Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 1 ...tioh.weebly.com/uploads/2/5/4/3/25433593/8week__chapter_1_.pdf · Microelectronic Circuits, Kyung Hee Univ. Spring, 2016

Microelectronic Circuits, Kyung Hee Univ. Spring, 2016

1

1.10.1. Physical Structure• pn junction structure

• p-type semiconductor• n-type semiconductor• metal contact for connection

Figure 1.35: Simplified physical structure of the pnjunction. (Actual geometries are given in Appendix A.) As

the pn junction implements the junction diode, its terminals are labeled anode and cathode.


2

1.10.2 Operation with Open-Circuit• Q: What is state of pn junction with open-circuit terminals?• A:

• p-type material contains majority of holes• these holes are neutralized by equal amount of bound

negative charge• n-type material contains majority of free electrons

• these electrons are neutralized by equal amount of bound positive charge


3

• Bound charge• charge of opposite polarity to free electrons / holes of a

given material• neutralizes the electrical charge of these majority carriers• does not affect concentration gradients


4

• Q: What happens when a pn-junction is newly formed – aka. when the p-type and n-type semiconductors first touch one another?

• A: See following slides…


5

Step #1: The p-type and n-type semiconductors are joined at the junction

Figure: The pn junction with no applied voltage (open-circuited terminals).

n-type semiconductor filled with free electrons

p-type semiconductor filled with holes junction


6

Step #1A: Bound charges are attracted (from environment) by free electrons and holes in the p-type and n-type semiconductors, respectively. They remain weakly “bound” to these majority carriers; however, they do not recombine.


positive bound charges

negative bound charges


7

Step #2: Diffusion begins. Those free electrons and holes which are closest to the junction will recombine and, essentially, eliminate one another.



8

Step #3: The depletion region begins to form – as diffusion occurs and free electrons recombine with holes.

The depletion region is filled with “uncovered” bound charges – who have lost the majority carriers to which they were linked.



9

• Q: Why does diffusion occur even when bound charges neutralize the electrical attraction of majority carriers to one another?

• A: Diffusion current, as shown in (1.43) and (1.44), is effected by a gradient in concentration of majority carriers – not an electrical attraction of these particles to one another.


10

Step #4: The “uncovered” bound charges effect a voltage differential across the depletion region. The magnitude of this barrier voltage (V0) differential grows, as diffusion continues.

volta

ge p

oten

tial

location (x)

barrier voltage (Vo)

No voltage differential exists across regions of the pn-junction outside of the depletion region because of the neutralizing effect of

positive and negative bound charges.


11

Step #5: The barrier voltage (V0) is an electric field whose polarity opposes the direction of diffusion current (ID). As the magnitude of V0increases, the magnitude of ID decreases.


diffusion current (ID)

drift current (IS)


12

Step #6: Equilibrium is reached, and diffusion ceases, once the magnitudes of diffusion and drift currents equal one another – resulting in no net flow.


drift current (IS)

Once equilibrium is achieved, no net current flow exists (Inet = ID – IS) within the pn-junction while under open-circuit condition.

p-type n-typedepletion region


13

The Drift Current IS and Equilibrium

• In addition to majority-carrier diffusion current (ID), a component of current due to minority carrier drift exists (IS).

• Specifically, some of the thermally generated electrons and holes in the p-type and n-type materials move toward and reach the edge of the depletion region.

• There, they experience the electric field (V0) in the depletion region and are swept across it.

• Unlike diffusion current, the polarity of V0 reinforces this drift current.


14

• Because these holes and free electrons are produced by thermal energy, IS is heavily dependent on temperature

• Any depletion-layer voltage, regardless of how small, will cause the transition across junction. Therefore IS is independent of V0.

• drift current (IS) – is the movement of these minority carriers.


15

0 barrier voltage thermal voltage

acceptor doping concentration donor doping concentration

concentration of free electrons... ...in intrinsic

2

sem

0

ic

(eq3.22)

TA

Di

VV

NN

n

A DT

i

N NV V

n

==

==

=

=

ln

onductor

• pn-junction built-in voltage (V0) – is the equilibrium value of barrier voltage

• Generally, it takes on a value between 0.6 and 0.9V for silicon at room temperature

• This voltage is applied across depletion region, not terminals of pn junction• Power cannot be drawn from V0


16

Note that the magnitude of drift current (IS) is unaffected by level of diffusion and / or V0. It will be, however, affected by temperature.



drift current (IS)


17

• Q: Is the depletion region always symmetrical? As shown on previous slides?

• A: The short answer is no.• Q: Why?

• A: Because, typically NA > ND.• When the concentration of doping agents (NA, ND) is

unequal, the width of depletion region will differ from side to side.

• The depletion region will extend deeper in to the “less doped” material, a requirement to uncover the same amount of charge.

• xp = width of depletion p-region• xn = width of depletion n-region


18

The depletion region will extend further in to region with “less” doping. However, the “number” of uncovered charges is the same.


19

3.4.2: Operation withOpen-Circuit Terminals

• Width of and Charge Stored in the Depletion Region• the question we ask here is, what happens once the open-circuit pn junction

reaches equilibrium???• typically NA > ND

• minority carrier concentrations at equilibrium (no voltage applied) are denoted by np0 and pn0

• because concentration of doping agents (NA, ND) is unequal, the width of depletion region will differfrom side to side

• the depletion region will extend deeper in to the “less doped” material, a requirement to uncover the same amount of charge

• xp = width of depletion p-region

• xn = width of depletion n-region

Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C.

dv/dx is dependent of Q/W

charge is equal, but width is different


20

pp

p

pp

p

pp

magnitude of charghe on -side of junction magnitude of electric charge

PP

P

cross-sectional area of junction penetration of depletion region into -side

co

nP

(eq3.23)

n

D

Q nq

x

n

An

D

N

Q qAx N

+ ===

==

+ =

pp

-pp

pp

pp

centration of donor atoms

magnitude of charghe on -side of junction magnitude of electric charge

cross-sectional area of junction penetration

P

P

P

fP

o

-(eq3.24)

p

Q nq

A

p A

x

Q qAx N=

==

=

=

pp

pp

depletion region into -side concentration of acceptor a

PsPtomA

pN =

• Q: How is the charge stored in both sides of the depletion region defined?

• A: Refer to equations to right. Note that these values should equal one another.


21

(eq3.25) n Ap A n D

p D

x NqAx N qAx N

x N= → =

• Q: What information can be derived from this equality?• A: In reality, the depletion region exists almost entirely

on one side of the pn-junction – due to great disparity between NA > ND.


22

ppp

pp

0

p width of depletion region electrical permiability of silicon (11.7 1.04 12 )

magnitude of electron charge concentration of acceptor ato

PP/

Pm

0

s

(eq3.22 1

6) 1

S

A

W

qF cm

Sn p

A D

N

W x x Vq N N

ε ε

ε

== = −

==

= + = +

E

pp

pp

pp0

concentration of donor atoms barrier / junction built-in volta Pge

PP

(eq3.27)

(eq3.28)

D

An

A D

Dp

NV

A D

Nx W

N N

Nx W

N N

==

=+

=+

• Note that both xp and xn

may be defined in terms of the depletion region width (W).


23

0

(eq3.29)

(eq3.30) 2

A DJ

A D

A DJ S

A D

N NQ Q Aq W

N N

N NQ A q V

N Nε

±

= = +

= +

• Note, also, the charge on either side of the depletion region may be calculated via (1.47) and (1.51).


24

• Q: What has been learned about the pn-junction? • A: composition

• The pn junction is composed of two silicon-based semiconductors, one doped to be p-type and the other n-type.

• A: majority carriers• Are generated by doping.• Holes are present on p-side, free electrons are

present on n-side.


25

• Q: What has been learned about the pn-junction? • A: bound charges

• Charge of majority carriers are neutralized electrically by bound charges.

• A: diffusion current ID• Those majority carriers close to the junction will

diffuse across, resulting in their elimination.


26

• Q: What has been learned about the pn-junction? • A: depletion region

• As these carriers disappear, they release bound charges and effect a voltage differential V0.

• A: depletion-layer voltage• As diffusion continues, the depletion layer voltage (V0)

grows, making diffusion more difficult and eventually bringing it to halt.


27

• Q: What has been learned about the pn-junction? • A: minority carriers

• Are generated thermally.• Free electrons are present on p-side, holes are

present on n-side.• A: drift current IS

• The depletion-layer voltage (V0) facilitates the flow of minority carriers to opposite side.

• A: open circuit equilibrium ID = IS


28

1.11.1. Qualitative Description of Junction Operation

• Figure to right shows pn-junction under three conditions:• (a) open-circuit – where a barrier voltage V0 exists.• (b) reverse bias – where a dc voltage VR is applied.• (c) forward bias – where a dc voltage VF is applied.

Figure 1.38: The pn junction in: (a) equilibrium; (b) reverse bias; (c) forward bias.


29

• Figure to right shows pn-junction under three conditions:• (a) open-circuit – where a barrier voltage V0 exists.• (b) reverse bias – where a dc voltage VR is applied.• (c) forward bias – where a dc voltage VF is applied.

Figure 3.11: The pn junction in: (a) equilibrium; (b) reverse bias;

(c) forward bias.

1) no voltage applied

2) voltage differential across depletion zone is V0

3) ID = IS

1) negative voltage applied

2) voltage differential across depletion zone is V0 + VR

3) ID < IS

1) positive voltage applied

2) voltage differential across depletion zone is V0 - VF

3) ID > IS


30

• reverse bias case• the externally applied voltage VR

adds to (aka. reinforces) the barrier voltage V0

• …increase effective barrier• this reduces rate of diffusion,

reducing ID• if VR > 1V, ID will fall to 0A

• the drift current IS is unaffected, but dependent on temperature

• result is that pn junction will conduct small drift current IS

• forward bias case• the externally applied voltage VF

subtracts from the barriervoltage V0

• …decrease effective barrier• this increases rate of diffusion,

increasing ID• k

• the drift current IS is unaffected, but dependent on temperature

• result is that pn junction will conduct significant current ID - IS

minimal current flows in reverse-bias case

significant current flows in forward-bias case


31

Reverse-Bias Casepp

p0p

00

width of depletion region electrical permiability of silicon (11.7 1.04 12 )

magn

replace with

itude of electron ch/

0

arge

PP

(eq3.31)2 1 1

( )

S

R

F cm

Sn p R

VV V

W

q

A D

W x x V Vq N N

ε ε

ε

== = −

+

=

= + = + +

action:

E

pp

pp

pp

p0 p

pp

concentration of acceptor atoms concentration of donor atoms

barrier / junction built-in voltage externally applied reverse-bias volta

P

PPg Pe

P

(eq3.3 22)

A

D

R

NN

V

J

V

Q A

==

==

=

0

pp

0

magnitude of charge store

0

d on either side of depletion re

replace with

gi Pon

( )

J

R

VV V

A DS R

A

Q

D

N Nq V V

N Nε

+

=

+ + action:

• Observe that increased barrier voltage will be accompanied by…

• (1) increase in stored uncovered charge on both sides of junction

• (2) wider depletion region

• Width of depletion region shown to right.


32

Forward-Bias Case

00

pp

pp

pp

0

width of depletion region electrical permiability of silicon (11.7 1.04 12 )

magnitude of electron charge con

replac

PP

P/

e with

02 1 1

( )

A

F

S F c

V

W

qm

Sn p F

A D

N

V V

W x x V Vq N N

ε ε

ε

== = −

=

−

=

= + = + −

action:

E

pp

pp

pp0

pp

centration of acceptor atoms concentration of donor atoms

barrier / junction built-in voltage externally applied forward-bias voltage

PP

P

0

P

2 (

D

F

A DJ S F

A D

NV

V

N NQ A q V V

N Nε

==

=

= − +

0

pp

0

magnitude of charge stored on either side of

rep

dep

lace wit

letion region

P

h

)

J

FV V

Q

V

=

−

action:

• Observe that decreased barriervoltage will be accompanied by…

• (1) decrease in stored uncovered charge on both sides of junction

• (2) smaller depletion region

• Width of depletion region shown to right.


33

1.11.2. The Current-Voltage Relationship of the Junction

• Q: What happens, exactly, when a forward-bias voltage (VF) is applied to the pn-junction?

• step #1: Initially, a small forward-bias voltage (VF) is applied. It, because of its polarity, pushes majority carriers (holes in p-region and electrons in n-region) toward the junction and reduces width of the depletion zone.

• Note, however, that this force is opposed by the built-in voltage built in voltage V0.


34

step #1: Initially, a small forward-bias voltage (VF) is applied. It, because of its polarity, pushes majority (holes in p-region and electrons in n-region) toward the junction and reduces width of the depletion zone.

Figure: The pn junction with applied voltage.

VF

Note that, in this figure, the smaller circles represent minority carriers and not bound charges – which are not considered here.


35

step #2: As the magnitude of VF increases, the depletion zone becomes thin enough such that the barrier voltage (V0 – VF) cannot stop diffusion current – as described in previous slides.


VF

Note that removing barrier voltage does not facilitate diffusion, it only removes the electromotive force which opposes it.


36

step #3: Majority carriers (free electrons in n-region and holes in p-region) cross the junction and become minority charge carriers in the near-neutral region.



drift current (IS)

VF


37

step #4: The concentration of minority charge carriers increases on either side of the junction. A steady-state gradient is reached as rate of majority carriers crossing the junction equals that of recombination.


min

ority

car

rier

conc

entr

atio

n

location (x)

VF

For the open-circuit condition, minority carriers are evenly distributed throughout the non-depletion regions. This

concentration is defined as either np0 or pn0.


38

step #4: The concentration of minority charge carriers increases on either side of the junction. A steady-state gradient is reached as rate of majority carriers crossing the junction equals that of recombination.

Figure: The pn junction with applied voltage

VF

min

ority

car

rier

conc

entr

atio

n

location (x)


39

step #5+: Diffusion current is maintained – in spite low diffusion lengths (e.g. microns) and recombination – by constant flow of both free electrons and holes towards the junction.

Figure: The pn junction with applied voltage

VF

flow of holes flow of electrons

flow of diffusion current (ID)

recombination


40

0

( ) = concentration of holes in -region as function of = thermal equilibrium concentration

2

0

= applied foward-bias voltage = thermal volt

/0

(eq3.7)

(eq3.33

( ))

n n n

n

p

pp

T

T

pp

p

PP

x n xpV

in

A

V Vn n n

VP

np

N

x p e

=

=

p

p

a

/0 0

e

/

g

0

excessconcentra

excess(eq3.34)

concentratio

tion

( 1)

(eq )

n

3.34

pp

V VTn n

P

V VTn

p e p

p e

= −

= −

• Q: How is the relationship between forward-bias voltage applied (V.) and minority-carrier holes and electrons defined?

• step #1: Employ (1.57).• This function describes

maximum minority carrier concentration at junction.

• step #2: Subtract pn0 from pn(x) to calculate the excess minority charge carriers.

The key aspect of (1.57) is that it relates the minority-charge carrier concentration at the junction boundary in terms of majority-charge

carrier on the opposite side.


41

0

/0

( ) /0

( ) //0 0

( ) = concentration of holes in -region as function of , = thermal eq

( 1)

(eq3.35

(eq3.35) (

( ) ( )

( 1)

)

)

n p

n n n n

Vn

n

V

p

T

x x Ln n n

x x LV VT

x

n

x p

p e

n n n

n

x p excess concentrati

px

on e

p e e

−

− −

− −

= +

= + −

p

p

p

uilibrium concentration = point of interest, edge of depletion region, = diffusion lengthn Px x L=

• Q: How is the relationship between forward-bias voltage applied (V.) and minority-carrier holes and electrons defined?

• step #3: Refer to (1.59).• This function describes the minority carrier concentration as a

function of location (x), boundary of depletion region (xn), and diffusion length (Lp).


42

3.5.2: The Current-VoltageRelationship of the Junction

Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)

steady-state minority carrier concentration on both sides of a pn-junction for which NA >> ND

excess concentration

“base” concentration


43

3.5.2: The Current-VoltageRelationship of the Junction

Oxford University PublishingMicroelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)

These excess concentrations effect steady-state diffusion current. However, how is this diffusion current defined?


44

[ ]

( ) //0

take derivative of

0

( ) //0

( ) /

0

( 1)

0

/

( )

( )

( 1)

(eq3.36) ( 1)

n pT

n p

x x LV VTn n p

n

p

T

nn

x x LV Vn

x x LV Vn

x

pe e

p pp

L

d x dp

dx dx

dp e e

dx

pJ qD e e

L

− −

− −

− −

− −

= +

+ −

= − − −

action: p

p

substitute in value from above

calculate ma

(

ximum

)

/0( ) ( 1)

n

Tp V V

d xdx

p np

DJ q p e

L= −

action:

actio

p

n:

max

• Q: For forward-biased case, how is diffusion current (ID) defined?

• step #1: Take derivative of (1.59) to define component of diffusion current attributed to flow of holes.

• step #2: Note that this value is maximum at x= xn. Oxford University Publishing

Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)


45

Q: For forward-biased case, how is diffusion current defined?

/0

/0

(eq3.37) maximum hole - diffusion concentration:

(eq3.38) maximum electron - diffusion concentration:

( ) ( 1)

( ) ( 1 )

T

T

p V Vp n n

p

V Vnn p p

n

Dx q p e

L

Dx q n e

L

+ = −

− = −

J

J

• step #3: Define the component of maximum diffusion current attributed to minority-carrier electrons – in method similar above.


46

Q: For forward-biased case, how is diffusion current defined?

+

= =

= + + −

= + −

= + −

2 2

0 0

subtitute in valuesfor ( ) and (- )

subtitut

/0

e/ and

/

/

0

2

( ) ( )

( 1)

( 1)

p n n p

n i D p i

T

T

A

p n n p

p V Vnn p

p n

p V Vni

p D n

x x

p n N n n N

A

I A x x

D DI A q p q n e

L L

D DI Aqn e

L N L N

action: J J

action:

J J

= +

= −

2

total current ( ) through junction is equal to area ( ) timesmaximum hole ( )

subt

and electron-diffusion ( ) current densities

/

itute

( 1)

p ns i

p

n

D

T

n A

p

D DI A

I

qnL N L

V VS

N

AJ J

I I eaction:

• step #4: Define total diffusion current as sum of components attributed to free electrons and holes.


47

2 / /( 1)(eq3. ( 140) )T T

S

p V V V Vni

n

I

Sp D A

D DI Aqn e I e

L N L N

= + − = −

• Q: For forward-biased case, how is diffusion current (ID) defined?

• A: This is an important equation which will be employed in future chapters.


48

• Q: Why is diffusion current (ID) dependent on the concentration gradient of minority (as opposed to majority) charge carriers?

• A: Essentially, it isn’t.• Equation (1.57) defines the minority-charge carrier

concentration in terms of the majority-charge carrier concentrations in “other” region.

• As such, the diffusion current (ID) is most dependent on two factors: applied forward-bias voltage (VF) and doping.


49

/(eq3.40) ( 1)TV VSI I e= −

• saturation current (IS) – is the maximum reverse current which will flow through pn-junction.

• It is proportional to cross-section of junction (A).

• Typical value is 10-18A.Figure 1.40: The pn junction I–V

characteristic.

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Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 1 ...tioh.weebly.com/uploads/2/5/4/3/25433593/8week__chapter_1_.pdf · Microelectronic Circuits, Kyung Hee Univ. Spring, 2016