Bipolar Junction Transistor (BJT)

1. Theory

Definition: A bipolar junction transistor is a three-layer (NPN or PNP) device with two back-to-back PN junctions, in which a small base current controls a much larger collector current.
Terminals: Emitter (heavily doped, injects carriers), base (thin and lightly doped), collector (moderately doped, collects carriers).
NPN and PNP: Both obey identical equations with electrons and holes, and all polarities, swapped; NPN is faster because electrons have higher mobility.
Bipolar conduction: Both carrier types matter: minority carriers carry the main current across the base, while majority carriers supply the base current.
Emitter injection efficiency: A heavily doped emitter and lightly doped base make almost all emitter current consist of carriers injected into the base ( $γ \to 1$ ).
Base transport factor: A base much narrower than the minority diffusion length lets nearly all injected carriers reach the collector without recombining ( $α_{T} \to 1$ ).

2. Working Principle

Forward-active mode: The base-emitter junction is forward biased and the base-collector junction reverse biased; injected electrons diffuse across the base and are swept into the collector.
Current gain: Collector current is $β$ times the base current, with $β$ typically 50 to 500.
Exponential control: Collector current rises exponentially with $V_{B E}$ ( $I_{C} = I_{S} exp (V_{B E} / V_{T})$ ), giving the highest transconductance per unit current of any transistor ( $g_{m} = I_{C} / V_{T}$ ).
Saturation and cut-off: Both junctions forward biased gives saturation (switch on, with stored base charge); both reverse biased gives cut-off (switch off).
Early effect: Rising $V_{C E}$ widens the collector depletion region into the base, narrowing it and slightly raising $I_{C}$ , which sets the output resistance.
High-current limits: High injection and the Kirk effect (base push-out) reduce gain and $f_{T}$ at high current density.
Breakdown: $B V_{C E O}$ with open base is lower than $B V_{C B O}$ because the transistor’s own gain amplifies the avalanche current.

3. Applications

Bandgap voltage references: The precisely predictable $V_{B E}$ and its temperature behaviour give the standard on-chip reference.
Translinear and logarithmic circuits: The exact exponential I-V law enables analog multipliers, log amplifiers and RMS detectors.
Precision low-noise analog front ends: Low $1/ f$ noise and tight $V_{B E}$ matching suit op-amp input stages and instrumentation amplifiers.
RF and mm-wave transceivers: SiGe HBTs dominate automotive radar and high-speed optical-link drivers and receivers.
Handset RF power amplifiers: GaAs HBTs are the standard power amplifier in mobile phones.

Name	Formula	Related Formulae	Variables/Constants
Ebers–Moll terminal currents	$I_{E} = I_{E S} [exp (\frac{V _{B E}}{V _{T}}) - 1] - α_{R} I_{C S} [exp (\frac{V _{B C}}{V _{T}}) - 1]$ $I_{C} = α_{F} I_{E S} [exp (\frac{V _{B E}}{V _{T}}) - 1] - I_{C S} [exp (\frac{V _{B C}}{V _{T}}) - 1]$	$α_{F} I_{E S} = α_{R} I_{C S} = I_{S}$ $I_{B} = I_{E} - I_{C}$	$I_{E S}, I_{C S} : e mi tt er an d co l l ec t or j u n c t i o n s a t u r a t i o n c u r r e n t s$ $α_{F}, α_{R} : f or w a r d an d r e v er se co mm o n - ba se c u r r e n t g ain s$ $V_{B E}, V_{B C} : ba se - e mi tt er an d ba se - co l l ec t or v o l t a g es$ $V_{T} : t h er ma l v o l t a g e$
Forward-active collector current	$I_{C} = I_{S} exp (\frac{V _{B E}}{V _{T}})$	$I_{S} = \frac{q A D _{n B} n _{i}^{2}}{N _{B} W _{B}} = \frac{q A n _{i}^{2}}{G _{B}}$	$I_{S} : t r an s p or t s a t u r a t i o n c u r r e n t$ $A : e mi tt er a r e a$ $W_{B} : q u a s i - n e u t r a l ba se w i d t h$ $N_{B} : ba se d o p in g$ $G_{B} = N_{B} W_{B} : ba se G u mm e l n u mb er$
Minority carrier profile in the base	$Δ n_{B} (x) = n_{B 0} exp (\frac{V _{B E}}{V _{T}}) (1 - \frac{x}{W _{B}})$	$n_{B 0} = \frac{n _{i}^{2}}{N _{B}}$	$Δ n_{B} (x) : e x cess e l ec t r o n co n ce n t r a t i o n in t h e ba se (l in e a r f or a s h or t ba se, W_{B} ≪ L_{n B})$ $n_{B 0} : e q u i l ib r i u m min or i t y co n ce n t r a t i o n in t h e ba se$
Current gain relations	$β = \frac{α}{1 - α}$	$I_{C} = β I_{B}, I_{E} = (β + 1) I_{B}$	$β : co mm o n - e mi tt er c u r r e n t g ain$ $α : co mm o n - ba se c u r r e n t g ain$
Emitter injection efficiency	$γ = [1 + \frac{D _{pE} W _{B} N _{B}}{D _{n B} L _{pE} N _{E}}]^{- 1}$	$α = γ α_{T}$	$γ : f r a c t i o n o f e mi tt er c u r r e n t c a r r i e d b y c a r r i er s inj ec t e d in t o t h e ba se (w i d e e mi tt er a ss u m e d)$ $D_{pE}, L_{pE} : min or i t y h o l e d i f f u s i o n coe f f i c i e n t an d l e n g t h in t h e e mi tt er$ $N_{E} : e mi tt er d o p in g$
Base transport factor	$α_{T} = \frac{1}{c o s h ( W _{B} / L _{n B} )} \approx 1 - \frac{W _{B}^{2}}{2 L _{n B}^{2}}$	$L_{n B} = D_{n B} τ_{n B}$	$α_{T} : f r a c t i o n o f inj ec t e d c a r r i er s t ha t r e a c h t h e co l l ec t or$ $L_{n B}, τ_{n B} : min or i t y e l ec t r o n d i f f u s i o n l e n g t h an d l i f e t im e in t h e ba se$
Common-emitter current gain (design form)	$β \approx [\frac{D _{pE} W _{B} N _{B}}{D _{n B} L _{pE} N _{E}} + \frac{W _{B}^{2}}{2 L _{n B}^{2}}]^{- 1}$	$\frac{1}{β} \approx (1 - γ) + (1 - α_{T})$	$(gain is maximized by a heavily doped emitter, a lightly doped narrow base, and a long base diffusion length)$
Early effect (base-width modulation)	$I_{C} = I_{S} exp (\frac{V _{B E}}{V _{T}}) (1 + \frac{V _{C E}}{V _{A}})$	$r_{o} = \frac{V _{A}}{I _{C}}, V_{A} = \frac{Q _{B}}{C _{j c}}$	$V_{A} : E a r l y v o l t a g e$ $r_{o} : o u tp u t r es i s t an ce$ $Q_{B} = q A N_{B} W_{B} : ba se c ha r g e$ $C_{j c} : co l l ec t or - ba se d e pl e t i o n c a p a c i t an ce$
Small-signal transconductance and input resistance	$g_{m} = \frac{I _{C}}{V _{T}}, r_{π} = \frac{β}{g _{m}} = \frac{β V _{T}}{I _{C}}$		$g_{m} : t r an sco n d u c t an ce$ $r_{π} : s ma l l - s i g na l ba se - e mi tt er in p u t r es i s t an ce$
Base transit time	$τ_{B} = \frac{W _{B}^{2}}{2 D _{n B}}$		$τ_{B} : m e an t im e f or min or i t y c a r r i er s t o d i f f u se a cr oss t h e ba se (r e d u ce d in g r a d e d - ba se d e v i ces b y t h e b u i l t - in f i e l d)$
Base–emitter capacitance	$C_{π} = C_{j e} + C_{d e}, C_{d e} = g_{m} τ_{F}$	$C_{j e} = depletion capacitance (see PN Junction Diode page)$	$C_{d e} : d i f f u s i o n c a p a c i t an ce f r o m s t or e d ba se c ha r g e$ $τ_{F} : f or w a r d t r an s i t t im e (\approx τ_{B} + τ_{E})$
Unity-gain cutoff frequency	$f_{T} = \frac{1}{2 π τ _{ec}}$	$τ_{ec} = \frac{C _{j e} + C _{j c}}{g _{m}} + τ_{B} + τ_{C}, τ_{C} = \frac{x _{C}}{2 v _{s a t}}$	$f_{T} : f r e q u e n cy a t w hi c h t h e co mm o n - e mi tt er c u r r e n t g ain f a l l s t o u ni t y$ $τ_{ec} : t o t a l e mi tt er - t o - co l l ec t or d e l a y t im e$ $x_{C} : co l l ec t or d e pl e t i o n w i d t h$
Maximum oscillation frequency	$f_{ma x} = \frac{f _{T}}{8 π R _{B} C _{j c}}$		$f_{ma x} : f r e q u e n cy a t w hi c h t h e u ni l a t er a l p o w er g ain f a l l s t o u ni t y$ $R_{B} : ba se ser i es r es i s t an ce$
Punch-through voltage	$V_{P T} = \frac{q N _{B} W _{B}^{2}}{2 ε _{s}} (1 + \frac{N _{B}}{N _{C}})$		$V_{P T} : co l l ec t or - ba se v o l t a g e a t w hi c h t h e d e pl e t i o n r e g i o n s p an s t h e e n t i r e ba se$ $N_{C} : co l l ec t or d o p in g$
Collector breakdown voltages	$B V_{C E O} \approx \frac{B V _{C B O}}{β ^{1/ n}}$	$B V_{C B O} \approx \frac{ε _{s} E _{cr i t}^{2}}{2 q N _{C}} (see PN Junction Diode / Avalanche Diode pages)$	$B V_{C B O} : co l l ec t or - ba se b r e ak d o w n v o l t a g e w i t h t h e e mi tt er o p e n$ $B V_{C E O} : co l l ec t or - e mi tt er b r e ak d o w n v o l t a g e w i t h t h e ba se o p e n$ $n : e m p i r i c a l m u l t i pl i c a t i o n e x p o n e n t (\approx 3 - 6)$
Kirk effect (high-current onset)	$J_{K} = q N_{C} v_{s a t} [1 + \frac{2 ε _{s} V _{C B}}{q N _{C} W _{C}^{2}}]$		$J_{K} : co l l ec t or c u r r e n t d e n s i t y a t w hi c h inj ec t e d e l ec t r o n c ha r g e c an ce l s t h e co l l ec t or s p a ce c ha r g e an d t h e ba se e f f ec t i v e l y w i d e n s$ $W_{C} : co l l ec t or e p i t a x ia l l a y er t hi c k n ess$
Storage time (saturation switching)	$t_{s} = τ_{S} ln [\frac{I _{B 1} - I _{B 2}}{I _{B, s a t} - I _{B 2}}]$	$I_{B, s a t} = \frac{I _{C, s a t}}{β _{F}}$	$t_{s} : d e l a y w hi l e s t or e d e x cess ba se c ha r g e i s r e m o v e d b e f or e t h e co l l ec t or c u r r e n t b e g in s t o f a l l$ $τ_{S} : s t or a g e t im e co n s t an t$ $I_{B 1}, I_{B 2} : f or w a r d an d r e v er se ba se d r i v e c u r r e n t s$

Important Questions

Ques: Why does the BJT page treat NPN and PNP as one device rather than two?

Both devices are built from the same two back-to-back junctions and obey the same drift-diffusion, continuity, and junction equations already on the Basic Semiconductor Equations and PN Junction Diode pages; the only change is which carrier is the minority in each region. Swapping $n \leftrightarrow p$ and reversing every voltage and current sign converts any NPN formula into its PNP counterpart exactly, so separate pages would be redundant duplicates. The real, quantitative difference is carrier mobility: electrons are faster than holes in most semiconductors, so an NPN has a shorter base transit time $τ_{B}$ and higher $f_{T}$ than a geometrically identical PNP, which is why NPN devices dominate high-speed designs and PNPs are typically used as complements. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Why must the emitter be heavily doped and the base lightly doped and narrow, and what does that cost?

The design form $β \approx [\frac{D _{pE} W _{B} N _{B}}{D _{n B} L _{pE} N _{E}} + \frac{W _{B}^{2}}{2 L _{n B}^{2}}]^{- 1}$ shows two loss mechanisms: holes back-injected from the base into the emitter (suppressed by making $N_{E} ≫ N_{B}$ , which pushes $γ \to 1$ ) and recombination in the base (suppressed by making $W_{B} ≪ L_{n B}$ , which pushes $α_{T} \to 1$ ). The cost is that a thin, lightly doped base has high base resistance $R_{B}$ (hurting $f_{ma x}$ and noise) and is more susceptible to the Early effect and punch-through, since the collector depletion region eats a larger fraction of it. BJT design is therefore a balance between gain, speed, output resistance, and breakdown voltage rather than maximizing any single quantity. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Does a BJT have a reverse recovery or storage time like a PN diode?

Yes, but the term shows up as storage time $t_{s}$ when the transistor is driven into saturation. In saturation both junctions are forward biased, so excess minority charge builds up in the base (and collector); on turn-off this charge must be removed before the collector current can fall, which is the same stored-charge physics behind the PN diode’s $τ ln (1 + I_{F} / I_{R})$ delay, just with the forward and reverse base drive currents setting the ratio. This is why switching circuits avoid deep saturation (for example with Baker clamps or Schottky-clamped bases) — keeping the device just out of saturation removes most of the storage delay. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: What is the Early effect and why does it set the output resistance?

As $V_{C B}$ increases, the collector depletion region extends further into the base, narrowing the quasi-neutral width $W_{B}$ . Since $I_{S} \propto 1/ W_{B}$ , the collector current rises slightly with $V_{C E}$ instead of staying flat, which appears as a finite slope in the output characteristics. Extrapolating those slopes back to the voltage axis gives the Early voltage $V_{A}$ , and the output resistance $r_{o} = V_{A} / I_{C}$ follows directly. A larger $V_{A}$ (a more heavily doped, wider base) means a flatter characteristic and higher voltage gain, again trading against current gain and speed. Reference: J.M. Early, “Effects of space-charge layer widening in junction transistors,” Proc. IRE 40, 1401 (1952); S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

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