Thank you very much for your help, cora.
I think most compact digital camera can do it if they have micro model (some brand call it macro) function. The shortest minimal distance, the better. Prefer external zoom lens to internal one. The external means you can see the lens move in and out when you run it. Normally the front part of the lens is small and can sit on the eye piece (normally eye piece has an edge slightly higher than central) of the microscope nicely, so you don't need tripod, or even save you an extension tube, even though it's quite easy to make such a tube.
Please refer to this linkage