Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
Introduction to Electronic Devices (Course Number 300331) Fall 2006 Bipolar Transistors Information: http://www.faculty.iu- Dr. Dietmar Knipp bremen.de/dknipp/ Assistant Professor of Electrical Engineering
Source: Apple
Ref.: Apple
Ref.: IBM Critical 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 101 dimension (m) Ref.: Palo Alto Research Center
Bipolar Transistor 1 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
Introduction to Electronic Devices 5 Bipolar Transistors 5.1 Introduction 5.2 Basic transistor operation 5.3 Transistor under zero bias 5.4 Transistor under bias conditions 5.4.1 Shockley Assumptions 5.4.2 The ideal transistor equation 5.4.3 The transistor equation in its general form 5.4.4 Modes of Operation 5.8.1 The active mode 5.8.2 The Saturation mode 5.8.3 The cutoff mode 5.8.4 The inversion mode 5.5 Transport and gain factors 5.5.1 The Emitter efficiency 5.5.2 The Transport factor 5.5.3 The Common-base current gain 5.5.5 The summary of the transport and gain factors
Bipolar Transistor 2 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.6 Transistor Design 5.6.1 The transport factor 5.6.2 The Emitter Efficiency 5.7 Bipolar Transistors as Amplifiers 5.7.1 Common base circuit 5.7.2 Common emitter circuit 5.7.3 The Early Effect 5.8 Transfer characteristic and gain 5.9 Device parameters 5.10 Equivalent circuit of a bipolar junction transistor
References
Bipolar Transistor 3 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.1 Introduction The 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.
Bipolar Transistor 4 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.1 Introduction A 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. Schematic cross section of a pnp The BJT device structure consists of two transistor. The transistor is pn junctions. The device can be implemented in a p-type implemented as an pnp or a npn substrate. The n-type and the p+- structure. Each of the doped regions is type regions are formed by connected with one of the terminals: diffusion of dopants in the p-type Base, Emitter or Collector. The three substrate. The electrodes are regions of a BJT are formed by the formed by metal contacts. diffusion of a doping profiles in a substrate. Ref.: M.S. Sze, Semiconductor Devices
Bipolar Transistor 5 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.1 Introduction The 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.
Bipolar Transistor 6 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.2 Basic transistor operation
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 pnp-transistor 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).
npn-transistor
Ref.: M.S. Sze, Semiconductor Devices
Bipolar Transistor 7 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.2 Basic transistor operation
On this slide the + and – signs indicate the direction of the current flow.
IB = IE − IC
The npn-structure is complementary pnp-transistor 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 pnp transistor.
npn-transistor Ref.: M.S. Sze, Semiconductor Devices
Bipolar Transistor 8 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.3 Bipolar Junction Transistors under zero bais At 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).
Bipolar Transistor 9 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
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. 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 Ref.: M.S. Sze, Semiconductor Devices
Bipolar Transistor 10 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
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 the incorporated 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.
Bipolar Transistor 11 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4 Transistor under bias conditions Before 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.
Bipolar Transistor 12 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4 Transistor under bias conditions Due 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 Ref.: M.S. Sze, Semiconductor Devices
Bipolar Transistor 13 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4 Transistor under bias conditions Due 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 the corresponding bands, because the product of the carrier concentration is below the square of the intrinsic carrier concentration.
Bipolar Transistor 14 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
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.)
Bipolar Transistor 15 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.2 The ideal transistor equation In 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.
∂2 p p − p n n n0 Diffusion equation for holes Dp 2 − = 0 ∂x τ pl
Bipolar Transistor 16 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.2 The ideal transistor equation Firstly 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
x x p ()x = p + C ⋅exp + C ⋅exp− n n0 1 B 2 B Lp Lp
where Lp and Ln are the hole and the electron diffusion length of the minority carriers.
Hole diffusion length Lp = Dpτ pl
Electron diffusion length Ln = Dnτ nl
Bipolar Transistor 17 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.2 The ideal transistor equation
The following boundary conditions are used to determine the constants C1 and C2: qVEB p (x =W )= 0 pn ()x = 0 = pn0 ⋅ exp and n kT
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 2 ni pn0 = NB
where NB is the donor concentration in the base. Solving the Diffusion equation leads to the following expression for the minority carrier concentration.
W − x W − x sinh sinh LB LB qVEB p p pn ()x = pn0 ⋅ exp −1 ⋅ + pn0 ⋅ 1− kT W W sinh sinh LB LB p p
Bipolar Transistor 18 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
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
qV x Minority carrier concentration in p ()x = p ⋅ exp EB −1 ⋅ 1− n n0 the base region kT W
The approximation is valid because the Diffusion length is large in comparison to the width of the base.
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.
Ref.: M.S. Sze, Semiconductor Devices Bipolar Transistor 19 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.2 The ideal transistor equation The minority carrier concentration in the emitter and the collector region can be obtained in a very similar way. qV x − x n ()x = n + n ⋅exp EB −1⋅exp E x ≤ −x E E0 E0 E E kT Ln x − x n ()x = n − n ⋅exp− C x ≥ x C C0 C0 C C Ln
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
qVEB nE ()x = −xE = nE0 ⋅ exp kT
qVCB nC ()x = xC = nC0 ⋅ exp− = 0 kT We assume that the emitter depth and the collector depth are much larger
than the diffusion length LE and LC for the minority carriers.
Bipolar Transistor 20 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.2 The ideal transistor equation Knowing the minority carrier concentration the various current components can be determined by solving the current density equation. dp j = qµ pF − qD ⋅ Current density for holes p p p dx
It is assumed that the overall current is determined by the diffusion current. The influence of the drift current is negligible.
Bipolar Transistor 21 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.2 The ideal transistor equation Further it is assumed that the hole and the electron diffusion current densities remain nearly constant throughout the depletion region. E E C C Ln >> x Ln >> x −W This is a valid approximation because the diffusion length of the emitter and collector is much larger than the width of the depletion regions.
qVEB x Minority carrier concentration in pn ()x = pn0 ⋅ exp −1 ⋅ 1− kT W the base region The current densities can be determined assuming a constant current density in the depletion region by B dp qADp pn0 qV n EB I Ep = A⋅− qDp ≅ exp Emitter hole current dx x=0 W kT in the base The collector current can be calculated in very similar way:
B dp qADp pn0 qV Collector hole current I = A⋅− qD n ≅ exp EB Cp p in the base dx x=W W kT
Bipolar Transistor 22 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.2 The ideal transistor equation
IEp is equal to ICp if W/Lp << 1. The electron current IEn corresponds to dn qAD E n qV Emitter electron E E n E0 EB I En = A⋅ − qDn = E exp −1 dx L kT current x=− xE n The collector current can be calculated in a similar way:
dn qADC n C n C 0 Collector ICn = A⋅ − qDC = dx LC electron current x=xC n
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. B E B Dp pn0 D n qV Dp pn0 I = I + I = qA⋅ + n E0 ⋅ exp EB −1 + qA E En Ep E W Ln kT W Emitter current
Bipolar Transistor 23 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.2 The ideal transistor equation The collector can be calculate accordingly.
B B C Dp pn0 qV Dp pn0 D n I = I + I = qA⋅ ⋅ exp EB −1 + qA + n C0 C Cn Cp C W kT W Ln Collector current The base current is the difference between the emitter and the collector current: E C Dn nE0 VEB Dn nC 0 I B = I E − IC = qA⋅ ⋅ exp −1 + Base current LE V LC n th n The current flow through the transistor is mainly determined by the minority carrier distribution in the base.
Bipolar Transistor 24 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.3 The transistor equation in its general form The 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:
qVEB qVCB IE = a11 ⋅ exp −1 − a12 ⋅ exp −1 Emitter current kT kT
qVEB qVCB IC = a21 ⋅ exp −1 − a22 ⋅ exp −1 Collector current kT kT
D p D n Dp pn0 a = qA⋅ p n0 + E E0 a = qA 11 W L 12 W E Coefficients
D p Dp pn0 D n p n0 a = qA + C C0 a21 = qA⋅ 22 W W LC
Bipolar Transistor 25 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.4 Modes of Operation Bipolar transistors can be operated in 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, Minority carrier distribution of a pnp •Cutoff mode and transistor under the four modes of •Inverted mode. operation: Active, Saturation, Cutoff and Inverted mode.
Ref.: M.S. Sze, Semiconductor Devices
Bipolar Transistor 26 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.4.1 Active Mode In 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 Mode In the saturation mode both junctions are forward biased. The minority carrier concentration for x=W is nonzero. The carrier concentration is:
qVCB pn ()x =W = pn0 exp kT The transistor operates as a switch.
Bipolar Transistor 27 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.4.4.3 Cutoff Mode In the cutoff mode both diodes are under reverse bias conditions. Under such conditions
pn ()(x = 0 = pn x =W = 0 )
The cutoff mode corresponds to the off mode of a transistor which is used as a switch.
5.4.4.4 Inverted Mode In 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.
Bipolar Transistor 28 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.5 Transport and gain factors The 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.
Base (n)
IE = IEp + IEn
ICp IEp Emitter Current I IC E Irec ICB0
IEn IC = ICp + ICn = ICp + ICB0
Collector Current Collector (p) Emitter (p) IBB
IB = IE − IC IB
Base Current Current components of a pnp transistor in the active mode.
Bipolar Transistor 29 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
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 should be 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.
Bipolar Transistor 30 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
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
IC ICp α0 = ≈ Common-base current gain IE IE
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.
Bipolar Transistor 31 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
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.
IC β0 = Common-emitter current gain IB
The common emitter current gain can be expressed in terms of the base current gain. The common-emitter current gain is given by
IC IC IE β0 = = IE − IC IE IE − IC IE
α0 β0 = Common-emitter current gain 1−α0
Bipolar Transistor 32 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
α5.5.2 Common-emitter current gain The common base factor can be described as the product of the emitter efficiency and base transport factor.
I I I = C = Ep ⋅ C = γα 0 T IEp + IEn IEp + IEn IEp
Bipolar Transistor 33 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.5.3 The Emitter efficiency The emitter efficiency γ is defined as the ratio of the emitter holes (for an pnp transistor) current versus the total emitter current.
IEp γ ≈ Emitter efficiency IEp + IEn
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.
IE = IEp + IEn Emitter efficiency IEp = γ ⋅ IE IEn = (1−γ )⋅ IE Later on the emitter efficiency will be correlated with the material properties and the device design.
Bipolar Transistor 34 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.5.4 The Transport Factor Base 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.
ICp I p ()x =W αT ≡ = ()<1 Base transport factor IEp I p x = 0
The transport factor should be close to 1. With increasing transport factor more holes are transported from the emitter to the collector.
Bipolar Transistor 35 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.5 Transport and gain factors The 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.
α = γα 0 T α Common-base current gain
For well-designed transistors IEn isγα small compared to IEp and ICp is close to IEp. Both γ and αT are approaching unity. Therefore, α0 is very close to 1. IEpγ IC = ICp + ICn = T IEp + ICn = T ⋅ + ICn =α0IE + ICB0 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. α0 β0 = 1−α0
Bipolar Transistor 36 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.5.5 Summary of the transport and gain factors
I =α ⋅ I + I Base (n) C 0 E CB0 Collector current
ICp =α0 ⋅ IE = γαT IE IEp = γ ⋅ IE I I C IB = (1−α0 )⋅ IE − ICB0 E Irec = ()1−αT ⋅γ ⋅ IE ICB0
IEn = ()1−γ ⋅ IE Emitter current
()1−α ⋅I Collector (p) Emitter (p) 0 E IE = IC + IB
Base current IB
Bipolar Transistor 37 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
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 factor Correlation between the transport factor and the material parameters and the device design. I I ()x =W Cp p Base transport factor αT ≡ = ()<1 IEp I p x = 0 The currents can be substituted by the diffusion current dp j = −qD ⋅ Current density for holes Dp p dx Leading to the following expression for the base transport factor
Bipolar Transistor 38 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.6.1 The transport factor Leading to the following expression for the base transport factor
dpn ()x dx x=W Base transport factor αT = <1 dpn ()x
dx x=o
Using the assumption that W/Lp<<1 leads to :
1 Base transport factor αT ≈ B <1 cosh()W Lp
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.
Bipolar Transistor 39 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.6.2 The Emitter Efficiency Correlation 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. I I (x = 0) Ep p Emitter efficiency γ = = ()(< )1 I Ep + I En I p x = 0 + I n x = − xE
The emitter efficiency can be rewritten in the following from E Dn ⋅ nE 0
1 LE Emitter efficiency ≈ 1 + B > 1 γ D p ⋅ pn 0 W The carrier concentration under thermal equilibrium are given by 2 2 ni ni pn0 = nE 0 = N B N E
Bipolar Transistor 40 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.6.2 The Emitter Efficiency
Finally the emitter efficiency is given by
1 γ = < 1 E Emitter efficiency Dn W N B 1 + B ⋅ E ⋅ D p L p N E
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/NE has 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!
α0 = γαT Common base current gain
Bipolar Transistor 41 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.7 Bipolar Transistors as Amplifiers Transistors 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.
VB VB VB
Rout RC Rout RC Rg Q1 Rg Q1 Rg Q1 Rout RC Vout Vin Vout V Vin out Vin
Common Base Common Emitter Common Collector circuits circuits circuits (emitter follower)
Bipolar Transistor 42 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.7.1 Common base circuit Input current: Emitter current Output current: Collector current Input voltage: Base/Emitter voltage Output voltage: Base/Collector voltage Common Base circuits
Input current: IE = f (VBE ,VBC )≈ f (VBE )
EB qVEB IE ≈ I0 ⋅ exp −1 kT Collector 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.
Ref.: M.S. Sze, Semiconductor Devices
Bipolar Transistor 43 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.7.1 Common base circuit Output current
Voltage controlled amplification: IC = f (VBE ,VBC )
IC = α0 ⋅ IE + IBC0
EB qVBE BC qVBC IC =α0 ⋅ I0 ⋅ exp −1 + I0 ⋅ exp −1 kT kT
Current controlled amplification: IC = f (VBC , IE )
IC =α0 ⋅ IE + IBC0
BC qVBC IC = α0 ⋅ IE + I0 ⋅ exp −1 kT
Bipolar Transistor 44 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
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.
Ref.: M.S. Sze, Semiconductor Devices
Bipolar Transistor 45 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.7.2 Common emitter circuit
Input current: IB = f (VBE ,VCE )
IB = ()1−α0 ⋅ IE − ICB0
EB qVBE BC qVBC IB = ()1−α0 ⋅ I0 ⋅ exp −1 − I0 ⋅ exp −1 kT kT
VBC = VBE −VCE
EB qVBE BC q IB = ()1−α0 ⋅ I0 ⋅ exp −1 − I0 ⋅ exp ()VBE −VCE −1 kT kT
Bipolar Transistor 46 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.7.2 Common emitter circuit Output currrent Voltage controlled amplification: IC = f (VBE ,VCE )
EB qVBE BC qVBC IC = α0 ⋅ I0 ⋅ exp −1 − I0 ⋅ exp −1 kT kT
VBC = VBE −VCE
EB qVBE BC q IC =α0 ⋅ I0 ⋅ exp −1 − I0 ⋅ exp ()VBE −VCE −1 kT kT
Bipolar Transistor 47 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.7.2 Common emitter circuit Output current Current controlled amplification: IC = f ()VCE , IB
IC − ICB0 IE = α0
IE = IC + IB α β
α0 ⋅ IB ICB0 α0 IC = α + ⋅ = 0 ⋅()IB + ICB0 α0 1− 0 α0 1− 0 β β 0 BC q IC = 0 ⋅ IB − ⋅ I0 ⋅ exp ()VBE −VCE −1 α0 kT
Bipolar Transistor 48 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.7.3 The Early effect In 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.
Bipolar Transistor 49 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.7.3 The Early effect Change of the width of the base collector diode in the active mode:
Mod BE BC BC wB = wB − lB − lB ≈ wB − lB
2ε ε N C wMod ≈ w − 0 Si ⋅ ()V BC +V −V ⋅ A B B bi BE CE B B C () q ND ⋅ ND + N A
()0 VCE IC = IC ⋅1+ VA
Output curves including the Early effect. The Early voltage can be extracted from the output curves. Ref.: M.S. Sze, Semiconductor Devices
Bipolar Transistor 50 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.8 Transfer characteristic and gain The 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
Bipolar Transistor 51 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.8 Transfer characteristic and gain In 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. Asα 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: I I Cp IC Ep IC γ 0 = ≈ = ⋅ ≈ ⋅αT IE IE IE IEp α
IC α DC current gain 0 ≈ ≈ T ⋅γ α IE
∂IC ∂IEp ∂IC α Differential current gain = = ⋅ ≈ T ⋅γ ∂IE ∂IE ∂IEp
Bipolar Transistor 52 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.8 Transfer characteristic and gain The 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:
IC β0 ≈ DC current gain IB
∂I β = C Differential current gain ∂IB
Furthermore, the common emitter current gain depends on the current level flowing through the transistor.
Bipolar Transistor 53 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.8 Transfer characteristic and gain For 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
β Current gain curves: DC and differential gain as a function of β0 I ∂I the collector current level. β ≈ C β = C 0 I B ∂IB
Ref.:M. Böhm, Microeletroncis
Bipolar Transistor 54 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.8 Transfer characteristic and gain For low current levels one of the assumptions of the Shockley model cannot be applied. The recombination current in the depletion regions cannot be ignored. I − I dep I γ = Ep rec < Ep Emitter efficiency I Ep + I En I Ep + I En
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.
I Ep γ = Emitter efficiency I Ep + I En
Bipolar Transistor 55 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.9 Device parameters In 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.
∂VBE rBE = Differential Input resistance VB ∂I B VCE =const.
Rout qVBE IB ≈ I0 exp −1 R kT C Rg Q1
Vout V kT in rBE ≈ Differential input q ⋅ IB resistance Common Emitter circuits
Bipolar Transistor 56 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.9 Device parameters The differential collector emitter resistance can be calculated by using the Early voltage.
∂VCE Differential output resistance rCE = ∂IC I B =const.
VA rCE ≈ IC
Ouput curves including the Early effect. The Early voltage can be extracted from the output curves.
Bipolar Transistor 57 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.9 Device parameters The reverse voltage ratio and the slope can be calculated by:
Reverse ∂VBE kT vr = vr ≈ voltage ratio ∂VCE qVA IB =const.
∂I qI S = C S ≈ C Slope ∂VBE kT VCE =const.
Bipolar Transistor 58 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.10 Equivalent circuit of a bipolar junction 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:
2-port v1 = h11 ⋅i1 + h12 ⋅ v2
v1 v2 i2 = h21 ⋅i1 + h22 ⋅ v2
The properties of the 2-port are given by the h-parameters (hybrid parameters).
Bipolar Transistor 59 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.10 Equivalent circuit of a bipolar junction transistor
The 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.
∂VBE ∂VBE dVBE = dIB ⋅ + dVCE ⋅ ∂IB ∂VCE VCE =const. IB =const. Linearize around the operating point. ∂IC ∂IC dIC = dIB ⋅ + dVCE ⋅ ∂IB ∂VCE VCE=const. IB =const.
dVBE = dIB ⋅ rBE + dVCE ⋅ vr Linearize around the operating point. 1 dIC = dIB ⋅ β + dVCE ⋅ rCE
Bipolar Transistor 60 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.10 Equivalent circuit of a bipolar junction transistor Due to the correlation between the common emitter circuit and the 2-port the h- parameters can be derived.
Common emitter circuit 2-port
v2 dV v1 BE dVCE
dV r v dI v1 h11 h12 i1 BE = BE r ⋅ B = ⋅ i h h v dIC β 1 rCE dVCE 2 21 22 2
h11 = rBE h12 = vr
h21 = β h22 =1 rCE Ref.: M. Böhm, Microeletroncis
Bipolar Transistor 61 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.10 Equivalent circuit of a bipolar junction transistor The 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.
i2 i1
DC or low frequency h 11 equivalent circuit of a v1 v common emitter h21 i1 1/h22 2 circuit. h12 v2
Bipolar Transistor 62 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
5.10 Equivalent circuit of a bipolar junction transistor High frequency equivalent circuit of a common emitter circuit.
Full hybrid π equivalent circuit model (Giacoletto model)
Rerf.: M. Shur, Introduction to Electronic Devices
Bipolar Transistor 63 Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
References Michael 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 junction diode, The bipolar junction transistor, Field effect devices, (Price: US$25 per book), Audience: under graduate students
Bipolar Transistor 64