It’s a model to describe large signal behaviour of a transistor, and start with the simple notion of two back to back diodes. For example the diodes seen at the two . It can be shown that (see S.M. Sze, Physics of Semiconductor Devices), therefore . where. More Complete Ebers-Moll Model. Model includes configurational. Ideal transistor model. Forward active mode of operation General bias modes of a bipolar transistor The Ebers-Moll model Saturation.

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Instead, they drift through the base-collector depletion region and end up as majority carriers in the collector region. The three main BJT amplifier topologies are:. That is, a PNP transistor is “on” when its base is pulled low relative to the emitter. 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 unapproximated Ebers—Moll equations used to describe the three currents in any operating region are given below. The forward- and reverse-bias transport factors are obtained by measuring the current gain in the forward active and reverse active mode of operation.

These views are related by the current—voltage mkdel of the base—emitter modrl, which is the usual exponential current—voltage curve of a p—n junction diode. For the specific case where the base-emitter and base-collector voltage are the same and the base doping is uniform, there can be no minority carrier diffusion in the base so that: It is less than unity due to recombination of charge carriers as they cross the base region. Ebers—Moll model for a PNP transistor.

These electrons diffuse through the base from the region of high concentration near the emitter toward the region of low concentration near the collector.

The emitter efficiency is obtained from: The device thus loses all gain when in this state. However, current in many metal conductors is due to the flow of electrons which, because they carry a negative charge, move in the direction opposite to conventional current.


The Ebers-Moll model describes all of these bias modes. Using the parameters identified in Figure 5. BJTs can be thought of as voltage-controlled current sourcesbut are more simply characterized as current-controlled current sources, or current amplifiers, due to the low impedance at the base.

In addition to normal breakdown ratings of the device, power BJTs are subject to a failure mode called secondary breakdownin which excessive current and normal imperfections in the silicon die cause portions of the silicon inside the device to become disproportionately hotter than the others. The Schottky diode clamps the base-collector voltage at a value, which is slightly lower than the turn-on voltage of the base-collector diode. In contrast, unipolar transistors, such as field-effect transistorsonly use one kind of charge carrier.

To further simplify this model, we will assume that all quasi-neutral regions in the device are much smaller than the minority-carrier diffusion lengths in these regions, so that the “short” diode expressions apply. Retrieved from ” https: These current sources depend on the current through each diode. The minority carrier lifetime in the base is 10 ns.

Ebers Moll Equations

You can help by adding to it. If the emitter-base junction is reverse biased into avalanche or Zener mode and charge flows for a short period of time, the current gain of the BJT will be permanently degraded. July Learn how and when to remove this template message.

The emitter current due to electrons and holes are obtained using the “short” diode expressions derived in section 4. This section may be too technical for most readers to understand. Holt, Reinhart, and Winston.

As shown, the term, xin the model represents a different BJT lead depending on the topology used.

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 omdel and base, which means the base must be lightly doped to obtain high injection efficiency, making its resistance relatively high. Cut-off requires little further analysis, while the reverse active mode ,oll operation is analogous to the forward active mode with the added complication that the areas of the base-emitter and base-collector junction, A E and A Cdiffer.


The saturation currents I E,s and I C,s are obtained by measuring the base-emitter base-collector diode saturation current modfl shorting the base-collector base-emitter diode. Darlington transistor Sziklai pair Cascode Long-tailed pair. The arrow on the symbol for bipolar transistors indicates the PN junction between base and emitter and points in the direction conventional current travels.

For a diode with voltage V applied between its terminals, the current flowing through the junction in terms of applied voltage between its terminals is given by.

Ebers-moll model of transistor

In addition, the collector-base area is typically larger than the emitter-base area, so that even fewer electrons make it from the collector into the emitter.

In the reverse active mode, we reverse the function of the emitter and the collector. A typical current gain for a silicon bipolar transistor is 50 – Two commonly used HBTs are silicon—germanium and aluminum gallium arsenide, though a wide variety of semiconductors may be used for the HBT structure.

In the active mode of operation, electrons are injected from the forward biased n-type emitter region into the p-type base where they diffuse as minority carriers to the reverse-biased n-type collector and are swept away by the electric field in the reverse-biased collector—base junction. Therefore, the base-collector junction is also forward biased.

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 beers 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.