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ECE 250 – Elec t ron ic Devic es 1

Electronic Device Modeling




Physics

• You should really take a semiconductor device h sics course.

• We can only cover a few basic ideas and

.




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

. – New – Silicon Carbide (SiC) – High voltage Schottky

diodes.




Elements

• Elements in the periodic table are grouped b the number of electrons in their valence

shell (most outer shell).

– Conductors – Valence shell is mostl em t 1

electron)

– Insulators – Valence shell is mostl full

– Semiconductors – Valence shell is half full.

Or is it half em t ?




Semiconductors

• Silicon and Germanium are group 4elements – the have 4 electrons in their

valence shell.

Valence

Electron

Si




Silicon

• When two silicon atoms are placed close toone another the valence electrons are

shared between the two atoms, forming a

covalent bond.Covalent

bond

Si Si




Si

Si




SiliconSi SiSi

Si

• n mpor an proper y o e -a om

silicon lattice structure is that valenceelectrons are available on the outer edge

of the silicon crystal so that other silicon

atoms can be added to form a large single

.




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

º ,

state so each covalent bond position is filled.

•

material, no electrons will move because they

.=> At 0 ºK, silicon is an insulator.




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.




em con uc ors• As temperature increases, more bonds are

broken creating more negative freeelectrons and more ositivel char ed

empty states. (Number of free electrons is a

function of temperature.)• To break a covalent bond, a valence

l r n m in minim m n r E

called the energy band gap. (Number of free




Insulators

• Elements that have a large energy band gapof 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

is accelerated through a 1 volt potential.




Electron Volt

−

joulec u

vo t coue

19 1106021

.

−

−

⎞⎛ ×=

×=

joules

coulomb19

10602.1−

×=

⎝

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




Conductors

• Elements that have a small energy band gapare conductors.

• These elements have a large number of free

electrons need very little energy to escape

.




Semiconductors

• Semiconductors have a band gap energy of about 1 eV

– Silicon = 1.1 eV

– = .

– Ge = 0.66 eV




Empty States

• An electron that has sufficient energy and isad acent to an em t state ma move into

the 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

Si Si Si Si Si Si

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 Si

Empty 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 theappearance that positive charges movethrough 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 chargedholes and negatively charged electrons.




Carrier Concentrations

• The concentrations of holes and freeelectrons are im ortant uantities in the

behavior of semiconductors.

•

of particles per unit volume, or

3cm




Intrinsic Semioconductor

• Definition – An intrinsic semiconductor isa sin le cr stal semiconductor with no other

types of atoms in the crystal.

– Pure silicon

– Pure germanium

– .




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 wehave one free electron and one hole.

• In an intrinsic semiconductor, the

concentration of holes and free electrons arethe same.




Intrinsic Semiconductors

• =i

intrinsic semiconductor.

semiconductor.




Intrinsic Carrier Concentration⎛ − Eg3

⎠⎝

=KT

ni

2

exp

of the semiconductor.

• g = an gap energy e

• B = material constant

⎟⎟ ⎞

⎜⎜⎛

33

#

o⋅




Intrinsic Carrier Concentration⎛ − Eg3

⎠⎝

=KT

ni

2

exp

• T = temperature (ºK)

’ - º.




Material Constants

Material Eg (eV)

B ( ) ( ) ⎟⎟ ⎠⎜⎜⎝ ⋅ 23

3

#

K cmo

Silicon 1.12 5.23×1015

Gallium

Arsenide

1.4 2.10×1014

Germanium 0.66 1.66×1014




Important Note:

oo uses a s g y eren Notation!

− ⎟ ⎠

⎜⎝

=KT

BT ni exp3

33




Book Material Constants

Material Eg (eV) B ( ) ( ) ⎟⎟ ⎠

⎞

⎜⎜⎝

⎛

⋅36

#

K cmo

Silicon 1.12 5.4×1031

34




Example

• Find the intrinsic carrier concentration of free electrons and holes in a silicon

semiconductor at room temperature.

35




MathCAD

eV 1.602 1019−⋅ coul⋅( ) 1⋅ volt⋅≡ K B 86.2 10

6−⋅ eV⋅:=

⋅:=

Bsi 5.23 1015⋅

1

cm3

K 1.5⋅

⋅:=

Egsi 1.12 eV⋅:=

ECE 250 El t i D i 36




MathCAD

ni Bsi T1.5

⋅ exp

si−

2 K B⋅ T⋅⋅:=

10 1= .

cm3

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





Extrinsic Semiconductors

• Since the concentrations of free electronsand holes is small in an intrinsic

semiconductor, only small currents are

ossible.• Impurities can be added to the

of free electrons and holes.






• An impurity would have one less or onemore electron in the valance shell than

silicon.

•would come from group 3 or group 5

.



ECE 250 Elec t ron ic Devic es 40




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

ECE 250 Elec t ron ic Devic es 41





• The group 5 atom is called a donorim urit since it donates a free electron.

• The group 5 atom has a net positive charge

move.

,created without adding holes.



ECE 250 Elec t ron ic Devic es


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

• Since boron has only 3 valence electrons,

its neighbors leaving one open bond

.





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 freeelectrons that will fill the o en bond

position, creating a hole in the silicon atom

whence it came.• The boron atom has a net negative charge

,

atom cannot move.




• Since boron accepts a valence electron, it iscalled an acce tor im urit .

• Acceptor impurities create excess holes but

.

• A semiconductor doped with an acceptor

p-type semiconductor.




Carrier Concentrations

• For any semiconductor in thermale uilibrium n =n 2 where

• no = the concentration of free electrons.

o .

• ni = the intrinsic carrier concentration

⎟ ⎞⎜⎛ −= Eg BT ni exp23




Extrinsic Carrier Concentrations

• For an n-type semiconductor with donor im urities the concentration of donor

impurities is Nd with units #/cm3.

• ,electrons in the n-type semiconductor is

o .




Extrinsic Carrier Concentrations

• Since no po=ni

2

for any semiconductor inthermal equilibrium, and

• For an n-type semiconductor, no ≈ Nd

d

io

N

n p

2

=

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



Current in Semiconductors

• The two processes that cause free electronsand holes to move in a semiconductor aredrift and diffusion.

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

• Diffusion – the movement of holes and

electrons due to variations inconcentrations.




Drift Current

• Assume that an electric field is applied to toa 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.dn

vs −

e • vdn is the drift velocity of

electrons.n J

r

•n

s e curren ens y

due to electrons.n-type




Drift Current-Electrons

• The electrons acquire a drift velocity of r

s

•

ndn −=

n units of cm2/(volt-sec).

• n .

• For low-doped silicon, a typical number is= 2 -n .



Drift Current Density-Electrons

• Current = charge per unit time (coul/sec).• =

specific area = amps/unit area = coul/(sec-

2




Drift Current Density-Electrons

E enenv J ndnn μ =−=• e = the charge on an electron = 1.602×10-19

coulombs.• n=concentration of electrons = #/cm3.

= 3.

223

chargecharge ampcmenvdn ===

secseccm cmcm⋅




Drift Current - Holes

• Holes – The Electric field

creates a force in the E r

same direction of the

electric field.dp

vr+

h • vdp is the drift velocity of

holes. p J

r

• p

s e curren ens y

due to holes.n-type




Drift Current-Holes

r

s

• Where μ p is the mobility of holes with units pdp =

o cm vo -sec .

• The units of vdp are cm/sec.

• For low-doped silicon, a typical number isμdp=480 cm2/volt-sec.




Mobility - Aside

• Note that μn> μ p.

• .

• P-type and n-type devices operate the same.

, - .



r r

dpvh

r

dnvs −

e

r

p n J

n-type n-type

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



Ohm’s Law

• Another form of Ohm’s law is J=σE• .

• Noting that

E ep E en J pn

rrr

μ μ +=

• andrv




Conductivity

We can find the conductivity of a

semiconductor as

pn epenσ +=




(Cover Them)




Excess Carriers

• So far we have assumed that thesemiconductor is in stead state.

• Suppose that we shine light on a

.• If the photons have sufficient energy, valence

create pairs of free electrons and holes.




Excess Carriers

called excess holes (δ p) and excess free.

• When excess holes and free electrons are

create , t ese concentrat on o o es an

free electrons increase above the thermal

equ r um va ue

n = n + δn = + δ



Excess Carriers

• Generation – Creates free electrons – hole

airs.

• Recombination – Eliminates free electrons

.• Excess Carrier Lifetime – The mean time

exist before recombination.

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