EEE 531: Semiconductor Device Theory I Instructor: Dragica Vasileska Department of Electrical Engineering Arizona State University Bipolar Junction Transistor EEE 531: Semiconductor Device Theory I Outline 1. Introduction 2. IV Characteristics of a BJT 3. Breakdown in BJT 4. Geometry Effects in BJT EEE 531: Semiconductor Device Theory I 1. Introduction Original point-contact transistor Inventors of the transistor: (1947) William Shockley, John Bardeen and Walter Brattain First grown transistor (1950) EEE 531: Semiconductor Device Theory I (A) Terminology and symbols PNP - transistor NPN - transistor E C E C B B E p+ n p C E n+ p n C + + V V V V EB CB BE + + BC B B • Both, pnp and npn transistors can be thought as two very closely spaced pn-junctions. • The base must be small to allow interaction between the two pn-junctions. EEE 531: Semiconductor Device Theory I • There are four regions of operation of a BJT transistor (example for a pnp BJT): V EB Forward active region Saturation region (emitter-base FB, collector-base RB) (both junctions forward biased) V CB Cutoff region Inverted active region (both junctions reverse biased) (emitter-base RB, collector-base FB) • Since it has three leads, there are three possible amplifier types: C E p p+ B B E C n V n V p+ n p EC EC V p+ V p V EB CB EB V B CB E C (a) Common-base (b) Common-emitter (c) Common-collector EEE 531: Semiconductor Device Theory I (B) Qualitative description of transistor operation p+ n p • Emitter doping is much larger than I { I Ep Cp base doping • Base doping larger than collector I I En Cn doping • Current components: I I B1 B3 I E I Ep I En I I B2 cn I I I I C Cp Cn E En C I B I E IC I B1 I B2 I B3 • I = current from electrons being bBa1ck injected into the forward-biased E emiter-base junction F E V • I = current due to electrons that reBp2lace the recombined electrons in the base • I = collector current due to I B3 I Cp thermally-generated electrons in the Ep collector that go in the base EEE 531: Semiconductor Device Theory I (C) Circuit definitions Base transport factor : T T ICp / I Ep Ideally it would be equal to unity (recombination in the base reduces its value) Emitter injection efficiency : I I Ep Ep Approaches unity if emitter doping is ICp I Ep I E much larger than base doping Alpha-dc: I I I IC Cp Cn Cp dc T I E I Ep I En I Ep I En Beta-dc: I I C C dc Current gain is large when dc I I I 1 dc B E C dc approaches unity EEE 531: Semiconductor Device Theory I Collector-reverse saturation current: I BC0 ICn IC ICp ICn dc I E I BC0 Collector current in common-emitter configuration: I dc BC0 IC dc IC I B I BC0 IC I B 1 dc 1 dc IC dc I B I EC0 I EC0 1 dc I BC0 Large current gain capability: Small base current I forces the E-B junction to be forward B biased and inject large number of holes which travel through the base to the collector. EEE 531: Semiconductor Device Theory I (D) Types of transistors Base • Discrete (double-diffused) Emitter p+np transistor 5 m 200 m Collector • Integrated-circuit n+pn transistor 6 m 200 m EEE 531: Semiconductor Device Theory I 2. IV-Characteristics of a BJT (A) General Considerations • Approximations made for derivation of the ideal IV-characteristics of a BJT: (1) no recombination in the base quasi-neutral region (2) no generation-recombination in the E-B and C-B depletion regions (3) one-dimensional current flow (4) no external sources • Notation: p+ n p N = N N = N N = N AE E DB B AC C L = L L = L L = L n E p B n C D = D D = D D = D n E p B n C n = n p = p n = n p0 E0 n0 B0 p0 C0 = = = n E p B n C EEE 531: Semiconductor Device Theory I • The carrier concentration variation for various regions of operation is shown below: E-B C-B p (0) B saturation n (0’) C n (0”) E p (W) B Forward p (x) n (x’) B C n (x”) active n E p C0 n B0 E0 p (W) x” B x’ 0” 0 Cut-off W 0’ • Assuming long emitter and collector regions, the solutions of the minority electrons continuity equation in the emitter and collector are of the form: VEB /VT x"/ LE nE (x") nE0 e 1 e VCB /VT x'/ LC nC (x') nC0 e 1 e EEE 531: Semiconductor Device Theory I • For the base region, the steady-state solution of the continuity equation for minority holes, of the form: d 2p p B B 0 2 2 dx LB using the boundary conditions: VEB /VT VCB /VT pB (0) pB0 e 1, pB (W ) pB0 e 1 is given by: sinh(W x) / L V /V p (x) p B e EB T 1 B B0 sinh W / LB sinhx / L V /V p B e CB T 1 B0 sinh W / LB Note: The presence of the sinh() terms means that recombination in the base quasi-neutral region is allowed. EEE 531: Semiconductor Device Theory I • Once we have the variation of n (x”), p (x) and n (x’), we can E B C calculate the corresponding diffusion current components: E-B C-B I =I (0”)+I (0) I =I (0’)+I (W) E nE pB I (0) C nC pB pB I (W) I (0”) pB I (x”) nE I (x) nE pB I (0’) I (x’) nC nC I =I (0)-I (W) x” B2 pB pB x’ 0” 0 W 0’ Base recombination current • Expressions for various diffusion current components: dnE dnC InE (0") AqDE , InC (0') AqDC dx" x"0" dx' x'0' dpB dpB I pB (0) AqDB , I pB (W ) AqDB dx x0 dx xW EEE 531: Semiconductor Device Theory I • Final results for the emitter, base and collector currents: D D 2 E B VEB /VT I E Aqni coth(W / LB ) e 1 LE N E LB N B D 1 2 B VCB /VT Aqni e 1 LB N B sinh(W / LB ) D 1 2 B VEB /VT IC Aqni e 1 LB N B sinh(W / LB ) D D 2 C B VCB /VT Aqni coth(W / LB ) e 1 LC NC LB N B D D 1 2 E B VEB /VT I B Aqni coth(W / LB ) e 1 LE N E LB N B sinh(W / LB ) D D 1 2 C B VCB /VT Aqni coth(W / LB ) e 1 LC NC LB N B sinh(W / LB ) EEE 531: Semiconductor Device Theory I • For short-base diodes, for which W/L <<1, we have: B x2 1 x cosh(x) 1 ; sinh(x) x; coth(x) 2 sinh(x) 2 • Therefore, for short-base diodes, the base current simplifies to: I I B1 B2 D DW 2 E B VEB /VT I B Aqni e 1 LE N E LB N B 2LB D D W 2 C B VCB /VT Aqni e 1 LC NC LB N B 2LB -I I B3 B2 • As W/L 0 (or ), the recombination base current I 0 . B B B2 EEE 531: Semiconductor Device Theory I (B) Current expressions for different biasing regimes Forward-active region: • E-B junction is forward biased, C-B junction is reverse- biased: D D 2 E B VEB /VT I E Aqni coth(W / LB )e I En I Ep LE N E LB N B D 1 2 B VEB /VT IC Aqni e ICp LB N B sinh(W / LB ) D D cosh(W / L ) 1 2 E B B VEB /VT I B Aqni e LE N E LB N B sinh(W / LB ) 2 DC DB cosh(W / LB ) 1 Aqni L N L N sinh(W / L ) C C B B B These terms vanish if there is no recombi- EEE 531: Semiconductor Device Theory I nation in the base • Graphical description of various current components: p+ n p I { }I I Ep Cp I E C I { I En Cn I I Recombination in the base B1 B3 I is ignored in this diagram. B • The emitter injection efficiency is given by: L N D L N D E E B coth(W / L ) E E B I L N D B WN D Ep B B E B E L N D short L N D I Ep I En E E B E E B 1 coth(W / LB ) base 1 LB N B DE WN B DE EEE 531: Semiconductor Device Theory I • The base transport factor is given by: I 1 W 2 Cp 1 T I cosh(W /L ) short 2L2 Ep B base B • Common-emitter current gain: L N D E E B coth(W / L ) L N D B L N D B B E E E B dc L N D short E E B 2 WNBDE 1 2 coth(W / LB )sinh (W /2LB ) base LBNBDE G = WN (Gummel number) B B • For a more general case of a non-uniform doping in the base, the Gummel number is given by: W G N (x)dx Typical values of G : B B B 0 EEE 531: Semiconductor Device Theory I Saturation region: • E-B and C-B junctions are both forward biased: D D 2 E B VEB /VT I E Aqni coth(W / LB )e LE N E LB N B D 2 B VCB /VT Aqni coth(W / LB )e I En I Ep - I Ep' LB N B D 1 2 B VEB /VT IC Aqni e LB N B sinh(W / LB ) D D 2 C B VCB /VT Aqni coth(W / LB )e ICp ICn ICp' LC NC LB N B I B I E IC Base current much larger than in forward-active regime ICn I B3 EEE 531: Semiconductor Device Theory I • Graphical description of various current components: p+ n p I { }I I Ep Cp I E C I ’{ } I ’ Ep Cp I I En { Cn I I Recombination in the base B1 B3 I is ignored in this diagram.