1. A 2D analog to a quantum well device has a length much longer than its width. Assume a 2D crystal with a length of 100 nm and width of 1 nm. Assume there are just enough electrons to begin to fill the first excited-state corresponding to the 1 nm direction. 100 a. What is the Fermi energy? b. How many electrons are in the device? C. What is the density of states (in energy units) just below and just above this level? Hint: All the equations needed are in the picture below. Assume the angle q is small. d. Based on this information, sketch the approximate density of states vs energy for energies that extend up to several excited states corresponding to the 1 nm direction. dk/ [Sin (0)] 80 60 k kw W = k Cos (0) 40 20 dk 20 40 60 80 100