President University Erwin Sitompul SDP 10/1

Dr.-Ing. Erwin SitompulPresident University

Lecture 10Semiconductor Device Physics

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Chapter 11BJT Static Characteristics

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The Ebers-Moll model is a large-signal equivalent circuit which describes both the active and saturation regions of BJT operation.

This model is to be used to calculate IC, IE for given VBE, VBC.

If only VEB is applied (VCB = 0): EB

EB

EB

E F0

C F F0

B F F0

( 1)( 1)

(1 ) ( 1)

qV kT

qV kT

qV kT

I I eI I eI I e

If only VCB is applied (VEB = 0):CB

CB

CB

C R0

E R R0

B R0 R

( 1)( 1)

(1 )( 1)

qV kT

qV kT

qV kT

I I eI I eI I e

EB

CB

BE BE E0 B0

E B B

BB0

B B

cosh( 1)

sinh

1 ( 1)sinh

qV kT

qV kT

W LD DI qA n p eL L W L

D p eL W L

EB

CB

BC B0

B B

BC BC0 B0

C B B

1 ( 1)sinh

cosh ( 1)

sinh

qV kT

qV kT

DI qA p eL W L

W LD Dn p eL L W L

IFO

IRO

Ebers-Moll ModelChapter 11 BJT Static Characteristics

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R : reverse common base gain

F : forward common base gain

B0BF F0 R R0

B Bsinh( )pDI I qA

L W L

CBEBC F F0 R0( 1) ( 1)qV kTqV kTI I e I e

fraction of E-B diode C-B diode currentcurrent that makes it

to the C-B junction

CBEBE F0 R R0( 1) ( 1)qV kTqV kTI I e I e

E-B diode fraction of C-B diode current current that makes it

to the E-B junction

Ebers-Moll ModelChapter 11 BJT Static Characteristics

Reciprocity relationship:

In the general case, when VEB and VCB are non-zero:

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Deviations, due to model limitations

Deviations from the IdealChapter 11 BJT Static Characteristics

Common base

Common emitter

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dc 2

E B

B E E B

B E E

E B

1

12

D N W WD N L LD N LD N W

Wx

DpB(x)

EBB0 ( 1)qV kTp e (VCB=0)

0

W

P+ N P

+ VEB

IE IC

Increasing –VCB

C dc B CE0I β I I

If –VCB increases→ W decreases→ dc increases→ IC increases

Base-Width ModulationChapter 11 BJT Static Characteristics

Common-Emitter ConfigurationActive Mode Operation Recalling two formulas,

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WB xnEB xnCB

Punch-ThroughChapter 11 BJT Static Characteristics

Punch-Through: E-B and C-B depletion regions in the base touch each other, so that W = 0.

As –VCB increases beyond the punch-through point, the E-B potential hill decreases and therefore increases the carrier injections and IC.

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Punch-through Avalanche

Increasing reverse bias of C-B junction

EC EB CB=V V V

Breakdown MechanismsChapter 11 BJT Static Characteristics

In the common-emitter configuration, for high output voltage VCE, the output current IC will increase rapidly due to the two mechanisms: punch-through and avalanche.

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pnp BJT

dc CB0C B

dc dc

α1 α 1 αM II IM M

M : multiplication factor

Avalanche MultiplicationChapter 11 BJT Static Characteristics

Holes [0] are injected into the base [1], then collected by the C-B junction.

Some holes in the C-B depletion region have enough energy do impact ionization [2].

The generated electrons are swept into the base [3], then injected into the emitter [4].

Each injected electron results in the injection of IEp/IEn holes from the emitter into the base [5].

For each pair created in the C-B depletion region by impact ionization, (IEp/IEn) + 1 > dc additional holes flow into the collector.

This means that carrier multiplication in C-B depletion region is internally amplified.

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Geometrical EffectsChapter 11 BJT Static Characteristics

Emitter area is not equal to collector area.Current does not flow in one

direction only.Series resistance.

Voltage drop occurs not only across the junction.

Current crowding.Due to lateral flow, current is

larger around emitter periphery than the collector periphery.

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diff

kT qx

Exdiff : exponential

decay constant

Graded BaseChapter 11 BJT Static Characteristics

Dopants are injected through diffusion.More or less falling exponential

distribution with distance into beneath of the semiconductor.

The doping within the base is not constant as assumed in ideal analysis.A function of position, having

maximum at E-B junction and minimum at C-B junction.

Creating a built-in electric field.The electric field enhances the

transport of minority carrier across the quasineutral width of the base. Increase of IE and IC.

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Due to recombination in emitter depletion region

Due to high level injection in base, base series resistance,

and current crowding

Gummel Plot

Figures of MeritChapter 11 BJT Static Characteristics

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E1 E2E1 E2 d p d pqD qD

dx dxD D

Continuity of hole current in emitter

(1 polysilicon; 2 Si) Shallower slope less JP

higher g,

E1 E2 E2 E2 E2

E1 E1

d p D d p d pdx D dx dx

D D D

Polysilicon Emitter BJTChapter 11 BJT Static Characteristics

dc is larger for a poly-Si emitter BJT as compared with an all-crystalline emitter BJT.

This is due to reduced dpE(x)/dx at the edge of the emitter depletion region.

Lower p

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Summary on BJT PerformanceChapter 11 BJT Static Characteristics

High gain (dc >> 1)One-sided emitter junction, so that emitter efficiency g

1Emitter doped much more heavily than base (NE >> NB).Narrow base, so base transport factor T 1.Quasi-neutral base width << minority-carrier diffusion length

(W << LB). IC determined only by IB (IC function of VCE or VCB)

One-sided collector junction, so that quasineutral base width W does not change drastically with changes in VCE or VCB.

Base doped more heavily than collector (NB > NC), W = WB – xnEB – xnCB for pnp BJT.