basic electronics 1b 2006

8/9/2019 Basic electronics 1b 2006

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The important thing to note for semiconductor operations is that the only e- of interest are the ones in the CB.

These e- in the CB are the only charge carriers that we care about in device physics. All of the previous

analysis holds for holes where the only holes of interest (the charge carriers) are located in the VB. A hole is

the empty state in the VB that we discussed previously. A hole can also be visualized as the motion of an

empty state on a bond (missing bond) of an atom that propagates when it is filled by an electron from a

neighboring bond.

The motion of this missing bond (hole) is exactly opposite to the electron that was just captured by the atom

with the missing bond. We can also can look at this in terms of the energy band diagram where the removal

of an e- from the VB creates and empty state in a vast sea of filled states. This empty state moves about

freely in the lattice (like a bubble in a liquid) because of the cooperative motion of the valence e-.

EE 329 Introduction to Electronics Spring 2006 14


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So what exactly is a hole? We know from quantum mechanics (QM) that electrons can move only between

allowed quantum states. If we envision a series of allowed states with each of them occupied by an electron

except for one at the end (empty state), and we apply a + charge at that end, we see the electrons moving

towards the + charge hopping from one allowed state to the next.

We now look at the process of e- and h+ creation in detail. At 0 K all the bonds are intact as shown below

and all the e- are in the VB and the CB is empty.



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Next we raise the temperature of the crystal and some of the covalent bonds begin breaking as shown below.

Note that by breaking a Si Si bond we always create an e- h+ pair (ehp).



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If we apply an external electric field we get movement of the e- and h+ (in opposite directions). Look at the

apparent motion of the empty state (hole) in the figure below as it moves to the right (equivalent to an e-

moving to the left). What we have here could be described as the motion of a positively charged particle and

this is what the hole represents. The interesting thing in a semiconductor is that this empty state actually

appears to have mass and momentum just like a real particle. Another interesting note is that the hole

generally has a different mass than the electron. From here on we will treat the electron and hole as

equivalent charge carrying particles with opposite charge and slightly different masses.



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Another way to look at this would be to take one e- from a perfect Si lattice. The lattice becomes + charged

and the Si atom that lost that e- will soon pull an e- from a nearby Si atom and this process will continue.

We know that the overall lattice is + charged, and we can say that the hole is the localization of that + charge

and is located wherever the missing e- is.

The key to making a useful semiconductor device is to precisely control the amount of charge carriers (CB e-

or VB h+) present. We cant do this simply by raising the temperature because that always creates e- and h+

in pairs. What we need is a different amount of e- or h+ in the lattice. This is where the principle of

semiconductor doping (adding impurities) comes into play. Pure undoped Si (intrinsic) is of very little use to

us as a semiconductor material since there are relatively few CB e- (and VB h+) at room temperature. Now

look at some numbers. There are approximately 5.02e22 Si atoms / cm3 in a Si lattice and since there are

four valence e- per atom, the total number of VB e- in the lattice is about 2.08e23 VB e- / cm3 or

bonds / cm3. At room temperature there is enough thermal energy present to break about 1e10 bonds / cm3

which means that we have 1e10 e- in the CB. This is not enough to make Si sufficiently electrically



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conductive for a useful semiconductor device. So what can we do to increase this number without just

increasing the temperature?

When we dope a semiconductor we intentionally add impurities atoms into the Si lattice that alter the ratio of

e- to h+. Normally when a Si bond breaks we get a CB e- and a VB hole. Now we will add either a Col III(usually B, called p doping or adding acceptors) or a Col V material (usually As, P or Sb, called n doping or

adding donors). Let us first consider the situation when we add B (see below). From the periodic table we

know that B has only 3 valence e- in its outer orbital. (Note that when we dope Si we usually add between

1e16 - 1e19 dopant atoms / cm3 into the lattice which means that we have between 1 in 20.8 million and 1 in

20.8 thousand dopant atoms in the lattice). So, in general each dopant B atom will be completely surrounded

by Si atoms. The B atom will bond with 4 neighboring Si atoms but what about its missing e-?



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The hole due to the missing e- in B becomes mobile and moves freely in the Si lattice. The opposite occurs

when we add P (As or Sb) into the Si lattice and this is shown below.

Now we have an extra e- for each donor atom. As we might guess, this e- will be only weakly attached to its

parent donor atom. The presence of these weakly bound e- causes discrete energy states to be formed within

the band gap and for n doping these states lie right below the bottom of the CB. In Si at room temperature

the extra e- in P lies 0.045eV below the CB edge, while in As it lies 0.054eV below the CB edge. In B on

the other hand the discrete energy state lies 0.045eV above the top of the VB. This is shown in the figurebelow.



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The lattice now looks like the following depending on the type of doping

What this means is that very little thermal energy is required for the extra e- in P to be elevated into the CB

where it becomes a useful charge carrier. The same occurs for the hole provided by B. At room temperature,

almost all of the 1e16 - 1e19 dopant atoms will be ionized which means that they have donated their extra

carrier into the CB (if e-) or VB (if h+). We no longer have only 1e10 carriers / cm3, but 6 to 9 orders of

magnitude more and with this large amount of carriers we can make a useful semiconductor device.

What happens to our doping levels as the temperature changes? At very low temperatures there will not be

sufficient energy for either the VB e- or the bandgap donor e- to make it into the CB and this is known as the

freeze-out region. At 0 K, all of the Si valence e- in the semiconductor lattice will reside in the VB and all of



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its states will be filled. The CB will be totally empty (see figure below). As we increase the temperature of

the lattice, thermal energy is now available to move some of the e- into the CB. Around 100 K, there is

sufficient energy for the dopant e- to make it into the CB, but not enough energy for the e- to make it all the

way from the VB (bond breaking). Here is where we can begin operating our semiconductor device and this

is called the extrinsic temperature region.

Up around 550 K the e- from the VB can start making the transition into the CB (bond breaking) and soon

their numbers swamp the numbers due from the dopants (remember there are about 2.08e23 VB e- / cm3

compared with a doping levels between 1e16 1e19) and we can no longer operate the device; this is called

the intrinsic temperature range. Remember in order to get a useful device we need a majority of one or the

other type of carrier. See the figures on the next page. Note the difference between Ge and Si with respectto the onset of the intrinsic temperature range.



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Remember that our actual bands are curved, but the density of available levels is so high at the bottom of the

CB (and top of the VB) that we can generally represent the bands as parallel flat lines for most device

applications. Any CB e- that has more than the minimum amount of energy tends to thermalize (by emitting

phonons) and fall to the lowest available CB energy state.

One important note in all of this is that the dopant atom must occupy a normal Si lattice site (substitutional),

not an interstitial site (in the middle) for it to have an energy state in the band gap. Remember we need to

increase the number of CB e- or VB h+ in Si in order to get useful electrical properties, and in order to do

this the B, P, or As impurity must sit on a substitutional site in order to get a state near the edges of the

bandgap. The problem with many interstitial impurities is that they tend to create states in the bandgap but

towards the center (deep level impurities) where they cause undesired leakage currents.

Adding impurities can also alter other properties of a material. Take diamond for example. What color is a

pure diamond (clear)? What color are many of diamonds found in nature (green or yellow)? What type of

substitutional impurities would you guess these are from (N and N2 impurities). Now what other colors are

diamonds (blue = B, green from radiation damage to the lattice, brown, pink and red due to other defects in

the lattice).

As a note, the band gap of Ge = 0.66 eV and GaAs = 1.42 eV. The distinction of metal, semiconductor and

insulator can be made on the basis of the concept of the bandgap. Most metal have little or no band gaps,

while insulators have high band gaps (eg. SiO2 = 8eV).



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Color

Wavelength

(um) nm eV

Far IR 100 100000 0.01

Fiber Optic 1.55 1550 0.80

Fiber Optic 1.3 1300 0.95IR 1 1000 1.24

Near IR 0.7 700 1.77

Deep Red 0.633 633 1.96

Red 0.616 616 2.01

Red Orange 0.607 607 2.04

Orange 0.595 595 2.08

Amber 0.588 588 2.11

Yellow 0.58 580 2.14

Green 0.565 565 2.19

EmeraldGreen 0.53 530 2.34

Blue 0.5 500 2.48Violet 0.39 390 3.18

near UV 0.35 350 3.54

UV 0.1 100 12.40

far UV 0.05 50 24.80

X-rays 0.01 10 124.00

You can also see how the size of the bandgap also helps determine the operating temperature range of the

semiconductor device (as we discussed previously). All else being equal, the larger the bandgap, the higher

the tempeature the semiconductor device will operate before it hits its intrinsic region. That is one of the

reasons that Si is preferred over Ge and also why GaAs operates at a higher temperature than Si. We can

also see that diamond will operate at an even higher temperature due to its band gap of around 5.6 eV.



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Carrier Properties

Now we look at the properties of the e- and h+ in more detail. First, both are charged particles (- and +) and

the magnitude of the charge is that of the e- = 1.6e-19 C. They also have mass but it is not a simple number.

It is dependent on many different parameters such as the semiconductor material and the direction of travelwithin the crystal, temperature etc.

First we note that the mass of an e- in a crystal is not the same as the mass of an e- in free space. It is

probably easier to think of the mass of the e- and h+ in a crystal as the proportionality constant between an

applied electric (E) field and the resulting acceleration of the particle (see figure below).

So when we apply an E field to a crystal and find that the acceleration is different, we can say that the mass

of the e- or h+ has changed. We then redefine our above equation and call the mass of the particle its

effective mass. Using this definition we can again treat the e- and h+ in the crystal in a classical Newtonian

manner instead of using quantum mechanics which actually governs the motion of particles in crystals. Wejust change the effective mass to fit the experimental parameters.

The effective masses we are most interested in are called the density of states effective masses (we will

discuss density of states soon). Their values are contained below (at 300 K) as ratios compared with the

mass of a free e-.



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Si / Ge / GaAs e- = 1.18, 0.55, 0.066

Si / Ge / GaAs h+ = 0.81, 0.36, 0.52

Note there is less of a difference between the different h+ masses.

We now reintroduce the term intrinsic semiconductor to mean one that is not doped (pure). We can also

define the intrinsic carrier concentration of a semiconductor as the number of ehp that are created (broken

bonds) which is strongly temperature dependent. Remember in this case the carriers are always created in

pairs.

Si / Ge / GaAs = 1e10 cm-3, 2e13, 2e6 broken bonds at room temperature. Note the values change as you

would expect from their respective band gaps; 1.12, 0.66 and 1.42 eV, also note that in Si there are a total of

2.08e23 bonds that can be broken so we are talking about 1 in 1e13 broken bonds in intrinsic Si at room

temperature. Again, this is why pure Si is not a good conductor at room temperature. See figure below.



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basic electronics 1b 2006

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