Bipolar junction transistor

The arrow on the symbol for bipolar transistors indicates the p–n junction between base and emitter and points in the direction in which conventional current travels.

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 the usual exponential current–voltage curve of a p–n junction (diode).[3]

The explanation for collector current is the concentration gradient of minority carriers in the base region.[3][4][5] Due to low-level injection (in which there are much fewer excess carriers than normal majority carriers) the ambipolar transport rates (in which the excess majority and minority carriers flow at the same rate) is in effect determined by the excess minority carriers.

Detailed transistor models of transistor action, such as the Gummel–Poon model, account for the distribution of this charge explicitly to explain transistor behaviour more exactly.[6] 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 ${\displaystyle \beta _{\text{F}}}$ times the base current. Some basic circuits can be designed by assuming that the base–emitter voltage is approximately constant and that collector current is β times the base current. However, to accurately and reliably design production BJT circuits, the voltage-control (for example, Ebers–Moll) model is required.[3] The voltage-control model requires an exponential function to be taken into account, but when it is linearized such that the transistor can be modeled 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 modeled as voltage-controlled current sources whose transconductance is proportional to their collector current. In general, transistor-level circuit analysis is performed using SPICE or a comparable analog-circuit simulator, so mathematical model complexity is usually not of much concern to the designer, but a simplified view of the characteristics allows designs to be created following a logical process.

Bipolar transistors, and particularly power transistors, have long base-storage times when they are driven into saturation; the base storage limits turn-off time in switching applications. A Baker clamp can prevent the transistor from heavily saturating, which reduces the amount of charge stored in the base and thus improves switching time.

The proportion of carriers 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 causes many more electrons to be injected from the emitter into the base than holes to be injected from the base into the emitter. A thin and lightly-doped base region means that most of the minority carriers that are injected into the base will diffuse to the collector and not recombine.

The common-emitter current gain is represented by β_F or the h-parameter h_FE; it is approximately the ratio of the DC collector current to the DC base current in forward-active region. (The F subscript is used to indicate the forward-active mode of operation.) It is typically greater than 50 for small-signal transistors, but can be smaller in transistors designed for high-power applications. Both injection efficiency and recombination in the base reduce the BJT gain.

Another useful characteristic is the common-base current gain, α_F. 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 0.980 and 0.998. It is less than unity due to recombination of charge carriers as they cross the base region.

Alpha and beta are related by the following identities:

${\displaystyle {\begin{aligned}\alpha _{\text{F}}&={\frac {I_{\text{C}}}{I_{\text{E}}}},&\beta _{\text{F}}&={\frac {I_{\text{C}}}{I_{\text{B}}}},\\\alpha _{\text{F}}&={\frac {\beta _{\text{F}}}{1+\beta _{\text{F}}}}&\iff \beta _{\text{F}}&={\frac {\alpha _{\text{F}}}{1-\alpha _{\text{F}}}}.\end{aligned}}}$

Beta is a convenient figure of merit to describe the performance of a bipolar transistor, but is not a fundamental physical property of the device. Bipolar transistors can be considered voltage-controlled devices (fundamentally the collector current is controlled by the base–emitter voltage; the base current could be considered a defect and is controlled by the characteristics of the base–emitter junction and recombination in the base). In many designs beta is assumed high enough so that base current has a negligible effect on the circuit. In some circuits (generally switching circuits), sufficient base current is supplied so that even the lowest beta value a particular device may have will still allow the required collector current to flow.

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

The diagram shows a schematic representation of an NPN transistor connected to two voltage sources. (The same description applies to a PNP transistor with reversed directions of current flow and applied voltage.) This applied voltage causes the lower P–N junction to become forward biased, allowing a flow of electrons from the emitter into the base. In active mode, the electric field existing between base and collector (caused by V_CE) will cause the majority of these electrons to cross the upper P–N junction into the collector to form the collector current I_C. 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, I_B. As shown in the diagram, the emitter current, I_E, is the total transistor current, which is the sum of the other terminal currents, (i.e., I_E = I_B + I_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 ${\displaystyle h_{\text{FE}}}$, and the value of this gain for small signals is referred to as ${\displaystyle h_{\text{fe}}}$. That is, when a small change in the currents occurs, and sufficient time has passed for the new condition to reach a steady state ${\displaystyle h_{\text{fe}}}$ is the ratio of the change in collector current to the change in base current. The symbol ${\displaystyle \beta }$ is used for both ${\displaystyle h_{\text{FE}}}$ and ${\displaystyle h_{\text{fe}}}$.[9]

The emitter current is related to ${\displaystyle V_{\text{BE}}}$ exponentially. At room temperature, an increase in ${\displaystyle V_{\text{BE}}}$ 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.

The germanium transistor was more common in the 1950s and 1960s but has a greater tendency to exhibit thermal runaway.

Various methods of manufacturing bipolar transistors were developed.[12]

• Point-contact transistor – first transistor ever constructed (December 1947), a bipolar transistor, limited commercial use due to high cost and noise.
  • Tetrode point-contact transistor – Point-contact transistor having two emitters. It became obsolete in the middle 1950s.
• Junction transistors
  • Grown-junction transistor – first bipolar junction transistor made.[13] Invented by William Shockley at Bell Labs on June 23, 1948.[14] Patent filed on June 26, 1948.
  • Alloy-junction transistor – emitter and collector alloy beads fused to base. Developed at General Electric and RCA[15] in 1951.
    • Micro-alloy transistor (MAT) – high-speed type of alloy junction transistor. Developed at Philco.[16]
    • Micro-alloy diffused transistor (MADT) – high-speed type of alloy junction transistor, speedier than MAT, a diffused-base transistor. Developed at Philco.
    • Post-alloy diffused transistor (PADT) – high-speed type of alloy junction transistor, speedier than MAT, a diffused-base transistor. Developed at Philips.
  • Tetrode transistor – high-speed variant of grown-junction transistor[17] or alloy junction transistor[18] with two connections to base.
  • Surface-barrier transistor – high-speed metal-barrier junction transistor. Developed at Philco[19] in 1953.[20]
  • Drift-field transistor – high-speed bipolar junction transistor. Invented by Herbert Kroemer[21][22] at the Central Bureau of Telecommunications Technology of the German Postal Service, in 1953.
  • Spacistor – around 1957.
  • Diffusion transistor – modern type bipolar junction transistor. Prototypes[23] developed at Bell Labs in 1954.
    • Diffused-base transistor – first implementation of diffusion transistor.
    • Mesa transistor – developed at Texas Instruments in 1957.
    • Planar transistor – the bipolar junction transistor that made mass-produced monolithic integrated circuits possible. Developed by Jean Hoerni[24] at Fairchild in 1959.
  • Epitaxial transistor[25] – a bipolar junction transistor made using vapor-phase deposition. See epitaxy. Allows very precise control of doping levels and gradients.

In 1954, Jewell James Ebers and John L. Moll introduced their mathematical model of transistor currents:[26]

Ebers–Moll model for an NPN transistor.[27] I_B, I_C and I_E are the base, collector and emitter currents; I_CD and I_ED are the collector and emitter diode currents; α_F and α_R are the forward and reverse common-base current gains.

Ebers–Moll model for a PNP transistor

Approximated Ebers–Moll model for an NPN transistor in the forward active mode. The collector diode is reverse-biased so I_CD is virtually zero. Most of the emitter diode current (α_F is nearly 1) is drawn from the collector, providing the amplification of the base current.

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

${\displaystyle {\begin{aligned}I_{\text{E}}&=I_{\text{ES}}\left(e^{\frac {V_{\text{BE}}}{V_{\text{T}}}}-1\right)\\I_{\text{C}}&=\alpha _{\text{F}}I_{\text{E}}\\I_{\text{B}}&=\left(1-\alpha _{\text{F}}\right)I_{\text{E}}\end{aligned}}}$

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

${\displaystyle J_{n\,({\text{base}})}={\frac {1}{W}}qD_{n}n_{bo}e^{\frac {V_{\text{EB}}}{V_{\text{T}}}}}$

where

• ${\displaystyle V_{\text{T}}}$ is the thermal voltage ${\displaystyle kT/q}$ (approximately 26 mV at 300 K ≈ room temperature).
• ${\displaystyle I_{\text{E}}}$ is the emitter current
• ${\displaystyle I_{\text{C}}}$ is the collector current
• ${\displaystyle \alpha _{\text{F}}}$ is the common base forward short-circuit current gain (0.98 to 0.998)
• ${\displaystyle I_{\text{ES}}}$ is the reverse saturation current of the base–emitter diode (on the order of 10⁻¹⁵ to 10⁻¹² amperes)
• ${\displaystyle V_{\text{BE}}}$ is the base–emitter voltage
• ${\displaystyle D_{n}}$ is the diffusion constant for electrons in the p-type base
• W is the base width

The ${\displaystyle \alpha }$ and forward ${\displaystyle \beta }$ parameters are as described previously. A reverse ${\displaystyle \beta }$ 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.[28]

${\displaystyle {\begin{aligned}i_{\text{C}}&=I_{\text{S}}\left[\left(e^{\frac {V_{\text{BE}}}{V_{\text{T}}}}-e^{\frac {V_{\text{BC}}}{V_{\text{T}}}}\right)-{\frac {1}{\beta _{\text{R}}}}\left(e^{\frac {V_{\text{BC}}}{V_{\text{T}}}}-1\right)\right]\\i_{\text{B}}&=I_{\text{S}}\left[{\frac {1}{\beta _{\text{F}}}}\left(e^{\frac {V_{\text{BE}}}{V_{\text{T}}}}-1\right)+{\frac {1}{\beta _{\text{R}}}}\left(e^{\frac {V_{\text{BC}}}{V_{\text{T}}}}-1\right)\right]\\i_{\text{E}}&=I_{\text{S}}\left[\left(e^{\frac {V_{\text{BE}}}{V_{\text{T}}}}-e^{\frac {V_{\text{BC}}}{V_{\text{T}}}}\right)+{\frac {1}{\beta _{\text{F}}}}\left(e^{\frac {V_{\text{BE}}}{V_{\text{T}}}}-1\right)\right]\end{aligned}}}$

where

• ${\displaystyle i_{\text{C}}}$ is the collector current
• ${\displaystyle i_{\text{B}}}$ is the base current
• ${\displaystyle i_{\text{E}}}$ is the emitter current
• ${\displaystyle \beta _{\text{F}}}$ is the forward common emitter current gain (20 to 500)
• ${\displaystyle \beta _{\text{R}}}$ is the reverse common emitter current gain (0 to 20)
• ${\displaystyle I_{\text{S}}}$ is the reverse saturation current (on the order of 10⁻¹⁵ to 10⁻¹² amperes)
• ${\displaystyle V_{\text{T}}}$ is the thermal voltage (approximately 26 mV at 300 K ≈ room temperature).
• ${\displaystyle V_{\text{BE}}}$ is the base–emitter voltage
• ${\displaystyle V_{\text{BC}}}$ is the base–collector voltage

Top: NPN base width for low collector–base reverse bias; Bottom: narrower NPN base width for large collector–base reverse bias. Hashed regions are depleted regions.

As the collector–base voltage (${\displaystyle V_{\text{CB}}=V_{\text{CE}}-V_{\text{BE}}}$) 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 (${\displaystyle i_{\text{C}}}$) and the forward common emitter current gain (${\displaystyle \beta _{\text{F}}}$) as given by:

${\displaystyle {\begin{aligned}i_{\text{C}}&=I_{\text{S}}\,e^{\frac {V_{\text{BE}}}{V_{\text{T}}}}\left(1+{\frac {V_{\text{CE}}}{V_{\text{A}}}}\right)\\\beta _{\text{F}}&=\beta _{{\text{F}}0}\left(1+{\frac {V_{\text{CB}}}{V_{\text{A}}}}\right)\\r_{\text{o}}&={\frac {V_{\text{A}}}{I_{\text{C}}}}\end{aligned}}}$

where:

• ${\displaystyle V_{\text{CE}}}$ is the collector–emitter voltage
• ${\displaystyle V_{\text{A}}}$ is the Early voltage (15 V to 150 V)
• ${\displaystyle \beta _{{\text{F}}0}}$ is forward common-emitter current gain when ${\displaystyle V_{\text{CB}}}$ = 0 V
• ${\displaystyle r_{\text{o}}}$ is the output impedance
• ${\displaystyle I_{\text{C}}}$ is the collector current

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.

The Gummel–Poon model[29] 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.[30] This model also includes the dependence of transistor ${\displaystyle \beta }$-values upon the direct current levels in the transistor, which are assumed current-independent in the Ebers–Moll model.[31]

Hybrid-pi model

The hybrid-pi model is a popular circuit model used for analyzing the small signal and AC behavior of bipolar junction and field effect transistors. Sometimes it is also called Giacoletto model because it was introduced by L.J. Giacoletto in 1969. The model can be quite accurate for low-frequency circuits and can easily be adapted for higher-frequency circuits with the addition of appropriate inter-electrode capacitances and other parasitic elements.

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, also known as the hybrid equivalent 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:

• Terminal 1, base
• Terminal 2, collector
• Terminal 3 (common), emitter; giving x to be e
• i_i, base current (i_b)
• i_o, collector current (i_c)
• V_in, base-to-emitter voltage (V_BE)
• V_o, collector-to-emitter voltage (V_CE)

and the h-parameters are given by:

• h_ix = h_ie for the common-emitter configuration, the input impedance of the transistor (corresponding to the base resistance r_pi).
• h_rx = h_re, a reverse transfer relationship, it represents the dependence of the transistor's (input) I_B–V_BE curve on the value of (output) V_CE. It is usually very small and is often neglected (assumed to be zero) at DC.
• h_fx = h_fe, the "forward" current-gain of the transistor, sometimes written h₂₁. This parameter, with lower case "fe" to imply small signal (AC) gain, or more often with capital letters for "FE" (specified as h_FE) to mean the "large signal" or DC current-gain (β_DC or often simply β), is one of the main parameters in datasheets, and may be given for a typical collector current and voltage or plotted as a function of collector current. See below.
• h_ox = 1/h_oe, the output impedance of transistor. The parameter h_oe usually corresponds to the output admittance of the bipolar transistor 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 h_oe and h_re parameters are neglected (that is, they are set to infinity and zero, respectively). 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.

The h refers to its being an h-parameter, a set of parameters named for their origin in a hybrid equivalent circuit model (see above). As with all h parameters, the choice of lower case or capitals for the letters that follow the "h" is significant; lower-case signifies "small signal" parameters, that is, the slope the particular relationship; upper-case letters imply "large signal" or DC values, the ratio of the voltages or currents. In the case of the very often used h_FE:

• F is from Forward current amplification also called the current gain.
• E refers to the transistor operating in a common Emitter (CE) configuration.

So h_FE (or hFE) refers to the (total; DC) collector current divided by the base current, and is dimensionless. It is a parameter that varies somewhat with collector current, but is often approximated as a constant; it is normally specified at a typical collector current and voltage, or graphed as a function of collector current.

Had capital letters not been used for used in the subscript, i.e. if it were written h_fe the parameter indicate small signal (AC) current gain, i.e. the slope of the Collector current versus Base current graph at a given point, which is often close to the hFE value unless the test frequency is high.

The Gummel–Poon SPICE model is often used, but it suffers from several limitations. For instance, reverse breakdown of the base–emitter diode is not captured by the SGP (SPICE Gummel–Poon) model, neither are thermal effects (self-heating) or quasi-saturation.[32] These have been addressed in various more advanced models which either focus on specific cases of application (Mextram, HICUM, Modella) or are designed for universal usage (VBIC).[33][34][35][36]

Emitter-coupled logic (ECL) use BJTs.

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.

The transistor parameters α and β characterize the current gain of the BJT. It is this gain that allows BJTs to be used as the building blocks of electronic amplifiers. The three main BJT amplifier topologies are:

• Common emitter
• Common base
• Common collector

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.[37]

Because base–emitter voltage varies as the logarithm 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.

Transistors may be deliberately made with a lower collector to emitter breakdown voltage than the collector to base breakdown voltage. If the emitter–base junction is reverse biased the collector emitter voltage may be maintained at a voltage just below breakdown. As soon as the base voltage is allowed to rise, and current flows avalanche occurs and impact ionization in the collector base depletion region rapidly floods the base with carriers and turns the transistor fully on. So long as the pulses are short enough and infrequent enough that the device is not damaged, this effect can be used to create very sharp falling edges.

Special avalanche transistor devices are made for this application.