Electrical conductivity in solids. Electronics and Microelectronics AE4B34EM. Splitting of discrete levels (Si) Covalent bond. Chemical Atomic bonds

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1 Electrical coductivity i solids Eergy bad structure lico atoms (the most commo semicoductor material) Electroics ad Microelectroics AE4B34EM 3. lecture Semicoductors N juctio Diodes Electros otetial eergy of the sigle silico atom Vacuum level The eistece of the well is give electrostatic force (Coulomb law) otetial eergy Bidig eergy Distace from atom ceter Discrete levels Atom Nucleus Slittig of discrete levels i the crystal Crystallie lattice a arragemet that is reeated eriodically It has the shortest distace betwee atoms lattice costat auli eclusio ricile: o two electros i its crystal ca eist i the same quatum state Therefore, the origial discrete levels will slit The real umber of layers deeds o the umber of atoms i a crystal For m 3 otetial eergy Distace from atom ceter Slittig of discrete levels () Eergy levels are for more atoms very close. We reflect these levels as so called eergy bad Four electros from each atom at highest levels forms valece electros Valece electros are furthers from the ucleus They forms mutual atoms relatio ad roerties of materials Bad ga the ga betwee the last occuied ad uoccuied bad atom crystal Bad ga Chemical Atomic bods Metalic bod electros bodig are delocalized over a lattice of atoms electro gas Ioic bod bodig electro is ot shared at all, but trasferred. I this tye of bod, the outer atomic orbital of oe atom has a vacacy which allows additio of oe or more electros Covalet bod oe or more electros (ofte a air of electros) are draw ito the sace betwee the two atomic uclei (oe from each atom) with oosite si At least a artial covalet bod is eeded for semicoductors Each atom has four valece electros Covalet bod Coductio bad E g Bad ga Valece bad Metal io Electro gas At low temerature At higher temerature Electrohole air At higher temerature electrohole air is cereated i bed structure diagram

2 Why silico is so oular? Křemík uvitř mookrystalu Easily accessible the secod most commo elemet i the Earth's crust Facecetered cubic structure Each silico atom has four eighbors with with covalet boud 28, ,33 g/cm 3 lico Why is silico so oular? Cheaest rearatio of highly ure silico Eistece of thermal oide laar Techology Relatively high resistivity of itrisic silico 23 kw Moocrystallie ad amorhous Crystallograhic defects Vacacy Moocrystallie Amorhous Iterstitial defect Frekel air Fermi level WF The Fermi Dirac distributio fuctio f FD gives the robability that a siglearticle state of eergy E would be occuied by a electro (at thermodyamic equilibrium) f FD (W F ) = 0,5 ecited electro Fermi level for two materials If we ut together two materials with differet Fermi level ositio, the level will comesate ad so called thermodyamic equilibrium is set Electros of coected material is demadig to get miimum Eergy Electros move to miimum eergy This will be imortat to elai the N juctio!

3 Electro eergy Isulators, metals, semicoductors Electric coductivity i solid states Bad ga width is crucial for the value of electrical coductivity Isulator Semicoductor Metal r resistivity: r = 1 / s r = W.cm r = W.cm r = W.cm Isulators: The magitude of the bad ga determies the differeces betwee isulators, semicoductors ad metals. The thermal ecitatio mechaism is ot a useful way to romote a electro to CB. Eve whe the meltig temerature is reached i a isulator. Eve very high electric fields is also uable to ecite electros across the bad ga i a isulator. CB (comletely emty) Eg > several electro volts VB (comletely full) Wide bad ga betwee VB ad CB Metals: Semicoductor eergy bads CB VB CB VB These two bads are artly filled. artly filled bads coducts well. This is the reaso why metals have high coductivity. Bad ga (Forbidde eergy ga) [Eg] Emty coductio bad At low temeratures the valace bad is full, ad the coductio bad is emty, they behave like isulators. The thermal eergy of the electros sittig at the to of the full bad is much lower tha that of the Eg at low temeratures. Touchig VB ad CB Overlaig VB ad CB No ga betwee valace bad ad coductio bad Full valace bad Semicoductor eergy bads Ecitatio mechaisms causig a e trasitio from the to of the valace bad (VB) to the bottom of the coductio bad (CB) eergy artially occuied coductio bad Forbidde eergy ga [Eg] e e e e artially occuied valace bad At higher temerature eough eergy is sulied to the e sittig at the to of the valace bad, e ca make a trasitio to the bottom of the coductio bad. Whe electro makes such a trasitio it leaves behid a missig electro state. This missig electro state is called as a hole. Hole behaves as a ositive charge carrier. Thermal eergy Thermal eergy = k. T = J/K 300 K =25 mev Ecitatio rate is roortioal to e(eg / kt) Electrical field For low fields, this mechaism does t romote electros to the CB i commo s/c s such as ad GaAs. A electric field of V/m ca rovide a eergy of the order of 1 ev. This field is eormous. Electromagetic radiatio c E h h ( J s) (310 m / s) / ( m) E( ev ) (i m) Eg artly filled CB artly filled VB Near ifrared h = Js c = m/s 1 ev= J 1.24 for lico Eg 1.1 ev ( m) 1.1m 1.1

4 Electro Cocetratio Hole Cocetratio Coclusios Holes cotribute to curret i valace bad (VB) as electros i coductio bad (CB). Hole is ot a free article. It ca oly eist withi the crystal. A hole is simly a vacat electro state. A trasitio results a equal umber of electros i CB ad holes i VB. This is a imortat roerty of itrisic, or udoed semicoductors. For etrisic, or doed, semicoductors this is o loger true. The drift velocity ad mobility At zero temerature, the free electro seed is relatig to thermal lattice vibratios (o electric field) If electric field is alied across a material, the drift velocity of electros ca be described by to the formula: v d =.E Electro ad hole coductivity Holes moves i the valece bad, electros i the coductio bad Holes movemet i the crystal lattice of the semicoductor Diffusio curret i semicoductors articles (electros, holes) are movig from areas of high cocetratios to a regio of low cocetratios. Diffusio curret is formed Hole movemet Hole movemet Electro movemet Hole movemet Diffusio curret desity of electros Diffusio curret desity of holes Electro movemet Electro movemet Doed (etrisic) Semicoductor Itrisic cocetratio of free carriers (electros, holes) is costat i the semicoductor at a give temerature Geeratio ad recombiatio rocess of electrohole airs is cotiuous rocess i semicoductors Electroic comoets Creatig of N juctio What is it good for? Geeratio of electrohole airs Recombiatio of electrohole airs The desig of electroic comoets eed various layers with differet cocetratios of electros ad holes We do this by imurity doig semicoductors

5 Doats Ntye semicoductor Semicoductor coductivity may easily be modified by itroducig imurities (Boro, hoshorus, Arse) ito their crystal lattice. The rocess of addig cotrolled imurities to a semicoductor is kow as doig. Tye of coductivity (ositive) 10,81 5B Boro Tye of coductivity N (Negativí) 30, hoshorus 74, As Doig by doors (elemet of the fifth grou, As) Majority carriers electros Miority carriers holes 5 Fied ositive io 5 Free electro E Di tye tye semicoductor Doig by accetors (elemet of the third grou B) Majority carriers holes Miority carriers electros Free electro tys N Juctio B 3 B 3 E Ai Fied egative io ioized accetors The N Juctio Metallurgical Juctio Na Nd Sace Charge Regio EField Electro Movemet h drift = h diffusio e diffusio = e drift ioized doors ioized accetors Na Metallurgical Juctio Sace Charge Regio EField Nd = = h drift h diffusio e diffusio e drift The N Juctio ioized doors Whe o eteral source is coected to the juctio, diffusio ad drift curret balace each other. Deletio regio icludes the ositively ad egatively charged regios. The sace charge regio does ot have ay free carriers. The width of the sace charge regio is roortioal to doat cocetratio. Metallurgical Juctio: The iterface where the ad tye materials meet Na & Nd: Rereset the amout of egative ad ositive doig i umber of carriers er cetimeter cubed. Usually i the rage of to 10 20

6 oteciál otetial Electric field Charge desity Charge desity Eergy level diagram for the juctio beforre thermal equilibrium Eergy level diagram for the juctio i thermal equilibrium Tye Tye N tye tye Electro Drift Electro Diffusio Neutral regio Tye Tye N Hole Diffussio Neutral regio Deletio regio Hole Drift Deletio Aroimatio, Electric Field ad otetial for juctio Abrut juctio tye E m tye qv bi area V bi At equilibrium, there is o bias, i.e. o alied voltage. The field takes the same sig as the charge The sig of the electric field is oosite to that of the otetial ; E v dv d tye Deletio Regio w whe N A tye N D The amout of ucovered egative charge o the left had side of the juctio must be equal to the amout of ositive charge o the right had side. Overall sacecharge eutrality coditio: N N A D The higher doed side of the juctio has the arrower deletio width Deletio Jiří Jakoveko Regio Electroics ad Microelectroics Deartmet of Microelectroics CTU Biased N juctio Forward bias: V > 0 Metal Cotact Ohmic Cotact (Rs~0) I Alied Electric Field The juctio is cosidered biased whe a eteral voltage is alied. There are two tyes of biasig: Forward bias ad Reverse bias. V alied Forward bias is formed by a ositive voltage o the aode Eteral voltage act agaist the barrier voltage. It results decreasig of otetial barrier. Vbi V. Deletio regio shriks. Holes i the valece bad of will drift to the N juctio. They ca overcome lower otetial barriers. The result is the ijectio of holes ito the N Holes i N become miority carriers ad recombie with majority electros Aalogical trasort rocess take lace i coductio bad with electros i the oosite directio. Equilibrium (zero bias) qv bi V bi Forward bias qvbi V Vbi V

7 oteciál otetial Eergy Reverse bias is formed by a egative voltage o the aode Eteral voltage act alog with the barrier voltage. It results icreasig of otetial barrier. Vbi V. Deletio regio shriks. Holes i the valece bad of ca ot drift to the N juctio. They ca ot overcome high otetial barriers. Mior holes i N, however, ca overcome the N juctio ad are etracted by regio The cocetratio of the holes i N is very small, ad the resultig curret will be small At room temerature the curret is ractically zero Aalogical rocess ca be described for mior electros i the oosite directio. Reverse bias: V < 0 Equilibrium (zero bias) qv bi V bi Reverse bias qvbi Vr V V bi R Aliyig bias to juctio Zero Bias Forward Bias Reverse Bias E q qv V bi V F c bi E v V bi Vbi V F qvbi Vr Vbi V R roerties of Diodes Ideal diode equatio V BR I S Reverse biased I D (ma) (A) Forward biased ~V V D V D = Bias Voltage I D = Curret through Diode. I D is Negative for Reverse Bias ad ositive for Forward Bias I S = Reverse Saturatio Curret V BR = Breakdow Voltage V = Barrier otetial Voltage D o D o qv qv JTotal q e 1 Jo e 1 L L kt kt multilyig by area ; qv I Io e 1 kt Ideal diode equatio Shockley equatio This equatio is valid for both forward ad reverse biases; just chage the sig of V.