EE105 Fall 015 Microelectroic Devices ad Circuits Prof. Mig C. Wu wu@eecs.berkeley.edu 511 Sutardja Dai Hall (SDH 6-1 Juctio -tye semicoductor i cotact with -tye Basic buildig blocks of semicoductor devices Diodes, Biolar juctio trasistors (BJ, Metal-oide-semicoductor field effect trasistors (MOSFE 6-1
Built-i Voltage At juctio, free electros from -side recombie with free holes from -side. Deletio regio has o electros or holes, but has fied (immobile charges from door ad accetor ios he fied charges establish a electric field, ad create a otetial differece betwee - ad -sides. his otetial is called built-i otetial! = V l A D # & i Eamle: A juctio with V : thermal voltage (= 6 mv at room tem -doig of 10 17 cm 3 ad : accetor cocetratio o -side -doig of 10 18 cm 3 : door cocetratio o -side i : itrisic carrier cocetratio = V l ' = 0.88 V # (=1.5 10 10 cm 3 i & at room tem 6-3 Electric Field Electrostatic Aalysis of Juctio (1 Ema A Charge desity: ( = # A Gauss Law: I oe dimesio: 6-4 E! da!! # = Q, =11.7ε 0 ε 0 = 8.854 10 14 F/cm E(A E( A = A( + E( = 0 (i charge eutral regio, = E( = # ote: ( + ( = (charge euality Maimum electrical field occurs at = 0 (juctio E ma = =
Electric Field Electrostatic Aalysis of Juctio ( E( = # V( = V( = # V( = ( + ( E('d' ( + ( + = ( + ( E ma = W, = A W + + W = e S ' 1 + 1 *, : Deletio Width ( + 6-5 Deletio Width Uder Bias W = e S + 1 # & V ( V is the alied voltage to the juctio, it's ositive for forward bias ad egative for reverse bias. Deletio width is wideed i reverse bias 6-6 3
Curret-Voltage (I-V Characteristics Uder forward bias, miority carriers at the edge of deletio regio is boosted u by (e V /V 1 : ( = 0 + 0 e V /V ( 1 e : hole diffusio legth i -tye Hole diffusio curret desity o -side d J = D ( = 0 e V /V ( 1 d = Similarly, electro diffusio curret desity i -side d J = ( = D 0 e V /V ( 1 d = L otal curret : ( A = A I = J + J I = I S e V /V 1 6-7 # 0 + D 0 L ' ev /V ( 1 & + D # L ' A & ( where I S = A i I-V Curve I = I S e V /V ( 1 where D I S = A i + D # L ' A & 6-8 4
Caacitace i Juctio (1: Deletio Caacitace (Maily Reverse Bias I comarisio, for a liear (ormal caacitor: C = Q V is a costat otal charge Ai deletio width at V = -V R Q J = A = A D W + W = 6-9 e S + 1 # & +V R ( As bias voltage chage, the amout of charge i the juctio chage. his is a oliear caacitor. he caacitace value is C j = dq J dv R = A + C j = A! # & + At zero bias, V R = 0 C j0 = A! # & + e S + 1 # & d dv 1 ( +V R 1 C j0 ote: ( +V R C j = A W herefore at V = -V R, C j = 1+ V R his is a variable caacitor, cotrollable by voltage! Caacitace i Juctio (: Diffusio Caacitace (Forward Bias Etra miority carriers stored outside juctio uder forward bias 6-10 Q = A shaded area uder ( Q = A 0 e V /V ( 1 e L d ( = L Q = A 0 e V /V 1 I = τ I has uit of time, its hysical meaig is miority carrier lifetime: τ = L Similarly, Q = τ I otal charge stored : Q = τ I +τ I = τ I τ is mea trasit time hese stored charges corresod to aother oliear caacitor call diffusio caacitace: ( C d = dq dv = d τ I dv = τ di dv C ' d = τ *,I ( + V 5
Summary of Juctio! Built-i otetial : = V l A D # & i Uder forward bias : ( I-V curve : I = I S e V /V 1! Diffusio caacitace : C d = τ # &I Uder revserse bias : egligible curret, I = I S Deletio caacitace : C j = Other imortat arameter : Deletio Width: W = e S V C j0 1+ V R + 1 # & V ( 6-11 E( = # V( = Detailed Derivatio of Juctio Potetial ( + ( E('d' (1 for :V( = E('d' = ('+ d' = ( '+ '= 6-1 '= = ( + ( for 0 < < : Because E( has differet eressio for < 0 ad > 0, the itegratio should be erformed i two searate rages, first from to 0, ad the from 0 to. We ca use V( = 0 from the above euatio for the first itgratio. herefore, V( = A (' = ' A ( D ( Built-i otetial : 0 d' * D, = + = V( = = (' 0 + D ( D ( + 6