-art design techniques and perform very respectably on the standard process.
MOSTEK was then selling 64-kibibit DRAM, the MK4164, apparently on an advanced 5-micron process.
I found a claim that NEC introduced 64-kilobit RAM on a 1.5 μm process in 1981, but not a reliable reference for it so far.
From that point onward, when an apples-to-apples comparison becomes possible, this site is an excellent resource. It describes the state of the industry in 1983 as:
256Kb development is at a maturing stage. NMOS 256Kb by Fujitsu with 2.5um NMOS triple poly process, 256Kb by NEC on 1.3um double poly process, 256Kb by Mitsubishi on 2um process, 256Kb by Motorola, 256Kb by Toshiba with 2um double poly process. Intel shows off industry-first CMOS DRAM with 64Kb on 1.2um process.
There was a leap to 1 megabit DRAM in 1984, using a 1 μm CMOS process.
4-megabit DRAM appeared in 1987, using an 800 nm process.
16-megabit DRAM appeared experimentally in 1988, and became mainstream in 1989 on a 500–600 nm process.
64-megabit DRAM became mainstream in 1991 on a 400 nm process.