OKANAGAN COLLEGE ELEN 236

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1 Semiconductor Theory

1.1 Conductor General Definition Any material that will support a generous flow of charge when a voltage source is applied across it

Insulator supports no charge when a voltage source is applied Semiconductor is somewhere in between

1.2 Conduction Scale Qualititatively, Insulators, semiconductors, and conductors fall on a scale looking like this:

• Placement of a material on the scale can be quantified. • This quantification is called resistivity. • Resistivity is denoted by the Greek symbol ρ (rho). • ρ = (Resistance x cross-sectional Area) / length = Ω x m2/m = Ω x m • Resistivity is a property of a type of material. Resistance is a property of something made

from that material. E.g., Ag resisitivity = 1.645x10-8

Perfect Insulator

Perfect Conductor

Insulators SemiConductors Conductors

Voltage Source

Conductor

Current flow

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Resistance of a Ag strand 10cm long and 1cm2 cross-sectional area is (1.645x10-8) x 0.1 / (1x10-4) = 1.645x10-5 Ω Resistance of a Ag strand 100m long and 1 cm2 cross-sectional area is (1.645x10-8) x 100 / (1x10-4) / 0.1 = 0.01645 Ω

• Resistance of two different Ag strands is different, but resistivity of Ag is same Examples:

Material Resistivity Copper 1.65x10-8 Ωm Gold 2.443x10-8 Ωm

Germanium 20-2300 Ωm Silicon ~500 Ωm Glass 1010 – 1014 Teflon 1016

A perfect conductor would have ρ = 0 A perfect insulator would have ρ = ∞. Of course neither of these actually exist. Note that sometimes we talk about conductivity; this is simply the reciprocal of resistivity.

1.3 Physical Basis of Conduction Conduction is simply the net movement of charged particles through a transmission medium. It is net movement because charged particles such as electrons are moving around all the time, but the net movement of charge in the non-conduction case is 0. The ease through which this transmission medium allows the charged particles to move determines the resistivity, which we discussed earlier. What we want to discuss now is what determines the ease of movement of the charged particles.

Generally, the charged particles that we care about are electrons. And the conductivity of a material depends on how many electrons are free for moving around – more free electrons on average means higher conductivity. To get an idea of what determines whether or not an electron is free, we need to look at the structure of atoms.

1.3.1 Atomic Structure and Orbitals A simplified model of an atom consists of a nucleus in the middle surrounded by a cloud of electrons around it. While we call the regions that electrons occupy orbitals, electrons do not actually orbit the nucleus in the way the planets orbit the sun, but these orbitals are well defined by quantum mechanics. So are you ready to learn about the wave functions of quantum mechanics? Actually for an understanding of the physical basis of conduction we don’t really need to know much about quantum mechanics except that it describes the regions that electrons can occupy, how we name these regions, and that these regions, or orbitals have different energy levels. The closer the orbital is to the nucleus, the lower the energy level. There is a naming/numbering system for the orbitals which describes the shell (main energy level), subshell (energy level within the main energy level), and number of electrons in the shell/subshell. The shell is an integer starting at 1, and the subshell is an integer starting at 0 and which must be less than the number for the shell. By convention, the subshells are not given numbers, but letters instead 0=s, 1=p, 2=d, 3=f, 4=g etc.

Wikipedia (http://en.wikipedia.org/wiki/Atomic_orbital) describes the naming convention as this:

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Where X is the shell number (or energy level), type is the subshell (s,p,d…), and y is the number of electrons in that orbital. For example, the first, and lowest energy orbital is 1s2 (pronounced "one s two"). In some cases (including in the text book), the shell is given a letter instead of a number starting at K.

Electrons in an atom start filling up orbitals starting at the lowest energy level, and work their way up. The outermost orbital containing electrons is called the valence shell or valence band. Therefore the valence band is the highest energy orbital associated with an atom … sort of …

The energy level above the valence band is called the conduction band, and if electrons can obtain energy from an external source (for example from heat) then they can jump into the conduction band and thus become free electrons. Application of an electric field (i.e., apply a voltage) will accelerate the free electrons along the field and thus create a current. The more electrons in the conduction band, the better the conductor (i.e., higher conductivity/lower resistivity).

So we can now say that metals such as copper, gold and silver must have a lot more free electrons in the conduction band than semiconductors such as silicon and germanium and insulators such as glass and mica. But why is this the case? The following diagram gives an indication of the reason

Conduction Band/Valence band diagrams for Insulator/Semiconductor/Conductor

As you can see it takes much more energy for electrons to move from the valence band to the conduction band in insulators and semiconds. This gap is called the bandgap, and conductors are good conductors because the bandgap is 0, therefore electrons in the valence band are also in the conduction band.

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1.3.1.1 More about Valence Shell The valence shell, which consists of the s subshell and the p sub-shell of the highest n shell that the atom has, has room for 8 electrons (2 from the s sub-shell and 6 from the p sub-shell). The more electrons it has occupying those 8 positions, the larger the bandgap is and therefore the better insulator (worse conductor) it is. When the valence shell has only 1 electron, it is an excellent conductor; when it has 8 electrons in it, it is an excellent insulator. The book states that a conductor has 1 electron, a semiconductor has 4, and an insulator has 8 … it is more like a gradient – an atom with 2 electrons in the valence shell (e.g. Fe) is a pretty good conductor too, while Sulfur which has 7 electrons in the valence shell is an good insulator. The semiconductor materials that we will exam in this course do have 4 electrons in the valence shell (i.e. Si and Ge)

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1.3.1.2 Example Atoms Cu/Ag/Au all have 1 atom in valence shell and are all excellent conductors

Fe/Ni both have 2 atoms in valence shell and are both good conductors Si/Ge both have 4 atoms in valence shell and are both semiconductors

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Sulfur has 6 atoms in valence shell and is a good insulator

1.3.2 Covalent Bonding All of the above descriptions apply to individual atoms, but what happens atoms are arranged in a group. Let’s look specifically at the two semiconductors, Si and Ge. When Si or Ge crystallize and solidify, adjacent atoms share electrons (this electron sharing is called covalent bonding). They share the electrons in such a way that the valence shell essentially becomes full with 8 electrons. The atoms form a tetrahedral structure where each atom is connected to 4 other atoms, and each atom contributes an electron to each connection. The following diagrams show the tetrahedral structure of Si. The structure on the left is silicon hydride, but if you replace the H’s with Si’s it would be a silicon crystal. The structure on the right is a diagram of several Si atoms in a crystal.

This covalent bonding is what makes Si and Ge good insulators when the crystals are very pure. Stay tuned to find out how Si/Ge can be made to be better conductors.

1.4 Conduction in Semiconductors

1.4.1 Electron-Hole Pairs At temperatures above absolute zero, electrons in the valence band of a Si/Ge crystal start moving around, and can sometimes gain enough energy to jump into the conduction band, thus becoming free. As mentioned before, the free electrons can now move and create a current in the presence of an electrical field. When the electron jumps to the conduction band, it leaves behind a hole in the electron cloud of the atom, and this hole behaves like a positive charge. After a short period of time, the electron will fall back into the hole (or the hole of another atom) and recreate a whole atom again. This process of leaving the valence band, and then falling back in is occurring all over inside the crystal. In Si, at any one time, 1010 electrons per cubic cm will be in the conduction band which means that it can conduct (although not nearly as well as Cu which has on the order of 1023 electrons/cm3 free electrons.

1.4.1.1 Current from Electrons and Holes As was just mentioned, Si/Ge can conduct, just not very well. On top of that, there is an idiosyncrasy in the way Si/Ge conduct (compared to metals). That idiosyncrasy is that current flow involves the flow of both the electrons, and the holes.

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That’s strange, how can a “hole” flow? After all, it’s just the absence of an electron, it’s not an actual existing entity. Well, wikipedia has a good analogy to help you imagine the concept of hole conduction:

Hole conduction can be explained by the following analogy. Imagine a row of people seated in an auditorium, where there are no spare chairs. Someone in the middle of the row wants to leave, so they jump over the back of the seat into an empty row, and walk out. The empty row is analogous to the conduction band, and the person walking out is analogous to a free electron.

Now imagine someone else comes along and wants to sit down. The empty row has a poor view; so he does not want to sit there. Instead, a person in the crowded row moves into the empty seat the first person left behind. The empty seat moves one spot closer to the edge and the person waiting to sit down. The next person follows, and the next, et cetera. One could say that the empty seat moves towards the edge of the row. Once the empty seat reaches the edge, the new person can sit down.

In the process everyone in the row has moved along. If those people were negatively charged (like electrons), this movement would constitute conduction. If the seats themselves were positively charged, then only the vacant seat would be positive. This is how hole conduction works.

You can see the full article at http://en.wikipedia.org/wiki/Electron_hole which has a good description of electron holes. The following diagram illustrates electron-hole conduction in a semiconductor:

1.4.2 Doping The idea of doping involves adding an impurity to the Si/Ge in order to promote the production of free electrons, or free holes. A semiconductor with more free electrons than free holes is called an N-type semiconductor. A semiconductor with more free holes than electrons is called a P-type semiconductor.

The concentration of the impurity determines the conductivity of the crystal. More impurity means more free electrons which means better conductivity. Highly doped semiconductors have concentrations of impurities on the order of 1018atoms/cm3 which makes the doping concentration with respect to the Si/Ge

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concentration on the order of 1 part per several thousand. Lightly doped semiconductors have concentrations of impurities with respect to the Si/Ge concentration on the order of parts per billion. Highly doped semiconductors can behave like metals (and are often used instead of metals in integrated circuit manufacturing).

1.4.2.1 N-type Doping Si/Ge has 4 valence electrons, now imagine replacing a large number of Si/Ge with an element that has 5 valence electrons such as Phosphorus, Arsenic or Antimony (these elements are called pentavalent due to having 5 valence electrons). Four of the valence electrons would be used up for creating bonds to four adjacent Si/Ge, but there will be one extra electron that is not bound to anything (except the impurity), and is therefore easily boosted into the conduction band to increase the number of free electrons of the crystal.

1.4.2.2 P-type Doping If instead of replacing Si/Ge atoms with pentavalent atoms, we use a trivalent atoms (3 atoms in valence shell) instead, then we get a crystal with a missing electron. As we know missing electrons are referred to as holes, and can conduct in the same way (but opposite direction) as electrons.

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1.4.2.3 Majority Carriers and Minority Carriers Another important concept in semiconductor conduction is the idea of majority and minority carriers. In any semiconductor, conduction occurs by the flow of electrons in one direction and a flow of holes in the other direction. In an undoped semiconductor, these flows would be equal and opposite, but in doped semiconductors, one flow is greater than the other. In n-type semiconductor, there are far more electrons than holes, so electrons are the majority carrier, and holes are the minority carrier. In p-type semiconductors, there are more holes than electrons, so holes are the majority carrier, and electrons are the minority carrier.

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1.5 The P-N Junction The way that electrons flow in doped semiconductors is all very interesting, but the really interesting effects occur when you have p-type semiconductor and an n-type semiconductor side-by-side1. The abrupt change from n-type semicondicutor to p-type semiconductor is called the P-N Junction.

There is a higher concentration of electrons in the n-type semiconductor, and so they diffuse across the p-n junction, and combine with the extra holes in the p-type semiconductor. When this occurs, a net negative charge starts to build up in the p-type material that now has more electrons, and a net positive charge starts to build up in the n-type material that now has fewer electrons. The net diffusion continues until the diffusion gradient is matched by the voltage potential gradient. In other words, the “force” causing electrons to move from high concentration to low concentration equals the force of the electric field caused by the now negatively charged p-type side and positively charged n-type side.

1 I say side-by-side, but they can’t simply be abutted together. See the text on page 883 on fabricating p-n junction.

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Once the semiconductor reaches equilibrium state, there is a region at the barrier that no longer has any majority carriers (all of the free electrons have combined with the extra holes). This region is called the depletion region because it is now depleted of majority carriers. The region also has a voltage across it due to the negatively charged p-type side and positively charged n-type side. This voltage is called the barrier voltage. As the text book says, it is best to think of this as a voltage that must be overcome in order for current to pass through it.

1.6 Introduction to the Diode The properties of the p-n junction make it useful for several important electronic devices. The most basic such device is the diode. A diode is simply a p-n junction with leads on it. A diode’s structure, and symbol are shown in the following figure:

1.6.1 Forward Biased Diode The following circuit shows a forward biased diode:

The positive terminal of the voltage source is connected to the p-material, and the negative terminal of the voltage source is connected to the n-material.

In this case, the negative terminal will drive free electrons in the n-material away from it towards and then across the junction. When in the p-material, the electrons will bind with holes. As more and more electrons cross the junction (the voltage source is supplying all of these electrons), more and more holes move across the p-material to be filled by electrons. There is therefore a flow of the majority carrier electrons in the n-material towards the junction, and a flow a majority carrier holes in the p-material also towards the junction resulting in a flow of current through the diode. Minority carriers also contribute to the flow but it is so insignificant that we can consider the diode current to be solely from the majority carriers.

It should be noted that the voltage that the voltage source supplies must be enough to overcome the barrier voltage first. When the voltage source is less than the barrier voltage, electrons from the n-material start to move into the depletion region from one end while holes from the p-material start to move into the depletion region from the other end. The depletion region will start to shrink; current will not flow until there is enough external voltage to close the depletion region completely, and that occurs when the external voltage equals or exceeds the barrier voltage.

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1.6.2 Reverse Biased Diode The following circuit shows a reverse biased diode:

The positive terminal of the voltage source is connected to the n-material, and the negative terminal of the voltage source is connected to the p-material.

The positive terminal will attract electrons from the n-material while the negative terminal will attract holes from the p-material towards it. Consequently, the depletion region will widen. No majority carriers flow across the depletion region, and therefore the majority current is zero.

There are still some minority carriers (thermally generated), and the electrons from the p-material will flow towards the positive terminal while holes from the n-material will flow towards the negative terminal resulting in a very small current. This current is called the saturation current, denoted Is and is generally on the order of nanoamps.

1.6.3 Breakdown Large reverse bias voltages can cause the junction to break down. Two types of breakdown can occur. The first kind is called avalanche breakdown, and this occurs when minority carriers are accelerated so quickly that they knock electrons out of other atoms in the seminconductor crystal. This leads to more electrons being knocked out, and this effect builds and builds creating an avalanche effect of free electrons. The diode can be destroyed if components external to the diode (i.e. resistors) do not limit the current. The breakdown occurs at a voltage called the Peak Reverse Voltage (PRV). The second kind of breakdown is called Zener breakdown, and we will examine this effect in a later section.