The Sinclair ZX80 and ZX81 have static RAM internally, which you wouldn't expect for a) a computer that's designed to be as cheap as possible and b) uses a Zilog Z80 which has built-in refresh circuitry.

The reason is that the designers saved a few chips by repurposing the Z80's refresh circuit as a counter/address generator, when generating the video signal. Specifically, it uses the instruction fetch cycle to read the character code from RAM, then it uses the refresh cycle to read the actual line of character data from the ROM. The ZX80 nominally clocks the Z80 at 3.25MHz, but a machine cycle is four clocks (two for fetch, two for refresh), so it's effectively the same speed as a 0.8125 MHz 6502.

I wrote a long section here about how the ZX80 uses the CPU to generate the screen and the extra logic that involves, but it was getting too long :) The ZX81 is basically just a cost-reduced ZX80 where all the discrete logic chips are moved into one semi-custom chip.

Doing this makes external RAM packs more expensive too. You couldn't use the real refresh address coming from the Z80 because the video generator would be hopping around a small range of addresses in the ROM, rather than covering the whole of RAM (or at least each row of the DRAM). The designer has two options:

1. Use static RAM in the external RAM pack, making it substantially more expensive for the RAM itself; 2. Use DRAM in the external RAM pack, and add extra refresh circuitry to refresh the DRAM when the main computer is using the refresh cycle doing its video madness.

I think most RAM packs did the second option.