6. Bipolar transistors
6.1. Device, constructive –technological features, circuit of insert
The bipolar transistorterms a three-electrode semiconductor device with two or more interactingelectron-hole junction. In the transistor alternate as an electrical conductivitythree regions of a semi-conductor, for what in a homogeneous semi-insulatingsubstrate of silicon Si-i the methods of epiplanar technique shape regions of acollector, basis and emitter, (fig. 6.1). For it in a plate Si-n, employee by acollector, the method of a local diffusion (introduction of atoms of dopingsubstance in a chip of a semi-conductor through some part of its surface) formsbase region (Si-p). In this region also method of a local diffusion formsemitter region (Si-n) with high density of a donor dopant. On boundary regionof emitter with base, and also on boundary of base region with collector areformed two electron-hole (p-n) junctions — emitter and collector (on a title ofextreme regions of transistor structure).
/>
Fig. 6.1. Planar n-p-n structureof the bipolar transistor
The junctions appearinteracting, if distance between them, called in breadth of basis />, is smaller diffusionlengths of mobile carriers of a charge. The diffusion length /> is a distance, whichtransits an electron and vacant electron site from a moment of occurrence in asemi-conductor up to a moment of a recombination />.
The area of collector junction always is more than the area of emitterjunction. The region of the emitter should have higher electrical conductivity,than basis and collector. An impurity concentration in the region of thetransistor owe corresponds as:
/>. (6.1)
Depending on the order ofalternation of regions as an electrical conductivity distinguish structuresp-n-p and n-p-n of types.
In a fig. 6.2 thestructures p-n-p and n-p-n and their legend on circuitries are shown.
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Fig. 6.2. Flat one-dimensionalmodel BT and legends
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Fig. 6.3. The circuits ofinsert of bipolar transistors
As a device of an electriccircuit, transistor use by such fashion, that one of its electrodes isentering, and another-output. The third electrode is common concerning an inputand exit. Depending on what electrode is common, distinguish three circuits ofinsert of the transistor: common-base (CB), common emitter (CE) and commoncollector (CC) (fig. 6.3).
6.2. Conditions of insert ofthe transistor. Static parameters.
Physical processes
By operation of the transistor the voltages fromexterior power supplys are affixed to its electrodes. Depending on polarityvoltages affixed to electrodes, each of p-n-junctions the transistor can beswitched on in direct or in the opposite direction. Four conditions of insertof the transistor are possible.
The table 6.1Title of junction
Insert
of junction
A title of a condition
of insert of the transistor
EJ
CJ
Backward
Backward Condition a splitting contact
EJ
CJ
Direct
Direct Condition of saturation
EJ
CJ
Direct
Backward Fissile condition
EJ
CJ
Backward
Direct Inverse condition
1. Condition asplitting contact. In a condition a splitting contact both p-n- junctionare backswitched on (high-ohmic state of a section E-C). In electrodes of thetransistor the thermal currents backswitched of junctions flow past which arestatic parameters of a condition the splitting contact. In each of threecircuits of insert of the transistor these parameters have particularmagnitudes. Their labels look like
for the circuitwith CB — />;
for the circuitwith CE — />;
for the circuitwith CC — />,
where the first index means anelectrode, in which the current flows past;
the second index – circuit ofinsert;
the third index — requirementin the rest of the circuit:
о — absence of a current in theother electrode — no-load operation,
s — short-circuit in the restof the circuit.
2. Condition ofsaturation. In a condition of saturation both p-n-junctions are directlyswitched on, the junctions saturated with mobile carriers of a charge, theirresistances are small. The section E-C has high conductance and it is possibleto consider it short-circuited.
Static parameters are thesaturation currents in electrodes the transistor /> andresidual voltages />. A voltage ratioand currents relevant electrodes give magnitudes of resistances of saturation:
/>; />.
3. Fissile condition.In a fig. 6.4 the flat one-dimensional model of the transistor is shown, whichemitter junction is switched on in a forward direction, and collector junction- in backward. Such insert corresponds to a fissile condition, and thetransistor has intensifying properties. The principle of operation of thetransistor in a fissile condition grounded on use of the following phenomena:
— injection of majoritycarriers through emitter junction;
— transport of injectedcarriers through basis owing to diffusions and drift;
— recombination ofnonequilibrium carriers in basis;
— extractions ofcarriers from basis in a collector by a region of collector junction.
The injection of carriersstipulates transiting through emitter p-n-junction of diffusive currents: hole /> and electronic />.
In an external circuit ofemitter the current of injection flows past
/>, (6.2)
where /> - hole current ofinjection of the emitter;
/> - electronic current ofinjection of the emitter.
For transistor structurep-n-p of a type the relation between admixtures in the emitter and basis isdefined, as:/>. Therefore />.
The relation betweencomponent of an emitter current is evaluated coefficient of injection
/> (6.3)
The injection of carriersfrom the emitter in basis rises density
minority carriers in basis.Their density on boundary of emitter junction for p-n-p of structure is definedby a relation
/> (6.4)
Appeared near to emitterjunction in basis a charge of vacant electron sites almost instantaneous,during a dielectric relaxation /> seconds,is cancelled by a charge of electrons affluent in basis from a radiant />. Circuit of a current theemitter — basis appears made and ensures course of an emitter current.Magnification near to emitter junction the electron concentrations and vacantelectron sites are established by a lapse rate of densities nonequilibriumcarriers in basis /> and />. Under an operation of lapse rates densities there is adiffusive driving of nonequilibrium vacant electron sites and electrons throughbasis from the emitter to a collector.
Diffusion of vacantelectron sites in basis is attended their recombination with by electrons. Onplace of recombined electrons in basis from the external circuits of a radiant /> act other electrons,establishing together with electrons leaving basis in the emitter, base currentrecombinations />. As breadth ofbasis is much less diffusion lengths of carriers />,a loss of carriers in basis at the expense of recombination is inappreciable,and current of a recombination /> on one,two order are less than a current />.
The vacant electron sitesinjected by the emitter in basis and which have reached collector backswitchedjunction, get in its accelerating region and are thrown in region of acollector. The collector current /> isestablished: />.
Process of transport of minoritynonequilibrium carriers through basis is evaluated by a transport coefficient />. Coefficient oftransport depends from breadth of basis /> anddiffusion length of vacant electron sites />:
/> (6.5)
Than more vacant electronsites is injected by the emitter in basis, than more them extract a collector,augmenting a collector current. Therefore current /> isproportional to an emitter current and is termed current controlled of acollector, which in view of relations (6.3) and (6.5) is defined by a relation(6.6) also records as follows:
/> (6.6)
/> - is termed as an integrated(static) transmission factor current of emitter in a collector circuit and inview of relations (6.3), (6,5) is defined by the following formula:
/>. (6.7)
Opportunity of control ofan output current of the transistor by change entering current is the importantproperty of the bipolar transistor, allowing to use it as a fissile device ofelectronic circuits.
Except for a controllablepart of a collector current />, in anelectrode
collector the unguided part ofa current — thermal current backswitched of junction flows past. It is similarto a current backswitched of a crystal diode and consequently has received atitle of a backward collector current />.
index c means, that it — current backswitched of collector junction,
index b — the measuringsoccur in the circuit with CB,
index 0 — the measuringsoccur at /> =0, i.e. No-load operationon an input.
The direction of abackward collector current /> coincideswith a direction of a controllable part of a collector current and consequently
/>. (6.8)
The current /> in a circuit of basis isguided towards to a base current of a recombination /> andbase current of injection />
/>. (6.9)
In an emitter circuit thecurrent of injection is the total of a collector current /> and base current />:
/>. (6.10)
The expressions (6.8) and(6.10) establish communication between currents of the transistor and valid forany circuit of insert.
The similar processesoccur in n-p-n the transistor to that by variance, that instead of vacantelectron sites it is necessary to speak about electrons and on the contrary.Positive directions of direct currents and supply voltages, relevant to afissile condition, are shown in a fig. 6.3.
Reverse voltage affixed oncollector junction, it is much more voltages directly switched of emitterjunction, and the currents are equal emitter circuits and collectorpractically. Therefore load power established variable component collectorcurrent, appears much more power expended on control by a circuital current ofthe emitter, hence transistor has intensifying properties. These qualities in acombination to a small overall dimensions, high reliability, longevity andprofitability have stipulated wide application of transistors in an electrontechnology.
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Fig. 6.4. Driving of carriersand currents in BT (fissile condition)
In the circuit with CE andCC (fig. 6.3) a current basises becomes control current, and the equation of acollector current (6.8) will be copied in the following aspect:
/>;
/>;
/>. (6.11)
where: /> - transmission factor of abase current in the circuit with CE:
/> - unguided part of a collector current inthe circuit with CE, or through current of the transistor.
For the circuit with CC anoutput current is the emitter current. Therefore
/>
or
/>,where/>. (6.12)
4. Inverse condition.In an inverse condition emitter junction backswitched, and the collectorjunction is under direct voltage. Therefore in comparison with a fissilecondition in an inverse condition the injection of carriers is carried outcollector junction, and extractions ofcarriers — emitter junction. Practically emitter and collector vary byfunctions and places in the circuit.
For the circuit with CB
/>. (6.13)
here /> - inverse coefficient oftransmission.
As the area of emitterjunction is much less than the area collector junction and />, />
For the circuit with CC
/>. (6.14)
For the circuit with CE
/>. (6.15)
6.3. Differential coefficientof transmission of a current
In the equation (6.7) foran integrated (static) transmission factor of an emitter current />. Coefficient of injection /> the efficiency of emitterjunction characterizes, and coefficient of diffusive transport /> characterizes processes inbasis, diffusive transport and recombination of carriers, with which attendsthis process; coefficient M is inlet for the account of processes in collectorjunction and almost always M=1. The equation of a collector current />, where /> is static parameter offissile condition of insert (fissile condition), displays link between directcurrents. Coefficient /> is defined bythe formula /> and this formula displayslink between stationary values of a control current /> andvalue of an output current />.
For variable signals, whichamplitude order much less grades of supply voltages, link between collectorcurrents and emitter is defined by derivation of a relation (6.7) as functionstwo arguments in the conjecture /> =const,i.e.
/>, or
/>. (6.16)
/> - differential transmissionfactor of an emitter current in circuit with CB, which always is more thanintegrated coefficient />. Calculations display, that at major levelsof injection, when /> (see of theformula (6.1), (6.4)), derivative /> aspiresto zero and />. Therefore for the analysis of a major signal integrated(static) coefficient /> is always used.
In consequent viewing isnot done variances between /> and />. Using a label />, but ineach case the applications of these magnitudes should be remembered a level ofinjection.
6.4. Ebers-Moll’s model
Links between currents andvoltages in the transistor for four conditions of insert are well compoundedwith convenient and clear mathematical Ebers-Moll’s model, grounded on a dualcircuit consisting of two diodes (emitter and collector), switched on meeting,and two current sources mapping interaction of these diodes (fig. 6.5).
/> (6.17)
/>. (6.18)
where /> and /> - thermal currents emitterand collector junctions accordingly, metered at short-circuit on exit and inputaccordingly (/> =0 and /> =0).
/>. (6.19)
where /> and /> - back currents of emitterand collector junctions measured accordingly at abruption of a collector andthe emitter. With the account (6.18), (6.19) relations (6.17) are conversed toan aspect
/>; (6.20)
/>; (6.21)
/>. (6.22)
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Fig. 6.5. Equivalent nonlinearEbers-Moll’s model for BT
In computing methods of theanalysis of transistor circuits with the help of a computer the widecirculation was received by nonlinear model of the Gummel-Pun’s transistor,which grounded on the solution of integrated relations for charges and linksexterior electrical performances a charge in basis of transistor structure. Itis very precise model explaining many physical effects, but its expositionneeds major number of parameters, so for the analysis in a wide frequency range25 parameters are necessary. The sequential simplification of Gummel-Pun’smodel eventually reduces in the elementary Ebers-Moll’s model. Therefore atthe analysis of the concrete circuits it is necessary to search for thereasonable compromise between an exactitude of the solution and complexity ofmodel.