Semiconductor diode

A semiconductor diode is a two-terminal device that conducts current in only one direction, made of two or more layers of which at least one is a semiconductor. An example is the pn-diode, made by joining a p-type semiconducting layer to an n-type semiconducting layer.

Electrical behavior

(PD) Image: John R. Brews
Nonideal pn-diode current-voltage characteristics.

The ideal diode has zero resistance for the forward bias polarity, and infinite resistance (conducts zero current) for the reverse voltage polarity. In other words, the semiconductor diode acts as an electrical rectifier.

The semiconductor diode is not ideal. As shown in the figure, the diode does not conduct appreciably until a nonzero knee voltage (also called the turn-on voltage or the cut-in voltage) is reached. Above this voltage the slope of the current-voltage curve is not infinite (on-resistance is not zero). In the reverse direction the diode conducts a nonzero leakage current (exaggerated by a smaller scale in the figure) and at a sufficiently large reverse voltage below the breakdown voltage the current increases very rapidly with more negative reverse voltages.

As shown in the figure, the on and off resistances are the reciprocal slopes of the current-voltage characteristic at a selected bias point:

$R=\left.{\frac {\Delta V}{\Delta I}}\right|_{V=V_{BIAS}}\ ,$

where R is the resistance and ΔI is the current change corresponding to the voltage change ΔV at the bias V = V_BIAS.

Types

Semiconductor diodes come in a large variety of types:

• pn-diode: The pn junction diode consists of an n-type semiconductor joined to a p-type semiconductor.
• Zener diode: The Zener diode is a special type of pn-diode made to operate in the reverse breakdown region, and used often as a voltage regulator. The breakdown voltage in these diodes is sometimes called the Zener voltage. Depending upon the voltage range designed for, the diode may break down by either Zener breakdown, an electron tunneling behavior, or by avalanche breakdown.
• Schottky diode: The Schottky diode is made using a metal such as aluminum or platinum, on a lightly doped semiconductor substrate.
• Tunnel diode: Like the Zener diode, the tunnel diode (or Esaki diode) is made up of heavily doped n- and p-type layers with a very abrupt transition between the two types. Conduction takes place by electron tunneling.
• Light-emitting diode: The light-emitting diode is designed to convert electrical current into light.
• Photodiode: The photodiode is the inverse of the light-emitting diode, acting as a photodetector, converting incident light to a detectable electric current.
• pin-diode: The pin-diode is made of three layers: an intrinsic (undoped) layer between the p- and n-type layers. Because of its rapid switching characteristics it is used in microwave and radio-frequency applications.
• Gunn diode: The Gunn diode is a transferred electron device based upon the Gunn effect in III-V semiconductors, and is used to generate microwave oscillations.
• Varactor: a pn-junction used in reverse bias as a voltage-variable capacitor for tuning radio receivers. The term varactor also is used for devices that behave like back-to-back Zener diodes.

Operation

Here, the operation of the simple pn junction diode is considered. The objective is to explain the various bias regimes in the figure. Operation is described using band-bending diagrams that show how the lowest conduction band energy and the highest valence band energy vary with position inside the diode under various bias conditions. For additional discussion, see the article Semiconductor.

Zero bias

(PD) Image: John R. Brews
Band-bending diagram for pn-junction diode at zero applied voltage. The depletion region is shaded.

The figure shows a band bending diagram for a pn-diode; that is, the band edges for the conduction band (upper line) and the valence band (lower line) are shown as a function of position on both sides of the junction between the p-type material (left side) and the n-type material (right side). When a p-type and an n-type region of the same semiconductor are brought together and the two diode contacts are short-circuited, the Fermi half-occupancy level (dashed horizontal straight line) is situated at a constant level. This level insures that in the field-free bulk on both sides of the junction the hole and electron occupancies are correct. (So, for example, it is not necessary for an electron to leave the n-side and travel to the p-side through the short circuit to adjust the occupancies.) However, a flat Fermi level requires the bands on the p-type side to move higher than the corresponding bands on the n-type side, forming a step or barrier in the band edges, labeled φ_B. This step changes the electron density on the n-side to become a Boltzmann factor exp(−φ_B/V_th) smaller on the p-side, to correspond to the lower electron density in p-region. Here the symbol V_th denotes the thermal voltage, V_th=k_BT/q ≈ 25 mV at T=290 kelvins. Similar considerations apply for the effect of the barrier upon the hole density in the n-region. As a result of this step in band edges, a region near the junction becomes depleted of both holes and electrons, forming an insulating region with no mobile charges. There are, however, fixed, immobile charges due to dopant ions. The absence of mobile charge in the depletion layer means that mobile charges are not present to balance the immobile charge contributed by the dopant ions: a negative charge on the p-type side due to acceptor dopant and as a positive charge on the n-type side due to donor dopant. The width of the depletion region adjusts so the negative acceptor charge on the p-side exactly balances the positive donor charge on the n-side, so there is no electric field outside the depletion region on either side.

In this band configuration no voltage is applied and no current flows through the diode. To force current through the diode a forward bias must be applied, as described next.

Forward bias

(PD) Image: John R. Brews
Band-bending diagram for pn-diode in forward bias. Diffusion drives carriers across the depletion region.

In forward bias the occupancy level for holes tends to stay at the level of the bulk p-type semiconductor while the occupancy level for electrons follows that for the bulk n--type. A forward bias lowers the separation of the p-type bulk band edges to be closer in energy to those of the n-type, and the two bulk half-occupancy levels are separated by an energy determined by the applied voltage. (The band bending diagram is made in units of volts, so no electron charge appears to convert V to energy.) As shown in the diagram, this reduction in band bending means the step in band edges is reduced by the applied voltage to φ_B-V. The reduced step in band edges also means that the depletion region narrows as holes are pushed into it from the p-side and electrons from the n-side. In crossing the depletion layer, the half-occupancy lines for holes and electrons are not flat, and become quasi-Fermi levels that depend upon the current level. In the bulk region on the p-side of the device, the electron half-occupancy line becomes coincident with that of the holes, and vice versa on the n-side.

The electrons in the n-type material are called majority carriers on that side, but any that make it to the p-type side are called minority carriers. The same descriptors apply to holes: they are majority carriers on the p-type side, and minority carriers on the n-type side. From the diagram half-occupancy levels in the depletion region, it is evident that, although the majority carrier densities in this region are reduced compared to the bulk (the band edges bend away from the half-occupancy line), when they cross over the boundary between n-type and p-type to become minority carriers, their concentration far exceeds the value found for minority carriers in the alien bulk material.

With a forward bias a current flows. This current is a diffusion current (that is a current driven by a concentration gradient) of holes across the depletion region from the p-side and of electrons in the opposite direction from the n-side. In bulk material where there are no fields, minority carriers have a very low concentration compared to majority carriers, for example, electron density on the p-side is a factor exp(−φ_B/V_th) lower than on the n-side.. When application of voltage V reduces the step in band edges, that results in carrier densities adjacent to the interface a Boltzmann factor exp(V/V_th) larger than the bulk values of the zero-bias case. These excess densities near the interface and the low densities in the bulk combine to set up a gradient in carrier concentration, and that gradient drives a diffusion of carriers from the interface into the bulk. The minority carriers injected into the bulk by diffusion are reduced in number as they travel into the bulk by recombination mechanisms that drive the excess concentrations toward the bulk values.

Recombination can occur by direct encounter with a majority carrier, annihilating both carriers, or through a recombination-generation center, a defect that alternately traps holes and electrons, assisting recombination. The minority carriers have a limited lifetime, and this lifetime in turn limits how far they can diffuse from the majority carrier side into the minority carrier side, the so-called diffusion length. In the LED recombination of electrons and holes is accompanied by emission of light of a wavelength related to the energy gap between valence and conduction bands, so the diode converts a portion of the forward current into light.

In the simple pn-diode the forward current increases exponentially with forward bias voltage due to the exponential increase in carrier densities, so there is always some current at even very small values of applied voltage. However, if one is interested in some particular current level, it will require a "knee" voltage before that current level is reached. For example, a very common choice in texts about circuits using silicon diodes is V_Knee = 0.7 V. Above the knee, of course, the current continues to increase exponentially. Some special diodes, such as some varactors, are designed deliberately to maintain a low current level up to some knee voltage in the forward direction.

Reverse bias

(PD) Image: John R. Brews
Band-bending for pn-diode in reverse bias

In reverse bias the occupancy level for holes again tends to stay at the level of the bulk p-type semiconductor while the occupancy level for electrons follows that for the bulk n--type. In this case, the p-type bulk band edges are raised relative to the n-type bulk by the applied bias, so the two bulk occupancy levels are separated again by an energy determined by the applied voltage. As shown in the diagram, this behavior means the depletion region widens as holes are pulled away from it on the p-side and electrons on the n-side.

When the reverse bias is applied, the electric field in the depletion region is increased, pulling the electrons and holes further apart than in the zero bias case. Thus, any current that flows is due to the very weak process of carrier generation inside the depletion region due to generation-recombination defects in this region. That very small current is the source of the leakage current under reverse bias. In the photodiode, reverse current is introduced using creation of holes and electrons in the depletion region by incident light, thus converting a portion of the incident light into an electric current.

When the reverse bias becomes very large, reaching the breakdown voltage, the generation process in the depletion region accelerates leading to an avalanche condition which can cause runaway and destroy the diode.

Diode law

The DC current-voltage behavior of the ideal pn-diode is governed by the Shockley diode equation:

$I=I_{R}\left(e^{v_{D}/V_{th}}-1\right)\ ,$

with v_D the DC voltage across the diode, and I_R the reverse saturation current, the current that flows when the diode is reverse biased (v_D large and negative). The symbol V_th denotes the thermal voltage, V_th=k_BT/q ≈ 25 mV at T=290 kelvins.

This equation does not model the non-deal behavior such as excess reverse leakage or breakdown phenomena. In many practical diodes this equation must be modified to read:

$I=I_{R}\left(e^{\frac {v_{D_{\ }}}{nV_{th}}}-1\right)\ ,$

where the ideality factor, n is introduced to model a slower rate of increase than predicted by the ideal diode law. Using this equation, the diode on-resistance is:

$R={\frac {1}{dI/dv_{D}}}\approx {\frac {nV_{th}}{I}}\ ,$

exhibiting a lower resistance the higher the current.

Capacitance

The depletion layer between the n- and p-sides of a pn-junction serves as an insulating region that separates the two diode contacts. Thus, the diode in reverse bias exhibits a capacitance, analogous to a parallel plate capacitor with a dielectric spacer between the contacts. (In forward bias, the junction conducts and therefore does not exhibit only a capacitance.) In reverse bias the width of the depletion layer is widened with increasing reverse bias, and the capacitance is accordingly decreased. Thus, the junction serves as a voltage-controllable capacitor.