ece 250 - lecture 1 - introduction to semiconductor...

ECE 250 – Electronic Devices 1

ECE 250ECE 250

Electronic Device Modeling


Introduction to SemiconductorIntroduction to Semiconductor Physics

• You should really take a semiconductor device physics course. p y

• We can only cover a few basic ideas and some simple calculationssome simple calculations.


Electronic Devices

• Most electronic devices are made out of semiconductors, insulators, and conductors.

• Semiconductors– Old Days – Germanium (Ge)– Now – Silicon (Si)– Now – Gallium Arsenide (GaAs) used for high speed

and optical devicesand optical devices.– New – Silicon Carbide (SiC) – High voltage Schottky

diodes.


Elements

• Elements in the periodic table are grouped by the number of electrons in their valence yshell (most outer shell).– Conductors – Valence shell is mostly empty (1Conductors Valence shell is mostly empty (1

electron)– Insulators – Valence shell is mostly fully– Semiconductors – Valence shell is half full.(Or is it half empty?)(Or is it half empty?)


Semiconductors

• Silicon and Germanium are group 4 elements – they have 4 electrons in their yvalence shell.

Valence Electron

Si


Silicon

• When two silicon atoms are placed close to one another, the valence electrons are ,shared between the two atoms, forming a covalent bond.

Covalent bond

Si Si


SiliconSilicon

Si

Si SiSi Si SiSi

Si


Si

SiliconSi SiSi

Si

Si

A i t t t f th 5 t•An important property of the 5-atom silicon lattice structure is that valence electrons are available on the outer edge of the silicon crystal so that other silicon yatoms can be added to form a large single silicon crystal.silicon crystal.


Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si


Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

•At 0 ºK each electron is in its lowest energy•At 0 K, each electron is in its lowest energy state so each covalent bond position is filled.•If a small electric field is applied to the•If a small electric field is applied to the material, no electrons will move because they are bound to their individual atomsare bound to their individual atoms.=> At 0 ºK, silicon is an insulator.


Silicon

• As temperature increases, the valence electrons gain thermal energy.g gy

• If a valence electron gains enough energy, it may break its covalent bond and and movemay break its covalent bond and and move away from its original position.

• This electron is free to move within the• This electron is free to move within the crystal.


Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si+

-Si Si Si Si Si Si

-

Si Si Si Si Si Si


Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si+

-

Si Si Si Si Si Si

Since the net charge of a crystal is zero, if a negatively (-) charged electron breaks its bond and moves away from its original position, a positively charged “empty state” is left in its original position.


Semicond ctorsSemiconductors• As temperature increases, more bonds are p

broken creating more negative free electrons and more positively charged p y gempty states. (Number of free electrons is a function of temperature.)p )

• To break a covalent bond, a valence electron must gain a minimum energy Eg,electron must gain a minimum energy Eg, called the energy band gap. (Number of free electrons is a function of Eg.)electrons is a function of Eg.)


Insulators

• Elements that have a large energy band gap of 3 to 6 eV are insulators because at room temperature, essentially no free electrons exist.

• Note: an eV is an electron volt. It is the amount of energy an electron will gain if itamount of energy an electron will gain if it is accelerated through a 1 volt potential.


Electron Volt( )( )llV 19 11060211 −( )( )

( ) joulecoul

voltcouleV19

19

110602.1

110602.11−

−

⎟⎠⎞

⎜⎝⎛×=

×=

( )joules

coulombcoul

1910602.1

110602.1−×=

⎟⎠

⎜⎝

Also, 1 eV = 1.518 ×10-22 BTU, but who cares.


Conductors

• Elements that have a small energy band gap are conductors.

• These elements have a large number of free electrons at room temperature because theelectrons at room temperature because the electrons need very little energy to escape from their covalent bondsfrom their covalent bonds.


Semiconductors

• Semiconductors have a band gap energy of about 1 eV– Silicon = 1.1 eV– GaAs = 1.4 eVGaAs 1.4 eV– Ge = 0.66 eV


Empty States

• An electron that has sufficient energy and is adjacent to an empty state may move into j p y ythe empty state, leaving an empty state behind.


Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si+

This electron can fill the empty

Si Si Si Si Si Sifill the empty

state.

Si Si Si Si Si SiEmpty state originally here.


Si Si Si Si Si Si

Si Si Si Si Si Si+

Si Si Si Si Si Si

Si Si Si Si Si SiEmpty state

Si Si Si Si Si Sinow here.


Si Si Si Si Si Si

Si Si Si Si Si Si+

Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si


Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si+

Si Si Si Si Si Si

Si Si Si Si Si Si


Empty States

• Moving empty states can give the appearance that positive charges move through the material.

• This moving empty state is modeled as a positively charged particle called a hole.

• In semiconductors, two types of “particles” contribute to the current: positively charged holes and negatively charged electrons.


Carrier Concentrations

• The concentrations of holes and free electrons are important quantities in the p qbehavior of semiconductors.

• Carrier concentration is given as the numberCarrier concentration is given as the number of particles per unit volume, or

• Carrier concentration = #• Carrier concentration = 3

#cm


Intrinsic Semioconductor

• Definition – An intrinsic semiconductor is a single crystal semiconductor with no other g ytypes of atoms in the crystal. – Pure siliconPure silicon– Pure germanium– Pure gallium arsenidePure gallium arsenide.


Carrier Concentration

• In an intrinsic semiconductor, the number of holes and free electrons are the same because they are thermally generated.

• If an electron breaks its covalent bond we have one free electron and one hole.

• In an intrinsic semiconductor, the concentration of holes and free electrons are the same.


Intrinsic Semiconductorsn

• = the concentration of free electrons in anin

the concentration of free electrons in an intrinsic semiconductor.

• = the concentration of holes in an intrinsic• = the concentration of holes in an intrinsic semiconductor.


Intrinsic Carrier Concentration⎟⎞

⎜⎛ − EgBT e p2

3

• B and Eg are determined by the properties

⎟⎠

⎜⎝

=KT

gBTni 2exp2

• B and Eg are determined by the properties of the semiconductor.E b d ( V)• Eg = band gap energy (eV)

• B = material constant

( ) ( ) ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

233

#

Kcm o( ) ( ) ⎠⎝ ⋅ 2Kcm


Intrinsic Carrier Concentration⎟⎞

⎜⎛ − EgBT e p2

3⎟⎠

⎜⎝

=KT

gBTni 2exp2

• T = temperature (ºK)• K = Boltzmann’s constant = 86 2×10-6 eV/ºK• K = Boltzmann s constant = 86.2×10 6 eV/ K


Material Constants⎞⎛Material Eg (eV) B

( ) ( ) ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⋅ 233

#

Kcm o

Silicon 1.12 5.23×1015

Gallium Arsenide

1.4 2.10×1014

Germanium 0.66 1.66×1014


Important Note:B k li htl diff tBook uses a slightly different

Notation!No o !

⎟⎞

⎜⎛ − Eg3 ⎟

⎠⎞

⎜⎝⎛=

KTEgBTni exp3


Book Material Constants

Material Eg (eV) B ( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅36

#Kcm o

Silicon 1.12 5.4×1031


Example

• Find the intrinsic carrier concentration of free electrons and holes in a silicon semiconductor at room temperature.


MathCAD

eV 1.602 10 19−⋅ coul⋅( ) 1⋅ volt⋅≡ KB 86.2 10 6−⋅eVK

⋅:=K

T 300 KT 300 K⋅:=Bsi 5.23 1015⋅

1

cm3 K1.5( )⋅⋅:= ( )

Egsi 1.12 eV⋅:=


MathCADEg⎛ ⎞

ni Bsi T1.5⋅ expEgsi−

2 KB⋅ T⋅

⎛⎜⎝

⎞⎟⎠

⋅:=⎝ ⎠

ni 1 5 1010×1

=ni 1.5 10×cm3

=

The concentration of silicon atoms in an intrinsic semiconductor is 5×1022 atoms/cm3.


Extrinsic Semiconductors

• Since the concentrations of free electrons and holes is small in an intrinsic semiconductor, only small currents are possible.p

• Impurities can be added to the semiconductor to increase the concentrationsemiconductor to increase the concentration of free electrons and holes.



• An impurity would have one less or one more electron in the valance shell than silicon.

• Impurities for group 4 type atoms (silicon)Impurities for group 4 type atoms (silicon) would come from group 3 or group 5 elementselements.



• The most common group 5 elements are phosphorous and arsenic.

• Group 5 elements have 5 electrons in the valence shell.

• Four of the electrons fill the covalent bonds in the silicon crystal structure.

• The 5th electron is loosely bound to the impurity atom and is a free electron at room temperature.


Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si P Si Si Si-

Si Si Si Si Si Si

Si Si Si Si Si Si



• The group 5 atom is called a donorimpurity since it donates a free electron.p y

• The group 5 atom has a net positive charge that is fixed in the crystal lattice and cannotthat is fixed in the crystal lattice and cannot move.

• With a donor impurity free electrons are• With a donor impurity, free electrons are created without adding holes.



• Adding impurities is called doping.• A semiconductor doped with donorA semiconductor doped with donor

impurities has excess free electron and is called an n-type semiconductorcalled an n type semiconductor.



• The most common group 3 impurity is boron which has 3 valence electrons.

• Since boron has only 3 valence electrons, the boron atom can only bond with three ofthe boron atom can only bond with three of its neighbors leaving one open bond positionposition.


Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si B Si Si Si

Si Si Si Si Si Si

Si Si Si Si Si Si



• At room temperature, silicon has free electrons that will fill the open bond pposition, creating a hole in the silicon atom whence it came.

• The boron atom has a net negative charge because of the extra electron but the boronbecause of the extra electron, but the boron atom cannot move.


Si Si Si Si Si Si

Si Si Si Si Si Si

Si Si B Si Si Si+

Si Si Si Si Si Si

Si Si Si Si Si Si



• Since boron accepts a valence electron, it is called an acceptor impurity.p p y

• Acceptor impurities create excess holes but do not create free electronsdo not create free electrons.

• A semiconductor doped with an acceptor impurity has extra holes and is called aimpurity has extra holes and is called a p-type semiconductor.


Carrier Concentrations

• For any semiconductor in thermal equilibrium nopo=ni

2, whereq opo i ,• no = the concentration of free electrons.• p = the concentration of holes• po = the concentration of holes.• ni = the intrinsic carrier concentration

⎟⎠⎞

⎜⎝⎛ −=

KTEgBTni 2

exp23

⎠⎝ KT2


Extrinsic Carrier Concentrations

• For an n-type semiconductor with donor impurities, the concentration of donor p ,impurities is Nd with units #/cm3.

• If Nd >> ni then the concentration of freeIf Nd >> ni, then the concentration of free electrons in the n-type semiconductor is approximately n ≈ Ndapproximately no ≈ Nd.



• Since nopo=ni2 for any semiconductor in

thermal equilibrium, and• For an n-type semiconductor, no ≈ Nd

2

d

io N

np2

=

• Where po is the concentration of holes in the n-type semiconductor.



• For a p-type semiconductor with acceptor impurities, the concentration of acceptor p , pimpurities is Na with units #/cm3.

• If N >> ni then the concentration of holesIf Na >> ni, then the concentration of holes in the p-type semiconductor is approximately p ≈ Napproximately po ≈ Na.



• Since nopo=ni2 for any semiconductor in

thermal equilibrium, and• For a p-type semiconductor, po ≈ Na

2

a

io N

nn2

=

• Where no is the concentration of free electrons in the p-type semiconductor.


Current in Semiconductors

• The two processes that cause free electrons and holes to move in a semiconductor are drift and diffusion.

• Drift – the movement of holes and electrons due to an electric field

• Diffusion – the movement of holes and electrons due to variations in concentrations.


Drift Current

• Assume that an electric field is applied to to a semiconductor.

• This field acts on holes and electrons.


Drift Current-Electrons

• Electrons – The Electric field creates a force in the E

r

opposite direction of the electric field – Attractive.

i h d if l i fdnvs −e

• vdn is the drift velocity of electrons.J i th t d it

nJr

• Jn is the current density due to electrons.n-type


Drift Current-Electrons

• The electrons acquire a drift velocity of

Evrs μ

• Where μ is the mobility of electrons with

Ev ndn μ−=

Where μn is the mobility of electrons with units of cm2/(volt-sec).

• The units of vd are cm/secThe units of vdn are cm/sec.• For low-doped silicon, a typical number is μ =1350 cm2/volt-secμn 1350 cm /volt sec.


Drift Current-Electronsr

Th i i ( ) i di h h

Ev ndns μ−=

• The minus sign (-) indicates that the electrons move in the opposite direction of th li d l t i fi ldthe applied electric field.


Drift Current Density-Electrons

• Current = charge per unit time (coul/sec).• Current density = current flowing through aCurrent density current flowing through a

specific area = amps/unit area = coul/(sec-cm2)cm )


Drift Current Density-Electrons

EenenvJ ndnn μ=−=

• e = the charge on an electron = 1.602×10-19

coulombs.• n=concentration of electrons = #/cm3.• en=charge/cm3• en=charge/cm .

223 seccharge

seccmcharge ampcmenvdn === 223 secseccm cmcm⋅


Drift Current - Holes

• Holes – The Electric field creates a force in the E

r

same direction of the electric field.

i h d if l i fdpvr+h

• vdp is the drift velocity of holes.J i th t d it

pJr

• Jp is the current density due to holes.n-type


Drift Current-Holes• The holes acquire a drift velocity of• The holes acquire a drift velocity of

Evrs μ=

• Where μp is the mobility of holes with units f 2/( lt )

Ev pdp μ=

of cm2/(volt-sec).• The units of vdp are cm/sec.• For low-doped silicon, a typical number is μdp=480 cm2/volt-sec.


Mobility - Aside

• Note that μn> μp.

• Electrons are faster than holesElectrons are faster than holes.• P-type and n-type devices operate the same.

However n type devices are fasterHowever, n-type devices are faster.


Drift Current Density-Holes

EJ EepepvJ pdpp μ==

• e = the charge on an electron = 1.602×10-19

coulombs.• p=concentration of holes = #/cm3.• ep=charge/cm3• ep=charge/cm .

223 seccharge

seccmcharge ampcmenvdp === 223 secseccm cmcmp ⋅


Drift CurrentDrift Current

Er

Er

Er+

Es

dpvr+hJr

dnvs −eJr

pJ nJ

n-type n-type

Drift current due to holes and electrons is in the same direction.


Total Drift Current

• Since the hole current and the electron current are in the same direction, the ,currents add.

• The total drift current is:The total drift current is:

rrrEepEenJ pn μμ +=


Ohm’s Law

• Another form of Ohm’s law is J=σE• σ is the conductivity of the materialσ is the conductivity of the material.• Noting that

EepEenJ pn

rrrμμ +=

• andEJrv

σ= EJ σ=


Conductivity

We can find the conductivity of a semiconductor as

pn epen μμσ +=


Diffusion CurrentsDiffusion Currents

(Cover Them)


Excess Carriers

• So far we have assumed that the semiconductor is in steady state.y

• Suppose that we shine light on a semiconductorsemiconductor.

• If the photons have sufficient energy, valence electrons may break their covalent bonds andelectrons may break their covalent bonds and create pairs of free electrons and holes.


Excess Carriers• These additional holes and electrons are• These additional holes and electrons are

called excess holes (δp) and excess free electrons (δn)electrons (δn).

• When excess holes and free electrons are d h i f h l dcreated, these concentration of holes and

free electrons increase above the thermal ilib i lequilibrium value

n = no+ δn p = po + δpo p po p


Excess Carriers

• In steady state, the generation of excess carriers will not cause the carrier concentration to increase indefinitely due to a process called recombination.p

• Electron-Hole Recombination – a free electron combines with a hole and bothelectron combines with a hole and both disappear.


Excess Carriers

• Generation – Creates free electrons – hole pairs.p

• Recombination – Eliminates free electrons and holes in pairsand holes in pairs.

• Excess Carrier Lifetime – The mean time over which an excess free electron and holeover which an excess free electron and hole exist before recombination.

ece 250 - lecture 1 - introduction to semiconductor...

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