半导体器件原理 1.12 Non-Ideal Effects in Bipolar Junction Transistor

About the other three operation modes of BJT, and some non-ideal effects, including the Early effect, base punchthrough, and breakdown.

# Reverse Active/Cutoff/Saturation Modes

• Reverse active mode: when the base-emitter junction is reverse biased and the base-collector junction is forward biased, electrons are injected from the collector to the base, then to the emitter. Operation is similar to forward active mode
  • The BJT still functions as a switch, which is controlled by the base-collector voltage
  • But the doping is not optimized for this mode, electron injection from the collector to the base has to be accomplished by a large hole current from the base to the collector
  • $\gamma$ is very small and $\beta$ is usually less than 1
  • Like using a large amount of running water to control the water flow in a small pipe
• Cutoff mode: when both the base-emitter junction and the base-collector junction are reverse biased, no current can flow through the junction. The connection between any two terminals of the BJT can be considered as open circuit
• Saturation mode: when both the base-emitter junction and the base-collector junction are forward biased, both emitter and collector inject electrons into the base
  • The minority carrier concentration in the base represents the superposition of the forward active and the reverse active cases, and its slope indicates the net current flow
  • We can calculate the carrier concentrations at the edges of the depletion regions of the base near the emitter and collector as:
  • If $V_{\text{C}}=V_{\text{E}}$, then $n_{\text{BC}}=n_{\text{BE}}$, the electron injections from the two sides balance out, no current flow through the device
    • Excess electrons at the base will recombine with holes, resulting a base hole current $I_{\text{B}p2}$
    • The base hole current will flow to both the emitter and collector, given by the slope of the minority carrier concentration at the emitter and the collector
    • The currents are mainly hole currents from the base to both the emitter and collector
    • When $n_{\text{BE}}\ne n_{\text{BC}}$, a net electron current flow will be observed in addition to the hole current from the base

# Current-Voltage Characteristics in the Saturation Mode

• From the forward active mode, we decrease $V_{\text{CE}}$ until it reaches the same as the base voltage, entering the saturation mode
• Further reduction of $V_{\text{CE}}$ will cause electrons to be injected from the collector to the base, balancing out some of the electron injection from the emitter to the base, leading to a decrease in the collector current $I_{\text{C}}$
• The hole current from the base to the collector increases, and contributes to a negative collector current that subtracts from the original collector current
• The collector current in the $I_{\text{C}}-V_{\text{CE}}$ curve is expected to drop when $V_{\text{CE}}$ is reduced below $V_{\text{BE}}$
• From the device perspective, the boundary between the forward active mode and the saturation mode is the point where $V_{\text{CE}}=V_{\text{BE}}$, which is called the saturation voltage $V_{\text{CEsat}}$
• Measurement results show that $I_{\text{C}}$ stays more or less constant after entering the saturation mode, until a much lower value than $V_{\text{BE}}$
  • Because carrier injection follows exponential scale instead of linear scale
  • For example
  • The electron injection from the collector to the base can be considered minimal, and the characteristics still follow those of the forward active mode
  • The drop in $I_{\text{C}}$ will not be noticeable until $V_{\text{CE}}$ drops to a very small value (e.g., $0.1\text{V}$)
• Based on the observed data, $V_{\text{CEsat}}$ is usually assigned a fixed value of $0.2\text{V}$, instead of a dependent value determined by $V_{\text{BE}}$.

# The Early Effect

Ideally, the collector voltage does not affect the collector current, thus $I_{\text{C}}$ is a flat line in the $I_{\text{C}}-V_{\text{CE}}$ curve in the forward active mode. But in reality, the collector voltage does have an effect on the collector current

• The collector current is given by the slope of minority carrier concentration at the base

  • When the collector voltage increases

    leading to a finite slope in the $I_{\text{C}}-V_{\text{CE}}$ curve

  • The characteristics are similar to the superposition of a BJT and a resistor in parallel, creating a permanent collector to emitter leakage path, hurting the gain of the transistor

  • The resistor is called the output resistance $r_O$

  • If all collector current at different $I_{\text{B}}$ are extrapolated back to the negative $V_{\text{CE}}$ axis, they will intersect at the same point $-V_{EA}$. $V_{EA}$ is called the Early voltage

  • The slope is given by

    $$\frac{\mathrm{d}{I}_{\text{C}}}{\mathrm{d}{V}_{\text{CE}}}=\frac{I_{\text{C}}}{V_{EA}+V_{\text{CE}}}$$

    Because $V_{EA}$ is usually very large with typical value of $300\text{V}$, the $V_{\text{CE}}$ in the denominator can be ignored for low voltage transistor applications

  • The output resistance can be expressed as

    $$r_O=\frac{V_{EA}}{I_{\text{C}}}$$

  • $V_{EA}$ of a BJT is not calculated, but measured or supplied by the device specifications

# Base Punchthrough

The early effect reduces the gain of the BJT, and should be minimized. This can be done if the change in $x_{\text{B}}$ is small compared to the original $x_{\text{B}}$, or to minimize $\frac{\mathrm{\Delta }{x}_{\text{B}}}{x_{\text{B}}}$

• Easiest way: increase the base width $W_{\text{B}}$
  • Not applicable, because it will increase more recombination in the base, reducing ${\alpha }_T$
• Another choice: minimize the change
  • $x_{d\text{BC}}$ is give by
  • This can be achieved by heavy base doping and light collector doping
  • This is why the collector is usually doped more lightly than the base
• For a BJT with extremely small base region, the depletion region at the base-emitter junction and the base-collector junction can touch each other
  • Base punchthrough: in extreme case of Early effect, the base start to lose control of the electron flow, and is unable to stop the current flow
  • Once the depletion regions touch, $V_{\text{CE}}$ can directly lower the barrier height, and the current show an exponential dependency on $V_{\text{CE}}$
  • Base punchthrough limits the minimum base width of a BJT
  • To avoid base punchthrough, the same method used to reduce Early effect can be applied
    • Large base width
    • Heavy base doping and light collector doping

# BJT breakdown

When a BJT is used as a switch, it is usually placed between two high voltage nodes to control the current flow. The highest voltage the BJT can withstand is limited by the breakdown voltage of the BJT.

• There are two ways to connect a BJT as a switch
  • In common base mode
    • When a high voltage is applied to the emitter, the BJT is in cutoff mode, and no current flows
    • When a negative voltage is applied, a current will flow through the load
    • The maximum voltage the BJT can withstand is determined by the breakdown voltage of the reverse biased base-collector junction
    • But the breakdown voltage also depends on the input, which can be high, low, or open
      • In most cases, the worst case with lowest breakdown voltage is when the input is open
      • This lowest breakdown voltage is denoted as $B{V}_{\text{CBO}}$: breakdown voltage in common-base configuration with emitter open
      • In this case, the BJT just has the base-collector junction reverse biased, and the breakdown voltage is the same as that of a PN junction
      • To increase breakdown voltage, the most effective way is to reduce doping on the lightly doped side (the collector side)
  • In common emitter mode
    • Again, the breakdown voltage is the lowest when the input is open
    • The breakdown voltage is denoted as $B{V}_{\text{CEO}}$: breakdown voltage in common-emitter configuration with base open
    • due to a possible feedback mechanism
      • Assume the base-collector junction is reverse biased at a particular voltage such that for every 10 electrons entering the base-collector diode, there is a probability of generating one electron/hole pair
      • Under normal condition, this voltage is not high enough to cause breakdown
      • But in common-emitter configuration, the hole generated in the impact ionization process will enter the base
      • As the base is open, the hole can only enter the emitter
      • To allow the hole to enter the emitter, an associated voltage results at the floating base
      • The ratio of the electron to hole current when the base emitter junction is lowered, is related to $\beta$
      • Assume $\beta =100$, a single hole entering the emitter will cause 100 electrons to be injected from the emitter to the base
      • These 100 electrons will enter the collector, causing 10 more electron/hole pairs to be generated
      • This positive feedback will cause a very high collector current, even though the initial voltage is not high enough to cause breakdown
    • To increase the breakdown voltage
      • Reduce the chance to generate the first electron/hole pair by reducing the electric field, achievable by reducing the collector doping
      • Reduce $\beta$ to trade off between gain and breakdown voltage

# Summary of BJT Design

• Very high emitter doping relative to base, to increase $\gamma$
• Very small base width, to increase ${\alpha }_T$
  • So that the BJT behaves more like an ideal switch with high gain
• Base width cannot be too small, limited by the Early effect and base punchthrough
• Collector doping should be low to reduce Early effect and increase breakdown voltage

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