Tunnel Diode - Electronic Devices - Electronics and Communication Engineering

Table of Contents
1. Introduction
2. Circuit symbol
3. Construction, materials and doping
4. Working principle
5. V-I characteristics of a tunnel diode
6. Current components in a tunnel diode
7. Peak voltage and peak current - derivation (tunneling model)
8. Small-signal (equivalent) model
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Introduction

Tunnel diode is a two-terminal, heavily doped semiconductor device that operates by the quantum mechanical tunneling effect. It was first investigated by Leo Esaki; for this discovery he received the Nobel Prize in Physics in 1973. Tunnel diodes are used for very low-voltage, very high-speed switching and for microwave-frequency applications where their negative resistance region is exploited.

Circuit symbol

The tunnel diode has an anode formed by the p-type material and a cathode formed by the n-type material. Its circuit symbol is similar to a PN junction diode but the device is identified by its characteristic properties rather than by a different symbol.

Construction, materials and doping

Tunnel diodes are fabricated from semiconductor materials with very heavy doping on both p and n sides. Typical doping concentrations are many orders of magnitude larger than those of a normal PN junction, producing a very narrow depletion layer (of the order of a few nanometres to about 10 nm). Because of such heavy doping the device shows significant tunneling current. Common materials used are germanium (Ge) and gallium arsenide (GaAs), which give favourable peak-to-valley characteristics for microwave use.

Working principle

Quantum tunneling

Classically, a charged particle must have energy at least equal to a potential barrier to cross it. Quantum mechanics allows a non-zero probability that a particle with energy less than the barrier will cross the barrier by tunneling. This probability falls rapidly as the barrier width and height increase.

The tunneling probability may be written qualitatively as

P α exp(-A · Eb · W)

Where P is the tunneling probability, Eb is the barrier energy (height), W is the barrier width and A is a constant related to material parameters. In a tunnel diode the barrier width is extremely small because of heavy doping, so tunneling across the junction becomes a dominant transport mechanism at small applied voltages.

Energy band diagrams and bias conditions

Understanding the V-I characteristics requires energy band diagrams of the heavily doped PN junction under different bias conditions:

• At zero bias the conduction-band states on the n side overlap in energy with valence-band states on the p side because heavy doping brings the Fermi levels close to band edges; this overlap allows tunneling of electrons even at small applied voltages.
• Under small forward bias the number of filled states on the n side that align with empty states on the p side increases, and tunneling current increases rapidly. This continues until the peak current is reached.
• As forward bias increases beyond the peak bias, the alignment of occupied and empty states deteriorates and the tunneling current decreases - this produces a region of negative slope (negative differential resistance) in the V-I curve.
• At still larger forward bias normal diffusion (thermionic) current of a forward-biased diode becomes dominant; the device then behaves like an ordinary diode past the valley point.
• Under reverse bias a high tunneling current is also possible because many filled states in the valence band of the p side align with empty states in the conduction band of the n side; thus reverse conduction is relatively large compared to a lightly doped PN junction.

V-I characteristics of a tunnel diode

The typical V-I characteristic of a tunnel diode shows three forward regions: a rising current region up to the peak, a decreasing current (negative resistance) region from peak to valley, and then an ordinary forward conduction region beyond the valley. In reverse bias the device also conducts significantly.

• At very small forward voltages the forward resistance is very small because tunneling dominates; current increases with voltage until the peak current (I_p) at peak voltage (V_p).
• When voltage increases beyond V_p the tunnel current falls and the net current decreases; the slope dI/dV is negative in this region - this is the negative resistance region. The negative resistance region continues until the valley point, where the current reaches a minimum (I_v) at voltage V_v.
• Beyond the valley region the diode behaves like an ordinary forward-biased diode and current increases rapidly with voltage.
• Tunnel diodes used for microwave and high-frequency applications often use Ge or GaAs because of more favourable peak and valley voltages and higher peak-to-valley current ratios.

Current components in a tunnel diode

The total current through a tunnel diode is the sum of three components:

I_t = I_tun + I_diode + I_excess

• Tunnel current (I_tun) - due to quantum tunneling across the narrow depletion region; dominant at low forward voltages and in reverse bias.
• Diode current (I_diode) - ordinary diffusion/thermionic current that follows the PN diode exponential law and becomes important at voltages beyond the valley point. It can be expressed as
  I_diode = I_do · (exp(V/(η·V_t)) - 1)
  where I_do is the reverse saturation current, V is the applied voltage, V_t is the thermal voltage (≈ kT/q) and η is the ideality factor (≈1 for Ge, ≈2 for Si in many cases).
• Excess current (I_excess) - additional leakage or parasitic tunneling via defects, impurities, or trap states; this sets the valley current and affects the minimum current in the negative resistance region.

A commonly used empirical form for the tunneling current is

I_tun = (V / R_O) · exp(-(V / V_O)^m)

where R_O is a characteristic resistance, V_O is a characteristic voltage (typical order 0.1-0.5 V for many devices) and m is an empirical exponent (often between 1 and 3).

Peak voltage and peak current - derivation (tunneling model)

For the empirical tunneling current I = (V / R_O) · exp(-(V / V_O)^m) the peak current occurs where dI/dV = 0. The derivation follows.

Differentiate I with respect to V and set derivative equal to zero to find V_peak.
dI/dV = (1 / R_O) · exp(-x) · [1 - V · (dx/dV)]
where x = (V / V_O)^m.
Compute dx/dV = m · (V / V_O)^m-1 · (1 / V_O) = m · (V / V_O)^m / V.
Therefore V · (dx/dV) = m · (V / V_O)^m.
Setting dI/dV = 0 gives
1 - m · (V / V_O)^m = 0
so

V_p = V_O · (1 / m)^1/m

The corresponding peak current is

I_p = (V_p / R_O) · exp(-(V_p / V_O)^m) = (V_O / R_O) · (1 / m)^1/m · exp(-1 / m)

Small-signal (equivalent) model

The small-signal equivalent of a tunnel diode in its negative resistance region typically includes the following elements:

• R_s - series (ohmic) resistance from the semiconductor bulk and contacts.
• -R_n - the negative resistance representing the slope of the DC V-I in the negative region; its magnitude is |R_n| = 1/|dI/dV| where dI/dV is negative.
• L_s - series inductance due to leads and packaging that may affect high-frequency behaviour.
• C or C_j - junction or depletion capacitance, approximately C = ε · A / W, where ε is the permittivity, A the junction area and W the depletion width; this capacitance affects the device response at microwave frequencies.

For the empirical tunneling model the small-signal conductance (dI/dV) can be expressed as

dI/dV = (1 / R_O) · exp(-(V / V_O)^m) · [1 - m · (V / V_O)^m]

Hence the small-signal resistance is

r = 1 / (dI/dV) = R_O · exp((V / V_O)^m) / [1 - m · (V / V_O)^m]

When the bracketed term is negative, the device exhibits negative differential resistance. At the point where the bracket term is zero the slope is zero (horizontal tangent on V-I) and the small-signal resistance becomes very large in magnitude.

Advantages and disadvantages

• Advantages: very high speed (tunneling is a fast quantum process), low noise, low power dissipation, simple two-terminal construction, good environmental immunity and long life when properly manufactured.
• Disadvantages: limited output voltage swing (small signal voltages), no isolation between input and output since it is a two-terminal device, manufacturing and matching for circuits can be more specialised, peak-to-valley current ratio limits usable negative resistance range.

Applications

Important applications that exploit the tunnel diode's negative resistance and fast response include:

• Very high-speed switching circuits where switching time is critical.
• Microwave and UHF oscillators and amplifiers using the negative resistance region to sustain oscillation.
• Frequency mixers and detectors in microwave front-ends.
• Relaxation oscillators, bistable devices and some specialised logic circuits where the negative resistance provides regenerative action.
• Low-noise amplifiers and detectors in niche, high-frequency systems.

Practical notes and typical parameters

• Because the tunnel diode relies on very heavy doping, its junction depletion region is extremely narrow (a few nanometres); careful fabrication and clean interfaces are required.
• Characteristic voltages V_O quoted in device models are often in the range of 0.1-0.5 V; the empirical exponent m typically lies between 1 and 3 and is dependent on device structure and material.
• The useful negative resistance region is limited in voltage extent; circuit designers must ensure correct biasing and loading so that the diode operates within the desired region (between V_p and V_v).

Summary

The tunnel diode is a heavily doped PN junction device that uses quantum tunneling to give extremely fast response and a distinctive V-I characteristic with a negative resistance region. It is valuable in specialised high-frequency and switching applications. Analysis of its behaviour combines the tunneling current model with ordinary diode current and parasitic contributions; device modelling and circuit design must take the peak, valley and small-signal resistance into account for stable and effective operation.