Band Theory of Semiconductors

 

Band Theory of Semiconductors When atom When atomss come come toge togeth ther er to form form a comp compou ound nd,, th thei eirr atom atom orbi orbita tall ener energi gies es mix mix to fo form rm mole molecu cula larr orbi orbita tall ener energi gies es.. As more more at atom omss be begi gin n to mi mixx an and d more more mole molecu cula larr orbi orbita tals ls are are form formed ed,, it is expe expect cted ed th that at many many of th thes esee en ener ergy gy leve levels ls wil illl star startt to be ver eryy clo close to, to, or even even com complet pletel elyy degen egener erat ate, e, in en ener ergy gy.. The hese se en ener erggy lev levels els are th then en said said to fo form rm bands of energy, as demonstrated in Figure 1.

Figure 1. An extremely oversimplified diagram of a  bandof energy. Z represents one atom with an arbitrary energy level. When more and more Z atoms interact to form a crystal lattice, they all have energy levels that are practically degenerate in energy. Thus, all of these energy levels become a  band, which is reprsented by the energy levels encased by the box.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Band Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Valence Band. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Conduction Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Conduction Fermi Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

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Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Intrinsic Semiconductors Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Extrinsic Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Answers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Outside Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Introduction According to the band theory, semiconductors will actually act as insulators at absolute zero. Above this temperature and yet still staying below the melting point of the solid, the metal would act as a semi semico cond nduc ucto tor. r.Se Semi mico cond nduc ucto tors rs are are clas classi sifi fied ed by th thee full fullyy occu occupi pied ed vale valenc ncee band band an and d unoc unoccu cupi pied ed co cond nduc ucti tion on band band.. Wi With th th thee smal smalll ba band nd ga gap p in be betw twee een n th thes esee two two band bands, s, it take takess a cert certai ain n amou amount nt of en ener ergy gy to exci excite te th thee elec electr tron onss fr from om th thee vale valenc ncee to cond conduc ucti tion on band band.. Thus Thus it foll follow owss th that at th thee hi high gher er th thee temp temper erat atur ure, e, th thee more more co cond nduc ucti tive ve th thee soli solid d wi will ll be.

Band Energy As stated stated previo previousl usly, y, contin continuou uouss  bands of en ener ergy gy are are form formed ed due due to th thee co comb mbin inat atio ions ns of mole molecu cula larr orbi orbita tals ls cl clos osee in ener energgy. Of cou course, rse, due to the mass amount ountss of diffe ifferren entt mole lecu cullar orbi orbittal mixi mixing ngs, s, band bandss of varyin ryingg en ener erggy wil will form. The difference between these band energies is known as the  band gap, as indicated in Figure 2.

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Figure 2. The blue boxes represent the conduction bands while the yellow boxes represent valence bands. The shading of the boxes is indicative of  electron density within the band. (a) band energies of an insulator (b) band energy of a semiconductor (c) band energy of a metal

The band theory looks at the jump of electrons across the band gap. In particular, the jump of electrons from their valence band to their conduction band across their Fermi energy level. This "jump" dictates optical and magnetic properties of the solid. Valence Band

The band of energy where all of the valence electrons reside and are involved in the highest energy molecular orbital. Conduction Band

The The band band en ener ergy gy wher wheree po posi siti tive ve or nega negati tive ve mobile charge carriers exis exist. t. Nega Negati tive ve mobi mobile le ch char arge ge ca carr rrie iers rs are are simp simply ly elec el ectr tron onss that hat had had eno enoug ugh h en ener erggy to es esca cap pe the valen alence ce band band and and ju jump mp to the co cond nduc ucttion ion ban band. Her Here, th they ey move ove free freely ly thro throug ugho hout ut the the crys crysta tall latt lattic icee an and d are are dire direct ctly ly in invo volv lved ed in th thee co cond nduc ucti tivi vity ty of semi semico cond nduc ucto tors rs.. Posi Positi tive ve mobi mobile le char charge ge carr carrie iers rs ar aree al also so re refe ferr rred ed to as holes.  Holes refer to the lack of an electron in the conduction band. In other word wo rds, s, a hole refe referrs to the fact fact th thaat with within in the the ban band the herre is a plac placee whe herre an elec electr troon  can exis existt (i (ie. e. nega negati tive ve mobi mobile le ch char arge ge carr carrie ier) r),, an and d ye yett the the el elec ectr tron on ceas ceases es to exis existt at th that at part partic icul ular ar lo loca cati tion on.. Beca Becaus usee th thee elec electr tron on has has th thee potential to be there and yet isn't there, it is referred to as positive mobile charge carrier.

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Fermi Level

This level refers to the highest occupied molecular orbital at absolute zero. It is usually found at the center between the valence and conduction conduction bands. The particles in this state each have have their own quantum st states ates and generally do do not interact with each other. When the temperature begins to rise above absolute zero, these particles will begin to occupy states above the Fermi level and states below the Fermi level become unoccupied.

Semiconductors Semi emicond conduc ucto torrs are def efin ined ed to ha havve cond conduc ucttivit ivityy in bet between ween an in insu sula lato torr and a co cond nduc ucttor. Due to thi hiss pro prope perrty, ty, se semi mico cond nduc ucto tors rs ar aree ve very ry comm common on in ever everyy day day elec electr tron onic icss si sinc ncee th they ey like likely ly wi will ll not not shor shortt ci circ rcui uitt like like a co cond nduc ucto tor. r. Th They ey get get thei theirr ch char arac acte teri rist stic ic cond conduc ucti tivi vity ty from from th thei eirr smal smalll band band gap. gap. Havi Having ng a band band gap gap pr prev even ents ts shor shortt ci circ rcui uits ts sinc sincee the electrons aren't continuously in the conduction band. A small band gap allows for the solid to have a strong enough flow of electrons from the valence to conduction bands in order to have some conductivity. El Elec ectr tron onss in the the cond conduc ucti tion on band band be beco come me free free from from th thee nucl nuclea earr ch char arge ge of th thee atom atom an and d th thus us ca can n move move fr free eely ly arou around nd th thee band band.. Thus Thus,, this this fr free ee-m -mov ovin ingg elec electr tron on is kn know own n as a negative charge carrier  sinc sincee havi having ng th thee elec electr tron on in th this is ba band nd ca caus uses es el elec ecttrica ricall cond conduc ucttiv ivit ityy of th thee so soli lid d. Whe hen n th thee el elec ectr tron on lea leaves th thee vale valen nce ban band, th thee sta state th then en becom ecomes es a  positive charge carrier, or a hole. Intrinsic Semiconductors

Pure semiconductors in which its properties are solely based off of the material itself. Here, the number of electrons in the conduction band equal the number of holes in the valence band. Theses semiconductors are also known as itypes. Extrinsic Semiconductors

Impure semiconductors that have been "doped" in order to enhance its conductivity. There are two types of  extrinsic semiconductors: p-type and n-type. A "dopant" atom is added to the lattice in order to draw electrons from the valence band. This atom is referred to as an acceptor . As more acceptors are added to the lattice, the number of  holes will begin to exceed the number of negative charge carriers, eventually leading to a p-type (positive type)  donors, "dopant" atoms that donate electrons to the semiconductor. N-type semiconductors semiconductors have a large number of  donors, conduction band.

Problems 1. How does the band gap indicate whether or not your substance is an insulator, semiconductor or conductor? 2. What is the purpose of a p-type semiconductor? An n-type? 3. What is the purpose of understanding band theory?

Answers 1. A very large band gap is indicative of an insulator--since it takes a great deal of energy for the electron to "jump" from the valence band to the conduction band, there will not likely be any conductivity. In conductors (metals) there is zero band gap, therefore the valence and conduction bands overlap. This allows for constant conductivity. Semiconductorss thus have a very small band gap, meaning that their conductivity is in between that of an insulator Semiconductor and conductor. 2. P-type conductors create an abundance of holes while n-types create an abundance of negatively charged carriers (conduction electrons) for the host material. 3. It explains a substance's metallic character (and thus its conductivity).

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Contributors • Mary Mary Mags Magsom ombo boll

References 1. Neamen Neamen,, Do Donal nald d (2006) (2006).. An Introduction to Semiconductor Devices (1st ed.) McGraw-Hill. 2. Housecroft, Cathernie Cathernie E.; Sharpe, Alan Alan G (2008). Inorganic Chemistry Chemistry (3rd ed.) Pearson Education Limited. Limited.

Outside Links • Semiconductors Semiconductors (Wikipedia) • Band Theory of Solids (very good website!) This page page viewe viewed d 9558 times The ChemWiki has 7709 Modules.

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