Bipolar transistors
6. Bipolar transistors
6.1. Device, constructive – technological
features, circuit of insert
The bipolar transistor terms a
threeelectrode semiconductor device with two or more interacting electronhole
junction. In
the transistor alternate as an electrical conductivity three regions of a
semiconductor, for what in a homogeneous semiinsulating substrate of silicon
Sii the methods of epiplanar technique shape regions of a collector, basis and
emitter, (fig. 6.1). For it in a plate Sin, employee by a collector, the
method of a local diffusion (introduction of atoms of doping substance in a chip
of a semiconductor through some part of its surface) forms base region (Sip).
In this region also method of a local diffusion forms emitter region (Sin)
with high density of a donor dopant. On boundary region of emitter with base,
and also on boundary of base region with collector are formed two electronhole
(pn) junctions  emitter and collector (on a title of extreme regions of
transistor structure).
Fig. 6.1. Planar npn structure of the
bipolar transistor
The junctions appear interacting, if
distance between them, called in breadth of basis _{}, is smaller diffusion lengths of mobile
carriers of a charge. The diffusion length _{} is a distance, which transits an electron and
vacant electron site from a moment of occurrence in a semiconductor up to a
moment of a recombination _{}.
The area of collector junction always is more than the area of emitter
junction. The region of the emitter should have higher electrical conductivity,
than basis and collector. An impurity concentration in the region of the
transistor owe corresponds as:
_{}.
(6.1)
Depending on the order of alternation
of regions as an electrical conductivity distinguish structures pnp and npn
of types.
In a fig. 6.2 the structures pnp and
npn and their legend on circuitries are shown.
Fig. 6.2. Flat onedimensional model BT
and legends
Fig. 6.3. The circuits of insert of
bipolar transistors
As a device of an electric circuit,
transistor use by such fashion, that one of its electrodes is entering, and
anotheroutput. The third electrode is common concerning an input and exit.
Depending on what electrode is common, distinguish three circuits of insert of
the transistor: commonbase (CB), common emitter (CE) and common collector (CC)
(fig. 6.3).
6.2. Conditions of insert of the
transistor. Static parameters.
Physical processes
By
operation of the transistor the voltages from exterior power supplys are
affixed to its electrodes. Depending on polarity voltages affixed to
electrodes, each of pnjunctions the transistor can be switched on in direct
or in the opposite direction. Four conditions of insert of the transistor are
possible.
The table 6.1
Title 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 a splitting
contact. In a condition a splitting contact both pn junction are backswitched
on (highohmic state of a section EC). In electrodes of the transistor the
thermal currents backswitched of junctions flow past which are static
parameters of a condition the splitting contact. In each of three circuits of
insert of the transistor these parameters have particular magnitudes. Their
labels look like
for the circuit with CB  _{};
for the circuit with CE  _{};
for the circuit with CC  _{},
where the first index means an electrode,
in which the current flows past;
the second index – circuit of insert;
the third index  requirement in the rest
of the circuit:
о  absence of a current in the other
electrode  noload operation,
s  shortcircuit in the rest of the
circuit.
2. Condition of saturation. In
a condition of saturation both pnjunctions are directly switched on, the
junctions saturated with mobile carriers of a charge, their resistances are
small. The section EC has high conductance and it is possible to consider it
shortcircuited.
Static parameters are the saturation
currents in electrodes the transistor _{} and residual voltages _{}. A voltage ratio and currents
relevant electrodes give magnitudes of resistances of saturation:
_{}; _{}.
3. Fissile condition. In a fig.
6.4 the flat onedimensional model of the transistor is shown, which emitter
junction is switched on in a forward direction, and collector junction  in
backward. Such insert corresponds to a fissile condition, and the transistor
has intensifying properties. The principle of operation of the transistor in a
fissile condition grounded on use of the following phenomena:
 injection of majority carriers
through emitter junction;
 transport of injected carriers
through basis owing to diffusions and drift;
 recombination of nonequilibrium
carriers in basis;
 extractions of carriers from
basis in a collector by a region of collector junction.
The injection of carriers stipulates
transiting through emitter pnjunction of diffusive currents: hole _{} and electronic _{}.
In an external circuit of emitter the
current of injection flows past
_{},
(6.2)
where _{}  hole current of injection of the emitter;
_{}  electronic current of injection of the
emitter.
For transistor structure pnp of a
type the relation between admixtures in the emitter and basis is defined, as:_{}. Therefore _{}.
The relation between component of an
emitter current is evaluated coefficient of injection
_{} (6.3)
The injection of carriers from the
emitter in basis rises density
_{}
(6.4)
Appeared near to emitter junction 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 the
emitter  basis appears made and ensures course of an emitter current.
Magnification near to emitter junction the electron concentrations and vacant
electron sites are established by a lapse rate of densities nonequilibrium
carriers in basis _{} and
_{}. Under an operation of lapse rates densities there is a diffusive
driving of nonequilibrium vacant electron sites and electrons through basis
from the emitter to a collector.
Diffusion of vacant electron sites in
basis is attended their recombination with by electrons. On place 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 current
recombinations _{}.
As breadth of basis 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 sites injected by
the emitter in basis and which have reached collector backswitched junction, get
in its accelerating region and are thrown in region of a collector. The
collector current _{} is
established: _{}.
Process of transport of minority
nonequilibrium carriers through basis is evaluated by a transport coefficient _{}. Coefficient of transport depends from breadth of basis
_{} and diffusion
length of vacant electron sites _{}:
_{}
(6.5)
Than more vacant electron sites is
injected by the emitter in basis, than more them extract a collector,
augmenting a collector current. Therefore current _{} is proportional to an emitter current and is
termed current controlled of a collector, 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 in view of relations
(6.3), (6,5) is defined by the following formula:
_{}.
(6.7)
Opportunity of control of an output
current of the transistor by change entering current is the important property
of the bipolar transistor, allowing to use it as a fissile device of electronic
circuits.
Except for a controllable part of a
collector current _{},
in an electrode
collector the unguided part of a current 
thermal current backswitched of junction flows past. It is similar to a current
backswitched of a crystal diode and consequently has received a title of a
backward collector current _{}.
index c means, that it  current
backswitched of collector junction,
index b  the measurings occur in the
circuit with CB,
index 0  the measurings occur at _{} =0, i.e. Noload operation
on an input.
The direction of a backward collector
current _{} coincides
with a direction of a controllable part of a collector current and consequently
_{}. (6.8)
The current _{} in a circuit of basis is guided
towards to a base current of a recombination _{} and base current of injection _{}
_{}.
(6.9)
In an emitter circuit the current 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 for any
circuit of insert.
The similar processes occur in npn
the transistor to that by variance, that instead of vacant electron sites it is
necessary to speak about electrons and on the contrary. Positive directions of
direct currents and supply voltages, relevant to a fissile condition, are shown
in a fig. 6.3.
Reverse voltage affixed on collector
junction, it is much more voltages directly switched of emitter junction, and
the currents are equal emitter circuits and collector practically. Therefore
load power established variable component collector current, appears much more
power expended on control by a circuital current of the emitter, hence
transistor has intensifying properties. These qualities in a combination to a small
overall dimensions, high reliability, longevity and profitability have
stipulated wide application of transistors in an electron technology.
Fig. 6.4. Driving of carriers and currents
in BT (fissile condition)
In the circuit with CE and CC (fig.
6.3) a current basises becomes control current, and the equation of a collector
current (6.8) will be copied in the following aspect:
_{};
_{};
_{}.
(6.11)
where: _{}  transmission factor of a base current in
the circuit with CE:
_{}  unguided part of a collector current in the
circuit with CE, or through current of the transistor.
For the circuit with CC an output
current is the emitter current. Therefore
_{}
or
_{},where_{}. (6.12)
4. Inverse condition. In an
inverse condition emitter junction backswitched, and the collector junction is
under direct voltage. Therefore in comparison with a fissile condition in an
inverse condition the injection of carriers is carried out collector junction,
and extractions of carriers  emitter junction.
Practically emitter and collector vary by functions and places in the circuit.
For the circuit with CB
_{}.
(6.13)
here _{}  inverse coefficient of transmission.
As the area of emitter junction 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 coefficient of
transmission of a current
In the equation (6.7) for an
integrated (static) transmission factor of an emitter current _{}. Coefficient of injection _{} the efficiency of emitter
junction characterizes, and coefficient of diffusive transport _{} characterizes processes in
basis, diffusive transport and recombination of carriers, with which attends
this process; coefficient M is inlet for the account of processes in collector
junction and almost always M=1. The equation of a collector current _{}, where _{} is static parameter of
fissile condition of insert (fissile condition), displays link between direct
currents. Coefficient _{} is
defined by the formula _{} and
this formula displays link between stationary values of a control current _{} and value of an output
current _{}.
For variable signals, which amplitude
order much less grades of supply voltages, link between collector currents and
emitter is defined by derivation of a relation (6.7) as functions two arguments
in the conjecture _{} =const,
i.e.
_{}, or
_{}.
(6.16)
_{}  differential transmission factor of an
emitter current in circuit with CB, which always is more than integrated
coefficient _{}. Calculations display, that at major levels of injection, when _{} (see of the formula (6.1),
(6.4)), derivative _{} aspires
to zero and _{}. Therefore for the analysis of a major signal integrated (static)
coefficient _{} is
always used.
In consequent viewing is not done
variances between _{} and
_{}. Using a label _{}, but in each case the applications of these
magnitudes should be remembered a level of injection.
6.4. EbersMoll’s model
Links between currents and voltages in
the transistor for four conditions of insert are well compounded with
convenient and clear mathematical EbersMoll’s model, grounded on a dual
circuit 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 emitter and collector
junctions accordingly, metered at shortcircuit on exit and input accordingly (_{} =0 and _{} =0).
_{}.
(6.19)
where _{} and _{}  back currents of emitter and collector
junctions measured accordingly at abruption of a collector and the emitter.
With the account (6.18), (6.19) relations (6.17) are conversed to an aspect
_{};
(6.20)
_{};
(6.21)
_{}. (6.22)
Fig. 6.5. Equivalent nonlinear
EbersMoll’s model for BT
In computing methods of the analysis of
transistor circuits with the help of a computer the wide circulation was
received by nonlinear model of the GummelPun’s transistor, which grounded on
the solution of integrated relations for charges and links exterior electrical
performances a charge in basis of transistor structure. It is very precise model
explaining many physical effects, but its exposition needs major number of
parameters, so for the analysis in a wide frequency range 25 parameters are
necessary. The sequential simplification of GummelPun’s model eventually
reduces in the elementary EbersMoll’s model. Therefore at the analysis of the
concrete circuits it is necessary to search for the reasonable compromise
between an exactitude of the solution and complexity of model.