Transcript Feature Selection/Extraction for Classification Problems

전자 회로 1
Lecture 4 (Diode)
2009. 03.
임한조
아주대학교 전자공학부
[email protected]
이 강의 노트는 전자공학부 곽노준 교수께서 08.03에 작성한 것으로 노트제공에 감사드림.
Overview
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Ideal Diode model
(Intrinsic) Semi-conductor characteristic
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Doping
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Majority/minority Carrier (Electrons & holes)
PN-junction
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Thermal ionization
Current components (Drift + Diffusion)
Bulti-in voltage (Barrier voltage)
Depletion region
Biasing (Reverse, Breakdown, Forward)
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The Ideal Diode
Diode symbol
i-v characteristic
Reverse direction
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Forward direction
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Simple application: Rectifier
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Another application: Logic gates
Y = AB C
Y = A + B + C
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Example
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Start from an appropriate assumption on a diode mode.
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Whether D1 is conducting or insulating.
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Nonlinear Elements (Semi-conductor)
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What is SEMI-conductor?
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Acts as a conductor in a situation.
Acts as an insulator in other situation.
In what situation?
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Depends on the input voltage or currents (and output)
 Input-output characteristic curve.
(voltage-current / current-current / voltage-voltage …)
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How to make a semi-conductor?
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Silicon (Si), Germanium (Ge)
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column 4 (covalent bonds)
+ impurities (column 3 or 5)
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Different types of solid
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Intrinsic silicon (Si)
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Silicon: our primary focus
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Atom number = 14
14 electrons in 3 shells: 2 ) 8 ) 4
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i.e., 4 electrons in outer “bonding” shell
Silicon forms a strong covalent bonds with 4 neighbors.
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Thermal ionization
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At room temperature, some of the covalent bonds are
broken by thermal ionization.
 Free electrons & holes  current conduction
ni = # of free electrons/holes = 1.5*10^10 carrier/cm^3 (at 300K)
Cf) # of atoms = 5*10^22 atoms/cm^3
 only very small number is ionized.
n  p  ni
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Temperature dependency
ni2  BT 3e  EG / kT
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(3.36)
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Current (moving carriers)
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Diffusion
Diffusivity
dp
J p  qDp
dx
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dn
J n  qDn
dx
(3.37)
(3.38)
Drift: by electric field
 drift   p E Mobility
(3.39)
J p drift  qp p E
(3.40a)
J n drift  qnnE
(3.40b)
J drift  q( p p  nn )E
(3.40c)
Dn/Dp = un/up ~= 2.5
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Resistivity
  1/ q( p p  nn )
Dn
n

Dp
p
 VT
(3.41)
(3.42)
Electrons are easier to move than holes
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Charge Drift  Current
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In thermal equilibrium, carriers are not stand still
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Brownian motion = collision
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Mean free time btw collision
But it goes nowhere (on average)
with no electric field
Application of E-field
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F=±qE
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Holes: +, Electrons: -
v(t) = at = ±qEt/m
m: mass of a charge
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Velocity randomization by collision
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Average velocity & Drift current
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Doped (extrinsic) semiconductor
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Donor (Group 5) – phosphorus
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N-type
ND: concentration of donor atoms
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Majority carrier:
By recombination:
Minority carrier:
Majority carrier concentration is
constant, while minority carrier
concentration does depend on
temperature.
Acceptor (Group 3) – boron
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P-type
NA: concentration of acceptor atoms
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pn- Junction (Diode)
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Electrons diffuse from the N-side to the P-side and recombine with holes
at the boundary. Holes diffuse from the P-side to the N-side and
recombine with electrons at the boundary. There is a region at the
boundary of charged atoms – called the space-charge region (also
called the depletion region; no mobile carriers in this region)
An electric field is created which results in a voltage drop across the
region – called the barrier voltage or built-in potential
In equilibrium, diffusion
current (ID) is balanced by drift
current (IS): ID = IS
Drift current comes from
(thermal) generation of
electron-hole pair.
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E-field and Built-in potential
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Junction Built-in voltage
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With no external biasing, the voltage across the
depletion region is
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Typically at room temperature, V0 ~= 0.6~0.8 V
Note that there is no measurable potential difference
between the n-type and p-type materials of pn junction
when in equilibrium. The electrochemical potentials
(Fermi levels) are the equal.
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Width of depletion region
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PN-junction
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Real Diode
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Abrupt PN-junction
Separate view
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Diffusion starts and
then balanced by drift
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Depletion approx.
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Space charge density & E-field
• Gauss equation
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Potential (Voltage)
• It is known that (we do not derive here)
Reference point @ n0 = p0 = ni
• Voltage barrier
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• Can also be calculated by
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Depletion width
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Overall charge neutrality:
Potential continuity at x = 0:
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Depletion width:
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Contact potential
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Potential difference across structure must be zero!!!
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Reverse-Bias
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Reverse-bias
 Increase the built-in potential:
V0  V0+VR
 Increased depletion region
 Decrease in diffusion current (ID)
while drift current (Is) remains the same.
 I = IS – ID : almost constant
Wdep
 2 s   1
1 
 

  V0  VR 

 q   NA ND 
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(3.52)
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Breakdown (large reverse bias)
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Zener breakdown (Vz < 5V)
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Increased depletion region
 larger electric field
 break covalent bonds
 electron-hole pair
Avalanche breakdown (Vz > 7V)
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Minority carrier with large kinetic energy
 collide with atoms
 break covalent bonds
 electron-hole pair
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Forward-Bias
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Very important!!!
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Summary: Forward-Bias
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Decrease the built-in potential
 Increase the number of carriers able to cross the barrier
 Diffusion current (ID) increase
While drift current (Is) remains the same
 Current flows from p to n
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Review
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Open circuit:
ID = IS
Reverse-bias:
I = IS - ID ~= IS
Breakdown
(large reverse-bias):
almost constant V
Forward-bias:
I = ID – IS ~=ID
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Current exponentially
increases
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Reference: Constants
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Thermal voltage
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Boltzmann constant (k)
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PV = NkT = nRT
k = 1.38×10−23 joule/kelvin
= 8.62×10−5 eV/kelvin.
= 1.38×10−16 erg/kelvin.
Magnitude of electron charge
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VT = kT/q = 0.25mV
q = 1.6×10-19 C
Permittivity of silicon
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