Exam 2 Study Guide Emphasizes Homeworks 5 through 9 Exam covers assigned sections of Chps. 3,4 & 5. Exam will also assume some basic information from the early part of the semester. It will assume you know the basic information from the earlier part of the semester that is required for this second part of the semesters.. Covers all class notes, starting with QM of a crystalline solid and ending with pn junction. Do all the reading assignments. Read my notes, especially Chps. 5, 6, 7, 8. Be able to solve all the homework problems without your notes. Re-do the derivations we did in class on your own. Equations given: Download formula sheet

Important Concepts on Energy Bands for Crystalline Solids: Including Semconductors Semiconductors and Metals are crystalline solids. Electrons exist only in allowed bands of energy. Bands are composed of many quantum states. Each band has approximately the same number of states as there are atoms in crystal. Bands that are completely filled with electrons cannot conduct electricity In semiconductors, at T=0 o K, all bands are either totally full or totally empty. The band with highest energy that is totally full is call the valence band (VB). The next highest band in energy is the conduction band (CB). In semiconductors there is an energy gap between the valence and conduction bands At T > 0 o T, some electrons obtain enough energy to jump the gap and exist in the conduction band. This process makes the conduction band partially full, and the valence band partially empty. Therefore, both of these bands can conduct at T > 0 o T

Important Concepts on Energy Bands and Conduction for Crystalline Solids: Including Semconductors States in the VB where electrons have left from are now empty. These empty states are called holes. Mathematically, holes act like positively charged electrons and are treated as such. The most popular semiconductor material is Silicon which composes more than 95% of our chips. Pure silicon is also called intrinsic silicon. In 1 cubic cm of intrinsic silicon at room temperature there are about electrons in the conduction band and holes in the valence band. In a metal at room temperature the CB is typically ½ full meaning that there are about conduction electrons/cm 3 Therefore, the conductivity of a metal is approximately greater than that of a semiconductor at 300 o K (recall current density: J=qnv).

Important Concepts on Energy Bands and Conduction for Crystalline Solids: Including Semconductors We usually want to increase and control the conductivity in semiconductors. We achieve this with doping. With doping we substitute impurities for silicon atoms into the lattice that give rise to mobile electron in the CB or mobile holes in the VB. In N-type material, the impurities give rise to electrons in the CB In P-type material, the impurities give rise to holes in the VB. N-type doping works as follows in Si: Silicon has 4 valence electrons. Phosphorous, which has 5 valence electrons, is substituted for a Si atom, leaving one of the 5 electrons essentially unbound. This electron enters the CB and can now be conducting. P-type dopants have 3 valence electrons. They accept electrons from the VB, leaving mobile holes in VB, which can now be conducting. Doping levels in semiconductors typically range from to /cm 3 Adding phosphorous atoms to Si will make it 10 7 times more conductive than intrinsic Si. Doped semiconductors are called extrinsic semiconductors. The fact that we can dope semiconductors to selectively control their conductivity allows for microelectronics to exist as we know it.

Important Concepts on Energy Bands and Conduction for Crystalline Solids: Including Semconductors By studying the band structure (QM states) we understand the doping and conduction possibilities of a semiconductors. The band structure also tells us the instantaneous (group) velocity of an electron (by the slope Vg=(1/hbar)(dE/dk) Band structure tells us effective mass, 1/m* = (1/hbar) 2 (d 2 E/d 2 k), by the curvature of the band near the minium. The effective mass and group velocity help to account for the quantum effects of crystal without having to solve the Schrodinger equation for every application. Mobility is another very important concept in semiconductors. It tells you the average velocity of a conduction electron (or hole) in the presence of an electric field. V avg = mobility x field (mobility = μ= qτ/m*) The mean free time between collisions is τ, which is also obtained using the band structure.

Exam Study Guide General Topics –Generation and Recombination –Drift Current –Diffusion Current –Built-in potential due to non-uniform doping: KNOW HOW TO EXPLAIN HOW BUILT IN POTENTIAL ARISES. –PN Junction in equilibrium, reverse bias and forward bias –Current components in PN junction –Qualitative and quantitative understanding of built in potential and balance of drift and diffusion. –Junction Capacitance and Diffusion Capacitance for a PN junction. –Depletion approximation and calculation of internal electric field and potential as a function of position. –Continuity equation –Derivation of carrier concentrations and current density as function of position in PN junction. –Know difference between minority and majority carriers.

PN Junction A PN junction is a contact between an N-type material and a P-type material. PN junction allows current to flow in one direction and not the other. The 2-terminal device that is made of a single PN junction is a diode. The PN junction structure is found in almost every electronic device (BJTs, MOSFETs, etc.) A PN junction has a built in potential barrier that arises due to non-uniform doping. (which is usually the same thing as saying different Fermi levels).

PN Junction To forward bias a PN junction apply a positive voltage on the P- side and the negative voltage (relatively speaking) on the N-side. When you forward bias a PN junction it reduces the potential barrier (and the built in electric field) and allows mobile electrons and holes to have a net current that is due to diffusion.