ECE Purdue Semiconductor Fundamentals L2.5: Quantum Mechanics - Density of States

This video is part of the course "Semiconductor Fundamentals" taught by Mark Lundstrom at Purdue University. The course can be found on nanoHUB.org at nanohub.org/courses/sfun or on edX at www.edx.org/course/semiconduc... .
This course provides the essential foundations required to understand the operation of semiconductor devices such as transistors, diodes, solar cells, light-emitting devices, and more. The material will primarily appeal to electrical engineering students whose interests are in applications of semiconductor devices in circuits and systems. The treatment is physical and intuitive, and not heavily mathematical.
Technology users will gain an understanding of the semiconductor physics that is the basis for devices. Semiconductor technology developers may find it a useful starting point for diving deeper into condensed matter physics, statistical mechanics, thermodynamics, and materials science. The course presents an electrical engineering perspective on semiconductors, but those in other fields may find it a useful introduction to the approach that has guided the development of semiconductor technology for the past 50+ years.

[@DW-iq8lt]

0:41 States within bands, 1:12 Density of states, 2:03 States in a finite volume of semiconductor, 9:00 Density of states in k-Space vs in Energy Space, 10:44 Parabolic band example 1: DOS for 1D nanowire, 14:55 Parabolic band example 2: DOS for 2D electrons, 17:28 Parabolic band example 3: DOS for 3D electrons, 18:58 Ellipsoidal band and valley degeneracy, 20:55 Comments on 3D DOS, 21:48 Graphs of DOS vs E in 1D/2D/3D.

[@chevestong]

Same timestamps but line-broken:
0:41 - States within bands
1:12 - Density of states
2:03 - States in a finite volume of semiconductor
9:00 - Density of states in k-Space vs in Energy Space
10:44 - Parabolic band example 1: DOS for 1D nanowire
14:55 - Parabolic band example 2: DOS for 2D electrons
17:28 - Parabolic band example 3: DOS for 3D electrons
18:58 - Ellipsoidal band and valley degeneracy
20:55 - Comments on 3D DOS
21:48 - Graphs of DOS vs E in 1D/2D/3D

[@wenhuihou3592]

On silde 14, the expression of dE should not have the En term.

[@chevestong]

At 14:30, why does the DOS approach infinity as we get closer to the bottom of the subband? I understand mathematically why (I see that E - E_j tends towards 0 in the equation) but, intuitively speaking, wouldn't the density of states converge at a numerical value? Or am I missing something here? Does it approach infinity because of the constant carrier generation/recombination that occurs at/by the bottom of the conduction band?

[@JustinCase-wy1wm]

The answer is on slide 7: since N(k)dk is constant, and dE goes to zero at the minimum of the parabola, D(E) must go to infinity.

[@jasonr.7887]

"Now I'm gonna drop the prime"

[@saye-zx3uy]

What about DOS of quantum dots?