## Write down the Schrodinger equation as the – (i) Electron trapped in 2D plane nanosheet (ii) Electron moving ill one-dimension/ nanowire.

** Ans. (i) Electron Trapped in 2D Plane Nanosheet –** When carriers are confined in one dimension, i.e., along-direction to a very small thickness t, and free to move along X and Y -direction. In nanophysics, it is the case of nanosheets where carriers are allowed to move along a two-dimensional plane (see fig. 1.37). X In this case, the modification of wave function and energy will be given by-

where, the quantum number n2 is called the sub-band index and for n = 1 the

carrier is assumed to be in the first sub-band.

* *

* (ii) *

*Electron Moving in One dimensional Nanowire**–*In nanowire, carriers are confined in both directions (say, Y and Z) to small dimension, t(assuming square crosssection, t2) and allowed to move freely along the’ length of x-axis, as shown in fig. I .38. In this case, the wave function and the energy will respectively be-

In nanophysics, motion of carriers in carbon nanotubes or similar kind of

nanowires can qualitatively be treated by the above equation, although the

actual bound states and energy expressions are more involved and compacted