8.3 Current-voltage characteristics

Current-voltage characteristics of diodes describe how current flows through these semiconductor devices under different voltage conditions. They're crucial for understanding diode behavior in circuits, from basic rectification to complex switching applications.

Diodes exhibit nonlinear I-V curves due to their unique structure. In forward bias, they conduct easily after a threshold voltage. In reverse bias, they block current until breakdown occurs. This behavior enables various applications in electronics, from power supplies to logic gates.

Current-voltage characteristics of diodes

• Current-voltage (I-V) characteristics describe the relationship between the current flowing through a diode and the voltage applied across it
• Understanding I-V characteristics is crucial for analyzing and designing semiconductor devices and circuits
• Diodes exhibit nonlinear I-V characteristics due to their unique properties and structure

Ideal diode vs real diode

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• Ideal diodes have zero resistance in the forward bias and infinite resistance in the reverse bias (open circuit)
• Real diodes have a small forward voltage drop (typically 0.6-0.7V for silicon diodes) and a finite reverse saturation current
• Real diodes also have non-zero reverse leakage current and capacitance effects

Forward bias vs reverse bias

• Forward bias occurs when the p-type region is connected to the positive terminal and the n-type region to the negative terminal
  • Reduces the depletion region width and allows current to flow easily
• Reverse bias occurs when the p-type region is connected to the negative terminal and the n-type region to the positive terminal
  • Increases the depletion region width and allows only a small leakage current to flow

Diode equation

• The diode equation relates the current flowing through a diode to the voltage applied across it: $I = I_s(e^{qV/nkT} - 1)$
  • $I_s$: reverse saturation current
  • $q$: elementary charge
  • $V$: voltage across the diode
  • $n$: ideality factor (typically between 1 and 2)
  • $k$: Boltzmann's constant
  • $T$: absolute temperature
• The exponential term in the diode equation leads to the nonlinear I-V characteristics

Diode current components

• Total diode current consists of two main components: diffusion current and drift current
• Diffusion current dominates in forward bias and is caused by the diffusion of majority carriers across the depletion region
• Drift current is caused by the drift of minority carriers in the depletion region and is significant in reverse bias

Diffusion current vs drift current

• Diffusion current is proportional to the gradient of the carrier concentration and is the main component of forward bias current
• Drift current is proportional to the electric field in the depletion region and is the main component of reverse bias current
• The relative magnitudes of diffusion and drift currents determine the shape of the diode I-V curve

Temperature dependence of diode current

• Diode current increases with temperature due to the increased thermal generation of carriers
• The reverse saturation current $I_s$ is strongly dependent on temperature and can be approximated by: $I_s \propto T^3e^{-E_g/kT}$
  • $E_g$: bandgap energy of the semiconductor
• Forward voltage drop decreases with increasing temperature (typically -2mV/°C for silicon diodes)

Breakdown mechanisms in diodes

• Breakdown in diodes occurs when the reverse bias voltage exceeds a certain threshold, leading to a sharp increase in reverse current
• Understanding breakdown mechanisms is important for designing high-voltage diodes and protection circuits

Zener breakdown

• Zener breakdown occurs in heavily doped p-n junctions with a narrow depletion region
• Under high reverse bias, the strong electric field in the depletion region causes tunneling of electrons from the valence band to the conduction band
• Zener breakdown is characterized by a sharp knee in the I-V curve and a constant reverse voltage (Zener voltage)

Avalanche breakdown

• Avalanche breakdown occurs in lightly doped p-n junctions with a wide depletion region
• Under high reverse bias, the strong electric field accelerates carriers, causing impact ionization and generating electron-hole pairs
• The newly generated carriers also undergo impact ionization, leading to an avalanche multiplication of current

Reverse breakdown voltage

• The reverse breakdown voltage $V_{BR}$ is the voltage at which the diode enters the breakdown region
• $V_{BR}$ depends on the doping concentrations, depletion region width, and the dominant breakdown mechanism (Zener or avalanche)
• Diodes with a specific $V_{BR}$ can be designed by controlling the doping profile and junction geometry

Diode equivalent circuits

• Diode equivalent circuits are simplified models that capture the essential behavior of diodes in different operating regions
• These models are used for circuit analysis and design, allowing for the prediction of diode performance in various applications

Ideal diode model

• The ideal diode model assumes zero forward voltage drop and infinite reverse resistance
• In forward bias, the diode acts as a short circuit, allowing current to flow freely
• In reverse bias, the diode acts as an open circuit, blocking any current flow

Constant voltage drop model

• The constant voltage drop model assumes a fixed forward voltage drop $V_D$ (typically 0.6-0.7V for silicon diodes) when the diode is forward biased
• In forward bias, the diode voltage remains constant at $V_D$, and the current is determined by the external circuit
• In reverse bias, the diode acts as an open circuit, similar to the ideal diode model

Piecewise linear model

• The piecewise linear model combines the constant voltage drop model in forward bias with a linear resistance in reverse bias
• In forward bias, the diode voltage is $V_D$, and the current is determined by the external circuit
• In reverse bias, the diode is modeled as a high resistance $R_R$, allowing for a small leakage current

Small-signal model of diodes

• The small-signal model is used for analyzing the behavior of diodes under small-signal excitation, such as in amplifiers and filters
• The model consists of a dynamic resistance $r_d$ in series with an ideal diode
• The dynamic resistance $r_d$ is given by: $r_d = \frac{nkT}{qI_D}$, where $I_D$ is the DC operating current
• The small-signal model is valid for small perturbations around the DC operating point

Diode capacitance effects

• Diodes exhibit capacitance effects due to the charge storage in the depletion region and the diffusion of carriers
• These capacitance effects influence the high-frequency behavior and switching characteristics of diodes

Depletion layer capacitance

• The depletion layer capacitance $C_j$ arises from the charge stored in the depletion region
• $C_j$ is voltage-dependent and decreases with increasing reverse bias voltage
• The depletion layer capacitance is given by: $C_j = \frac{C_{j0}}{\sqrt{1 + V_R/V_{bi}}}$
  • $C_{j0}$: zero-bias junction capacitance
  • $V_R$: reverse bias voltage
  • $V_{bi}$: built-in potential

Diffusion capacitance

• The diffusion capacitance $C_d$ is caused by the diffusion of minority carriers in the neutral regions
• $C_d$ is proportional to the forward bias current and is significant at high injection levels
• The diffusion capacitance is given by: $C_d = \frac{\tau I_D}{nkT/q}$
  • $\tau$: carrier lifetime
  • $I_D$: forward bias current

Diode switching characteristics

• The capacitance effects in diodes influence their switching characteristics, such as the turn-on and turn-off times
• During turn-on, the diode capacitances must be charged, leading to a delay in the current rise time
• During turn-off, the stored charge in the diode must be removed, resulting in a reverse recovery current and a delay in the voltage rise time

Applications of diode I-V characteristics

• The unique I-V characteristics of diodes enable various applications in electronic circuits
• Understanding the I-V characteristics is crucial for selecting the appropriate diodes and designing circuits that leverage their properties

Rectifiers and power supplies

• Diodes are commonly used in rectifier circuits to convert AC to DC
• The nonlinear I-V characteristics allow diodes to conduct current only in one direction, enabling the rectification of AC signals
• Half-wave rectifiers use a single diode to produce a pulsating DC output, while full-wave rectifiers use multiple diodes to produce a more stable DC output

Voltage regulators using Zener diodes

• Zener diodes, which exhibit a sharp breakdown voltage, are used in voltage regulator circuits
• By operating the Zener diode in the reverse breakdown region, a stable reference voltage can be obtained
• The Zener diode is connected in parallel with the load, and a series resistor limits the current through the diode

Diode clipping and clamping circuits

• Diode clipping circuits use the forward voltage drop of diodes to limit the amplitude of an input signal
• Series clipping circuits place the diode in series with the load, while parallel clipping circuits place the diode in parallel with the load
• Clamping circuits use diodes to shift the DC level of an AC signal, either by clamping the signal to a positive or negative DC level

Diodes in logic gates and switches

• Diodes can be used to implement simple logic gates, such as AND and OR gates
• The nonlinear I-V characteristics enable diodes to perform switching functions, allowing or blocking current flow based on the input conditions
• Diode-resistor logic (DRL) and diode-transistor logic (DTL) are examples of logic families that utilize diodes in combination with resistors and transistors