Introduction to Semiconductors

Add Your Comments

Like it says – Johnathan Smith

Semiconductors are materials that do not conduct electricity as freely as conductors, but still have some free charge to move around unlike insulators. Some more common semiconductors are silicon and germanium. Semiconductors typically have resistances between 10^-4 and 10^8 ohms.

The characteristics of conductors, semiconductors, and insulators can be explained using band theory. The lowest band that is occupied as zero temperature is the valence band and does not contribute to the conduction of electricity. The next highest unfilled band is called the conduction band. The energy level between the valence band and the conduction band is very high for insulators so that the electrons cannot bridge the gap normally at normal temperatures.

Diagram

Figure 1: Band layout of an insulator, very large energy gap

Conductors have their valence and conduction bands overlap so that free electrons participate in the flow of current.

Diagram

Figure 2: Band layout of a typical metal

Semiconductors on the other hand have a small energy gap between the bands and typically require around one electron-volt to jump over the gap.

Diagram

Figure 3: Band layout of a semiconductor

There are some different types of semiconductors around, including elemental and intrinsic. Some elemental semiconductors are silicon and germanium. Compound semiconductors are made up of two or more atoms that combine to make a semiconductor. GaAs and InP are examples of compound semiconductors.

In addition to the makeup differences in different types of semiconductors, there are also differences between intrinsic semiconductors and extrinsic semiconductors. Intrinsic semiconductors are made up of a pure material and do not require any additional doping or additions to make the material a semiconductor. Intrinsic semiconductors have what may seem like an unusual property that as temperature is increased their conductivity increases as well, unlike metals that decrease conductivity with increases in temperature.

The reason is that as temperature is increased more electrons have the energy to get kicked up to an energy state so that they are available to move freely in the material. As electrons move around in an intrinsic semiconductor they leave what is called a hole. The holes move in the opposite directions of the electrons and have opposite charge. There are as many holes as free moving electrons in an intrinsic semiconductor.
{mospagebreak}

Extrinsic semiconductors are ones that require doping to be made into semiconductors. Perfect crystal lattices of silicon are actually insulative. Silicon has four valence electrons that are all occupied with covalent bonding in a perfect crystal and that leads to having no free electrons to have a net movement throughout the crystal so that it acts as an insulator.

When silicon is doped with a material such as boron or aluminum, it becomes what is known as a p-type semiconductor. Boron and aluminum both have only three electrons in their valence shell and thus a hole is left. The hole allows an electron to float through to fill it.

Diagram

Figure 4: p-type semiconductor

In a similar manner, silicon can be doped with atoms such as phosphorus or arsenic that have five valence electrons and then an extra electron is put into the crystal. These types of semiconductors are called n-type.

Diagram

Figure 5: n-type semiconductor

The temperature dependence of extrinsic semiconductor band gaps is governed by the equation

Diagram

where a and ß are parameters dependent upon the material being studied. The resulting graph of the function shows that as temperature increases the band gap energy decreases as temperature increases.

Different types of semiconductors can be placed together as well to give n-p and p-n junctions. Using different type semiconductors next to each other can give rise to a diode, a device that only allows current to flow in one direction.

The flow of current in the reverse direction is very minimal until a sufficient voltage is reached to breakdown the junction, which is normally large. In flowing current forward across a diode a small voltage, around .7V for silicon, is needed to have the resistance of the semiconductor drop very low.

Diagram

Figure 6: A voltage vs. current diagram for a typical diode

Diagram

Figure 7: Current does not flow since the potential is setup opposite the diode

Diagram

Figure 8: Current flows since the diode is setup the same as the voltage


{mospagebreak}

Transistors are made by using n-p-n or p-n-p sandwiches of semiconductors. In such devices it seems at first glance that because it appears as two diodes back to back that no current would flow with a small voltage across the device, which would be true if it were not for the middle portion to have a small current added. When the middle portion of the semiconductor sandwich has a proper current applied it can switch the transistor to allow or disallow current flow.

N-P-N type transistors can be activated by having the middle, or base, section has a high enough voltage applied to it. P-N-P type transistors have the base sections brought to a low voltage to achieve current flow however.

Diagram

Figure 9: Layout of an NPN transistor

Diagram

Figure 10: Layout of a PNP transistor

Another type of sandwiching that can occur is p-i-n, where i is the intrinsic type semiconductor. Essentially a p-i-n diode is like a pn diode except with an added resistance in the forward bias as well. The middle layer in a pin diode has basically all of the potential difference across it for a forward bias.

Some lasers have also been made using pn junctions in semiconductors through the combination of holes and electrons at the junction. The devices required high current and were very inefficient. In an effort to make a more efficient laser it was discovered that using a heterostructure design made a more efficient laser. An example of a heterostructure would be where there is a Pn junction with the P having a larger band gap than the n.

Sources

I very highly recommend visiting the britneyspears.ac site as it is very amusing, even if you are not into all the physics of what is happening.

Britney Spears.ac
Encyclobeamia
How Stuff Works
Think Quest
Engr.sjsu
Colorado.edu
{mospagebreak}

I was fortunate enough to have several people email me about the article on semiconductors, and one in particular, Marco Russ, a graduate student in solid state physics, pointed out some very good clarifications and corrections to the original article. Marco also gave me a much better graph for diodes based on experimental data. His comments are below shown in full without editing.

“Semiconductors typically have resistances between 10^-4 and 10^8 ohms”

This only makes sense if you speak of specific resistances in ohms*m.
Anyway, it´s typical for semiconductors that they don´t have a typical
resistance! An immense range of resistances can be achieved, as is
obvious from the numbers you mention!

“The lowest band that is occupied as zero temperature is the valence
band and does not contribute to the conduction of electricity.”

*The valence band is the highest completely filled band at zero temperature!

*”The next highest unfilled band is called the conduction band”

The next highest band is the conduction band. It is unfilled only for
insulators and semiconductors and only at zero T.

“The energy level between the valence band and the conduction band is
very high for insulators so that the electrons cannot bridge the gap
normally at normal temperatures.”

I think you mean the energetic gap, not an “energy level”.

“There are some different types of semiconductors around, including
elemental and intrinsic.”

I guess you mean “… including elemental (like Si) and compound
semiconductors (like GaAs).”

“Intrinsic semiconductors are made up of a pure material and do not
require any additional doping or additions to make the material a
semiconductor”

Intrinsic semiconductors are undoped semiconductors, or semiconductors
where an equal amount of p- and n-doping is present. No semiconductor
needs doping to make it a semiconductor! Intrinsic means that the
“conducting” electrons are thermally activated from the valence band.

BTW, the temperature dependence of the band gap is very small for
realistic temperatures. In the range from 0K to 300K, the difference is
typically 10%; for realistic temperature differences during the
operation of a device, the band gap difference is about 1%.

While your description of the diodes/transistors isn´t wrong, I would
like to mention that a typical modern transistor found in your computer
is not a npn/pnp transistor, but a MOSFET, a completely different device.

and

Si is THE standard semiconductor. However, the number of intrinsic
carriers is very small (about 10^10/cm^3) for T = 300K. The conductivity

sigma = e x number of carriers x mobility of carriers

is about 3×10^-6 Ohm^-1 cm^-1.

Depending on the application, this could indeed be called
insulating behaviour. However, keep in mind that there is no fundamental
difference between an insulators and a semiconductors – both have a band
gap and an empty conduction band a 0K. Materials with a large band gap >
4eV are typically called insulators while Si has a band gap of about 1,1eV.

The second characteristic of a semiconductor is that its conductivity
can be changed of a very large range by doping/illumination etc, and this
can be done with Si.

So, if you can change the conductivity of a material from almost
insulating to almost metallic, it´s a semiconductor… 😉

For some physical parameters of Si and other semiconductors take a look HERE.
There, even AlN is classified as a semiconductor and AlNi has a band gap
of about 6eV!

Graph

Many thanks to Marco Russ for the corrections and clarifications.

Johnathan Smith

Leave a Reply

Your email address will not be published. Required fields are marked *