Lecture 2. Dopant Compensation
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1 Lecture 2 OUTLINE Bac Semicoductor Phycs (cot d) (cotd) Carrier ad uo PN uctio iodes Electrostatics Caacitace Readig: Chater EE105 Srig 2008 Lecture 1, 2, Slide 1 Prof. Wu, UC Berkeley oat Comesatio N tye semicoductor ca be coverted ito P tye material by couter doig it with accetors such that N > N. comesated semicoductor material has both accetors ad doors. N tye material (N > N ) P tye material (N > N ) N N 2 i N N N N 2 i N N EE105 Srig 2008 Lecture 2, Slide 2 Prof. Wu, UC Berkeley EE105 Fall
2 Tyes of Charge i a Semicoductor Negative charges: Coductio electros (dety ) Ioized accetor atoms (dety N ) Potive charges: Holes (dety ) Ioized door atoms (dety N ) The et charge dety (C/cm 3 ) i a semicoductor is ρ q ( + ) N N EE105 Srig 2008 Lecture 2, Slide 3 Prof. Wu, UC Berkeley Carrier rift The rocess i which charged articles move because of a electric field is called. Charged articles withi a semicoductor move with a average velocity roortioal to the electric field. The roortioality costat is the carrier mobility. Hole velocity Electro velocity h v μ E EE105 Srig 2008 Lecture 2, Slide 4 Prof. Wu, UC Berkeley v e μ E Notatio: μ hole mobility (cm 2 /V s) μ electro mobility (cm 2 /V s) EE105 Fall
3 Velocity Saturatio I reality, carrier velocities saturate at a uer limit, called the saturatio velocity (v sat ). Esat 4 10 V/cm μ0 μ 1+ be μ0 vsat b μ v 0 0E 1+ μ v sat E EE105 Srig 2008 Lecture 2, Slide 5 Prof. Wu, UC Berkeley rift Curret rift curret is roortioal to the carrier velocity ad carrier cocetratio: v h t volume from which all holes cross lae i time t v h t # of holes crosg lae i time t q v h t charge crosg lae i time t qv h charge crosg lae er uit time hole curret Hole curret er uit area (i.e. curret dety), qv h EE105 Srig 2008 Lecture 2, Slide 6 Prof. Wu, UC Berkeley EE105 Fall
4 Coductivity ad Restivity I a semicoductor, both electros ad holes coduct curret: qμ E q ( μ E ), tot, tot,, + Coductivity σ q μ + q μ q( μ + μ ) E σe,, qμ E + qμ E [uit: mho/cm S/cm] Restivity 1 ρ [Uit: Ω-cm] σ Tyical restivity rage for Si: 10 3 ~ 10 3 Ω cm EE105 Srig 2008 Lecture 2, Slide 7 Prof. Wu, UC Berkeley Restivity Examle Estimate the restivity of a Si samle doed with hoshorus to a cocetratio of cm 3 ad boro to a cocetratio of cm 3. The electro mobility ad hole mobility are 800 cm 2 /Vs ad 300 cm 2 /Vs, resectively. EE105 Srig 2008 Lecture 2, Slide 8 Prof. Wu, UC Berkeley EE105 Fall
5 Electrical Restace I + V _ W homogeeously doed samle t L Restace V R I L ρ Wt (Uit: ohms) where ρ is the restivity EE105 Srig 2008 Lecture 2, Slide 9 Prof. Wu, UC Berkeley Carrier iffuo ue to thermally iduced radom motio, mobile articles ted to move from a regio of high cocetratio to a regio of low cocetratio. alogy: ik drolet i water Curret flow due to mobile charge uo is roortioal to the carrier cocetratio gradiet. The roortioality costat is the uo costat. q d EE105 Srig 2008 Lecture 2, Slide 10 Prof. Wu, UC Berkeley Notatio: hole uo costat (cm 2 /s) electro uo costat (cm 2 /s) EE105 Fall
6 iffuo Examles Liear cocetratio rofile costat uo curret x N 1 L No-liear cocetratio rofile varyig uo curret x N ex L d, d q N q L, d q qn x ex L L d d EE105 Srig 2008 Lecture 2, Slide 11 Prof. Wu, UC Berkeley iffuo Curret iffuo curret withi a semicoductor costs of hole ad electro comoets:, tot, d q, d d q( ) q d Thetotal curret flowig i a semicoductor is the sum of curret ad uo curret: tot, +, +, +, EE105 Srig 2008 Lecture 2, Slide 12 Prof. Wu, UC Berkeley EE105 Fall
7 The Eistei Relatio The characteristic costats for ad uo are related: μ kt q Note that (300K) kt q 26mV at room temerature This is ofte referred to as the thermal voltage. EE105 Srig 2008 Lecture 2, Slide 13 Prof. Wu, UC Berkeley The PN uctio iode Whe a P tye semicoductor regio ad a N tye semicoductor regio are i cotact, a PN juctio diode d is formed. V + I EE105 Srig 2008 Lecture 2, Slide 14 Prof. Wu, UC Berkeley EE105 Fall
8 iode Oeratig Regios I order to uderstad the oeratio of a diode, it is ecessary to study its behavior i three oeratio regios: equilibrium, lb reverse bias, ad forward dbias. V 0 V < 0 V > 0 EE105 Srig 2008 Lecture 2, Slide 15 Prof. Wu, UC Berkeley Carrier iffuo across the uctio Because of the erece i hole ad electro cocetratios o each de of the juctio, carriers use across the juctio: Notatio: electro cocetratio o N tye de (cm 3 ) hole cocetratio o N tye de (cm 3 ) hole cocetratio o P tye de (cm 3 ) electro cocetratio o P tye de (cm 3 ) EE105 Srig 2008 Lecture 2, Slide 16 Prof. Wu, UC Berkeley EE105 Fall
9 eletio Regio s coductio electros ad holes use across the juctio, they leave behid ioized doats. Thus, a regio that is deleted of mobile carriers is formed. The charge dety i the deletio regio is ot zero. The carriers which use across the juctio recombie with majority carriers, i.e. they are aihilated. quaeutral regio widthw de quaeutral regio EE105 Srig 2008 Lecture 2, Slide 17 Prof. Wu, UC Berkeley The eletio roximatio -b ρ(x) qn a x I the deletio regio o the N de: de qn ρ Gauss s Law ε ε qn E ε ( x + b) I the deletio regio o the P de: de ρ qn ε ε qn ε -qn E ( a x ) ε F/cm EE105 Srig 2008 Lecture 2, Slide 18 Prof. Wu, UC Berkeley an bn EE105 Fall
10 Potetial istributio I the deletio regio, the electric otetial is quadratic ce the electric field is liear The otetial erece betwee the N ad the P de is called built i otetial, V 0 dv E V E V 0 -b V(x) 0 a x EE105 Srig 2008 Lecture 2, Slide 19 Prof. Wu, UC Berkeley PN uctio i Equilibrium I equilibrium, the ad uo comoets of curret are balaced; therefore the et curret flowig across the juctio is zero.,,,, tot, +, +, +, 0 EE105 Srig 2008 Lecture 2, Slide 20 Prof. Wu, UC Berkeley EE105 Fall
11 Built i Potetial, V 0 Because of the electric field i the deletio regio, there exists a otetial dro across the juctio: d dv d qμe q μ a d μ dv b kt N V ( b ) V ( a ) l l 2 μ q / N ( ) i V 0 kt q N N l 2 EE105 Srig 2008 Lecture 2, Slide 21 Prof. Wu, UC Berkeley i b a (Uit: Volts) Built I Potetial Examle Estimate the built i otetial for PN juctio below. N P N cm -3 N cm kt NN q i ( ) ( ) ( ) V l 26mV l 26mV l 10 kt Note: l(10) 26mV mV q V 60mV mV 0 EE105 Srig 2008 Lecture 2, Slide 22 Prof. Wu, UC Berkeley EE105 Fall
12 PN uctio uder Reverse Bias reverse bias icreases the otetial dro across the juctio. s a result, the magitude of the electric field icreasesad ad the width ofthe deletio regio wides. W 2ε 1 1 de + q + N N ( V V ) 0 R EE105 Srig 2008 Lecture 2, Slide 23 Prof. Wu, UC Berkeley iode Curret uder Reverse Bias I equilibrium, the built i otetial effectively revets carriers from ug across the juctio. Uder reverse bias, the otetial dro across the juctio icreases; therefore, egligible uo curret flows. very small curret flows, limited by the rate at which miority carriers use from the qua eutral regios ito the deletio regio. EE105 Srig 2008 Lecture 2, Slide 24 Prof. Wu, UC Berkeley EE105 Fall
13 PN uctio Caacitace reverse biased PN juctio ca be viewed as a caacitor. The deletio width (W de ) ad hece the juctio caacitace (C j ) varies with V R. C j ε W 2 [F/cm ] de EE105 Srig 2008 Lecture 2, Slide 25 Prof. Wu, UC Berkeley Voltage eedet Caacitace C j C j0 V 1+ V R 0 V C j0 ε q 2 N N N + N 1 V 0 ε F/cm is the ermittivity of lico EE105 Srig 2008 Lecture 2, Slide 26 Prof. Wu, UC Berkeley EE105 Fall
14 Reverse Biased iode licatio very imortat alicatio of a reverse biased PN juctio is i a voltage cotrolled oscillator (VCO), which huses a LC tak. By chagig V R, we ca chage C, which chages the oscillatio frequecy. 1 1 f res 2 2π LC EE105 Srig 2008 Lecture 2, Slide 27 Prof. Wu, UC Berkeley Summary Curret flowig i a semicoductor is comrised of d d ad uo comoets: tot qμ E + qμe + q q regio deleted dof mobile charge exists it at the juctio betwee P tye ad N tye materials. built i otetial dro (V 0 ) across this regio is established by the charge dety rofile; it ooses uo of carriers across the juctio. reverse bias voltage serves to ehace the otetial dro across the deletio regio, resultig i very little () curret flowig across the juctio. The width of the deletio regio (W de ) is a fuctio of the bias voltage (V ). W de 2ε 1 1 q + N N ( V V ) 0 kt N N V 0 l 2 q EE105 Srig 2008 Lecture 2, Slide 28 Prof. Wu, UC Berkeley i EE105 Fall
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