Power Electronics
Part 1: Introduction and pn junction
Department of Astronautical,
Electrical and Energetic Engineering
Prof. Giulio De Donato
Introduction
Power Electronic Concepts (1/2)
Power Electronic Concepts (2/2)
Basic Semiconductor Physics
• free carrier density:
– metals (Cu, Ag, etc) : 1023 cm-3 → conductivity 107 S/m
– insulators (quartz, Al oxide, etc): 103 cm-3 → 10-10 S/m
– Semiconductors (Si, Ge, etc): 108-1019 cm-3 → 100-10-3 S/m
• In semiconductors, free carrier density can be changed by orders of
magnitude by introducing impurities in the material or by applying
electric fields.
Silicon crystal
(second most
abundant element
in the earth’s crust)
Electrons and Holes
Text
Text
•
•
•
•
•
n2i
3
Eg
kT
⇡ BT e
thermal ionization equilibrium:
Eg - energy gap 1.12 eV for Si
k - Boltzmann’s constant 8.62x10-5 eV/K
B - 5.4x1031 1/(K cm3) for Si
at room temperature ni is about 1.5x1010 carriers/cm3, i.e. 1 in every
billion atoms in Si is ionized (A silicon crystal has about 5x1022 atoms/
cm3) !!!!
Doped Semiconductors
• elements from column III (e.g. B, Al, Ga) are acceptors.
• elements from column V (e.g. P, As, Sb) are donors.
• law of mass action:
p0 n0 = n2i
• space charge neutrality:
• in p-type material:
p0 + N d = n 0 + N a
Na >> ni
Nd ⇡ 0
p0 ⇡ N a
n2i
n0 ⇡
Na
• the above expression for n0, shows that the minority
carrier density is strongly dependent on T.
Recombination
• Recombination mechanisms:
– direct recombination of electrons and holes.
– trapping of carriers by impurities.
• Excess hole density δp must be equal to excess electron density δn.
• simple rate equation:
d( n)
=
dt
n
⌧
τ - excess-carrier lifetime
τ0 is the lifetime for δn<<nb
• for large δn
(>1017
cm-3 =
nb), τ decreases as δn increases:
• furthermore, as T increases, τ also increases.
• short τ - higher on state losses.
• long τ - longer switching times for minority carrier devices.
⌧=
⌧0
1+
( n)2
n2b
Drift and Diffusion
• Free carriers move via two
mechanisms:
– drift due to an impressed electric
field;
– diffusion due to variations in the
spatial density of free carriers.
• Drift component of current density:
Jdrif t = qµn nE + qµp pE
• Diffusion component of current
density:
dn
dp
Jdif f = Jn + Jp = qDn
qDp
dx
dx
• Diffusion constants and mobility
constants are related by the Einstein
equation:
Dp
Dn
kT
=
=
µp
µn
q
pn-Junctions
• Some of the majority carriers on either
side of the junction will diffuse across it to
the opposite side, where they are in the
minority.
• This creates a space charge layer on
either side of the junction, due to the
immobile ionized impurities that are left
behind.
• The resulting space charge density gives
rise to an electric field.
Potential Barrier at Thermal Equilibrium (1/2)
• The electric field can be calculated by
using Poisson’s equation.
• For a step junction, Poisson’s equation
is:
dE
=
dx
qNa
✏
qNd
=
✏
xp < x < 0
0 < x < xn
• integrating from x = -xp to x = xn the
expressions for the electric field are:
qNa (x + xp )
✏
qNd (x xn )
=
✏
E(x) =
xp < x < 0
0 < x < xn
Potential Barrier at Thermal Equilibrium (2/2)
• Integrating the field across the
depletion layer yields the potential
barrier or contact potential:
Z xn
qNa x2p + qNd x2n
E(x)dx = c =
2✏
xp
• An equilibrium is reached when the
carrier flux caused by diffusion is
counterbalanced by the carrier flux
due to drift.
• In equilibrium, the hole flux and
electron flux separately sum to zero.
• The contact potential cannot be
s
measured!!!!!
• Width of depletion layer: W0 = 2✏ c (Na + Nd )
qNa Nd
Reverse Bias of pn-Junction
• When junction is reverse biased, the
potential barrier increases to ϕc+V.
• The width of the depletion layer
increases to W(V) = xn(V)+xp(V).
• The total negative charge in the p-type
region must equal the total positive
charge in the n-type region of the
depletion layer:
qNa xp (V ) = qNd xn (V )
• total step junction depletion layer width:
p
W (V ) = W0 1
(V /
c)
• Probability of any majority carrier
diffusing across the junction becomes
vanishingly small.
•
Reverse saturation current Is due to gradients in minority carrier densities.
Forward Bias of pn-Junction
•
•
•
•
When pn junction is forward biased, the
potential barrier is reduced and the
depletion layer shrinks.
The equilibrium between drift and
diffusion is upset in favour of diffusion.
carrier injection in the regions
immediately adjacent to the depletion
layer.
minority-carrier diffusion length for
electrons
p in p-type region:
Ln =
•
for holes in n-type region:
Lp =
•
•
D n ⌧n
p
D p ⌧p
minority carrier density at the edge of
the depletion layer:
n2i qV
pn (0) =
e kT
Nd
The minority carrier densities will vary by orders of magnitude as the
voltage is changed relatively little.
I-V Characteristic of a pn-Junction
• In steady state forward-bias conditions, the
excess-carrier distributions remain constant
in time.
• The carriers that are lost by recombination
are replaced by the forward-bias current
density:
Qn
Qp
J=
⌧n
+
⌧p
• expressions for Qp and Qn:
h
Qp = q pn (0)
h
Qn = q np (0)
n2i i
Lp
Nd
n2i i
Ln
Na
• i-v characteristic of the pn-junction:
i
h L
Lp ih qV
n
2
J = qni
+
e kT 1
N a ⌧n
N d ⌧p
Breakdown
•
•
•
Possible breakdown mechanisms:
- Zener effect if VBD < 5V (not present in power diodes!!)
- avalanche effect if VBD > 7V
Zener breakdown occurs when the electric field in the depletion layer
increases to the point where it can break the covalent bonds and
generate electron-hole pairs. These are swept by the electric field
across the pn-junction and constitute a reverse current across the
junction. Once the Zener effect starts, a large number of carriers can
be generated with a negligible increase in junction voltage.
Avalanche breakdown occurs when minority carriers that cross the
depletion layer under the influence of the electric field gain sufficient
kinetic energy to be able to break covalent bonds in atoms with
which they collide. The carrier liberated in this process, know as impact
ionization, may have sufficiently high energy to be able to instigate an
avalanche effect that results in large reverse currents with negligible
change in the voltage drop across the pn-junction.
s
elec. field and voltage for av. BD: EBD =
2
2Eg m
✏(Na + Nd )EBD
BVBD ⇡
qt2
2qNa Nd