# Bipolar junction transistor: Wikis

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# Encyclopedia

A bipolar (junction) transistor (BJT) is a three-terminal electronic device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons and holes. Charge flow in a BJT is due to bidirectional diffusion of charge carriers across a junction between two regions of different charge concentrations. This mode of operation is contrasted with unipolar transistors, such as field-effect transistors, in which only one carrier type is involved in charge flow due to drift. By design, most of the BJT collector current is due to the flow of charges injected from a high-concentration emitter into the base where they are minority carriers that diffuse toward the collector, and so BJTs are classified as minority-carrier devices.

 PNP NPN
Schematic symbols for
PNP- and NPN-type
BJTs.

## Introduction

NPN BJT with forward-biased E–B junction and reverse-biased B–C junction

An NPN transistor can be considered as two diodes with a shared anode. In typical operation, the emitter–base junction is forward biased and the base–collector junction is reverse biased. In an NPN transistor, for example, when a positive voltage is applied to the base–emitter junction, the equilibrium between thermally generated carriers and the repelling electric field of the depletion region becomes unbalanced, allowing thermally excited electrons to inject into the base region. These electrons wander (or "diffuse") through the base from the region of high concentration near the emitter towards the region of low concentration near the collector. The electrons in the base are called minority carriers because the base is doped p-type which would make holes the majority carrier in the base.

To minimize the percentage of carriers that recombine before reaching the collector–base junction, the transistor's base region must be thin enough that carriers can diffuse across it in much less time than the semiconductor's minority carrier lifetime. In particular, the thickness of the base must be much less than the diffusion length of the electrons. The collector–base junction is reverse-biased, and so little electron injection occurs from the collector to the base, but electrons that diffuse through the base towards the collector are swept into the collector by the electric field in the depletion region of the collector–base junction. The thin shared base and asymmetric collector–emitter doping is what differentiates a bipolar transistor from two separate and oppositely biased diodes connected in series.

### Voltage, current, and charge control

The collector–emitter current can be viewed as being controlled by the base–emitter current (current control), or by the base–emitter voltage (voltage control). These views are related by the current–voltage relation of the base–emitter junction, which is just the usual exponential current–voltage curve of a p-n junction (diode).[1]

The physical explanation for collector current is the amount of minority-carrier charge in the base region.[1][2][3] Detailed models of transistor action, such as the Gummel–Poon model, account for the distribution of this charge explicitly to explain transistor behavior more exactly.[4] The charge-control view easily handles phototransistors, where minority carriers in the base region are created by the absorption of photons, and handles the dynamics of turn-off, or recovery time, which depends on charge in the base region recombining. However, because base charge is not a signal that is visible at the terminals, the current- and voltage-control views are generally used in circuit design and analysis.

In analog circuit design, the current-control view is sometimes used because it is approximately linear. That is, the collector current is approximately βF times the base current. Some basic circuits can be designed by assuming that the emitter–base voltage is approximately constant, and that collector current is beta times the base current. However, to accurately and reliably design production BJT circuits, the voltage-control (for example, Ebers–Moll) model is required[1]. The voltage-control model requires an exponential function to be taken into account, but when it is linearized such that the transistor can be modelled as a transconductance, as in the Ebers–Moll model, design for circuits such as differential amplifiers again becomes a mostly linear problem, so the voltage-control view is often preferred. For translinear circuits, in which the exponential I–V curve is key to the operation, the transistors are usually modelled as voltage controlled with transconductance proportional to collector current. In general, transistor level circuit design is performed using SPICE or a comparable analogue circuit simulator, so model complexity is usually not of much concern to the designer.

### Turn-on, turn-off, and storage delay

The Bipolar transistor exhibits a few delay characteristics when turning on and off. Most transistors, and especially power transistors, exhibit long base storage time that limits maximum frequency of operation in switching applications. One method for reducing this storage time is by using a Baker clamp.

### Transistor 'alpha' and 'beta'

The proportion of electrons able to cross the base and reach the collector is a measure of the BJT efficiency. The heavy doping of the emitter region and light doping of the base region cause many more electrons to be injected from the emitter into the base than holes to be injected from the base into the emitter. The common-emitter current gain is represented by βF or hfe; it is approximately the ratio of the DC collector current to the DC base current in forward-active region. It is typically greater than 100 for small-signal transistors but can be smaller in transistors designed for high-power applications. Another important parameter is the common-base current gain, αF. The common-base current gain is approximately the gain of current from emitter to collector in the forward-active region. This ratio usually has a value close to unity; between 0.98 and 0.998. Alpha and beta are more precisely related by the following identities (NPN transistor):

$\alpha_T = \frac{I_{\text{C}}}{I_{\text{E}}}$
$\beta_F = \frac{I_{\text{C}}}{I_{\text{B}}}$
$\beta_F = \frac{\alpha_{T}}{1 - \alpha_{T}}\iff \alpha_{T} = \frac{\beta_F}{\beta_F+1}$

## Structure

Simplified cross section of a planar NPN bipolar junction transistor
Die of a KSY34 high-frequency NPN transistor, base and emitter connected via bonded wires

A BJT consists of three differently doped semiconductor regions, the emitter region, the base region and the collector region. These regions are, respectively, p type, n type and p type in a PNP, and n type, p type and n type in a NPN transistor. Each semiconductor region is connected to a terminal, appropriately labeled: emitter (E), base (B) and collector (C).

The base is physically located between the emitter and the collector and is made from lightly doped, high resistivity material. The collector surrounds the emitter region, making it almost impossible for the electrons injected into the base region to escape being collected, thus making the resulting value of α very close to unity, and so, giving the transistor a large β. A cross section view of a BJT indicates that the collector–base junction has a much larger area than the emitter–base junction.

The bipolar junction transistor, unlike other transistors, is usually not a symmetrical device. This means that interchanging the collector and the emitter makes the transistor leave the forward active mode and start to operate in reverse mode. Because the transistor's internal structure is usually optimized for forward-mode operation, interchanging the collector and the emitter makes the values of α and β in reverse operation much smaller than those in forward operation; often the α of the reverse mode is lower than 0.5. The lack of symmetry is primarily due to the doping ratios of the emitter and the collector. The emitter is heavily doped, while the collector is lightly doped, allowing a large reverse bias voltage to be applied before the collector–base junction breaks down. The collector–base junction is reverse biased in normal operation. The reason the emitter is heavily doped is to increase the emitter injection efficiency: the ratio of carriers injected by the emitter to those injected by the base. For high current gain, most of the carriers injected into the emitter–base junction must come from the emitter.

The low-performance "lateral" bipolar transistors sometimes used in CMOS processes are sometimes designed symmetrically, that is, with no difference between forward and backward operation.

Small changes in the voltage applied across the base–emitter terminals causes the current that flows between the emitter and the collector to change significantly. This effect can be used to amplify the input voltage or current. BJTs can be thought of as voltage-controlled current sources, but are more simply characterized as current-controlled current sources, or current amplifiers, due to the low impedance at the base.

Early transistors were made from germanium but most modern BJTs are made from silicon. A significant minority are also now made from gallium arsenide, especially for very high speed applications (see HBT, below).

### NPN

The symbol of an NPN Bipolar Junction Transistor.

NPN is one of the two types of bipolar transistors, in which the letters "N" and "P" refer to the majority charge carriers inside the different regions of the transistor. Most bipolar transistors used today are NPN, because electron mobility is higher than hole mobility in semiconductors, allowing greater currents and faster operation.

NPN transistors consist of a layer of P-doped semiconductor (the "base") between two N-doped layers. A small current entering the base in common-emitter mode is amplified in the collector output. In other terms, an NPN transistor is "on" when its base is pulled high relative to the emitter.

The arrow in the NPN transistor symbol is on the emitter leg and points in the direction of the conventional current flow when the device is in forward active mode.

One mnemonic device for identifying the symbol for the NPN transistor is "not pointing in, or 'not pointing, no' "[5]

### PNP

The other type of BJT is the PNP with the letters "P" and "N" referring to the majority charge carriers inside the different regions of the transistor.

The symbol of a PNP Bipolar Junction Transistor.

PNP transistors consist of a layer of N-doped semiconductor between two layers of P-doped material. A small current leaving the base in common-emitter mode is amplified in the collector output. In other terms, a PNP transistor is "on" when its base is pulled low relative to the emitter.

The arrow in the PNP transistor symbol is on the emitter leg and points in the direction of the conventional current flow when the device is in forward active mode.

One mnemonic device for identifying the symbol for the PNP transistor is "pointing in proudly, or 'pointing in - pah'."[5]

### Heterojunction bipolar transistor

Bands in graded heterojunction NPN bipolar transistor. Barriers indicated for electrons to move from emitter to base, and for holes to be injected backward from base to emitter; Also, grading of bandgap in base assists electron transport in base region; Light colors indicate depleted regions

The heterojunction bipolar transistor (HBT) is an improvement of the BJT that can handle signals of very high frequencies up to several hundred GHz. It is common in modern ultrafast circuits, mostly RF systems.[6][7] Heterojunction transistors have different semiconductors for the elements of the transistor. Usually the emitter is composed of a larger bandgap material than the base. The figure shows that this difference in bandgap allows the barrier for holes to inject backward into the base, denoted in figure as Δφp, to be made large, while the barrier for electrons to inject into the base Δφn is made low. This barrier arrangement helps reduce minority carrier injection from the base when the emitter-base junction is under forward bias, and thus reduces base current and increases emitter injection efficiency.

The improved injection of carriers into the base allows the base to have a higher doping level, resulting in lower resistance to access the base electrode. In the more traditional BJT, also referred to as homojunction BJT, the efficiency of carrier injection from the emitter to the base is primarily determined by the doping ratio between the emitter and base, which means the base must be lightly doped to obtain high injection efficiency, making its resistance relatively high. In addition, higher doping in the base can improve figures of merit like the Early voltage by lessening base narrowing.

The grading of composition in the base, for example, by progressively increasing the amount of germanium in a SiGe transistor, causes a gradient in bandgap in the neutral base, denoted in the figure by ΔφG, providing a "built-in" field that assists electron transport across the base. That drift component of transport aids the normal diffusive transport, increasing the frequency response of the transistor by shortening the transit time across the base.

Two commonly used HBTs are silicon–germanium and aluminum gallium arsenide, though a wide variety of semiconductors may be used for the HBT structure. HBT structures are usually grown by epitaxy techniques like MOCVD and MBE.

## Regions of operation

Bipolar transistors have five distinct regions of operation, defined mostly by applied bias:

• Forward-active (or simply, active): The base–emitter junction is forward biased and the base–collector junction is reverse biased. Most bipolar transistors are designed to afford the greatest common-emitter current gain, βF, in forward-active mode. If this is the case, the collector–emitter current is approximately proportional to the base current, but many times larger, for small base current variations.
• Reverse-active (or inverse-active or inverted): By reversing the biasing conditions of the forward-active region, a bipolar transistor goes into reverse-active mode. In this mode, the emitter and collector regions switch roles. Because most BJTs are designed to maximize current gain in forward-active mode, the βF in inverted mode is several (2–3 for the ordinary germanium transistor) times smaller. This transistor mode is seldom used, usually being considered only for failsafe conditions and some types of bipolar logic. The reverse bias breakdown voltage to the base may be an order of magnitude lower in this region.
• Saturation: With both junctions forward-biased, a BJT is in saturation mode and facilitates high current conduction from the emitter to the collector. This mode corresponds to a logical "on", or a closed switch.
• Cutoff: In cutoff, biasing conditions opposite of saturation (both junctions reverse biased) are present. There is very little current flow, which corresponds to a logical "off", or an open switch.
• Avalanche breakdown region

Although these regions are well defined for sufficiently large applied voltage, they overlap somewhat for small (less than a few hundred millivolts) biases. For example, in the typical grounded-emitter configuration of an NPN BJT used as a pulldown switch in digital logic, the "off" state never involves a reverse-biased junction because the base voltage never goes below ground; nevertheless the forward bias is close enough to zero that essentially no current flows, so this end of the forward active region can be regarded as the cutoff region.

### Active-mode NPN transistors in circuits

Structure and use of NPN transistor. Arrow according to schematic.

The diagram opposite is a schematic representation of an NPN transistor connected to two voltage sources. To make the transistor conduct appreciable current (on the order of 1 mA) from C to E, VBE must be above a minimum value sometimes referred to as the cut-in voltage. The cut-in voltage is usually about 600 mV for silicon BJTs at room temperature but can be different depending on the type of transistor and its biasing. This applied voltage causes the lower P-N junction to 'turn-on' allowing a flow of electrons from the emitter into the base. In active mode, the electric field existing between base and collector (caused by VCE) will cause the majority of these electrons to cross the upper P-N junction into the collector to form the collector current IC. The remainder of the electrons recombine with holes, the majority carriers in the base, making a current through the base connection to form the base current, IB. As shown in the diagram, the emitter current, IE, is the total transistor current, which is the sum of the other terminal currents (i.e., $I_{\text{E}} = I_{\text{B}} + I_{\text{C}}\,$).

In the diagram, the arrows representing current point in the direction of conventional current – the flow of electrons is in the opposite direction of the arrows because electrons carry negative electric charge. In active mode, the ratio of the collector current to the base current is called the DC current gain. This gain is usually 100 or more, but robust circuit designs do not depend on the exact value (for example see op-amp). The value of this gain for DC signals is referred to as hFE, and the value of this gain for AC signals is referred to as hfe. However, when there is no particular frequency range of interest, the symbol β is used[citation needed].

It should also be noted that the emitter current is related to VBE exponentially. At room temperature, an increase in VBE by approximately 60 mV increases the emitter current by a factor of 10. Because the base current is approximately proportional to the collector and emitter currents, they vary in the same way.

### Active-mode PNP transistors in circuits

Structure and use of PNP transistor.

The diagram opposite is a schematic representation of a PNP transistor connected to two voltage sources. To make the transistor conduct appreciable current (on the order of 1 mA) from E to C, VEB must be above a minimum value sometimes referred to as the cut-in voltage. The cut-in voltage is usually about 600 mV for silicon BJTs at room temperature but can be different depending on the type of transistor and its biasing. This applied voltage causes the upper P-N junction to 'turn-on' allowing a flow of holes from the emitter into the base. In active mode, the electric field existing between the emitter and the collector (caused by VCE) causes the majority of these holes to cross the lower P-N junction into the collector to form the collector current IC. The remainder of the holes recombine with electrons, the majority carriers in the base, making a current through the base connection to form the base current, IB. As shown in the diagram, the emitter current, IE, is the total transistor current, which is the sum of the other terminal currents (i.e., $I_{\text{E}} = I_{\text{B}} + I_{\text{C}}\,$).

In the diagram, the arrows representing current point in the direction of conventional current – the flow of holes is in the same direction of the arrows because holes carry positive electric charge. In active mode, the ratio of the collector current to the base current is called the DC current gain. This gain is usually 100 or more, but robust circuit designs do not depend on the exact value. The value of this gain for DC signals is referred to as hFE, and the value of this gain for AC signals is referred to as hfe. However, when there is no particular frequency range of interest, the symbol β is used[citation needed].

It should also be noted that the emitter current is related to VEB exponentially. At room temperature, an increase in VEB by approximately 60 mV increases the emitter current by a factor of 10. Because the base current is approximately proportional to the collector and emitter currents, they vary in the same way.

## History

The bipolar point-contact transistor was invented in December 1947 at the Bell Telephone Laboratories by John Bardeen and Walter Brattain under the direction of William Shockley. The junction version known as the bipolar junction transistor, invented by Shockley in 1948, enjoyed three decades as the device of choice in the design of discrete and integrated circuits. Nowadays, the use of the BJT has declined in favour of CMOS technology in the design of digital integrated circuits.

### Germanium transistors

The germanium transistor was more common in the 1950s and 1960s, and while it exhibits a lower "cut off" voltage, typically around 0.2 V, making it more suitable for some applications, it also has a greater tendency to exhibit thermal runaway.

### Early manufacturing techniques

Various methods of manufacturing bipolar junction transistors were developed[8].

## Theory and modeling

In the discussion below, focus is on the NPN bipolar transistor. In the NPN transistor in what is called active mode the base-emitter voltage VBE and collector-base voltage VCB are positive, forward biasing the emitter-base junction and reverse-biasing the collector-base junction. In active mode of operation, electrons are injected from the forward biased n-type emitter region into the p-type base where they diffuse to the reverse biased n-type collector and are swept away by the electric field in the reverse biased collector-base junction. For a figure describing forward and reverse bias, see the end of the article semiconductor diodes.

### Large-signal models

#### Ebers–Moll model

The DC emitter and collector currents in active mode are well modeled by an approximation to the Ebers–Moll model:

Ebers–Moll Model for NPN Transistor
Ebers–Moll Model for PNP Transistor
$I_{\text{E}} = I_{\text{ES}} \left(e^{\frac{V_{\text{BE}}}{V_{\text{T}}}} - 1\right)$
$I_{\text{C}} = \alpha_T I_{\text{ES}} \left(e^{\frac{V_{\text{BE}}}{V_{\text{T}}}} - 1\right)$

The base internal current is mainly by diffusion (see Fick's law) and

$J_n(\text{base}) = \frac{q D_n n_{bo}}{W} e^{\frac{V_{\text{EB}}}{V_{\text{T}}}}$

where

• VT is the thermal voltage kT / q (approximately 26 mV at 300 K ≈ room temperature).
• IE is the emitter current
• IC is the collector current
• αT is the common base forward short circuit current gain (0.98 to 0.998)
• IES is the reverse saturation current of the base–emitter diode (on the order of 10−15 to 10−12 amperes)
• VBE is the base–emitter voltage
• Dn is the diffusion constant for electrons in the p-type base
• W is the base width

The α and forward β parameters are as described previously. A reverse β is sometimes included in the model.

The unapproximated Ebers–Moll equations used to describe the three currents in any operating region are given below. These equations are based on the transport model for a bipolar junction transistor.[21]

$i_{\text{C}} = I_{\text{S}}\left(e^{\frac{V_{\text{BE}}}{V_{\text{T}}}} - e^{\frac{V_{\text{BC}}}{V_{\text{T}}}}\right) - \frac{I_{\text{S}}}{\beta_R}\left(e^{\frac{V_{\text{BC}}}{V_{\text{T}}}} - 1\right)$
$i_{\text{B}} = \frac{I_{\text{S}}}{\beta_F}\left(e^{\frac{V_{\text{BE}}}{V_{\text{T}}}} - 1\right) + \frac{I_{\text{S}}}{\beta_R}\left(e^{\frac{V_{\text{BC}}}{V_{\text{T}}}} - 1\right)$
$i_{\text{E}} = I_{\text{S}}\left(e^{\frac{V_{\text{BE}}}{V_{\text{T}}}} - e^{\frac{V_{\text{BC}}}{V_{\text{T}}}}\right) + \frac{I_{\text{S}}}{\beta_F}\left(e^{\frac{V_{\text{BE}}}{V_{\text{T}}}} - 1\right)$

where

• iC is the collector current
• iB is the base current
• iE is the emitter current
• βF is the forward common emitter current gain (20 to 500)
• βR is the reverse common emitter current gain (0 to 20)
• IS is the reverse saturation current (on the order of 10−15 to 10−12 amperes)
• VT is the thermal voltage (approximately 26 mV at 300 K ≈ room temperature).
• VBE is the base–emitter voltage
• VBC is the base–collector voltage
##### Base-width modulation
Top: PNP base width for low collector-base reverse bias; Bottom: narrower PNP base width for large collector-base reverse bias. Light colors are depleted regions.

As the applied collector–base voltage (VBC) varies, the collector–base depletion region varies in size. An increase in the collector–base voltage, for example, causes a greater reverse bias across the collector–base junction, increasing the collector–base depletion region width, and decreasing the width of the base. This variation in base width often is called the "Early effect" after its discoverer James M. Early.

Narrowing of the base width has two consequences:

• There is a lesser chance for recombination within the "smaller" base region.
• The charge gradient is increased across the base, and consequently, the current of minority carriers injected across the emitter junction increases.

Both factors increase the collector or "output" current of the transistor in response to an increase in the collector–base voltage.

In the forward-active region, the Early effect modifies the collector current (iC) and the forward common emitter current gain (βF) as given by:[citation needed]

$i_{\text{C}} = I_{\text{S}} \, e^{\frac{v_{\text{BE}}}{V_{\text{T}}}} \left(1 + \frac{V_{\text{CB}}}{V_{\text{A}}}\right)$
$\beta_F = \beta_{F0}\left(1 + \frac{V_{\text{CB}}}{V_{\text{A}}}\right)$
$r_{\text{o}} = \frac{V_{\text{A}}}{I_{\text{C}}}$

where:

• VCB is the collector–base voltage
• VA is the Early voltage (15 V to 150 V)
• βF0 is forward common-emitter current gain when VCB = 0 V
• ro is the output impedance
• IC is the collector current
##### Current–voltage characteristics

The following assumptions are involved when deriving ideal current-voltage characteristics of the BJT[22]

• Low level injection
• Uniform doping in each region with abrupt junctions
• One-dimensional current flow
• Negligible recombination-generation in space charge regions
• Negligible electric fields outside of space charge regions.

It is important to characterize the minority diffusion currents induced by injection of carriers.

With regard to pn-junction diode, a key relation is the diffusion equation.

$\frac{d^2 \Delta p_{\text{B}} (x)}{dx^2} = \frac{\Delta p_{\text{B}} (x)}{L_{\text{B}}^2}$

A solution of this equation is below, and two boundary conditions are used to solve and find C1 and C2.

$\Delta p_{\text{B}} (x) = C_1 e^{x/L_{\text{B}}} + C_2 e^{-x/L_{\text{B}}}$

The following equations apply to the emitter and collector region, respectively, and the origins 0, 0', and 0'' apply to the base, collector, and emitter.

$\Delta n_{\text{B}} (x'') = A_1 e^{x''/L_{\text{B}}} + A_2 e^{-x''/L_{\text{B}}}$
$\Delta n_{\text{c}} (x') = B_1 e^{x'/L_{\text{B}}} + B_2 e^{-x'/L_{\text{B}}}$

A boundary condition of the emitter is below:

$\Delta n_{\text{E}} (0'') = n_{\text{E}O} ( \exp (q V_{\text{EB}} / kT) - 1)\;$

The values of the constants A1 and B1 are zero due to the following conditions of the emitter and collector regions as $x'' \rightarrow 0$ and $x' \rightarrow 0$.

$\Delta n_{\text{E}} (x'') \rightarrow 0$
$\Delta n_{\text{c}} (x') \rightarrow 0$

Because A1 = B1 = 0, the values of ΔnE(0'') and Δnc(0') are A2 and B2, respectively.

$\Delta n_{\text{E}} (x'') = n_{\text{E}0} (\exp (q V_{\text{EB}} / kT) - 1) \exp(-x''/L_{\text{E}})\;$
$\Delta n_{\text{C}} (x') = n_{\text{C}0} (\exp (q V_{\text{CB}} / kT) - 1) \exp(-x'/L_{\text{C}})\;$

Expressions of IEn and ICn can be evaluated.

$I_{\text{E}n} = - q A D_{\text{E}} \frac{d \Delta_{\text{E}} (x'')}{dx} |_{x''=0''}$
$I_{\text{C}n} = -q A \frac{D_{\text{C}}}{L_{\text{C}}} n_{\text{C}0} ( \exp ( q V_{\text{CB}} / kT) - 1)$

Because insignificant recombination occurs, the second derivative of ΔpB(x) is zero. There is therefore a linear relationship between excess hole density and x.

$\Delta p_{\text{B}} (x) = D_1 x + D_2\;$

The following are boundary conditions of ΔpB.

$\Delta p_{\text{B}} (0) = D_2\;$
$\Delta p_{\text{B}} (W) = D_1 W + \Delta p_{\text{B}} (0)\;$

Substitute into the above linear relation.

$\Delta p_{\text{B}} (x) = - \left ( \frac{ \Delta p_{\text{B}} (0) - \Delta p_{\text{B}} (W) }{W} \right ) x + \Delta p_{\text{B}} (0)$.

With this result, derive value of IEp.

$I_{\text{E}p} (0) = - q A D_{\text{B}} \frac{d \Delta p_{\text{B}}}{dx}|_{x=0}$
$I_{\text{E}p} (0) = \frac{q A D_{\text{B}}}{W} \left ( \Delta p_{\text{B}} (0) - \Delta p_{\text{B}} (W) \right )$

Use the expressions of IEp, IEn, ΔpB(0), and ΔpB(W) to develop an expression of the emitter current.

$\Delta p_{\text{B}}(W) = p_{\text{B}0} \exp ( q V_{\text{CB}}/kT)\;$
$\Delta p_{\text{B}}(0) = p_{\text{B}0} \exp ( q V_{\text{EB}}/kT))\;$
$I_{\text{E}} = qA \left ( \left ( \frac{D_{\text{E}} n_{\text{E}0}}{L_{\text{E}}} + \frac{D_{\text{B}} p_{\text{B}0}}{W} \right ) \left ( \exp \left ( \frac{q V_{\text{EB}}}{kT} \right ) - 1 \right ) - \left ( \frac{D_{\text{B}}}{W} p_{\text{B}0} \right ) \left ( \exp \left ( \frac {q V_{\text{CB}}}{k T} \right ) - 1 \right ) \right )$

Similarly, an expression of the collector current is derived.

$I_{\text{C}p} (W) = I_{\text{E}p} (0)\;$
$I_{\text{C}} = I_{\text{C}p} (W) + I_{\text{C}n} (0')\;$
$I_{\text{C}} = q A \left ( \left ( \frac{D_{\text{B}}}{W} p_{\text{B}0} \right ) ( \exp (q V_{\text{EB}} / kT ) -1 ) - \left ( \frac{ D_{\text{C}} n_{\text{C}0} }{ L_{\text{C}} } + \frac{ D_{\text{B}} p_{\text{B}0} }{ W } \right ) ( \exp (q V_{\text{CB}} / kT ) -1 ) \right )$

An expression of the base current is found with the previous results.

$I_{\text{B}} = I_{\text{E}} - I_{\text{C}}\;$
$I_{\text{B}} = q A \left ( \frac{D_{\text{E}}}{L_{\text{E}}} n_{\text{E}0} ( \exp ( q V_{\text{EB}} / kT ) - 1) + \frac{D_{\text{C}}}{L_{\text{C}}} n_{\text{C}0} ( \exp ( q V_{\text{CB}} / k T ) - 1 ) \right )$
##### Punchthrough

When the base–collector voltage reaches a certain (device specific) value, the base–collector depletion region boundary meets the base–emitter depletion region boundary. When in this state the transistor effectively has no base.The device thus loses all gain when in this state.

#### Gummel–Poon charge-control model

The Gummel–Poon model[23] is a detailed charge-controlled model of BJT dynamics, which has been adopted and elaborated by others to explain transistor dynamics in greater detail than the terminal-based models typically do [2]. This model also includes the dependence of transistor β-values upon the dc current levels in the transistor, which are assumed current-independent in the Ebers–Moll model.[24]

### Small-signal models

#### h-parameter model

Generalized h-parameter model of an NPN BJT.
replace x with e, b or c for CE, CB and CC topologies respectively.

Another model commonly used to analyze BJT circuits is the "h-parameter" model, closely related to the hybrid-pi model and the y-parameter two-port, but using input current and output voltage as independent variables, rather than input and output voltages. This two-port network is particularly suited to BJTs as it lends itself easily to the analysis of circuit behaviour, and may be used to develop further accurate models. As shown, the term "x" in the model represents a different BJT lead depending on the topology used. For common-emitter mode the various symbols take on the specific values as:

• x = 'e' because it is a common-emitter topology
• Terminal 1 = Base
• Terminal 2 = Collector
• Terminal 3 = Emitter
• iin = Base current (ib)
• io = Collector current (ic)
• Vin = Base-to-emitter voltage (VBE)
• Vo = Collector-to-emitter voltage (VCE)

and the h-parameters are given by –

• hix = hie – The input impedance of the transistor (corresponding to the emitter resistance re).
• hrx = hre – Represents the dependence of the transistor's IBVBE curve on the value of VCE. It is usually very small and is often neglected (assumed to be zero).
• hfx = hfe – The current-gain of the transistor. This parameter is often specified as hFE or the DC current-gain (βDC) in datasheets.
• hox = hoe – The output impedance of transistor. This term is usually specified as an admittance and has to be inverted to convert it to an impedance.

As shown, the h-parameters have lower-case subscripts and hence signify AC conditions or analyses. For DC conditions they are specified in upper-case. For the CE topology, an approximate h-parameter model is commonly used which further simplifies the circuit analysis. For this the hoe and hre parameters are neglected (that is, they are set to infinity and zero, respectively). It should also be noted that the h-parameter model as shown is suited to low-frequency, small-signal analysis. For high-frequency analyses the inter-electrode capacitances that are important at high frequencies must be added.

## Applications

The BJT remains a device that excels in some applications, such as discrete circuit design, due to the very wide selection of BJT types available, and because of its high transconductance and output resistance compared to MOSFETs. The BJT is also the choice for demanding analog circuits, especially for very-high-frequency applications, such as radio-frequency circuits for wireless systems. Bipolar transistors can be combined with MOSFETs in an integrated circuit by using a BiCMOS process of wafer fabrication to create circuits that take advantage of the application strengths of both types of transistor.

### Temperature sensors

Because of the known temperature and current dependence of the forward-biased base–emitter junction voltage, the BJT can be used to measure temperature by subtracting two voltages at two different bias currents in a known ratio [3].

### Logarithmic converters

Because base–emitter voltage varies as the log of the base–emitter and collector–emitter currents, a BJT can also be used to compute logarithms and anti-logarithms. A diode can also perform these nonlinear functions, but the transistor provides more circuit flexibility.

## Vulnerabilities

Exposure of the transistor to ionizing radiation causes radiation damage. Radiation causes a buildup of 'defects' in the base region that act as recombination centers. The resulting reduction in minority carrier lifetime causes gradual loss of gain of the transistor.

Power BJTs are subject to a failure mode called secondary breakdown, in which excessive current and normal imperfections in the silicon die cause portions of the silicon inside the device become disproportionately hotter than the others. The doped silicon has a negative temperature coefficient, meaning that it conducts more current at higher temperatures. Thus, the hottest part of the die conducts the most current, causing its conductivity to increase, which then causes it to become progressively hotter again, until the device fails internally. The thermal runaway process associated with secondary breakdown, once triggered, occurs almost instantly and may catastrophically damage the transistor package.

## References

1. ^ a b c (2nd ed.). Cambridge University Press. ISBN 9780521370950.
2. ^ Juin Jei Liou and Jiann S. Yuan (1998). Semiconductor Device Physics and Simulation. Springer. ISBN 0306457245.
3. ^ General Electric (1962). Transistor Manual (6th ed.). p. 12.  "If the principle of space charge neutrality is used in the analysis of the transistor, it is evident that the collector current is controlled by means of the positive charge (hole concentration) in the base region. ... When a transistor is used at higher frequencies, the fundamental limitation is the time it takes the carriers to diffuse across the base region..." (same in 4th and 5th editions)
4. ^ Paolo Antognetti and Giuseppe Massobrio (1993). Semiconductor Device Modeling with Spice. McGraw–Hill Professional. ISBN 0071349553.
5. ^ a b Alphonse J. Sistino (1996). Essentials of electronic circuitry. CRC Press. p. 64, 102. ISBN 9780824796938.
6. ^ D.V. Morgan, Robin H. Williams (Editors) (1991). Physics and Technology of Heterojunction Devices. London: Institution of Electrical Engineers (Peter Peregrinus Ltd.). ISBN 0863412041.
7. ^ Peter Ashburn (2003). SiGe Heterojunction Bipolar Transistors. New York: Wiley. Chapter 10. ISBN 0470848383.
8. ^ Third case study – the solid state advent (PDF)
9. ^ TRANSISTOR MUSEUM Historic Transistor Photo Gallery BELL LABS TYPE M1752
10. ^ Morris, Peter Robin (1990). "4.2". A History of the World Semiconductor Industry. IEE History of Technology Series 12. London: Peter Peregrinus Ltd.. p. 29. ISBN 0 86341 227 0.
11. ^ TRANSISTOR MUSEUM Historic Transistor Photo Gallery RCA TA153
12. ^ High Speed Switching Transistor Handbook (2nd ed.). Motorola. 1963. p. 17. [1]
13. ^ TRANSISTOR MUSEUM Historic Transistor Photo Gallery WESTERN ELECTRIC 3N22
14. ^ The Tetrode Power Transistor PDF
15. ^ TRANSISTOR MUSEUM Historic Transistor Photo Gallery PHILCO A01
16. ^ TRANSISTOR MUSEUM Historic Transistor Photo Gallery Surface Barrier Transistor
17. ^ Herb’s Bipolar Transistors IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 48, NO. 11, NOVEMBER 2001 PDF
18. ^ Influence of Mobility and Lifetime Variations on Drift-Field Effects in Silicon-Junction Devices PDF
19. ^ TRANSISTOR MUSEUM Historic Transistor Photo Gallery BELL LABS PROTOTYPE DIFFUSED BASE TRIODE
20. ^ TRANSISTOR MUSEUM Historic Transistor Photo Gallery FAIRCHILD 2N1613
21. ^ A.S. Sedra and K.C. Smith (2004). Microelectronic Circuits (5th ed.). New York: Oxford. Eqs. 4.103–4.110, p. 305. ISBN 0-19-514251-9.
22. ^ R S Muller, Kamins TI & Chan M (2003). Device electronics for integrated circuits (Third Edition ed.). New York: Wiley. p. 280 ff. ISBN 0-471-59398-2.
23. ^ H. K. Gummel and R. C. Poon, "An integral charge control model of bipolar transistors," Bell Syst. Tech. J., vol. 49, pp. 827–852, May–June 1970
24. ^ A.S. Sedra and K.C. Smith (2004). Microelectronic Circuits (5th ed.). New York: Oxford. p. 509. ISBN 0-19-514251-9.