Editing Bipolar junction transistor (section)

=== 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 the usual exponential current–voltage curve of a p–n junction (diode).<ref name="Horowitz 1989">{{cite book |last1=Horowitz |first1=Paul |author-link1=Paul Horowitz |last2=Hill |first2=Winfield |author-link2=Winfield Hill |title=The Art of Electronics |edition=2nd |date=1989 |publisher=Cambridge University Press |isbn=978-0-521-37095-0 |url=https://books.google.com/books?id=bkOMDgwFA28C |access-date=June 22, 2023 }}</ref>

The explanation for collector current is the concentration gradient of minority carriers in the base region.<ref name="Horowitz 1989" /><ref>{{cite book |title=Semiconductor Device Physics and Simulation |first1=Juin Jei |last1=Liou |first2=Jiann S. |last2=Yuan |publisher=Springer |date=1998 |isbn=978-0-306-45724-1 |url=https://books.google.com/books?id=y343FTN1TU0C&q=charge-controlled+bjt+physics&pg=PA166 }}</ref><ref>{{cite book | title = Transistor Manual |author=General Electric |edition=6th |date=1962 |page=12 |bibcode = 1964trma.book.....C }} "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).</ref> Due to [[low-level injection]] (in which there are many fewer excess carriers than normal majority carriers) the [[Ambipolar diffusion|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 behavior more exactly.<ref>{{cite book |title=Semiconductor Device Modeling with Spice |first1=Paolo |last1=Antognetti |first2=Giuseppe |last2=Massobrio |publisher=McGraw–Hill Professional |date=1993 |isbn=978-0-07-134955-0 |url=https://books.google.com/books?id=5IBYU9xrGaIC&q=gummel-poon+charge+model&pg=PA96 }}</ref> The charge-control view easily handles [[phototransistor]]s, where minority carriers in the base region are created by the absorption of [[photon]]s, 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 <math>\beta_\text{F}</math> 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 model (e.g. the [[Ebers–Moll model]]) is required.<ref name="Horowitz 1989" /> 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 circuit]]s, 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.