BJT Operation

The Bipolar Junction Transistor (BJT) is the foundation of analog amplifier design and forms the basis for understanding all three-terminal semiconductor devices. Unlike a diode that simply rectifies, a BJT controls a large collector current using a small base current, enabling amplification. Active mode operation, carrier injection across junctions, and base width modulation are the core physical processes that govern BJT behavior and appear consistently in GATE.

Core Concept Explanation

A BJT consists of three alternating semiconductor layers: Emitter, Base, and Collector. For an NPN transistor, the emitter is N-type heavily doped, the base is P-type lightly doped and physically thin, and the collector is N-type moderately doped. This creates two PN junctions: the emitter-base junction (J_E) and the collector-base junction (J_C).

In active mode, J_E is forward biased and J_C is reverse biased. Forward biasing J_E causes the emitter to inject a large number of electrons into the thin P-type base. Because the base is very thin and lightly doped, most of these injected electrons diffuse across the base without recombining. They reach the edge of the reverse-biased J_C depletion region, where the strong electric field sweeps them into the collector. This constitutes the collector current IC, which is nearly equal to the emitter current IE.

The fraction of injected electrons that recombine in the base before reaching the collector constitutes the base current IB. Since the base is thin and lightly doped, the recombination probability is low and IB is small. The current gain beta (β) = IC / IB can range from 50 to several hundred, meaning a small base current controls a large collector current. This is the transistor amplification action.

Mathematical Expression

Two fundamental current gain parameters define BJT behavior. The common-base current gain alpha (α) = IC / IE represents the fraction of emitter current reaching the collector. It is always less than unity (typically 0.95 to 0.999). The common-emitter current gain beta (β) = IC / IB = α / (1 - α). Because α is close to 1, (1 - α) is small and β becomes large.

The collector current in active mode is given by IC = IS × exp(VBE / VT) × (1 + VCE / VA), where IS is the saturation current, VBE is the base-emitter voltage, VT is the thermal voltage, and VA is the Early voltage, which characterizes base width modulation. If VA is large (ideal device), IC is approximately IS × exp(VBE/VT), independent of VCE.

Base width modulation (the Early effect) occurs because the reverse bias on J_C changes the width of the collector depletion region, which extends into the base. As VCE increases, the depletion region penetrates deeper into the base, effectively reducing the base width W_B. A narrower base reduces recombination, increases α, and increases IC slightly. When IC vs VCE is plotted, this appears as an upward slope in the active region. Extrapolating these lines back to the voltage axis gives the Early voltage VA.

Practical Understanding

The physical requirement for high β is a thin, lightly doped base. A thin base means fewer recombination events. Light base doping means fewer majority carriers (holes in NPN) available for recombination with injected minority carriers. Modern BJTs use base widths on the order of tens of nanometers, achieving β values of 100 to 500.

The Early effect has practical consequences in analog design. In a common-emitter amplifier, finite VA means the transistor does not have infinite output impedance. The small signal output resistance is ro = VA / IC. A high VA (large ro) means the transistor approximates an ideal current source more closely, which is desirable in high-gain amplifiers and current mirrors.

Given:
β = 100, IB = 20 μA = 20e-6 A
Early voltage VA = 80 V, VCE = 5 V
IC without Early effect: IC0 = β × IB

Why this formula applies:
Active mode operation; collector current with Early effect correction.

Formula:
IC0 = β × IB
IC_actual = IC0 × (1 + VCE / VA)

Substitution:
IC0 = 100 × 20e-6 = 2 mA
IC_actual = 2e-3 × (1 + 5/80)

Calculation:
1 + 5/80 = 1 + 0.0625 = 1.0625
IC_actual = 2e-3 × 1.0625

Final Answer:
IC_actual = 2.125 mA  (Early effect causes 6.25% increase over ideal)

Exam Tip: In active mode, remember J_E forward and J_C reverse. β = α/(1-α); if α = 0.99, β = 99. The Early effect increases IC with VCE; ro = VA/IC is the small signal output resistance due to the Early effect.

• Active mode: J_E forward biased, J_C reverse biased; this is the amplification mode.
• Electrons injected from emitter into base, diffuse across thin base, swept into collector by reverse-biased junction field.
• IB arises from recombination in base and reverse injection from base to emitter.
• β = IC/IB = α/(1-α); high β requires thin, lightly doped base.
• Early effect: increasing VCE narrows base width, increases IC slightly; modeled by Early voltage VA.

Quick Revision

• Active mode conditions: VBE > 0 (forward), VBC < 0 (reverse) for NPN.
• α = IC/IE (always < 1), β = IC/IB, β = α/(1-α).
• IE = IC + IB (KCL at transistor node).
• Early effect: IC increases with VCE due to base width narrowing; ro = VA/IC.
• GATE trap: α close to 1 does not mean β is also close to 1; β = α/(1-α) amplifies small (1-α) into large β.
• Thin, lightly doped base maximizes β by minimizing recombination.
• Saturation: both junctions forward; Cutoff: both reverse; neither mode amplifies.