Introduction to Electronic Devices - Jacobs University Bremen · 2 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp Bipolar Transistor Introduction to Electronic Devices

1

Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp

Bipolar Transistor

Source: Apple

Ref.: IBM

101110-110-210-310-410-510-610-8Critical

dimension (m)

Ref.: Apple

Ref.: Palo Alto Research Center

10-7

Introduction to Electronic Devices(Course Number 300331) Fall 2006

Bipolar Transistors

Dr. Dietmar Knipp

Assistant Professor of Electrical Engineering

Information:http://www.faculty.iu-bremen.de/dknipp/

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Bipolar Transistor

Introduction to Electronic Devices5 Bipolar Transistors

5.1 Introduction5.2 Basic transistor operation5.3 Transistor under zero bias 5.4 Transistor under bias conditions

5.4.1 Shockley Assumptions5.4.2 The ideal transistor equation5.4.3 The transistor equation in its general form5.4.4 Modes of Operation

5.8.1 The active mode5.8.2 The Saturation mode5.8.3 The cutoff mode5.8.4 The inversion mode

5.5 Transport and gain factors5.5.1 The Emitter efficiency5.5.2 The Transport factor5.5.3 The Common-base current gain5.5.5 The summary of the transport and gain factors

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Bipolar Transistor

5.6 Transistor Design 5.6.1 The transport factor5.6.2 The Emitter Efficiency

5.7 Bipolar Transistors as Amplifiers5.7.1 Common base circuit 5.7.2 Common emitter circuit5.7.3 The Early Effect

5.8 Transfer characteristic and gain5.9 Device parameters5.10 Equivalent circuit of a bipolar junction transistor

References

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Bipolar Transistor

5.1 IntroductionThe transistor (Germanium point contact transistor) was invited by Barttain, Bardeen and Shockley in 1947. As the name already implies it is a bipolar device (like a diode), which means that both electrons and holes (minority and majority carriers) contribute to the overall current flow.

The bipolar junction transistor (BJT) is one of the most important semiconductor devices. The transistor is used for high speed circuits, analog circuits and power applications.

The underlying electronic transport mechanisms of bipolar junction transistors (BJT) and diodes are similar. Both devices are diffusion controlled devices. Therefore, the influence of the drift current on the total current is negligible.

The operating principle of bipolar devices is different from the behavior of unipolar device like a Field Effect Transistors (FETs), where the current is either controlled by electrons or holes. Furthermore, a field effect transistor is a drift controlled electronic device.

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Bipolar Transistor

5.1 IntroductionA bipolar transistor (like all other transistors) is a three (four) terminal device. The device consists of an input and an output loop. The device is designed in such a ways that small input changes of a current or/and a voltage result in large changes of the output current or/and voltage.

The BJT device structure consists of two pn junctions. The device can be implemented as an pnp or a npnstructure. Each of the doped regions is connected with one of the terminals: Base, Emitter or Collector. The three regions of a BJT are formed by the diffusion of a doping profiles in a substrate.

Schematic cross section of a pnptransistor. The transistor is implemented in a p-type substrate. The n-type and the p+-type regions are formed by diffusion of dopants in the p-type substrate. The electrodes are formed by metal contacts.

Ref.: M.S. Sze, Semiconductor Devices

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Bipolar Transistor

5.1 IntroductionThe operation principle of a bipolar transistor relies on the fact that the base region of the transistor is a very thin region, so that the two diodes affect each other. The thickness of the base in controlled by the manufacturing (diffusion) process.

In terms of applications pure analog integrated circuits are getting less important. Nowadays the technology shifts towards BiCMOS technology. BiCMOS is a combination of bipolar technology and metal oxide semiconductor technology (technology required to manufacture field effect transistors). It allows the realization of analog and digital circuits on a single chip.

5.2 Basic transistor operation

The two possible device structures of a bipolar transistor or Pnp- and a npn-structures. Bipolar transistors can operate in four modes of operation, depending on the voltage applied to the base-emitter and the base-collector junction. The four modes of operation are: Active mode, inversion mode, cutoff mode, Saturation mode.

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Bipolar Transistor


In order to realize an amplifier the BJT will be operated in the active mode. In the following the basic operating principle of a bipolar transistor in the active mode will be presented.

The + and – signs indicate the polarities of the voltages applied to the terminals under normal operating conditions (active mode).

In the active mode the emitter base diode is forward biased (VEB>0) and the base collector diode is reverse biased (VCB<0).

pnp-transistor

npn-transistor


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Bipolar Transistor

pnp-transistor

npn-transistor Ref.: M.S. Sze, Semiconductor Devices


On this slide the + and – signs indicate the direction of the current flow.

The npn-structure is complementary to the pnp structure. As a consequence the current flow and the voltage polarities are reversed. In the following we will discuss the electronic transport of a pnptransistor.

CEB III −=

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Bipolar Transistor

5.3 Bipolar Junction Transistors under zero baisAt first the BJT will be studied in thermal equilibrium. All three terminals of the device are grounded.

Under thermal equilibrium the Fermi level is constant throughout the entire device structure. As a consequence the derivative of the Fermi level is zero, so that the overall current flowing through the device is zero.

The following device structure is used for the discussion: The emitter is (much) heavier doped than the base and the base is again heavier doped than the collector. The base region is much shorter than the emitter and the collector region. The base width of the base region is much shorter than the diffusion length of the minority carriers. Therefore, the two pn-junctions affect each other.

If the base-region would be much longer than the diffusion length of the minority carriers in the base region of the two pn-junctions would behave like two separate diodes. The operation of the diodes would be independent of each other.

The electric field distribution in the BJT can be calculated by solving the Poisson equation. As a consequence of the doping profile in the individual regions of the device the maximum electric field and the built-in voltage for the base/emitter junctions is higher than the maximum electric field and the built-in voltage for the base/collector junction (under thermal equilibrium).

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Bipolar Transistor

pnp-transistor


(a) pnp-transistor under thermal equilibrium (all terminals grounded).

(b) Doping profile of an abrupt pnp structure, (c) Electric field profile,

(d) Energy band diagram

5.3 Bipolar Junction Transistor under zero bias

Throughout the following discussion it is assumed that two abrupt junctions are formed. As a consequence the electric field distribution outside of the depletion regions is zero.

The formation of the space charge region for a BJT is comparable with the formation of the space charge region of a diode.

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Bipolar Transistor

5.3 Bipolar Junction Transistor under zero bias

There are technological and a physical reasons for the different doping profiles in the individual regions of the device:

Technological:The fabrication of a BJT requires two diffusion steps to form three regions with different doping concentrations. In the first diffusion step the base has to be formed and the already existing dopants in the material (in the substrate) have to be compensated or over compensated. In the second diffusion step the doping concentration has to be increased again to compensate theincorporated dopants of the first diffusion step.

Physical:The goal of the transistor design is the realization of transistors with high current and/or voltage gain. High current and voltages gains can be achieved if the doping concentration in the base is lower than the doping concentration in the emitter. The underlying physical reasons for this particular behavior will be discussed in the chapter on transport and gain factors.

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Bipolar Transistor

5.4 Transistor under bias conditionsBefore deriving the ideal bipolar junction transistor equations the basic operating principle of BJT under biasing conditions will be described. Here we will concentrate on a common base bipolar transistor in active mode as this is the most important mode of operation. In this case the base/emitter junction is in forward bias and the base/collector junction operates under reverse bias conditions. The input and the output loop share the base terminal. Therefore, the circuit is called a common base circuit.

As a consequence of the applied bias voltages the width of the depletion regions is changed. Since the base emitter junctions is under forward bias holes are injected via the emitter and electrons are injected via the base. At the same time the base collector junction is reverse biased and the current flow should be small. However, as the width of the base region is very short the holes injected in the emitter diffuse through the base so that they reach the base collector depletion region, where the holes „float up“ into the collector region. Therefore, the collector collects the holes „floating up“. The emitter is called emitter because holes are emitted, which are collected by the collector (BJT in the active mode). Most of the emitted holes reach the collector region.

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Bipolar Transistor

5.4 Transistor under bias conditionsDue to the forward bias applied to the base/emitter junction the external electric field lowers the electric field caused by the built-in voltage. The width of the space charge region and the electric field is reduced. The opposite behavior is observed for the reverse biased diode. Here the external electric field enhances the internal electric field, so that the width of the space charge region is extended.


(a) pnp-transistor under bias conditions. The transistor operates

in the active mode. (b) Doping profile of an abrupt pnp

structure, (c) Electric field profile,

(d) Energy band diagram

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Bipolar Transistor

5.4 Transistor under bias conditionsDue to the applied bias voltages the Fermi level split up into quasi Fermi levels. For the pn junction under forward bias the quasi Fermi levels shift closer to the corresponding bands. This means that the quasi Fermi level for the electrons shift closer to the conduction band, whereas the quasi Fermi level for the holes shifts closer to the valence band. For the reverse bias diode the opposite behavior is observed. The Quasi Fermi levels shift away from thecorresponding bands, because the product of the carrier concentration is below the square of the intrinsic carrier concentration.

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Bipolar Transistor

5.4.1 Shockley Assumptions

In order to derive the ideal transistor equation the Shockley assumptions have to be fulfilled. The assumptions for deriving the ideal transistor equations are comparable with the assumptions used for deriving the ideal diode equation.

• Uniform doping throughout the individual regions of the device, so that abrupt junctions are formed at the emitter/base and the collector/base interface.

• The hole drift current in the base region and the collector saturation current are negligible.

• Low-level injection for the forward biased diodes

• Non losses due to generation and recombination in the depletion regions of the base/emitter junction and the base/collector junction

•No series resistance in the device (No voltage drop across the neutral regions.)

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Bipolar Transistor

5.4.2 The ideal transistor equationIn the active mode the base/emitter junction is forward biased and the base/collector junction is reverse biased.

Under forward bias conditions of the base emitter diode holes are injected from the emitter region into the base region. Subsequently the holes diffuse across the base region and reach the collector junction.

In order to determine the ideal transistor equation the Diffusion equation has to be solved. It can be assumed that the current flow in the base is determined by the diffusion rather than the drift of carriers. As a consequence the electric field in the base can be ignored.

The Diffusion equation has to be solved for the forward biased base/emitter junction which can be described by an asymmetric pn-junction.

002

2

=−

−∂∂

pl

nnnp

ppxpD

τDiffusion equation for holes

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Bipolar Transistor

5.4.2 The ideal transistor equationFirstly we determine the minority carrier distribution (i.e. hole concentration in the n-type base region). In a second step the current flow can be obtained from the minority-carrier gradient.

The general solution of the Diffusion equation is given by

where Lp and Ln are the hole and the electron diffusion length of the minority carriers.

( )

−⋅+

⋅+= B

pBp

nn LxC

LxCpxp expexp 210

plpp DL τ=

nlnn DL τ=

Hole diffusion length

Electron diffusion length

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Bipolar Transistor

5.4.2 The ideal transistor equationThe following boundary conditions are used to determine the constants C1and C2:

and

where pn0 is the equilibrium minority carrier concentration in the base. It is important to note that the minority carrier concentration has to be zero for x=W. The minority carrier concentration in thermal equilibrium can be calculated by

where NB is the donor concentration in the base. Solving the Diffusion equation leads to the following expression for the minority carrier concentration.

( )

⋅==kTqVpxp EB

nn exp0 0( ) 0==Wxpn

B

in N

np2

0 =

( )

−

−⋅+

−

⋅

−

⋅=

Bp

Bp

n

Bp

BpEB

nn

LW

LxW

p

LW

LxW

kTqVpxp

sinh

sinh1

sinh

sinh1exp 00

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Bipolar Transistor

5.4.2 The ideal transistor equation

The sinh(x) function can be approximated by x for x << 1, so that the electron concentration results to

The approximation is valid because the Diffusion length is large in comparison to the width of the base.

( )

−⋅

−

⋅=

Wx

kTqVpxp EB

nn 11exp0Minority carrier concentration in the base region


The minority carrier concentration (holes) is approximation by a straight line because the width of the base is much smaller than the diffusion length for the holes.

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Bipolar Transistor

5.4.2 The ideal transistor equationThe minority carrier concentration in the emitter and the collector region can be obtained in a very similar way.

where nE0 and nC0 are the equilibrium electron concentration. At the boundaries between the neutral region and the space charge region the carrier concentration can be simplifies to

We assume that the emitter depth and the collector depth are much larger than the diffusion length LE and LC for the minority carriers.

( ) EEn

EEBEEE xx

Lxx

kTqVnnxn −≤

−⋅

−

⋅+= exp1exp00

( ) CCn

CCCC xx

Lxxnnxn ≥

−−⋅−= exp00

( )

⋅=−=kTqVnxxn EB

EEE exp0

( ) 0exp0 =

−⋅==kTVq

nxxn CBCCC

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Bipolar Transistor

5.4.2 The ideal transistor equationKnowing the minority carrier concentration the various current components can be determined by solving the current density equation.

It is assumed that the overall current is determined by the diffusion current. The influence of the drift current is negligible.

dxdpqDpFqj ppp ⋅−= µ Current density for holes

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Bipolar Transistor

5.4.2 The ideal transistor equationFurther it is assumed that the hole and the electron diffusion current densities remain nearly constant throughout the depletion region.

This is a valid approximation because the diffusion length of the emitter and collector is much larger than the width of the depletion regions.

The current densities can be determined assuming a constant current density in the depletion region by

The collector current can be calculated in very similar way:

EEn xL >> WxL CC

n −>>

( )

−⋅

−

⋅=

Wx

kTqVpxp EB

nn 11exp0Minority carrier concentration in

the base region

≅

−⋅=

= kTqV

WpqAD

dxdpqDAI EBn

Bp

x

npEp exp0

0

≅

−⋅=

= kTqV

WpqAD

dxdpqDAI EBn

Bp

Wx

npCp exp0

Emitter hole currentin the base

Collector hole currentin the base

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Bipolar Transistor

5.4.2 The ideal transistor equationIEp is equal to ICp if W/Lp << 1. The electron current IEn corresponds to

The collector current can be calculated in a similar way:

where DE and DC are the minority carrier diffusion constants in the emitter and the collector region.

The overall emitter can be calculated by the sum of the electron and the hole current.

Emitter electron

current

−

=

−⋅=

−=

1exp0

kTqV

LnqAD

dxdnqDAI EB

En

EEn

xx

EEnEn

E

Collector electron currentC

n

CCn

xx

CCCn L

nqADdxdnqDAI

C

0=

−⋅=

=

Emitter current

WpD

qAkTqV

LnD

WpD

qAIII nBpEB

En

EEnn

Bp

EpEnE000 1exp +

−

⋅

+⋅=+=

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Bipolar Transistor

5.4.2 The ideal transistor equationThe collector can be calculate accordingly.

The base current is the difference between the emitter and the collector current:

The current flow through the transistor is mainly determined by the minority carrier distribution in the base.

Collector current

++

−

⋅⋅=+= C

n

CCnn

BpEBn

Bp

CpCnC LnD

WpD

qAkTqV

WpD

qAIII 000 1exp

Base current

+

−

⋅⋅=−= C

n

CCn

th

EBEn

EEn

CEB LnD

VV

LnDqAIII 00 1exp

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Bipolar Transistor

5.4.3 The transistor equation in its general formThe current voltage characteristic can be expressed in general terms which facilitates the discussion of the different modes of operation. The current-voltage characteristic can be described by the following set of equations:

Emitter current

−

⋅−

−

⋅= 1exp1exp 1211 kT

qVakTqVaI CBEB

E

Collector current

−

⋅−

−

⋅= 1exp1exp 2221 kT

qVakTqVaI CBEB

C

WpD

qAa np 012 =

+⋅=

E

EEnp

LnD

WpD

qAa 0011

+=

C

CCnp

LnD

WpD

qAa 0022

WpD

qAa np 021 ⋅=

Coefficients

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Bipolar Transistor

5.4.4 Modes of OperationBipolar transistors can be operatedin four modes of operation, depending on the voltages applied to the base-emitter and the base-collector junction. So far we have considered the active mode, where the base-emitter junction is forward biased and the base collector junction is reverse biased.

Modes of operation:

•Active mode,

•Saturation mode,

•Cutoff mode and

•Inverted mode.

Minority carrier distribution of a pnptransistor under the four modes of operation: Active, Saturation, Cutoff and Inverted mode.


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Bipolar Transistor

5.4.4.1 Active ModeIn the active mode the base/emitter junction is forward biased and the base/collector junction is reverse biased. The device behavior in the active mode was discussed in the chapter “Ideal transistor equation”.

The derived ideal transistor equations indicate that all three currents, base, emitter and collector current are independent of the base/collector voltage. Therefore, the currents are only controlled by the base/emitter voltage, the device design and the material properties.

5.4.4.2 Saturation ModeIn the saturation mode both junctions are forward biased. The minority carrier concentration for x=W is nonzero. The carrier concentration is:

The transistor operates as a switch.

( )

==kTqVpWxp CB

nn exp0

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Bipolar Transistor

5.4.4.3 Cutoff ModeIn the cutoff mode both diodes are under reverse bias conditions. Under such conditions

The cutoff mode corresponds to the off mode of a transistor which is used as a switch.

5.4.4.4 Inverted ModeIn the inverted mode the base-emitter junction is reverse biased, whereas the base-collector junction is forward biased. In the inverted mode the emitter behaves like the collector in the active mode and vice versa (The collector behaves like the emitter in the active mode). As the doping concentration typically decreases from the emitter to the collector the emitter efficiency of the transistor is lower in the inverted mode. Therefore, the current gain is reduced in comparison to the active mode.

( ) ( ) 00 ==== Wxpxp nn

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Bipolar Transistor

5.5 Transport and gain factorsThe schematic sketch illustrates the different internal current components of a pnp transistor. The red arrows indicate a hole currents, whereas the blue arrows correspond to the electron currents.

Current components of a pnp transistor in the active mode.

CpI

EnI

recI

EpI

BBI

0CBI

Collector (p) Emitter (p)

Base (n)

EI CI

BI

Emitter Current

EnEpE III +=

0CBCpCnCpC IIIII +=+=

Collector Current

CEB III −=

Base Current

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Bipolar Transistor

5.5 Transport and gain factors

IBB corresponds to the electrons injected via the base that recombine with holes (which reach the base) from the emitter.

IEn is the electron current being injected from the base to the emitter. IEn shouldbe as low as possible. It can be minimized by using heavy doping of the emitter or using a heterostructure.

ICB0 is a thermally generated current in the depletion region of the base and the collector. In the active mode the base collector diode is under reverse bias conditions. Therefore, the electrons are flowing from the p- to the n-region. The current ICB0 corresponds to the leakage current of the base collector diode.

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Bipolar Transistor

5.5.1 Common base current gain

In the first sep the common base and the common emitter current gain is introduced. The common base circuit is the most basic transistor circuit. The base is used as a terminal for the input and the output loop. Therefore, the circuit is called the common base circuit. The common base current gain is defined as the current reaching the collector versus the injected emitter current. The current gain for a common base circuit is very close to 1. Therefore, the common base is not used as a current amplifier. The common base circuit is typically used as a voltage amplifier (the common base circuit has a large voltage gain). The common-base current gain is given by

The electron collector current for a pnp transistor is typically small in comparison to the emitter hole current, so that influence of the electron current can be ignored.

Common-base current gainE

Cp

E

C

II

II

≈=0α

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Bipolar Transistor

5.5.2 Common-emitter current gain

The common emitter gain is defined as the current reaching the collector versus the base current. The current gain for a common base circuit is typically much larger than 1.

The common emitter current gain can be expressed in terms of the base current gain. The common-emitter current gain is given by

Common-emitter current gainB

C

II

=0β

ECEE

EC

CE

C

IIIIII

III

−=

−=0β

0

00 1 α

αβ−

= Common-emitter current gain

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Bipolar Transistor

5.5.2 Common-emitter current gainThe common base factor can be described as the product of the emitter efficiency and base transport factor.

TEp

C

EnEp

Ep

EnEp

C

II

III

III γαα =

⋅

+=

+=0

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Bipolar Transistor

5.5.3 The Emitter efficiencyThe emitter efficiency γ is defined as the ratio of the emitter holes (for an pnptransistor) current versus the total emitter current.

As the emitter electron current does not contribute to the current flowing from the emitter to the collector the emitter electron current should be minimized. With other word: The emitter efficiency should be maximized.The emitter efficiency allows the description of the electron and hole emitter currents in terms of the overall emitter current.

Later on the emitter efficiency will be correlated with the material properties and the device design.

Emitter efficiencyEnEp

Ep

III+

≈γ

Emitter efficiency( ) EEn II ⋅−= γ1EEp II ⋅= γEnEpE III +=

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Bipolar Transistor

5.5.4 The Transport FactorBase transport factor is the ratio of the holes reaching the collector versus the holes injected from the emitter. Therefore, the transport factor αT is defined as the ratio of emitter minority current and the collector minority current.

The transport factor should be close to 1. With increasing transport factor more holes are transported from the emitter to the collector.

Base transport factor( )( ) 1

0<

==

=≡xIWxI

II

p

p

Ep

CpTα

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Bipolar Transistor

5.5 Transport and gain factorsThe common-base current gain is the product of the emitter efficiency and the transport factor. Both of these parameters have to be maximized to achieve a high current gain. The common-base current gain should be close to 1.

For well-designed transistors IEn is small compared to IEp and ICp is close to IEp. Both γ and αT are approaching unity. Therefore, α0 is very close to 1.

The importance of maximizing the common-base current gain gets clear when considering the equation of the common-emitter gain. Increasing the common-base current gain from 90% to 99% leads to an increase of the common-emitter gain from 9 to 99.

Common-base current gainTγαα =0

00 CBECnEp

TCnEpTCnCpC IIII

IIIII +=+

⋅=+=+= α

γγαα

0

00 1 α

αβ−

=

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Bipolar Transistor

ETECp III γαα =⋅= 0

( ) EEn II ⋅−= γ1

( ) ETrec II ⋅⋅−= γα1

EEp II ⋅= γ

( ) EI⋅− 01 α

0CBI

Collector (p)Emitter (p)

Base (n)

EI CI

BI

5.5.5 Summary of the transport and gain factors

00 CBEC III +⋅=α

( ) 001 CBEB III −⋅−= α

BCE III +=

Collector current

Emitter current

Base current

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Bipolar Transistor

5.6 Transistor Design In the following the influence of the material properties and the device design on the transport and the gain factors will be discussed.

5.6.1 The transport factorCorrelation between the transport factor and the material parameters and the device design.

The currents can be substituted by the diffusion current

Leading to the following expression for the base transport factor

Base transport factor( )( ) 1

0<

==

=≡xIWxI

II

p

p

Ep

CpTα

dxdpqDj pDp ⋅−= Current density for holes

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Bipolar Transistor

5.6.1 The transport factorLeading to the following expression for the base transport factor

Using the assumption that W/Lp<<1 leads to :

Based on the equation for the transport factor the transistor can be optimized:

•To get a large transport factor the width of the base should be small and the Diffusion length should be large!•The transport factor should be high to achieve a high current gain!•The Diffusion length is getting large for low levels of doping in the base.

Base transport factor

( )

( ) 1<=

=

=

ox

n

Wx

n

T

dxxdp

dxxdp

α

Base transport factor( ) 1cosh

1<≈ B

pT LW

α

40


Bipolar Transistor

5.6.2 The Emitter EfficiencyCorrelation between the emitter efficiency and the material parameters and the device design. The emitter efficiency should be high to achieve a high current gain. The emitter efficiency can be rewritten in the following form.

The emitter efficiency can be rewritten in the following from

The carrier concentration under thermal equilibrium are given by

Emitter efficiency( )

( ) ( ) 10

0<

−=+=

==

+=

Enp

p

EnEp

Ep

xxIxIxI

III

γ

Emitter efficiency111

0

0

>⋅

⋅

+≈

WpD

LnD

nBp

E

EEn

γ

B

in N

np2

0 =E

iE N

nn2

0 =

41


Bipolar Transistor

5.6.2 The Emitter Efficiency

Finally the emitter efficiency is given by

Based on the equation for the emitter efficiency the transistor can be optimized:

To get a large emitter efficiency and therefore a high current gain the ratio NB/NEhas to be as small as possible, which means that the doping concentration in the emitter should be much higher than the doping concentration in the base.

To get a large transport factor and therefore a high current gain the width of the base should be small!

Emitter efficiency1

1

1<

⋅⋅+=

E

BEp

Bp

En

NN

LW

DD

γ

Common base current gainTγαα =0

42


Bipolar Transistor

Common Collector circuits (emitter follower)

Common Emitter circuits

VB

Rg

Rout

Q1

Vin

Vout

RC

Common Base circuits

Vout

Q1Rg

Rout

VB

Vin

RCQ1

Rout

Rg

Vin

VB

Vout

RC

5.7 Bipolar Transistors as AmplifiersTransistors can be implemented as common base, common emitter and common collector circuit. In the following the I/V characteristic of the individual circuits will be discussed. Independent of the circuit implementation the circuit can be described by

Input curves (input current) as a function of the input voltage. The output voltage is typically used as a parameter for the plot.

Output curves (output current) as a function of the output voltage. The input current or the input voltage is typically used as a parameter for the plot.

43


Bipolar Transistor

5.7.1 Common base circuit Input current: Emitter current

Output current: Collector current

Input voltage: Base/Emitter voltage

Output voltage: Base/Collector voltageCommon Base circuits


( ) ( )BEBCBEE VfVVfI ≈= ,

−

⋅≈ 1exp0 kTqVII EBEB

E

Input current:

The base/collector voltage has only a minor effect on the input curve. Therefore, the influence of the base/collector voltage on the emitter current can be neglected.

Col

lect

orC

urre

nt

44


Bipolar Transistor

5.7.1 Common base circuitOutput current

Voltage controlled amplification:

Current controlled amplification:

( )BCBEC VVfI ,=

00 BCEC III +⋅=α

−

⋅+

−

⋅⋅= 1exp1exp 000 kT

qVIkTqVII BCBCBEEB

C α

( )EBCC IVfI ,=

00 BCEC III +⋅=α

−

⋅+⋅= 1exp00 kTqVIII BCBC

EC α

45


Bipolar Transistor

5.7.2 Common emitter circuit Input current: Base current

Output current: Collector current

Input voltage: Base/Emitter voltage

Output voltage: Collector/Emitter voltage

Common Emitter Circuits and collector current as a function of the emitter/collector voltage.


46


Bipolar Transistor

5.7.2 Common emitter circuit

Input current:

( ) 001 CBEB III −⋅−= α

( )CEBEB VVfI ,=

( )

−

⋅−

−

⋅⋅−= 1exp1exp1 000 kT

qVIkTqVII BCBCBEEB

B α

CEBEBC VVV −=

( ) ( )

−

−⋅−

−

⋅⋅−= 1exp1exp1 000 CEBE

BCBEEBB VV

kTqI

kTqVII α

47


Bipolar Transistor

5.7.2 Common emitter circuit Output currrent

Voltage controlled amplification: ( )CEBEC VVfI ,=

−

⋅−

−

⋅⋅= 1exp1exp 000 kT

qVIkTqVII BCBCBEEB

C α

CEBEBC VVV −=

( )

−

−⋅−

−

⋅⋅= 1exp1exp 000 CEBE

BCBEEBC VV

kTqI

kTqVII α

48


Bipolar Transistor

5.7.2 Common emitter circuit

Output current

Current controlled amplification: ( )BCEC IVfI ,=

0

0

αCBC

EIII −

=

( )

−

−⋅⋅−⋅= 1exp0

0

00 CEBE

BCBC VV

kTqIII

αββ

BCE III +=

( )0000

0

0

0

0

0

11αβ

αα

ααα

CBBCBB

C IIIII +⋅=−

⋅+−⋅

=

49


Bipolar Transistor

5.7.3 The Early effectIn the common emitter (common collector) configuration the collector current (emitter current) should be independent of VCE. This is only the case for an ideal transistor, where the width of the base region is assumed to be constant for different applied voltages VCE. Since the width of the depletion region is modulated by the applied voltage VCE, the base width is a function of the applied bias voltage. With increasing reverse bias applied on the output side of the common emitter or common collector circuit the width of the base is reduce. We speak about base width modulation. Due to the reduced width of the base the collector current and the common emitter gain is increased.

The deviation from the model of an ideal bipolar transistor is described by the Early effect. The Early effect can be characterized by the Early voltage. The early voltage corresponds to the intersection of the extrapolated output curves with the voltage axis.

50


Bipolar Transistor

Output curves including the Early effect. The Early voltage can be extracted from the output curves.

5.7.3 The Early effectChange of the width of the base collector diode in the active mode:

( )

+⋅=

A

CECC V

VII 10


BCBB

BCB

BEBB

ModB lwllww −≈−−=

( ) ( )CABD

BD

CA

CEBEBCbi

SiB

ModB NNN

NVVVq

ww+⋅

⋅−+⋅−≈εε02

51


Bipolar Transistor

5.8 Transfer characteristic and gainThe Common emitter circuit is the most important BJT based circuit. The circuit exhibits a high current gain so that it can be used as a current amplifier. The relationship between the input current (base current) and the output current (collector current) is linear over several orders if magnitude, which assumes that the current gain is constant. However, for low and high current levels the current gain drops.

Transfer Curve: Collector current as a function of the base current.

Ref.:M. Böhm, Microeletroncis

52


Bipolar Transistor

5.8 Transfer characteristic and gainIn the following we will discuss the influence of the operating point on the DC and the differential current gain for different circuits.

So far we concentrated in our discussion on the DC current gains α0 and β0. As part of an amplifier the differential current gain of the transistor might be of more interest. The DC and differential common base current gain can be defined by:

γαα ⋅≈≈ TE

C

II

0

γαα ⋅≈∂∂

⋅∂∂

=∂∂

= TEp

C

E

Ep

E

C

II

II

II

DC current gain

Differential current gain

TEp

C

E

Ep

E

C

E

Cp

II

II

II

II

αγα ⋅≈⋅=≈=0

53


Bipolar Transistor

5.8 Transfer characteristic and gainThe common base DC and differential current gain is more ore less equal. Furthermore, the common base current gain can be assumed to be constant for different current levels.

For the common emitter circuit the situation is different. Here the DC and the differential current gain is calculated to be:

Furthermore, the common emitter current gain depends on the current level flowing through the transistor.

B

C

II∂∂

=β Differential current gain

B

C

II

≈0β DC current gain

54


Bipolar Transistor

5.8 Transfer characteristic and gainFor medium current levels the current gain can be considered to be constant or slightly increasing. The slight increase is caused by the Early effect. The influence of the Early effect on the current gain has already be discussed. The widening of the depletion region of the reverse biased base/collector junction leads to a slow increase of the current gain with increasing collector current levels.

β

β0

B

C

II

≈0βB

C

II∂∂

=β

β, β0

Current gain curves: DC and differential gain as a function of the collector current level.

Ref.:M. Böhm, Microeletroncis

55


Bipolar Transistor

5.8 Transfer characteristic and gainFor low current levels one of the assumptions of the Shockley model cannot be applied. The recombination current in the depletion regions cannot be ignored.

For high current levels another assumptions of the Shockley model is not fulfilled. The assumption of weak injection is not fulfilled anymore.The strong injection of carriers via the emitter into the base leads to an increase of the minority carrier concentration. As a consequence the hole diffusion current in the emitter IEn is increased and the emitter efficiency is reduced.

EnEp

Ep

EnEp

deprecEp

III

IIII

+<

+−

=γ Emitter efficiency

EnEp

Ep

III+

=γ Emitter efficiency

56


Bipolar Transistor

.constVB

BEBE

CEIVr

=∂∂

= Differential Input resistance

BBE Iq

kTr⋅

≈

−

≈ 1exp0 kTqVII BE

B

5.9 Device parametersIn addition to the gain factors several other parameters are of major importance. In particular when it comes to the design of BJT based circuits. Therefore, the most important device parameters will be introduced in the following.

Differential input resistance

VB

Rg

Rout

Q1

Vin

Vout

Common Emitter circuits

RC

57


Bipolar Transistor

.constIC

CECE

BIVr

=∂∂

= Differential output resistance

Ouput curves including the Early effect. The Early voltage canbe extracted from the output curves.

C

ACE I

Vr ≈

5.9 Device parametersThe differential collector emitter resistance can be calculated by using the Early voltage.

58


Bipolar Transistor

.constICE

BEr

BVVv

=∂∂

=Reverse voltage ratio

.constVBE

C

CEVIS

=∂∂

=kTqIS C≈

Ar qV

kTv ≈

Slope

5.9 Device parametersThe reverse voltage ratio and the slope can be calculated by:

59


Bipolar Transistor

So far we discussed I/V characteristic of BJTs. In the following a procedure will be described, which allows to derive an equivalent circuit for the BJT. In order to implement a BJT in a circuit simulator like SPICE the transistor has to be described by an equivalent circuit.

We will start the description by using a 2-port theory. We assume that the input and the output loop of the transistor is described by:

The properties of the 2-port are given by the h-parameters (hybrid parameters).

2121111 vhihv ⋅+⋅=

2221212 vhihi ⋅+⋅=

2-port

v1 v2

5.10 Equivalent circuit of a bipolar junction transistor

60


Bipolar Transistor

5.10 Equivalent circuit of a bipolar junction transistorThe BJT parameters VBE and IC can be described as a function of the parameters IB and VCE leading to VBE=f(IB,VCE) and IC(IB,VCE). In the next step the base emitter voltage and the collector current can be linearized around the operating point.

.. constICE

BECE

constVB

BEBBE

BCEVVdV

IVdIdV

== ∂∂⋅+

∂∂⋅=

.. constICE

CCE

VB

CBC

BconstCEVIdV

IIdIdI

=∂∂

⋅+∂∂⋅=

=

Linearize around the operating point.

Linearize around the operating point.

rCEBEBBE vdVrdIdV ⋅+⋅=

CECEBC r

dVdIdI 1⋅+⋅= β

61


Bipolar Transistor

⋅

=

CE

B

CE

rBE

C

BE

dVdI

rvr

dIdV

1β

Common emitter circuit 2-port

dVBE dVCEv1

v2

⋅

=

2

1

2221

1211

2

1

vi

hhhh

iv

CE

rBE

rhhvhrh12221

1211

====

βRef.: M. Böhm, Microeletroncis

5.10 Equivalent circuit of a bipolar junction transistorDue to the correlation between the common emitter circuit and the 2-port the h-parameters can be derived.

62


Bipolar Transistor

v1

i1

h11

h12 v2

h21 i1 1/h22

i2

v2

5.10 Equivalent circuit of a bipolar junction transistorThe three basic bipolar transistor circuits can be described by a 2-port circuit. The equivalent circuit of a common emitter circuit is shown on the slides. The equivalent circuit represents the DC or low frequency equivalent circuit. Due to the correlation between the common emitter circuit and the 2-port the h-parameters can be derived.

DC or low frequency equivalent circuit of a common emitter circuit.

63


Bipolar Transistor

Full hybrid π equivalent circuit model (Giacoletto model)

Rerf.: M. Shur, Introduction to Electronic Devices

5.10 Equivalent circuit of a bipolar junction transistorHigh frequency equivalent circuit of a common emitter circuit.

64


Bipolar Transistor

ReferencesMichael Shur, Introduction to Electronic Devices, John Wiley & Sons; (January 1996).(Price: US$100), Audience: under graduate students

Simon M. Sze, Semiconductor Devices, Physics and Technology, John Wiley & Sons; 2nd Edition (2001). (Price: US$115), Audience: under graduate students

R.F. Pierret, G.W. Neudeck, Modular Series on Solid State Devices, Volumes in the Series: Semicondcutor Fundamentals, The pn junctiondiode, The bipolar junction transistor, Field effect devices,(Price: US$25 per book), Audience: under graduate students

Documents

Introduction to Electronic Devices - Jacobs University Bremen · 2 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp Bipolar Transistor Introduction to Electronic Devices