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. B • Important note: As V becomes more positive, the number of holes injected from CB the collector into the base and afterwards in the emitter increases. The collector hole flux is opposite to the flux of holes arriving from the emitter, and the two currents subtract, which leads to a reduction of the emitter as well as the collector currents.
EEE 531: Semiconductor Device Theory I Cutoff region: • E-B and C-B junctions are both reverse biased. For short- base diode with no recombination in the base, this leads to:
2 DE 2 DC I E Aqni I En , IC Aqni ICn LE N E LC NC
2 DE DC 2 DC I B I E IC Aqni Aqni LE N E LC NC LC NC p+ n p I I E C I En I Cn
I I Recombination in the base B1 I B3 B is ignored in this diagram.
EEE 531: Semiconductor Device Theory I (C) Form of the input and output characteristics Common-base configuration: I C I Forward active E V <-3V saturation CB T I 0 E V =0 CB I =0 I E BC0 V V EB cutoff BC Common-emitter configuration: I V = 0 Forward active I C CB B V = 0 saturation EC I 0 B V > 3V EC T I =0 I B V EC0 EB V cutoff EC EEE 531: Semiconductor Device Theory I • Note on the collector-base reverse saturation current:
C E I Cn V >0 BC B
I =I B BC0
Minority electrons in the collector that are within L from the C-B V C BC junction are collected by the high electric field into the base.
EEE 531: Semiconductor Device Theory I • Why is I much larger than I ? EC0 BC0
I En I C E Cn I I Ep Cp V > 0 EC I =0 B B I = I E EC0 I Ep I EC0 ICn ICp I BC0 I Ep dc 1 I BC0, dc ICn The electrons injected from the collector into the base and then into the emitter forward bias the E-B junction . This leads to large hole injection from the emitter into the base and then into the collector. In summary, relatively small number of electrons into the emitter forces injection of large number of holes into the base (transistor action) which gives I >> I . EC0 BC0 EEE 531: Semiconductor Device Theory I (D) Ebers-Moll equations • The simplest large-signal equivalent circuit of an ideal (intrinsic) BJT consists of two diodes and two current-controlled current sources: I F I V /V I R I I I e EB T 1 E C F F 0 V /V I I e CB T 1 I I R R0 R R F F I B • Using the results for I and I , we can calculate various coefficient: E C
VEB /VT VCB /VT I E I F 0 e 1 R I R0 e 1
VEB /VT VCB /VT IC F I F 0 e 1 I R0 e 1 • The reciprocity relation for a two-port network requires that:
F I F 0 R I R0
EEE 531: Semiconductor Device Theory I (E) Early effect • In deriving the IV-characteristics of a BJT, we have assumed that , dc , I and I to be constant and independent of the applied voltage. dc BC0 EC0 • If we consider a BJT in the forward active mode, when the reverse bias of the C-B junction increases, the width of the C-B depletion region increases, which makes the width of the base quasi-neutral region W eff to decrease:
Weff W (metallurgical) xdeb xdcb • The common-emitter current gain, taking into account the effective width of the base quasi-neutral region (assuming =1) is then given by: 1 1 W L 2 dc T 2 eff B • The common-emitter current gain can be approximated with: 2 L dc 2 B dc 1 W dc eff EEE 531: Semiconductor Device Theory I • Graphical illustration of the Early (base-width modulation) effect: W ’ eff W E eff C
B • If we approximate the collector current with the hole current:
D V /V D V /V I I Aqn2 B e EB T Aqn2 B e EB T C Cp i W i B GB (WB ) N B (x)dx o I n(W ) W I we find: C I B B C C Early voltage VBC GB VBC VA • Since W / V <0, we have that I / V > 0, i.e. I increases. B BC C BC C
EEE 531: Semiconductor Device Theory I • Empirically, it is found that a linear interpolation of the collector current dependence on V is adequate in most cases: EC IC dc I B I EC0 1VEC /VA dc I B I EC0 1VEC /VA
qGBWB where the Early voltage is given by: VA k A ks0
• Graphical illustration of the Early effect:
I Another effect contributing C to the slope is due to generation currents in the C-B junction: Generated holes drift to the collector. Generated electrons drift into V the base and then the emitter, -|V | EC thus forcing much larger hole A injection (transistor action). EEE 531: Semiconductor Device Theory I (F) Deviations from the ideal model: There are several factors that lead to deviation from the ideal model predictions: Breakdown effects Geometry effects Generation-recombination in the depletion regions
3. Breakdown in BJT’s • There are two important mechanisms for breakdown in BJT’s: (1) punch-through breakdown (2) avalanche breakdown (similar to the one in pn- junctions)
EEE 531: Semiconductor Device Theory I • The punch-through breakdown occurs when the reverse-bias C-B voltage is so large that the C-B and the E-B depletion regions merge. • The emitter-base barrier height for holes is affected by V , BC i.e. small increase in V is needed for large increase in I . BC C
V increasing BC p+ n p Note: Punch-through voltage is usually much larger than the avalanche breakdown voltage.
• The mechanism of avalanche breakdown in BJT’s depend on the circuit configuration (common-emitter or common- base configuration).
EEE 531: Semiconductor Device Theory I • For a common-base configuration, the avalanche breakdown in the C-B junction (open emitter) BV is obtained via the BC maximum (breakdown) electric field F (~300 kV/cm for BR Si and 400 kV/cm for GaAs): k F 2 1 1 k F 2 s 0 BR s 0 BR BVBC 2q N B NC 2qNC • The increase in current for voltages higher than BV is BC reflected via the multiplication factor in the current expres- sion. It equals one under normal operating conditions, and exceeds unity when avalanche breakdown occurs. • When the emitter is open, the multiplication factor for the C-B junction is: m 1 V b M 1 BC CB BV BC
EEE 531: Semiconductor Device Theory I • For a common-emitter configuration, the collector-emitter breakdown voltage BV is related to BV : EC BC
I E IC Open base configuration M I BC BC0 IC M BC dc I E I BC0 IC M EC I EC0 1 dcM BC M (1 ) BC dc 1/ mb M EC BVEC BVBC 1 dc 1 dcM BC r o
t 50 Much smaller than BV c M M BC a EC BC f 40 due to transistor action. n o i t 30 a c i l 20 p i t l
u 10
M Reverse voltage 20 40
EEE 531: Semiconductor Device Theory I I I C C
V V EC BV BC BV BC0 EC0
Common-base output Common-emitter output characteristics characteristics
EEE 531: Semiconductor Device Theory I 4. Geometry effects • The geometry effects include: (1) Bulk and contact resistance effects (2) Current crowding effect
B E B Base contacts p+ n+ p+ p n n+ Emitter contacts collector • Base current flows in the direction parallel to the E-B junction, which gives rise to base spreading resistance. • When V is much larger than V , most of the emitter BB’ T current is concentrated near the edges of the E-B junction.
EEE 531: Semiconductor Device Theory I Generation-recombination in the depletion region ln(I ) Current crowding, high-level C injection series resistence ln(I ) B I • Reverse-biased C-B junction C dc I adds a generation current to I . B C • Forward-biased E-B junction has recombination current. I is C g-r current not affected by the recombina- V EB tion in the E-B junction. modification: dc Current dc crowding or r • Low-current levels C recombination current • large current levels high-level injection and g-r series resistance ln(I ) EEE 531: Semiconductor Device Theory I C