Fall-2003 PH-31 A. La Rosa JUNCTIONS I. HARNESSING ELECTRICAL CONDUCTIVITY IN SEMICONDUCTOR MATERIALS Itrisic coductivity (Pure silico) Extrisic coductivity (Silico doed with selected differet atoms) II. ENERGY LEVELS DIAGRAM -material, -material Diode: ad materials laced together III. CHEMICAL POTENTIAL (FERMI LEVEL) IV. COMPARISON of CHARGE-CARRIER POPULATION at EACH SIDE of the JUNCTION V. FORWARD BIAS, REVERSE BIAS I. HARNESSING ELECTRICAL CONDUCTIVITY IN SEMICONDUCTOR MATERIALS Let s take Silico as a yical examle of semicoductor material. A Silico atom has valece electros. Joied by covalet bods, Si atoms form a lattice structure costituted by two itereetratig eriodic fcc lattices, havig 5x10 22 Si-atoms/cm 3 (8 atoms i a cube of side 5.3 Agstros). At zero temerature Silico is a isulator because all its valece electros articiate i the bodig. It lacks electros that ca wader free aroud the crystal structure. At T=0, coductivity σ= 0. At T = 0 K Si: [Ne]3s 2 3 2 Itrisic coductivity Here we cosider a Si material free of foreig atoms (just ure silico atoms). Thermal geeratio of coductio electros At room temerature (kt ~ 0.025 ev), thermal agitatio of the crystallie host rovides eergy to electros ad there is a o-vaishig robability (~ e -Eg/2kT ) that some of them will be able to break away from the (E g =1.12 ev) bodig ad, At T = 300 K Hole Free electro
cosequetly, set almost free to wader aroud the crystal: they become coductio electros. These electros are able to articiate i the coductivity of silico uder the resece of a exteral electric field. A tyical value of the cocetratio of coductio electros geerated i this maer, at room temerature, is o ~1.x10 10 e - /cm 3. Geeratio of holes Notice that the creatio of a ew coductio electro leaves their Si atoms with oe bodig vacacy. This bodig vacacy is called a hole. Holes cotribute to the coductivity. Ideed, uder the resece of a exteral electric field, a boded electro from a Si atom earby will have a tedecy to filli this bodig vacacy (the fact that the Si atom hostig the hole is a ositive io hels the rocess) ad eeds very little eergy to do that. Whe that haes a ew hole (with its associated ositive io) is left behid, which triggers the creatio of aother hole, ad so o. The et result: a et ositive charge is trasorted alog the fillig of holes. Sice a hole is created simultaeously with a coductio electro, the cocetratio of holes o equals the cocetratio of electros: o = o. This situatio could be chaged if selected foreiger atoms are itroduced i the silico crystallie structure. Extrisic coductivity -tye: Si crystal doed with door atoms (5 e - i their valece shell). Four e - articiate i the bodig with Si atoms, while the fifth becomes almost free of ay bodig. With a little bit of eergy this fifth e- becomes free to wader aroud the etire silico material. Examle of doig level: 10 16 arseic atoms/cm 3. -tye: Si doed with accetors 3 Hole Accetors Doors atoms (3 valece e - ). (Boro 5 Free electro atoms, for examle). The three e - articiate i the bodig with Si atoms, creatig a bod vacacy to be filled-i, that is, accetor atoms create holes, which articiate i the coductivity (as exlaied above). So, the resece of doors ad accetors icreases the electrical coductivity of the material.
II. ENERGY LEVELS DIAGRAM Silico ENERGY LEVELS DIAGRAM Eergy (electros) Coductio bad E g Badga Valece bad Forbidde levels Eergy levels available to be occuied by electros -material ad -material -material -material ENERGY LEVELS DIAGRAM Eergy (electros) + + + + door atoms accetors atoms - - - - e - e - x Electrically eutral material Electrically eutral material Materials laced together Eergy (electros) N A accetors - - - - - - Electrically eutral regio Charged regio = (x) + + + + + + + + + - - + + + + + + + + + N D doors/cm 3 regio Built-i electric field Case: N A > N D Deletio regio Electrically eutral Whe the ad samles are laced together, electros ad holes diffuse ad recombie, leavig behid ubalaced egative ad ositive regios that ed u costitutig what is called the deletio regio.
III. CHEMICAL POTENTIAL (FERMI LEVEL) At temerature T, semicoductor materials are characterized by their Chemical Potetial, a eergy level located somewhere i the bad-ga; its exact locatio deedig o the doig (accetors ad doors) cocetratios. Eergy (e - ) Chemical otetial Chemical otetial Eergy (e - ) - - + - + ε + i Built-i iteral electric field = (x) Electrostatic otetial Eergy of e - Fermi level Whe the materials are joied, electros diffuse from to (leavig behid ubalaced ositive door ios) ad recombie with hole i the regio (thus creatig egative accetor ios. holes diffuse from to. While diffusio takes lace, a electric filed build-u that ooses the diffusio rocess. Whe equilibrium is reached a sigle Fermi level characterizes the whole system (the - juctio). ev o V o ε = 0 ε = 0
IV. Comariso of charge-carrier oulatio at each side of the juctio : cocetratio of e - i the -side : cocetratio of e - i the -side : cocetratio of holes i the -side : cocetratio of holes i the -side The sub-idex 0 stads for values whe the system is i equilibrium Eergy - f o e V o o (-side)= o (-side) = o e - carrier desity oulatio -regio -regio Similarly: From thermodyamics cosideratios: o = o e - q Vo/kT 1 Electrostatic otetial o ε o (-side) = o V o P o (-side) = o -regio -regio hole + carrier desity oulatio From thermodyamics cosideratios: o = o e -qvo/kt 2 From 1 ad 2 :
o o = o o 3 I other words: o o (-side) = o o (-side) Miority ad majority carriers : cocetratio of holes i the -side : cocetratio of holes i the -side The sub-idex 0 stads for values whe the system is i equilibrium majority carriers o o miority carriers (x) Electrostatic otetial o From thermodyamics cosideratios: V o o = o e -q Vo/kT o -regio -regio
Forward bias + - Eergy of e - ε f Eergy of e - e V o e (V o ) Reverse bias V R + - Eergy of e - ε R Eergy of e - V R V R e V o V R e (V o +V R )
Origi of the drift curret I o + - ε f Eergy of e - Drift of thermally geerated electros Thermally geerated e-h airs Thermally geerated e-h airs Drift of thermally geerated holes I o Electros thermally geerated ear the juctio are swet by the iteral electric field that exists across the juctio. Similar situatio haes to the thermally geerated holes. The drift mechaism illustrated i the figure above costitute the origi of the uavoidable drift curret I 0. Notice, the electros ad hole will be swet by whatever electric field is reset across the juctio, regardless of the actual value of ε. That is, the rate of charges crossig the juctio is somehow ideedet of the forward or reverse bias voltages. Oce they are geerated earby the juctio, ay electric field will swee them across. Thus, I 0 deeds oly o how fast are the e-h airs geerated, which is iflueced by the badga E g ad temerature.
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