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Diodes

Semiconductor Devices

Semiconductors have many applications in modern electronics. We describe some basic semiconductor devices in this section. A great advantage of using semiconductors for circuit elements is the fact that many thousands or millions of semiconductor devices can be combined on the same tiny piece of silicon and connected by conducting paths. The resulting structure is called an integrated circuit (ic), and ic chips are the basis of many modern devices, from computers and smartphones to the internet and global communications networks.

Diodes

Perhaps the simplest device that can be created with a semiconductor is a diode. A diode is a circuit element that allows electric current to flow in only one direction, like a one-way valve. A diode is created by joining a p-type semiconductor to an n-type semiconductor (this figure). The junction between these materials is called a p-n junction. A comparison of the energy bands of a silicon-based diode is shown in this figure (b). The positions of the valence and conduction bands are the same, but the impurity levels are quite different. When a p-n junction is formed, electrons from the conduction band of the n-type material diffuse to the p-side, where they combine with holes in the valence band. This migration of charge leaves positive ionized donor ions on the n-side and negative ionized acceptor ions on the p-side, producing a narrow double layer of charge at the pn junction called the depletion layer. The electric field associated with the depletion layer prevents further diffusion. The potential energy for electrons across the p-n junction is given by this figure.

Figure a shows two blocks place side by side, in contact. The left one is labeled p and the right one is labeled n. Figure b shows a valence band at the bottom and a conduction band at the top. There are holes within the valance band on the left, labeled holes at the top of the valence band. There are electrons above the conduction line on the right, labeled electrons at the bottom of the conduction band. Impurity bands are shown above the holes and below the electrons.

(a) Representation of a p-n junction. (b) A comparison of the energy bands of p-type and n-type silicon prior to equilibrium.

Figure a shows two blocks place side by side, in contact. The left one is labeled p and the right one is labeled n. Minus signs are shown in the p block near the side in contact. Plus signs are shown in the n block near the side in contact. Figure b shows a valence band at the bottom and a conduction line at the top. The valence band is higher on the left side almost reaching the central line between the two bands. There are holes with the valence band at the top, on the left. The conduction line is lower on the right, almost reaching the central line between the two bands. There are electrons just above the line, on the right. The displacement of the bands is labeled eV subscript 0, potential difference prevents diffusion of electrons from n side to p side.

At equilibrium, (a) excess charge resides near the interface and the net current is zero, and (b) the potential energy difference for electrons (in light blue) prevents further diffusion of electrons into the p-side.

The behavior of a semiconductor diode can now be understood. If the positive side of the battery is connected to the n-type material, the depletion layer is widened, and the potential energy difference across the p-n junction is increased. Few or none of the electrons (holes) have enough energy to climb the potential barrier, and current is significantly reduced. This is called the reverse bias configuration. On the other hand, if the positive side of a battery is connected to the p-type material, the depletion layer is narrowed, the potential energy difference across the p-n junction is reduced, and electrons (holes) flow easily. This is called the forward bias configuration of the diode. In sum, the diode allows current to flow freely in one direction but prevents current flow in the opposite direction. In this sense, the semiconductor diode is a one-way valve.

We can estimate the mathematical relationship between the current and voltage for a diode using the electric potential concept. Consider N negatively charged majority carriers (electrons donated by impurity atoms) in the n-type material and a potential barrier V across the p-n junction. According to the Maxwell-Boltzmann distribution, the fraction of electrons that have enough energy to diffuse across the potential barrier is \(N{e}^{\text{−}eV\text{/}{k}_{\text{B}}T}\). However, if a battery of voltage \({V}_{b}\) is applied in the forward-bias configuration, this fraction improves to \(N{e}^{\text{−}e(V-{V}_{b})\text{/}{k}_{\text{B}}T}\). The electric current due to the majority carriers from the n-side to the p-side is therefore

\(I=N{e}^{\text{−}eV\text{/}{k}_{\text{B}}T}\;{e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}={I}_{0}{e}^{e{V}_{b}\text{/}{k}_{\text{B}}T},\)

where \({I}_{0}\) is the current with no applied voltage and T is the temperature. Current due to the minority carriers (thermal excitation of electrons from the valence band to the conduction band on the p-side and subsequent attraction to the n-side) is \(\text{−}{I}_{0}\), independent of the bias voltage. The net current is therefore

Note:

\({I}_{\text{net}}={I}_{0}({e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}-1).\)

A sample graph of the current versus bias voltage is given in this figure. In the forward bias configuration, small changes in the bias voltage lead to large changes in the current. In the reverse bias configuration, the current is \({I}_{\text{net}}\approx \text{−}{I}_{0}\). For extreme values of reverse bias, the atoms in the material are ionized which triggers an avalanche of current. This case occurs at the breakdown voltage.

Graph of I subscript net versus V. An arrow pointing right from the y axis is labeled forward bias. An arrow pointing left from the y axis is labeled reverse bias. The curve goes up and right in the first quadrant and then becomes almost vertical at higher values of x and y. It crosses the positive x axis into the fourth quadrant  and then the negative y axis at minus I subscript 0. It travels left in a horizontal line till a point where it turns sharply down into what becomes an almost vertical line. The x value of the turning point is labeled breakdown voltage.

Current versus voltage across a p-n junction (diode). In the forward bias configuration, electric current flows easily. However, in the reverse bias configuration, electric current flow very little.

Example: Diode Current

Attaching the positive end of a battery to the p-side and the negative end to the n-side of a semiconductor diode produces a current of \(4.5\;×\;{10}^{-1}\;\text{A}\text{.}\) The reverse saturation current is \(2.2\;×\;{10}^{-8}\;\text{A}\text{.}\) (The reverse saturation current is the current of a diode in a reverse bias configuration such as this.) The battery voltage is 0.12 V. What is the diode temperature?

Strategy

The first arrangement is a forward bias configuration, and the second is the reverse bias configuration. In either case, this figure gives the current.

Solution

The current in the forward and reverse bias configurations is given by

\({I}_{\text{net}}={I}_{0}({e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}-1).\)

The current with no bias is related to the reverse saturation current by

\({I}_{0}\approx -{I}_{\text{sat}}=2.2\;×\;{10}^{-8}.\)

Therefore

\(\cfrac{{I}_{\text{net}}}{{I}_{0}}=\cfrac{4.5\;×\;{10}^{-1}\;\text{A}}{2.2\;×\;{10}^{-8}\;\text{A}}=2.0\;×\;{10}^{8}.\)

This can be written as

\(\cfrac{{I}_{\text{net}}}{{I}_{0}}+1={e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}.\)

This ratio is much greater than one, so the second term on the left-hand side of the equation vanishes. Taking the natural log of both sides gives

\(\cfrac{e{V}_{b}}{{k}_{\text{B}}T}=19.\)

The temperature is therefore

\(T=\cfrac{e{V}_{b}}{{k}_{\text{B}}}\left(\cfrac{1}{19}\right)=\cfrac{e(0.12\;\text{V})}{8.617\;×\;{10}^{-5}\;\text{eV}\text{/}\text{K}}\left(\cfrac{1}{19}\right)=73\;\text{K}\text{.}\)

Significance

The current moving through a diode in the forward and reverse bias configuration is sensitive to the temperature of the diode. If the potential energy supplied by the battery is large compared to the thermal energy of the diode’s surroundings, \({k}_{\text{B}}T,\) then the forward bias current is very large compared to the reverse saturation current.

Resource:

Create a pn junction and observe the behavior of a simple circuit for forward and reverse bias voltages. Visit this site to learn more about semiconductor diodes.

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