The Bipolar Junction Transistor N Physical Structure: Oxide-Isolated, Low-Voltage, High-Frequency Design

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The Bipolar Junction Transistor n Physical Structure: oxide-isolated, low-voltage, high-frequency design ... typical of the bipolar transistor found in a BiCMOS process, such as the MicroLinear tile array chips used in the laboratory experiments

n+ polysilicon contact metal contact to base to n+ emitter region metal contact to collector

p-type base

+ + A p n n A' n+ buried layer n+ buried layer

p-type substrate field oxide n+ - p - n sandwich (intrinsic npn transistor) (a)

(emitter)

(base) edge of n+ buried layer

field oxide

A A'

+ p p n+

+ n emitter area, AE

(intrinsic npn transistor) (collector) (b)

EECS 105 Fall 1998 Lecture 19 Circuit Symbol and Terminal Characteristics n As with MOSFETs, we have two devices that have complementary characterisitcs, in this case the npn transistor and the pnp transistor The direction of the diode arrow indicates whether the central layer (the base) is n or p

C E IC IE + + + VEB B V B − V + CE EC − IB VBE − IB − − −I −I E E C C (a) (b)

npn pnp

normal operation: normal operation: I positive V positive C CE -IC positive VEC positive I positive V = 0.7 V B BE -IB positive VEB = 0.7 V -IE positive IE positive n The pnp usually has a very different physical structure ... we will concentrate on the npn and then consider the pnp briefly

EECS 105 Fall 1998 Lecture 19 npn BJT Collector Characteristics

n Similar test circuit as for n-channel MOSFET ... except IB is controlled instead of VBE (for convenience)

= IC IC(IB, VCE)

+ V − CE

(a)

I C = µ (µA) IB 2.5 A 300 = µ IB 2 A 250

200 I = 1.5 µA (saturation) B

150 = µ (forward active) IB 1 A 100 = IB 500 nA 50 I = 0 (cutoff) −3 −2 −1 B

1 2 3 4 5 6 VCE (V) = µ −4 IB 1 A (reverse active) −8 = µ IB 2 A

(b)

EECS 105 Fall 1998 Lecture 19 Regions of Operation n Constant-current region is called forward active ... corresponds to MOSFET saturation region (!?!)

β IC = F IB = IS exp[VBE/Vth](1 + VCE / VA) ...

-1 λ (VA) is like for MOSFET n Constant-voltage region is called saturation ... corresponds to MOSFET triode region

≈ VCE VCE() sat = 0.1V or 0.2 V

n Cutoff ... corresponds to MOSFET cutoff region n Reverse active ... terminal voltages for npn sandwich are flipped so that VCE is negative and VBC = 0.7 V. Only occasionally useful.

Boundary between saturation and forward-active regions:

> > VCE VCE() sat and IB 0

... much easier to apply this test than VDS > VDS(sat)

EECS 105 Fall 1998 Lecture 19 Small-Signal Model of the Forward-Active npn BJT n Transconductance (same concept as for MOSFET):

∂ iC gm = ∂ vBE Q ⁄ vBE Vth Ebers-Moll (forward-active): iC = ISe

iC iC

+ IC ic I = C Q slope gm

IC Q v + BE VBE VBE vbe

0.2 0.4 0.6 vBE VBE

Evaluating the derivative, we find that

I V⁄ V I ------S- BE th C gm ==e ------Vth Vth

EECS 105 Fall 1998 Lecture 19 Input Resistance n The collector current is a function of the base current in the forward-active β region (recall IC = FIB). At the operating point Q, we define ∂i β C o = ∂ iB Q

β β β and so ic = o ib. (Note that the “DC beta” F and the small-signal o are both highly variable from device to device) n Since the base current is therefore a function of the base-emitter voltage, we define the input resistance rπ as:

∂i ∂i ∂i –1 B B C -----1- rπ ==∂ ∂ ∂ =β gm vBE iC vBE o Q Q Q n Solving for the input resistance

ββ β oo V th kT o rπ==------=------gmIC qIC

n For a high input resistance (often desirable), we need a high current gain or a low DC bias current.

EECS 105 Fall 1998 Lecture 19 Output Resistance n The Ebers-Moll model has perfect current source behavior in the forward-active region -- actual characteristics show some increase:

− V VAn CE

n Why? Base width shrinks due to encroachment by base-collector depletion region

Approximate model: introduce Early voltage VAn to model increase in iC

v ⁄ V v BE thCE Model: iC =ISe 1 + ------VAn

n Output resistance: ∂i I –1C ≅ ------C ro= ∂ vCE VAn Q

EECS 105 Fall 1998 Lecture 19 Complete Small-Signal Model n Add the depletion capacitance from the base-emitter junction to find the total base-emitter capacitance: Cπ = CjE + Cb

CjE = 2CjEo

CjEo is proportional to the emitter-base junction area (AE) n Depletion capacitance from the base-collector junction: Cµ Cµ C = ------o - µ ⁄ φ 1 + VCB Bc

Cµo is proportional to the base-collector junction area (AC) + n Depletion capacitance from collector (n buried layer) to bulk: Ccs C C = ------cso cs ⁄ φ 1 + VCS Bs

Ccso is proportional to the collector-substrate junction area (AS)

base collector i ib Cµ c

+ + r r b + c C v g v π r cs Cπ π rπ m o − vce vbe substrate

rex − − emitter

EECS 105 Fall 1998 Lecture 19 Numerical Values of Small-Signal Elements

ib ic + collector + base +

g vπ r vbe vπ rπ m o vce − − − emitter n Transconductance:

µ g = 4 mS = 4 x 10-3 S IC = 100 A, Vth = 25 mV --> m

Note: gm varies linearly with collector current and is independent of device geometry, in contrast to the MOSFET

n Input resistance:

β µ rπ = 25 kΩ o = 100, IC = 100 A, Vth = 25 mV -->

n Output resistance:

µ r = 350 kΩ IC = 100 A, VAn = 35 V --> o

VAn = Early voltage increases with increasing base width and decreases with decreasing base doping.

EECS 105 Fall 1998 Lecture 19 npn BJT SPICE model

Close correspondence to Ebers-Moll and small-signal models

Name Parameter Description Units

IS transport saturation current [IS]Amps β BF ideal maximum forward beta [ F]None

VAF forward Early voltage [VAn] Volts β BR ideal maximum reverse beta [ R]None

RB zero bias base resistance [rb]Ohms

RE emitter resistance [rex]Ohms

RC collector resistance [rc]Ohms

CJE B-E zero-bias depletion capacitance [CjEo] Farads φ VJE B-E built-in potential [ Be] Volts MJE B-E junction exponential factor None

CJC B-C zero-bias depletion capacitance [Cµo] Farads φ VJC B-C built-in potential [ Bc] Volts MJC B-C junction exponential factor None

CJS substrate zero-bias depletion capacitance [Ccso] Farads φ VJS substrate built-in potential [ Bs] Volts MJS substrate junction exponential factor None τ TF ideal forward transit time [ F] Seconds

.MODEL MODQN NPN IS=1E-17 BF=100 VAF=25 TF=50P + CJE=8E-15 VJE=0.95 MJE=0.5 CJC=22E-15 VJC=0.79 MJC=0.5 + CJS=41E-15 VJS=0.71 MJS=0.5 RB=250 RC=200 RE=5

EECS 105 Fall 1998 Lecture 19