Introductory Notes, Electrons in Solids

ECE G201, Solid State Devices

McGruer

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Electrons and Quantum Mechanics

• Chapter 1. Electron Energy States in Semiconductors.• Supplement 1A. Introduction to Quantum Mechanics

Text well written – read everything!!

Why “quantum mechanics”? – It is a description of very

small systems, like electrons. Energy is “quantized” – it exists in discrete packets or quanta.

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Big Picture, QM

• For many purposes, the quantum analysis of semiconductors leads to pseudo-classical mechanics, where me me* and then classical mechanics is used. (me* is the effective mass)

• Much of the behavior of semiconductor devices can be understood in this limit, and with a basic understanding of electron energy levels.

• However, many modern devices (nanoscale devices) + many device phenomena are inherently quantum in nature, so at the graduate level, we need at least a basic understanding of the principles of quantum mechanics.

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First, the most important subject in understanding semiconductors and central to quantum mechanics:

Chapter 1, Electron Energy, Electron Energy States in Semiconductors.

Look at Bohr atom (details in the text)•Nucleus very heavy compared with the electron so we assume that the electron orbits around the nucleus. (corrections for this assumption are about 0.1%)

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Concept of potential energy or potential is critical in quantum mechanics.

For two charged particles (assume point charges),

, where q is the charge on an electron.

Force = -gradient of the potential energy.

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20

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44 r

q

r

QQF

Force = - gradient of the potential energy.

Now, integrate both sides.

As electrical engineers, we know that the definition of zeor potential (zero voltage) is arbitrary.

(Are we talking about voltage here???)

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4 r

drqFdrdE

dr

dEEF

P

PP

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