非理想效应、电荷控制模型、基渡时间

1 . Lecture #18 ANNOUNCEMENTS • Lowest quiz score will be dropped for each student • No Discussion and Office Hours next week • Design Project will be posted online tomorrow OUTLINE The Bipolar Junction Transistor – Gummel numbers – Charge-control model – Base transit time Spring 2003 EE130 Lecture 18, Slide 1 Current Formulas for NPN BJT Long Emitter and Long Collector: I E = qA [( DE LE pE 0 + DB LB nB 0 cosh(W / LB ) sinh(W / LB ) )(e qVBE / kT − 1) − ( DB LB )( nB 0 sinh(W1 / LB ) e qVBC / kT − 1 )] = qA[( ) ( )(e )] cosh(W / LB ) IC DB LB nB 0 sinh(W1 / LB ) ( e qVBE / kT − 1) − DC LC pC 0 + DB LB nB 0 sinh(W / LB ) qVBC / kT −1 Short Emitter and Short Collector: I E = qA [( DE WE′ pE 0 + DB LB nB 0 cosh(W / LB ) sinh(W / LB ) )(e qVBE / kT − 1) − ( DB LB )( nB 0 sinh(W1 / LB ) e qVBC / kT − 1 )] I C = qA [( DB LB ) nB 0 sinh(W1 / LB ) (e qVBE / kT − 1) − (DC WC′ pC 0 + DB LB nB 0 cosh(W / LB ) sinh(W / LB ) )(e qVBC / kT )] −1 Spring 2003 EE130 Lecture 18, Slide 2 1 

2 . Review: BJT Breakdown Mechanisms • In the common-emitter configuration, for high output voltage VCE, the output current IC will increase rapidly due to one of two mechanisms: – punch-through – avalanche Spring 2003 EE130 Lecture 18, Slide 3 Review: Punch-Through E-B and E-B depletion regions in the base touch, so that W = 0 As |VCB| increases, the potential barrier to hole injection decreases and therefore IC increases Spring 2003 EE130 Lecture 18, Slide 4 2 

3 . Review: Avalanche • Holes are injected into the base, then PNP BJT: collected by the B-C junction – Some holes in the B-C depletion region have enough energy to generate EHP [1] – The generated electrons are swept into the base [3], then injected into the emitter [4] – Each injected electron results in the injection of IEp/IEn holes from the emitter into the base [0] → For each EHP created in the C-B depletion region by impact ionization, IEp/IEn+1>βdc additional holes flow into the collector i.e. carrier multiplication in C-B depletion region is internally amplified VCB 0 VCE 0 = where VCB0 = reverse breakdown voltage of the C-B junction ( β dc + 1)1 / m Spring 2003 EE130 Lecture 18, Slide 5 2≤m≤6 Base Gummel Number 2 W ni N B Base Gummel number GB ≡ ∫ 2 dx 0 ni B DB = total integrated base dopant dose (atoms/cm2) divided by DB For a uniformly doped base with negligible band-gap narrowing, N BW GB = DB 2 qn A qVEB / kT IC ≅ i GB e ( −1 ) Spring 2003 EE130 Lecture 18, Slide 6 3 

4 .Emitter Gummel Number w/ Poly-Si Emitter ni N E ( −WE′ ) 2 2 −WE′ ni N E Emitter Gummel number GE ≡ ∫ dx + ni E ( −WE′ ) S p 2 2 0 ni E DE where Sp = DEpoly/WEpoly is the surface recombination velocity For a uniformly doped emitter, ni  WE′ 1  2 GE = N E 2 + niE  DE S p  2 I B ≅ i (e qVEB / kT − 1) qn A GE Spring 2003 EE130 Lecture 18, Slide 7 Charge Control Model A PNP BJT biased in the forward-active mode will have excess minority-carrier charge QB stored in the quasi-neutral base: ∆pB ( x, t ) = ∆pB (0, t )(1 − Wx ) W qAW∆pB (0, t ) QB = qA ∫ ∆pB ( x, t )dx = 0 2 dQB Q = iB − B dt τB Spring 2003 EE130 Lecture 18, Slide 8 4 

5 . Base Transit Time τt W qAW∆pB (0, t ) QB = qA ∫ ∆pB ( x, t )dx = 0 2 ∂∆pB ( x, t ) qADB ∆pB (0, t ) Q Q ic = − qADB = = 2 B = B ∂x x =W W W / 2 DB τ t W2 τt ≡ 2 DB • time required for minority carriers to diffuse across the base • sets the switching speed limit of the transistor Spring 2003 EE130 Lecture 18, Slide 9 Relationship between τt and τB τ B ≅ β dcτ t Spring 2003 EE130 Lecture 18, Slide 10 5 

6 . Drift Transistor: Built-in Base Field The base transit time can be reduced by building into the base a drift field that aids the flow of electrons. • Fixed EgB , NB decreases from emitter end to collector end. E - B C Ec Ef Ev • Fixed NB , EgB decreases from emitter end to collector end. E - B C 1 dEC Ec Ef = q dx Ev Spring 2003 EE130 Lecture 18, Slide 11 6