Semiconductor substrates suitable for making thin vertical current conducting devices are made by providing a relatively thick semiconducting substrate with at least one conductivity type having a thickness of from about 100 .mu.m to 700 .mu.m. At least one active device region is optionally first formed on a first side. Then the semiconducting substrate is thinned in at least one selected region on the other side below at least partially where the active device will be on the first side so as to have the selected region thinned to a thickness ranging from about 10 .mu.m to 400 .mu.m to form at least one deep trench. The depth of the thinning of the semiconducting substrate is controlled when the substrate has more than one conductivity type layers or more than one conductivity type layer concentrations so that either (a) some of the first thinned conductivity type layer or some of the first thinned conductivity type layer concentration remains or (b) the thinning proceeds all the way through the first conductivity type layer or all the way through the first conductivity type layer concentration. A conductivity type dopant can be optionally formed in the semiconductor substrate in the thinned selected region on the second side. Finally, a current electrode is formed on the second side in contact with said thinned selected region or said conductivity type dopant in said thinned selected region. In the event the at least one active device region was not initially formed in the first step, then it can be formed at the end.