The semiconductor channels 2022A-B and 2032A-B have a varying width that decrease along the first portion 1900A and increase along the second portion 1900B with increasing height in the Z-direction. The widths of the semiconductor channel segments 2022A-B and 2032A-B are defined as W1 at the top of the semiconductor device 500, W2 at the bottom of the semiconductor device 500 near the substrate, and W3 at the point of the semiconductor device in between the first portion 1900A and the second portion 1900B. In some embodiments, both W1 and W2 are greater than W3 as shown in FIG. 19B. In some embodiments, W1 is equal to W2. The varying width of the semiconductor channel segments 2022A-B and 2032A-B are designed to keep cell current constant with varying channel lengths. The length of the word lines 1902 in the Y-direction, Ly1, Ly2, and Ly3, result from the formation of the trenches. These lengths do not affect the channel lengths Lx1, Lx2, and Lx3 shown in FIG. 19A.
FIGS. 20A-B illustrate plots of semiconductor channel thickness versus channel length and cell current versus channel length that correspond to the embodiment of the semiconductor device 500 shown in FIGS. 19A-B.