Chapter 1. Electronics and Semiconductorstioh.weebly.com/uploads/2/5/4/3/25433593/7week__chapter_1_.pdf · Chapter 1. Electronics and Semiconductors Tong In Oh. Microelectronic Circuits,

Microelectronic Circuits, Kyung Hee Univ. Spring, 2016

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Chapter 1. Electronics and Semiconductors

Tong In Oh


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Objective• Basic properties of semiconductors (silicon)• How doping a pure silicon crystal dramatically changes its electrical

conductivity• Two mechanisms of current flows in semiconductors: drift, diffusion of

charge carriers• Structure and operation of the pn junction


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1.7 Intrinsic Semiconductors• Semiconductor: a material whose conductivity lies between that of

conductors (copper) and insulators (glass)• Single-element: such as germanium and silicon (Ⅳ in the periodic table)• Compound: such as gallium-arsenide (GaAs)

(combining elements of groups Ⅲ and Ⅴ or Ⅱ and Ⅵ )


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• Valence electron – is an electron that participates in the formation of chemical bonds

• Atoms with one or two valence electrons more than a closed shell are highly reactive because the extra electrons are easily removed to form positive ions.

• Covalent bond – is a form of chemical bond in which two atoms share a pair of atoms.

• It is a stable balance of attractive and repulsive forcesbetween atoms when they share electrons.


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• Silicon atom• four valence electrons• requires four more to complete outermost shell• each pair of shared forms a covalent bond• the atoms form a lattice structure

Figure 1.28 Two-dimensional representation of the silicon crystal. The circles represent the inner core of silicon atoms, with +4

indicating its positive charge of +4q, which is neutralized by the charge of the four valence electrons. Observe how the covalent bonds are formed by sharing of the valence electrons. At 0K, all bonds are intact and no free electrons are available for current

conduction.


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• silicon at low temps• all covalent bonds – are intact• no electrons – are available for conduction• conducitivity – is zero

• silicon at room temp• some covalent bonds – break, freeing an electron and creating hole, due to

thermal energy :thermal generation• some electrons – will wander from their parent atoms, becoming available for

conduction• Holes – fill up the “hole”• conductivity – is greater than zero

The process of freeing electrons, creating holes, and filling them facilitates current flow…


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3.1: Intrinsic Semiconductors• silicon at low temps:

• all covalent bonds are intact• no electrons are available for conduction• conducitivity is zero • silicon at room temp:

• sufficient thermal energy exists to break some covalent bonds, freeing an electron and creating hole

• a free electron may wander from its parent atom

• a hole will attract neighboring electrons

the process of freeing electrons, creating holes, and filling them facilitates current flow

Figure 1.29: At room temperature, some of the covalent bonds are broken by thermal generation. Each broken bond gives rise to a free

electron and a hole, both of which become available for current conduction.


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• intrinsic semiconductor – is one which is not doped• One example is pure silicon.

• generation – is the process of free electrons and holes being created.

• generation rate – is speed with which this occurs.• recombination – is the process of free electrons and holes

disappearing.• recombination rate – is speed with which this occurs.

Generation may be effected by thermal energy. As such, both generation and recombination rates will be (at least in

part) a function of temperature.


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• thermal generation – effects a equal concentration of free electrons and holes.

• Therefore, electrons move randomly throughout the material.

• In thermal equilibrium, generation and recombination rates are equal.


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• In thermal equilibrium, the behavior below applies…• ni = number of free electrons and holes / unit volume of

intrinsic semiconductor at a given temperature• p = number of holes• n = number of free electrons

• 𝑛𝑛 = 𝑝𝑝 = 𝑛𝑛𝑖𝑖


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• ni = number of free electrons and holes in a unit volume for intrinsic semiconductor

• B = parameter which is 7.3E15 cm-3K-3/2 for silicon• T = temperature (K)• Eg = bandgap energy which is 1.12eV for silicon• k = Boltzman constant (8.62E-5 eV/K)

• 𝑝𝑝𝑛𝑛 = 𝑛𝑛𝑖𝑖2 (𝑛𝑛𝑖𝑖 ≈ 1.5 × 1010/𝑐𝑐𝑐𝑐3 for silicon at room temperature)

/ 23 / 2

equal to and

gE kT

p n

in BT e−=


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• Q: Why can thermal generation not be used to effect meaningful current conduction?

• A: Silicon crystal structure described previously is not sufficiently conductive at room temperature.

• Additionally, a dependence on temperature is not desirable.

• Q: How can this “problem” be fixed?• A: doping

doping – is the intentional introduction of impurities into an extremely pure (intrinsic) semiconductor for the

purpose changing carrier concentrations.


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1.8 Doped Semiconductors

• n-type semiconductor• Silicon is doped with element having a valence of 5.• To increase the concentration of free electrons (n).• One example is phosphorus, which is a donor.• Bound charge: positive charge of phosphorus atom


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• n-type doped semiconductor• If ND is much greater than ni …

• concentration of donor atoms is ND• Then the concentration of free electrons in the n-type is

defined as below.

The key here is that number of free electrons (aka. conductivity) is dependent on doping concentration, not

temperature…

they will be equal...

number numberfree donor

e-trons atomsin -type

( ) ( ) n D

n

n N≈


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• n-type semiconductor• pn will have the same dependence on temperature as ni

2

• the concentration of free electrons (nn) will be much larger than holes• electrons are the majority charge carriers• holes are the minority charge carrier

• n-type semiconductor• Q: How can one find the

concentration?• A: Use the formula to right,

adapted for the n-type semiconductor.

number number numberof holes of free of freein n-type electrons electrons

in n-type and holes

: combine this with equationon previous

in

sli

thermalequ

d

2

i

2

e

l.

(eq3.5)

n n i

in

D

p n n

np

n

× =

≈

action


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• p-type semiconductor• Silicon is doped with element having a valence of 3.• To increase the concentration of holes (p).• One example is boron, which is an acceptor.


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• p-type doped semiconductor• If NA is much greater than ni …

• concentration of acceptor atoms is NA• Then the concentration of holes in the p-type is defined

as below.

they will be equal...

numbernumberacceptorholes

atomsin-type

(eq3.6) ( ) ( )p A

p

p N≈


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• p-type semiconductor• Q: How can one find the

concentration?• A: Use the formula to right,

adapted for the p-type semiconductor.

numbernumber numberof freeof holes of free

electronsin -type electronsand holes

: combine this with equationon

in -typein thermal

e

previous slide

qu

2

il

2

.

(eq3.7)

pp

p p i

ip

A

p n n

nn

n

× =

≈

action

• p-type semiconductor• np will have the same dependence on temperature as ni

2

• the concentration of holes (pn) will be much larger than holes• holes are the majority charge carriers• free electrons are the minority charge carrier


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1.9.1 Drift Current

• Q: What happens when an electrical field (E) is applied to a semiconductor crystal?

• A: Holes are accelerated in the direction of E, free electrons are repelled.

Figure 1.32: An electric field E established in a bar of silicon causes the holes to drift in the direction of E and the free electrons to drift in the opposite direction. Both the hole and

electron drift currents are in the direction of E.


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• Q: How is the velocity of these holes defined?

.E (volts / cm)

.µp (cm2/Vs) = 480 for silicon

.µn (cm2/Vs) = 1350 for silicon

note that electrons move with velocity 2.5 times higherthan holes

p pp p

p pp p

hole mobility electron mobilityelectric field electric fie

P PP Pld

(eq3.8) (eq3.9)

p n

p drift p n drif n

E E

tv E v E

µ µ

µ µ− −

= == =

= = −


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• Assume that, for the single-crystal silicon bar on previous slide, the concentration of holes is defined as p and electrons as n.

• Q: What is the current component attributed to the flow of holes (not electrons)?


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• step #1: Consider a plane perpendicular to the x direction.• step #2: Define the hole charge that crosses this plane.

pp

pp

current flow attributed to holes cross-sectional area of silicon

magnitude of the electron charge concentration of holes

drift velocity of holes

(eq3.10)

p

p drift

IA

p p dr f

qp

v

i tI Aqpv−

==

==

=

−=

PART A: What is the current component attributed to the flow of holes (not electrons)?


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step #3: Substitute in µpE. step #4: Define current

density as Jp = Ip / A. µ

µ

==

==

==

=

pp

pp

current flow attributed to holes cross-sectional area of silicon

magnitude of the electron charge concentration of holes

hole mobility electric field

p

p

IA

qp

p

E

pI Aqp E

solution

(eq3.11) p pJ qp Eµ=

PART A: What is the current component attributed to the flow of holes (not electrons)?


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pp

pp

current flow attributed to electrons cross-sectional area of silicon

magnitude of the electron charge concentration of free electrons

electron mobility electric field

n

n

n n d

I

rift

Aqn

E

I Aqv

µ

==

=

−

=

==

= −

this is conductivity ( )

(eq3.12)

(eq3.13 )) (

n n

p n p n

J qn E

J J J q p n Eσ

µ

µ µ

=

= + = +

• Q: What is the current component attributed to the flow of electrons (not holes)?

• A: to the right…• Q: How is total drift current defined?

• A: to the right…

𝐼𝐼𝑛𝑛 = −𝐴𝐴𝐴𝐴𝑛𝑛𝑣𝑣𝑛𝑛−𝑑𝑑𝑑𝑑𝑖𝑖𝑑𝑑𝑑𝑑


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• conductivity (σ.) – relates current density (J) and electrical field (E)

• resistivity (ρ.) – relates current density (J) and electrical field (E) Ohm's Law

1( )

(eq3.14)

(eq3.16)

(eq3.15)

(eq3.1

( )

/

1

(

7)

(

)(

1

p n

p

p n

n

p n

q p n

q p

J E

q

q p

p n

J E

q p n

n

σ

σ

µ µ

ρµ

µ µ

µ

ρµ µ

=

= +

=

=

+

+

+


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1.9.2 Diffusion Current• carrier diffusion – is the flow of charge carriers from area of high

concentration to low concentration.• It requires non-uniform distribution of carriers.

• diffusion current – is the current flow that results from diffusion.


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• Take the following example…• inject holes – By some unspecified

process, one injects holes in to the left side of a silicon bar.

• concentration profile arises –Because of this continuous hole inject, a concentration profile arises.

• diffusion occurs – Because of this concentration gradient, holes will flow from left to right.

Figure 1.33: A bar of silicon (a) into which holes are injected, thus creating the hole concentration profile along the x axis, shown in

(b). The holes diffuse in the positive direction of x and give rise to a hole-diffusion current in the same direction. Note that we are not

showing the circuit to which the silicon bar is connected.

inject holes

concentration profile arises

diffusion occurs


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p

pp

2

p

pp

J current flow density attributed to holes magnitude of the electron charge

diffusion constant of (12cm /s for silicon h ) (

JJoles

(( )

eq3.19)

p

p

p

Jq

Dx

pd x

J qDdx

==

=

= −

p

hole diffusion current density :p

pp

pp

) hole concentration at point / gradient of hole concentration

current flow density attributed t

JJ

o

(eq3 .2 ) ( )

0

n

n

xd dx

n

J

d xJ qD

dx

==

=

= −

p

electron diffusion current den ty : n

si

pp

pp

pp

2

pp

free electrons diffusion constant of electrons

( ) free electron concentration at point / gradient of free electron concentra

(

tion

35cm /s for siliconJ

)J

J

J

nDx x

d dx

===

nn

• Q: How is diffusion current defined?


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1.9.3 Relationship Between D and µ

the relationship between diffusion constantand mobility is defined by thermal voltage

(eq3.21) pnT

n p

DDV

µ µ= =

• Q: What is the relationship between diffusion constant (D) and mobility (µ)?

• A: thermal voltage (VT)• Q: What is this value?

• A: at T = 300K, VT = 25.9mV known as Einstein

Relationship


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drift current density (Jdrift) effected by – an electric field (E).

diffusion current density (Jdiff) effected by – concentration gradient in free electrons and holes.

pp

pp

cross-sectional area of silicon, magnitude of the electron charge, concentration of holes, concentration of free elect

Jr Jons,

( )

A qp

drift p drift n drift

n

p nJ J J q p n Eµ µ

= == =

− −= + = +drift current density :

pp

2

hole mobility, electron mobility, electric field

diffusion constant of holes (12 m s

J

c /

( ) (

)

p n

p

diff p diff n diff p n

E

D

d x d xJ J J qD qD

dx dx

µ µ

− −

= = =

=

= + = − −diffusion currep

nt densityn

:

pp

pp

2 for silicon), diffusion constant of electrons (35cm /s for silicon),( ) hole concentration at point , ( ) free electron concentration at point ,

/ gradient of hole concent

JJ

ration,

nDx x x x

d dx

== ==

p np p

p / gradient of free electron concentrat nJiod dx=n


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Homeworks• Example 1.8

Documents

Chapter 1. Electronics and Semiconductorstioh.weebly.com/uploads/2/5/4/3/25433593/7week__chapter_1_.pdf · Chapter 1. Electronics and Semiconductors Tong In Oh. Microelectronic Circuits,