6.1. Device, constructive
technological features, circuit of insert

The bipolar transistor
terms a three-electrode semiconductor device with two or more interacting
electron-hole junction. In the transistor alternate as an electrical conductivity
three regions of a semi-conductor, for what in a homogeneous semi-insulating
substrate of silicon Si-i the methods of epiplanar technique shape regions of a
collector, basis and emitter, (fig. 6.1). For it in a plate Si-n, employee by a
collector, the method of a local diffusion (introduction of atoms of doping
substance in a chip of a semi-conductor through some part of its surface) forms
base region (Si-p). In this region also method of a local diffusion forms
emitter region (Si-n) 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 electron-hole (p-n) junctions - emitter and collector (on a title of
extreme regions of transistor structure).

Fig. 6.1. Planar n-p-n 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
semi-conductor 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
p-n-p and n-p-n of types.

In a fig. 6.2 the
structures p-n-p and n-p-n and their legend on circuitries are shown.

Fig. 6.2. Flat one-dimensional
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 another-output. The third electrode is common concerning an input
and exit. Depending on what electrode is common, distinguish three circuits of
insert of the transistor: common-base (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 p-n-junctions 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 p-n- junction
are backswitched on (high-ohmic state of a section E-C). 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:

î - absence of a current in the
other electrode - no-load operation,

s - short-circuit in the rest
of the circuit.

2. Condition of
saturation. In a condition of saturation both p-n-junctions are directly
switched on, the junctions saturated with mobile carriers of a charge, their
resistances are small. The section E-C has high conductance and it is possible
to consider it short-circuited.

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 one-dimensional 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 p-n-junction 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
p-n-p 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

minority carriers in basis.
Their density on boundary of emitter junction for p-n-p of structure is defined
by a relation

(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. No-load 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 n-p-n 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. Ebers-Moll’s model

Links between currents and
voltages in the transistor for four conditions of insert are well compounded
with convenient and clear mathematical Ebers-Moll’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 short-circuit 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
Ebers-Moll’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 Gummel-Pun’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 Gummel-Pun’s
model eventually reduces in the elementary Ebers-Moll’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.