ELEC 435 ELECTRONICS I
Bipolar Junction Transistors
Physical Operation
Sec 5.1 of Sedra & Smith
Equations for intrinsic silicon:
Resistivity of a bar of intrinsic Si:
ρ = 1 / [ q ( p μ p + n μ n) ]
where
μp
μn
= mobility of holes = 480 cm2/V.sec
= mobility of electrons = 1350 cm2 /V.sec
q = magnitude of the electron charge = 1.6 X 10-19 coulomb
n =
p =
concentration of free electrons (carriers/cm3)
concentration of free holes (carriers/cm3)
For intrinsic Si:
n = p = ni
ni = BT3 eEG/kT
EG = bandgap energy = 1.12 electro volts (eV) for Si
k = Boltzmann’s constant = 8.62 X 10 -5 eV/oK
T = absolute temperature in oKelvin
B = material dependent parameter = 5.4 X 1031 for Si
ni
= 1.5 X 1010 carriers/ cm3 at T = 300 oK
For a pn junction we have
i = Is ev / nVT
VT = kT/q thermal voltage
k = Boltzmann’s constant = 8.62 X 10 -5 eV/oK
T = absolute temperature in oKelvin
q = magnitude of the electron charge = 1.6 X 10-19 coulomb
VT = 25 mV
at T = 300 oK
Bar of intrinsic Si with a non-uniform hole concentration p
Diffusion current:
J p = - q Dp ( dp /dx)
Note that the slope is negative, resulting in a positive current in the x
direction.
Jp = current density in Amp/cm2
Dp = diffusion constant or diffusivity of holes. Typical value = 12 cm2/sec
Bar of intrinsic Si with a non-uniform electrons concentration n
Diffusion current:
Jn = q Dn ( dn /dx)
Jn = current density in Amp/cm2
Dn = diffusion constant or diffusivity of electrons. Typical value = 34cm2/sec
Drift Current
• Drift current occurs when an electric field, E, is applied across
a piece of Si.
• Free e- and h+ are accelerated by the electric field E, and
acquire a velocity components called drift velocity.
• The current density due to the drift velocity is :
Jn(drift) = q n μn E ;
Jp(drift) = q p μp E
Holes will drift in the same direction that E
μp = mobility of the h+, typically 480 cm2/V
μn = mobility of the e-, typically 1350 cm2/V
The total drift current is:
J(drift) = q (n μn + p μp ) E
therefore the resistivity ( Ω . cm ) is:
ρ = 1 / [ q ( p μ p + n μ n) ]
Einstein relationship:
Dn /μn = Dp /μp = VT
Doping a Silicon Crystal
In a n-type material (phosphorous impurity), the concentration of
free electrons (nno) is
nn0 ≈ ND
In a p-type material (Boron impurity), the concentration of free
holes (ppo) is
pp0 ≈ NA
In thermal equilibrium the product of electrons and hole
concentrations remains constant
nn0 pn0 = ni2
pn0 = ni2 / ND
np0 pp0 = ni2;
np0 = ni2 / NA
pn0 = minority carriers (holes) in the n-type material
np0 = minority carriers (electrons) in the p-type material
Simplified Structure if the npn transistor
Emitter-Base Junction (EBJ)
Collector-Base Junction (CBJ)
• In Bipolar Structures, there are two types of carriers:
electrons and holes.
• Both carriers participate in the current-conduction process.
BJT Modes of Operation
Mode
EBJ
CBJ
Cutoff
Reverse
Reverse
Active
Forward
Reverse
Reverse active Reverse
Forward
Saturation
Forward
Forward
Note:
BJT = Bipolar Junction Transistor
Operation of the npn transistor in the Active Mode
VBE causes the p-type base to be forward biased
VCB causes the n-type collector to be reverse-biased
Current Flow: due mainly to diffusion currents 1
• Component1: electrons injected from the emitter into the base
• Component2: holes injected from the base into the emitter
Generally
ND >> NA, therefore
component 1 >> component 2
Currents due to thermally generated minority carriers, are usually
very small and are neglected in this analysis.
1Note:
iE = electrons from E to B + holes from B to E
iE is out of the Emitter ( i.e. opposite to the direction of the
electron flow)
e- that are injected from E to B:
• are minority carriers in the p-type base region
• because the base is usually very thin, the concentration will be highest
(np(0)) at the emitter side and lowest (zero) at the collector side.
The reason for the zero concentration at the collector side of the base is
that the VCB causes the e- to be swept across the CBJ depletion region.
The Collector Current
• Most of the diffusing
depletion region.
e- will reach the boundary of the Collector-Base
• Because the Collector is more positive than the Base ( vCB volts),
these successful e- will be swept across the CBJ depletion region
into the Collector.
• They will be “collected” to constitute the collector current iC
ic = Is evBE /VT
Is = AE q Dn np0 / W
np0 = ni2 / NA
saturation current
Is = AE q Dn ni2/(NA W)
AE = cross-sectional area of the base-emitter junction
Dn = electron diffussivity in the Base
W = effective width of the base
The Collector Current (cont.)
• Note that the magnitude of ic is independent of vBE, as long as
the Collector is positive with respect to the Base, the e- that reach
the Collector side of the Base region will be swept into the Collector
and register as Collector current.
• Note that the saturation current, Is , is inversely proportional to
the Base width W and is directly proportional to the area of the
EBJ.
• Typical range of Is is 10-12 to 10-18 Amp
• Because Is is proportional to ni , it is a strong function of
temperature, approximately doubling for every 5oC rise in
temperature.