Junction Theory & Different Types of Diodes & Their Characteristics - 2

Table of Contents
1. Diode Resistance
2. Transition or Space-Charge (Depletion-Region) Capacitance (\(C_{T}\))
3. Diffusion (Storage) Capacitance (\(C_{D}\))
4. Diode Applications
5. Breakdown Diodes (Zener and Avalanche Diodes)
6. Tunnel Diode
7. Characteristics of a Tunnel Diode
8. Summary
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Diode Resistance

Static (or DC) resistance of a diode is defined as the ratio of the voltage across the diode to the current through it, that is the ratio V/I for a given operating point. Typical values for a silicon planar epitaxial diode are: forward voltage \(V_{F}=0.8\) V at forward current \(I_{F}=10\) mA (corresponding to \(R_{F}=80\ \Omega\)) and reverse leakage current \(I_{R}=0.1\ \mu\)A at reverse voltage \(V_{R}=50\) V (corresponding to \(R_{R}=500\) MΩ).

Dynamic (or incremental) resistance is important for small-signal operation. It is defined as the reciprocal of the slope of the current-voltage characteristic:

\(\displaystyle r=\frac{dV}{dI}\)

The dynamic conductance is the reciprocal of dynamic resistance:

\(\displaystyle g=\frac{1}{r}=\frac{dI}{dV}\)

For the ideal diode equation \(I=I_{0}\bigl(e^{V/(\eta V_{T})}-1\bigr)\), where \(I_{0}\) is the reverse saturation current, \(\eta\) is the ideality factor and \(V_{T}=kT/q\) is the thermal voltage, the incremental conductance for \(|V/(\eta V_{T})|\gg 1\) and in forward bias (\(I\gg I_{0}\)) is approximately

\(\displaystyle g=\frac{dI}{dV}\approx\frac{I}{\eta V_{T}}\)

and hence the dynamic resistance is

\(\displaystyle r\approx\frac{\eta V_{T}}{I}\)

Thus when forward current is large, r is small; under large reverse bias the conductance is very small and r is very large.

The piecewise linear characterization of a semiconductor diode.

For an avalanche diode in the breakdown region, the dynamic resistance in that region is commonly denoted \(R_{f}\). For such diodes the breakdown voltage is often written \(V_{y}\) or \(V_{z}\).

Transition or Space-Charge (Depletion-Region) Capacitance (\(C_{T}\))

The depletion region of a p-n junction consists of uncovered, immobile ions on the p- and n-sides. These oppositely charged layers separated by the depletion width behave like the plates of a parallel-plate capacitor. The transition (or junction) capacitance is

\(\displaystyle C_{T}=\frac{\varepsilon A}{W}\)

where \(\varepsilon=\varepsilon_{0}\varepsilon_{r}\) is the permittivity of the semiconductor, \(A\) is the junction cross-sectional area and \(W\) is the total depletion width.

The condition of charge neutrality across the depletion region is

\(N_{A}W_{p}=N_{D}W_{n}\)

where \(N_{A}\) and \(N_{D}\) are the acceptor and donor concentrations, and \(W_{p}\) and \(W_{n}\) are the depletion widths on the p- and n-sides respectively.

For a one-sided step junction (a useful approximation when \(N_{A}\ll N_{D}\) or vice versa) the barrier potential \(V_{B}\) and depletion width relations can be written. The effective barrier potential is

\(\displaystyle V_{B}=\frac{q N_{A} W^{2}}{2\varepsilon}\)

In the general case the total depletion width is

\(\displaystyle W=\sqrt{\frac{2\varepsilon(V_{0}-V)}{q}\cdot\frac{N_{A}+N_{D}}{N_{A}N_{D}}}\)

where \(V\) is the applied voltage (positive for forward bias) and \(V_{0}\) is the built-in contact potential (barrier potential). The barrier seen by carriers is \(V_{B}=V_{0}-V\).

• With no external bias (\(V=0\)) the depletion width of a typical p-n junction diode is of the order of 0.5 μm. The stored opposite charges separated by this distance give a junction capacitance typically around 20 pF for small signal diodes.
• Under forward bias the effective barrier \(V_{B}=V_{0}-V\) is reduced, the depletion width \(W\) decreases and the transition capacitance \(C_{T}\) increases. Under reverse bias the barrier \(V_{B}=V_{0}-(-V)=V_{0}+V\) increases, \(W\) increases and \(C_{T}\) decreases.
• Values of \(C_{T}\) range typically from 5 pF to 200 pF for many signal diodes; high-power diodes can have larger junction capacitances. The voltage-dependent capacitance property is used in varactor diodes (varicaps) for tunable filters and oscillator tuning circuits.

Diffusion (Storage) Capacitance (\(C_{D}\))

Diffusion capacitance appears when the junction is forward biased and is due to the change in injected charge stored in the quasi-neutral regions outside the depletion layer. It is defined as the rate of change of stored charge with voltage:

\(\displaystyle C_{D}=\frac{dQ}{dV}\)

For a forward biased diode, the diffusion capacitance is proportional to the forward current and may be written approximately as

\(\displaystyle C_{D}=\frac{\tau I}{\eta V_{T}}\)

where \(\tau\) is the mean minority-carrier lifetime. Typical values of \(C_{D}\) range from 10 pF up to 1000 pF; larger values correspond to diodes carrying larger forward current. The effect of \(C_{D}\) is negligible in reverse bias.

\(C_{D}\) decreases with increasing frequency because it is associated with carrier storage; at high frequencies carriers cannot respond fast enough and the effective \(C_{D}\) falls.

Although \(C_{D}\) can be much larger than \(C_{T}\) under forward bias, the diode time constant \(rC_{D}\) may still be moderate because the dynamic forward resistance \(r\) is small. The relation between the time constant and carrier lifetime is

\(\displaystyle rC_{D}=\tau\)

Hence the diode time constant equals the mean minority-carrier lifetime, which may range from a few nanoseconds to hundreds of microseconds depending on device design and materials.

Charge-Control Description of a Diode

The charge-control model relates diode current to the stored excess minority-carrier charge. The basic relation is

\(\displaystyle I=\frac{Q}{\tau}\)

or equivalently, for a single carrier diffusion region modeled by a diffusion length \(L_{p}\),

\(\displaystyle I=\frac{Q D_{p}}{L_{p}^{2}}\)

where \(Q\) is the total stored excess minority charge, \(D_{p}\) is the diffusion coefficient and \(\tau\) is the carrier lifetime. This expresses that in steady state the forward current supplies minority carriers at the same rate at which they recombine and disappear.

Diode Applications

An ideal p-n junction diode is a two-terminal, polarity-sensitive device: it conducts with low resistance when forward biased and blocks (high resistance) when reverse biased. Because of these properties diodes find many practical applications.

• Rectifiers in d.c. power supplies
• Switches in digital logic circuits and computer input/output protection
• Clamping networks used as DC restorers in television receivers and as voltage multipliers
• Clipping circuits and waveform shaping in computers, radar, radio and TV receivers
• Demodulators (detectors) in radio and TV receivers

Specialised forms of the p-n junction produced by different doping and construction are used as:

• Photodiodes and avalanche photodiodes (APD) for optical detection
• Zener diodes for voltage regulation
• Varactor (varicap) diodes for voltage-controlled tuning in radio and TV receivers
• Light-emitting diodes (LEDs) for displays
• Laser diodes for optical communications
• Tunnel diodes in microwave and high-speed switching applications

Breakdown Diodes (Zener and Avalanche Diodes)

Diodes that are designed to operate reliably in the reverse-breakdown region are used as voltage-reference or regulator devices. Such diodes are commonly called Zener diodes (for low breakdown voltages where the Zener effect is significant) or avalanche diodes (for higher breakdown voltages dominated by avalanche multiplication).

When reverse biased beyond a certain voltage the diode enters the breakdown region and a large reverse current flows while the voltage across the diode remains nearly constant. This property enables regulation: changes in load current or supply voltage produce only small changes in diode voltage within the breakdown region.

Two physical mechanisms for breakdown are important:

• Avalanche multiplication: Thermally generated carriers gain enough kinetic energy in the strong electric field to ionise atoms by impact, producing additional carriers and leading to a multiplication process. Avalanche breakdown dominates at breakdown voltages above roughly 6 V and has a positive temperature coefficient (breakdown voltage increases with temperature).
• Zener tunnelling: In very high field regions (typically for breakdown voltages below about 6 V), electrons can tunnel directly from the valence band to the conduction band through the high field region; this is the Zener effect and it produces a negative temperature coefficient (Zener voltage decreases with temperature).

The junction capacitance of breakdown diodes is the transition capacitance \(C_{T}\). High-power avalanche diodes can exhibit large capacitances; values from about 10 pF up to 10,000 pF are common depending on geometry and design.

(a) The volt-ampere Characteristic of an avalanche, or Zener, diode.
(b) A circuit in which such a diode is used to regulate the voltage across R_L against changes due to variations in load current and supply voltage.

Tunnel Diode

Tunnel diodes are heavily doped p-n junction devices first reported by Esaki in 1958. Heavy doping (impurity levels ≈ 10¹⁹/cm³) reduces the depletion width to the order of 10^-6 cm (≈100 Å), thin enough that carriers can quantum mechanically tunnel through the potential barrier.

Tunnelling phenomenon

Classically, a particle must have energy at least equal to the barrier height to cross it. Quantum mechanics, via the Schrödinger equation, shows a finite probability that an electron will penetrate and pass through a sufficiently thin barrier even if its energy is less than the barrier height-this is tunnelling. In heavily doped p-n junctions the tunnelling current dominates the I-V characteristic near zero bias, giving rise to unusual features.

(a) symbol for a tunnel diode (b) small-signal model of a tunnel diode in the negative resistance region (c) The volt-ampere characteristic of a tunnel diode.

Characteristics of a Tunnel Diode

The tunnel diode I-V characteristic exhibits a negative resistance region between a peak current \(I_{p}\) and a valley current \(I_{v}\). The typical shape is:

• At small forward bias the tunnelling current rises to a peak \(I_{p}\) at voltage \(V_{p}\).
• As voltage increases further the tunnelling probability for carriers decreases and the current falls to a minimum valley value \(I_{v}\) at voltage \(V_{v}\). Between \(V_{p}\) and \(V_{v}\) the device shows negative differential resistance \(\frac{dI}{dV} < 0\).
• Beyond the valley the normal forward diffusion current dominates and current rises again.

The negative resistance region makes the tunnel diode useful as an ultra-high speed switch and as an oscillator at microwave frequencies. Typical switching speeds are extremely fast-nanoseconds to picoseconds-and devices have been used where very low-noise, high-speed switching or microwave generation is required.

Tunnel diode applications

• Ultra-high speed switching (ns to ps range)
• Logic and memory circuits where very fast bistable elements are required
• Microwave oscillators and amplifiers
• Relaxation oscillators and pulse generators

Advantages and disadvantages

Advantages

1. Low noise
2. Simple operation
3. Very high speed
4. Low power consumption

Disadvantages

1. Very limited voltage range of useful operation (typically about 1 V or less across the negative resistance region)
2. Being a two-terminal device, there is no input-output isolation

Summary

This chapter has covered key small-signal and large-signal parameters of junction diodes: static and dynamic resistance, transition and diffusion capacitances, the charge-control description linking stored charge and current, practical diode applications, the physics and use of breakdown (Zener/avalanche) diodes, and the special properties and applications of Esaki (tunnel) diodes. The mathematical relations presented (for \(r\), \(g\), \(C_{T}\), \(C_{D}\), and \(W\)) are the standard design and analysis formulas used in semiconductor device and circuit studies.