Basic Physics of Semiconductors (1)

Section 2.1

Eat your broccoli before having desert.

Need to know your device physics before getting started with circuit design.

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Atom is the smallest particle of an element. Nucleus consists of positively charged particles called protons and uncharged particles called neutrons.The negative charged particles are called electrons.

Electrons orbit the nucleus of an atom at certain distance from the nucleus. Electrons near the nucleus have less energy than those in more distant orbits

Valence Electrons• Valence electrons: electrons in the outermost

shell.– Electrons that are in orbits farther from the

nucleus have higher energy and are less tightly bound to the atom than those close to the nucleus.

– Electrons with the highest energy exist in the outermost shell of an atom and are relatively loosely bound to the atom.

Silicon Atom

Silicon is the most popular material in microelectronics. It has four valence electrons.

(Nice tutorial on making silicon wafer, http://www.youtube.com/watch?v=aWVywhzuHnQ)

Sharing of Electrons in Silicon

A silicon atom with its four valence electrons shares an electron with each of its four neighbors. This effectively creates eight shares valence electrons for each atom and produces a state of chemical stability.

The sharing of valence electrons produce the covalent bonds that hold the atoms together; each valence electron is attracted equally by the two adjacent atoms which share it.

As electrical engineers, we are primarily interested in how we can get the electrons to move. We need to introduce a couple of concepts:•Holes•Free electrons•Bandgap•Electron density

At T=0K Electrons gain thermal energy and break away from the bonds. They begin to act as “free

charge carriers”—free electron.

An electron leave behind a void because the bond is now incomplete.

A void is called a hole. A hole can absorban free electron if one becomes available.

One electron has traveled from right to left.One hole has traveled from left to right.

Movement of electrons and holes

Bandgap Energy

Q:Does any thermal energy create free electrons (and holes) in silicon?

A: No. A minimum energy—called the “bandgap energy” is required todislodge an electron from a covalent bond. For silicon, the bandgapenergy is 1.12 eV.

Note: eV represents the energy necessary to move one electron acrossA potential difference of 1V. 1 eV =1.6 x 10-19 J

Insulators display a higher Eg . (e.g. 2.5 eV for diamond)Semiconductors usually have a moderate Eg between 1 eV and 1.5 eV.

Electron DensityQ: How many free electrons are created at a given temperature?

15 3 2 35 2 10 exp electrons cm2

gi

En T

kT

where k=1.38 x 10-23 J/K is called the Boltzmann constant.

As expected, materials having a larger bandgap (Eg)exhibit a smaller ni . Also, as T pproaches zero, ni approaches zero.

electron density

Making sense of electron density

Determine the electron density in silicon at T=300K.Use the electron density formula with Eg=1.12 eV, ni @ 300 T is 1.08 x 1010 Electrons per cm3.

Silicon has 5 x 1022 atoms per cm3.

What this means is that there is only one electron for 5 x 1012 atoms at room temperature.

How do we increase the electron density?

Intrinsic Semiconductor

The pure silicon has few electrons in comparison to the numbers ofatoms. Therefore, it is somewhat resistive.

In an intrinsic semiconductors, the electron density(n or ni) is equal to the hole density (p). (each electron is created by leaving behind

a hole.)

So

np=ni2

electronholes

Can we use something other than silicon?

Phosphorus has 5 valence electrons. The 5th electron is “unattached”.This electron is free to move and serves as a charge carrier.

Doping

The controlled addition of an impurity such as phosphorus to an intrinsic (pure)semiconductor is called “doping”. And phosphorus itself is a dopant.

Providing many more free electrons than in the intrinsic state, the doped silicon crystal is now called “extrinsic,” more specifically, an “ n-type” semiconductor to emphasize the abundance of free electrons.

Hole density in an n-type semiconductor

Many of the new electrons donated by the dopant “recombine” with the holes that were created in the intrinsic material. As a consequence,in an n-type semiconductor. The hole density will drop below its intrinsic level.

np=ni2

In an n-type semiconductor, Electrons are the majority carriers.Holes are the minority carriers.

If a voltage is applied across an n-type materials, the current consisting predominantly of electrons is produced!

if we dope silicon with an atom that provides an insufficientnumber of electrons, then we may obtain many incomplete covalent bonds.

A boron has only 3 valence electrons and can form only 3 covalent bonds. Therefore, it contains a hole and is ready to absorb a free electron.

Summary

MajorityCarriers Dn N 2

MinorityCarriers i

D

np

N

MajorityCarriers Ap N 2

MinorityCarriers i

A

nn

N

In n-type material,

In p-type material,

Applications # 1:Hot-Point Probe Test

Hot probe=soldering ironCold probe=probe at room temperature.

The electrons around the hot probe have higher thermal velocity, therefore on average move toward the cold side at a higher rate than the electrons on the cold side move to the hot side.

The imbalance causes the electrons to accumulate on the cold side and build up a negative voltage, which can be detected by a voltmeter.

Application #2: Thermoelectric Generator

Early satelite use decay of radioactive material as the heat source.It is also possible to use waste energy from automobile as the heat source.

The same concept is also used for energy harvesting from a wrist watch. (22 uW of power)

A material can conduct current in response to a potential difference.

The field accelerates the charge carriers in the material, forcing some to flow from one end to the other. Movement of charge carriers due to an electric field is called “drift.”

a

ab bV Edx

MobilityWe expect the carrier velocity to be proportional to the electric field strength (E).

v E

Mobility: 1350 cm2/(VS) for electrons 480 cm2/(VS) for holes.

since electrons move in a direction opposite to the electric field, we must express the velocity vector as

nev E

phv E

For electrons

For holes

Example 2.5

A uniform piece of n-type of silicon that is 1 um long senses a voltage of 1 V. Determine the velocity of the electrons.

# of charges passing x1 in 1 s

Divide the current by Wh gives you the current density

In the presence of both electrons and holes:

if the electric field approaches sufficiently high levels, the velocity no longer follows the electric field linearly. This is because the carriers collide with the lattice so frequently and the time between the collisions is so short that they cannot accelerate much.

Building a Resistor on Silicon

Building a Resistor on Doped Silicon

Problem: the mobility is a function of temperature. So the resistance will change with T.

Diffusion

Suppose a drop of ink falls into a glass of water. Introducing a high local concentration of ink molecules, the drop begins to “diffuse,” that is, the ink molecules tend to flow from a region of high concentration to regions of low concentration. This mechanism is called “diffusion.”

if charge carriers are “dropped” (injected) into a semiconductor so as to create a nonuniform density. Even in the absence of an electric field, the carriers move toward regions of low concentration, thereby carrying an electric current so long as the nonuniformity is sustained.

Diffusion current due to Holes

Diffusion Current Due to Electron

Divide by area to get current density

Einstein Relation

μ and D are related via D/ μ=kT/q

Overflow Material

http://www.youtube.com/watch?v=RHAso1yM-D4