Basic Physics of Semiconductors (1)

Section 2.1

Tentative Schedule

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Day

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Topic

Diagnostic Test Lab protocol, cleaning procedure, Linus/Cadence intro Fundamental concepts from Electric Circuits Basic device physics I-V characteristics of a diode (Simulation) Physics of PN junction diode Application of diodes: diode logic/Review Diode logic circuit Characteristics of BJT Test #1 Physics of a BJT

Section

2.1

2.2-2.3

4.1-4.3

Physics Matters!

Eat your broccoli before having desert.

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

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Review of High School Chemistry

• • • •

Terminology Energy of an Electron Valence Electron Covalent Bond

Terminology

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 .

Energy of an Electron

Less Energy More Energy 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 nucleus. higher energy and are less tightly bound to the atom than those close to the – 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 atoms which share it. covalent bonds that hold the atoms together; each valence electron is attracted equally by the two adjacent

• • • • 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

Generation of

Free

Electrons

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

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

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

Movement of electrons and holes

One electron One hole has traveled from right to left.

has traveled from left to right.

Bandgap Energy

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

A : No. A minimum dislodge an electron from a covalent bond. For silicon, the bandgap energy is 1.12 eV. energy—called the “bandgap energy” is required to Note: eV represents the energy necessary to move one electron across A potential difference of 1V. 1 eV =1.6 x 10 -19 J Insulators display a higher E g . (e.g. 2.5 eV for diamond ) Semiconductors usually have a moderate Eg between 1 eV and 1.5 eV.

Electron Density

Q: How many free electrons are created at a given temperature? electron density

n i

   15

T

exp 

E g

2

kT

 3 where k=1.38 x 10 -23 Boltzmann constant. J/K is called the As expected, materials having a larger bandgap (E g )exhibit a smaller n

i

. Also, as T pproaches zero, n i approaches zero.

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 10 10 Electrons per cm 3 .

Silicon has 5 x 10 22 atoms per cm 3 .

What this means is that there is only one temperature.

electron for 5 x 10 12 atoms at room How do we increase the electron density?

Intrinsic Semiconductor

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

In an intrinsic semiconductors, the electron density(n or n a hole.) So

nn=n i 2

i ) is equal to the hole density (p). (each electron is created by leaving behind

np=n i 2

electron holes

Can we use something other than silicon?

Add Phosphorous to Silicon to Create an silicon

Phosphorus has 5 valence electrons. This electron is free The 5 th electron is “unattached”.

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=n i 2

This equation is true whether we are dealing with an intrinsic or extrinsic semiconductor.

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!

Add Boron to Silicon to Create a p-type Silicon

if we dope silicon with an atom that provides an insufficient number 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

In n-type material, MajorityCarriers MinorityCarriers  

N n i

2 

D N D

In p-type material, MajorityCarriers MinorityCarriers

n i

2

N A



N A

V ab

  

b a Edx

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 .”

Mobility

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

v

 

E

 Mobility: 1350 cm 2 /(VS) for electrons 480 cm 2 /(VS) for holes.

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

v e

  

n



E

 For electrons 

v h

 

p



E

 For holes

Mobility of Various Doped Semiconductor

Devices of higher mobility can be used to make higher speed transistors!

Drift Current

Drift current is composed of the drift current due to holes and the drift current due to electrons.

Concept of a Current Density

The current density is the charge per second crossing a unit area .

Velocity Saturation

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.

Microscopic View of Charge Movement

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

Where does the – sign come from?

Diffusion Current Due to Electron

Summary

μ and D are related via D/ μ=kT/q This is known as Einstein’s relation

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