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Lecture 2

Semiconductor Physics

Semiconductor Physics 1-1

Outline Bond model: electrons and holes

Electron-hole pair generation and recombination

Intrinsic semiconductor

Doping: Extrinsic semiconductor

Charge Neutrality

Introduction to Charge Carrier Transport


Test Yourself

Can you differentiate between: Semiconductors

Conductors

Insulators

What is the difference between charge carriers and free charge carriers ?


Semiconductor Materials

Three most used semiconductors: carbon (C), silicon (Si) and germanium (Ge)


Carbon Silicon Germanium

Silicon (most common semiconductor material)

Bond Model

Si is column IV of the periodic table

Electronic structure of silicon atom: 10 core electrons (tightly bound)

4 valence electrons (loosely bound, responsible for most of the chemical properties

Other semiconductors: Single crystal: Ge, C (diamond form)

Compound: GaAs, InP, InGaAs, InGaAsP, GaP, ZnSe, CdTe (on the average, 4 valence electrons per atom)


Silicon crystal structure


Diamond structure: atoms tetrahedrally bonded by sharing valence electrons

covalent bonding

Each atom shares 4 electrons

eight covalent electrons associated with each atom

Si atomic density:

5 x 1022 cm-3

Simple “flattened” model of Si crystal

This bonding of atoms, strengthened by the sharing of

electrons, is called covalent bonding

Molecules or ions tend to be more stable when the outermost electron shells of their constituent atoms contain eight electrons


At 0 oK: • All bonds are satisfied (all valence electrons engaged in

bonding) • No “free” electrons (or holes)

Creation of electron-hole pair At room temperature (default 27 oC or 300 oK),

approximately 1.5X 1010 free carriers in 1 cm3 of intrinsic silicon material Intrinsic semiconductor material means material has

been refined to a very low level of impurities


Creation of electron-hole pair Electron-hole pairs in a silicon crystal. Free

electrons are being generated continuously while some recombine with holes

Electrons and holes

in semiconductors are

“fuzzier”: they span

many atomic sites


At finite temperature, some bonds are broken • “free” electrons – Mobile negative charge -1.6 x 10-19 C • “free” holes – Mobile positive charge, +1.6 x 10-19 C

Definitions

“electron” means free electron Not concerned with bonding electrons or

core electrons

Define: n ≡ free electron concentration [cm-3]

p ≡ free hole concentration [cm-3]

Mass action law (at thermal equilibrium)

Where ni ≡ intrinsic carrier concentration [cm−3 ]


pnni .2

Generation and Recombination Generation: break-up of covalent bond to form

electron and hole pairs In an intrinsic semiconductor, the number of holes is equal to the

number of free electrons

Generate new hole-electron pairs per unit volume per second requires energy from thermal or optical sources

Generation rate: G = Gthermal + Goptical + …. [cm−3. s−1 ]

Recombination: formation of covalent bond by bringing together electron and hole Releases energy in thermal or optical form

Recombination rate R [cm−3. s−1 ]

1 recombination event requires 1 electron + 1 hole

On an average, a hole (an electron) will exist for ζp (ζ n) seconds before recombination. This time is called the mean lifetime of the hole (electron)


Intrinsic Semiconductors Thermal Equilibrium

Steady state plus absence of external energy sources

With increasing temperature, the density of hole-electron pairs (free charge carriers) increases in an intrinsic semiconductor.

where ni ≡ intrinsic carrier concentration [cm−3 ] EG0 is the energy gap (the energy required to break a covalent

bond) at 0 K k is the Boltzmann constant in electron volts per degree

kelvin (J/K) [k = 1.38x10-23 J/K] A is a material-dependent constant independent of T


kT

E

i

G

eATn0

32

pnni .2

Intrinsic Semiconductors

In Si at 300 K (“room temperature”): ni ≈ 1x1010 cm-3

In a sufficiently pure Si wafer at 300K (“intrinsic semiconductor):

• Assume thermal equilibrium: n = p = ni ≈ 1 ×1010 cm−3

ni is a very strong function of temperature T ↑ ⇒ ni ↑

Why ?


Effect of Temperature on Conductivity

Conductor resistance increase with increase in heat (number of

free charge carriers decreases)

have a positive temperature coefficient

Semiconductor resistance decrease (i.e., conductivity increase) with

increase in heat (number of free charge carriers increases)

have a negative temperature coefficient


Controlling the properties of a Semiconductor

Doping = engineered introduction of foreign atoms to modify semiconductor electrical properties

Doping is the process of deliberately adding impurities to the crystal during manufacturing and increases the number of current carries (electrons or holes) Impurities (extraneous elements)

Doping process create n-type and p-type of semiconductors

A semiconductor material that has been subjected to the doping process is called an extrinsic material


Doping

Silicon: 4 valence electrons Each Si atom bonds to four

others Replace some Si atoms with atoms

that do not have four valence electrons

These atoms will have: - an extra electron (group V) Donors

- an extra hole (group III) Acceptors

Doping increases the number of carriers


Donors Introduce electrons to semiconductors (but not

holes)

For Si, group V elements (dopants) with 5 valence electrons (Arsenic “As”, phosphorus “P”, antimony “Sb”)


Donors 4 of five electrons participate in bonding

The 5th electron easy to release at room temperature, each donor releases 1 electron that is available

for conduction1 conduction

Donor site become positively charged (fixed charge)

Define:

Nd ≡ donor concentration [cm-3] If Nd << ni doping is irrelevant

• Intrinsic semiconductor → n = p = ni

If Nd >> ni, doping controls carrier

concentration

Extrinsic semiconductor ⇒

n = Nd and p = ni2/ Nd

Note: n >> p : n-type semiconductor

In general: Nd ≈ 1015

1020 atom or electron m-3 Semiconductor Physics 1-19

Acceptors Introduce holes to semiconductors (but not

electrons)

For Si, group III elements with 3 valence electrons (usually Boron(B) , Gallium (Ga) and Indium (In))


Acceptors 3 electrons participate in bonding

one bonding site “unsatisfied” making it easy to “accept” neighboring bonding electron to complete all bonds at room temperature, each acceptor “releases”

hole that is available for conduction

Acceptor site become

negatively charged

(fixed charge)


Acceptors

Define: Na ≡ acceptor concentration [cm-3] If Na << ni doping is irrelevant

• Intrinsic semiconductor → n = p = ni

If Na >> ni, doping controls carrier concentration

Extrinsic semiconductor ⇒ p = Na and n = ni2/ Na

Note: p >> n : p-type semiconductor

In general: Na ≈ 1015 1020 cm-3


Energy levels of donors and acceptors.


Summary of Charge Carriers


Majority and Minority Carriers

• n-type material, the electron is called majority carrier and hole the minority carrier

• p-type material, the hole is called majority carrier and electron the minority carrier


Charge Neutrality The semiconductor remains charge neutral even

when it has been doped Overall charge neutrality must be satisfied

In general: the net charge density ρ (C/cm3) in a semiconductor = ρ = q (p − n + Nd − Na) Where q: electric (elementary) charge = 1.6 Х 10-19 C


+ −

Charge Neutrality

Example Let us examine this for: Nd = 1017 cm-3, Na = 0

Then, n = Nd = 1017 cm−3, p = ni2/Nd = 103 cm−3

Using the equation ρ = q (p − n + Nd − Na), we find that ρ ≠ 0 !!

What is wrong??


Charge Neutrality

Nothing wrong!

We just made the approximation when we assumed that n = Nd

We should really solve the following system of equations (for Na=0):


p − n + Nd = 0 n.p = ni2

n2 - n. Nd - ni2 = 0 n ≠ Nd

+

Charge Carrier Transport

Any motion of free charge carriers in a semiconductor leads to a current

Different causes for having motion Associated random motion due to the thermal

energy (Thermal Motion)

Motion can be caused by an electric field due to an externally applied voltage (Carrier Drift)

Motion from regions where the carrier density is high to regions where the carrier density is low (Carrier Diffusion)


Thermal Motion In thermal equilibrium, carriers are not

sitting still: Undergo collisions with vibrating Si atoms

(Brownian motion)

Electrostatically interact with each other and with ionized (charged) dopants


Thermal Motion (cont’d) Characteristic time constant of thermal motion

mean free time between collisions • Tc ≡ Collison time (seconds)

In between collisions, carriers acquire high velocity: • vth ≡ thermal velocity (cm/second)

Characteristic length of thermal motion: • λ ≡ mean free path [cm] = vth Tc

Example: Put numbers for Si at room temperature (27 oC or 300 oK): Tc ≈ 10−13 seconds, vth ≈ 107 cm/second ⇒ λ ≈ 0.01 μm

Carriers undergo many collisions as they travel



Lecture Summary Covered material Continue Semiconductor Materials

Types of semiconductors Two types of “carriers” (mobile charge particles):

• electrons and holes

Creation of electron-hole pairs Doping

• Donors n-type semiconductor material • Acceptors p-type semiconductor material

Important equations under thermal equilibrium conditions: (p − n + Nd − Na = 0) and (n.p = ni

2)

Material to be covered next lecture Continue Semiconductor Physics

Carrier Transport (Carrier Drift and Carrier Diffusion)

pn junctions (or diodes) Basics