半导体器件原理 1.7 Real PN Junction Charateristics

About non-ideal PN junction characteristics, PN junction turn-on, breakdown, temperature effects, and how to design a PN junction.

# Ideal Diode Current in Log Scale

• When $V_A$ is small, $-1$ takes dominance, and $I$ decreases quickly in log scale
• When $V_A$ is large, $e^{\frac{q{V}_A}{kT}}$ takes dominance, and $I$ increases linearly in log scale
• The slope of the linear region can indicate how abruptly we can turn on the diode with applied voltage
  • $$\text{slope}=\frac{q}{kT}\log e$$
  • The unit of slope in log scale is a bit difficult to express, so we tend to refer$$\text{swing (}S\text{)}=\frac{1}{\text{slope}}=\frac{kT}{q}\ln 10$$
  • Once $T$ is known, $S$ is fixed

  • A Very Important Reference

    At room temperature:

    • $S=60\text{mV/dec}$
      • This means that for every increase of $60\text{mV}$ in the applied voltage $V_A$, the current $I$ increases by 10 times (one decade).
      • Remember this value
      • A smaller swing means a steeper slope, which means the diode can be turned on more abruptly with a smaller change in voltage
    • $V_{\text{th}}=\frac{kT}{q}=25\text{mV}$
      • Or $26\text{mV}$, depending on the round off method
      • The thermal voltage
      • With the same unit as voltage

# Recombination Current in the Depletion Region

• The characteristics of a real diode differs from the real one
  • At low current, measured current is usually higher than the ideal one
  • When $V_A$ increases to close to $V_{bi}$, the increase in the measured current slows down
  • 
• The ideal equation assumes no recombination happens in the depletion region
• However, in reality, recombinations happen in the depletion region
• As discussed in the previous chapter, recombination is a mechanism that encourages a higher current flow
• Therefore, recombination in the depletion region leads to higher majority carrier current
  • This current can be ignored when $V_A$ is large
  • When $V_A$ is small, this current is observable

# High Level Injection

• The ideal equation assumes the number of injected minority carriers does not effect the majority carrier concentration
• However, when $V_A$ is large, the number of injected minority carriers can be comparable to the majority carrier concentration at equilibrium
• On the P side:
  • Electrons are injected from the N side
  • High level electron injection causes accumulation of negative charges
  • This accumulation of negative charges repels holes, causing holes to accumulate on the P side near the depletion region
  • This creates a diffusion force which drives holes away against its motion in the ideal forward bias case
  • This is the high-level injection effect
  • The accumulation of holes is insignificant when $V_A$ is small
  • But can be very significant when $V_A$ is large
• The high-level injection effect always takes place first at the lightly doped side (because the majority carrier concentration is lower)

# Complete PN Junction Turn-on

• When we further increase $V_A$ beyond $V_{bi}$, the depletion region disappears
• As discussed in Chapter 1.5, the diode now behaves like a resistor
  • $I$ becomes proportional to $V_A$
  • Gives a straight line in linear scale
  • Shows saturating behavior in log scale

• When you see the current increases with voltage, the diode is most likely to be in the resistive region already
  • So the ideal diode equation is only valid for the $I-V$ curve close to zero, or before the diode turns on
• Fully turn-on region: the resistive region when the depletion region disappears
• Turn-on voltage $V_{\text{ON}}$: Measured by extending the straight line in $I-V$ curve to cut the $V$ axis
  • 
  • The turn-on voltage for a silicon diode is assumed to be around $0.7\text{V}$

# PN Junction Breakdown

• The ideal equation shows that the current remains small for any negative $V_A$
• However, in reality, when $V_A$ is negative and large enough, the current increases rapidly in the negative direction
• This is called reverse breakdown
• Two different mechanisms can cause reverse breakdown
  • Avalanche breakdown
    • A high electric field is created in the depletion region when $V_A$ is negative and large
    • This high electric field can accelerate carriers to very high speeds
    • These high-speed carriers can collide with atoms in the crystal lattice and generate electron-hole pairs
    • When the reverse bias is high enough, the additional electron-hole pairs, together with the original carriers, can create more collisions and generate even more electron-hole pairs, resulting in a large reverse current
    • It is like a avalanche caused by a small snowball
  • Zener breakdown
    • Recall the equation used to calculate the depletion region width:$$x_d=\sqrt{\frac{2{\epsilon }_{\text{Si}}{V}_{bi}}{q}(\frac{1}{N_A}+\frac{1}{N_D})}$$
    • When the doping concentration is very high, the depletion region width can be very small
    • For a narrow junction with high reverse bias voltage, the lateral separation between the conduction band and the valence band can be very small
    • This allows electrons in the valence band to tunnel through the energy barrier to the conduction
    • This tunneling effect can create a large reverse current
• Breakdown may not be destructive
  • If the current is limited, the diode can recover after the reverse bias is removed
  • What really destroys the diode is the heat generated by the large current, melting the junction

# Temperature Effects

• At high temperature, the impact of carriers added by doping is less significant
  • Both sides of the junction behave more like intrinsic semiconductors
  • $V_{bi}$ and $V_{\text{ON}}$ decreases
  • The junction will be less effective as a rectifier, more like a resistor
  • $I_D$ increases, leading to a higher reverse saturation current
  • The slope of the ideal region decreases, leading to a larger swing $S$, making the diode more conductive, the current becomes less sensitive to voltage change, and is more difficult to turn off
  • Rectifying properties are degraded

# PN Junction Design

• The current follows a more complicated 2D or 3D pattern
• For the heavily doped side, the resistance is relatively low and close to ideal, it can be doped as heavily as possible, subjective to the solid solubility limit
• The lightly doped side controls the properties of the diode
  • If we simply connect metal to the lightly doped side, the series resistance will be very high
  • The metal-semiconductor contact resistance is usually very high
  • And the current may concentrate on a small area, due to the non-uniform resistance distribution
• We wish to decrease the resistance by adopting a higher doping concentration, but this may significantly decrease the breakdown voltage
• Design goal: select a high enough doping concentration to reduce the series resistance, while maintaining a high enough breakdown voltage

• The breakdown condition is related to the maximum electric field in the depletion region
• The avalanche breakdown voltage can be plotted against the doping concentration on the lightly doped side
• Once the doping concentration passes a certain value, the Zener breakdown will take over
  • Once the electric field/slope of the band is known, the lateral separation between the conduction band and the valence band (tunneling distance) can be calculated
• It is important to understand how the electric field changes with doping concentration

• Recall how we calculate the depletion region width
  • $$x_{p/n}\approx \sqrt{\frac{2{\epsilon }_{\text{Si}}(V_{bi}-V_A)}{q}\frac{1}{N_{A/D}}}$$
  • According to Gauss’s law, the electric field in the depletion region is$$\frac{\mathrm{d}E}{\mathrm{d}x}=\frac{\rho }{{\epsilon }_{\text{Si}}}$$Thus$${\overrightarrow{E}}_{\text{max}}=-\frac{q{N}_{A/D}{x}_{p/n}}{{\epsilon }_{\text{Si}}}$$
  • Now we have$${\overrightarrow{E}}_{\text{max}}=-\sqrt{\frac{2q{N}_{A/D}(V_{bi}-V_A)}{{\epsilon }_{\text{Si}}}}$$
• Now we have the relationship between the maximum electric field and the doping concentration
• To choose a proper doping concentration, we begin with an arbitrary concentration
• Then we can calculate $|{\overrightarrow{E}}_{\text{max}}|$
• We compare $|{\overrightarrow{E}}_{\text{max}}|$ with $E_{\text{BD}}$, which can be found in the avalanche breakdown curve
• If $|{\overrightarrow{E}}_{\text{max}}|<E_{\text{BD}}$, the doping concentration is acceptable
• Else, we need to reduce the doping concentration and repeat the process
• As an engineer, make sure to leave enough margin

• Besides the depletion region, a diode also consists of neutral regions
• The neutral regions contribute little to the rectifying properties of the diode, but contribute to the series resistance
  • We can increase the doping concentration to reduce the resistance
• We can also add another P contact to make the resistance more uniform at different locations

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