semi-conductor & diodesnicadd.niu.edu/~piot/phys_375/lesson_7.pdf20 60 100 140 i d i s for v d
TRANSCRIPT
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P. Piot, PHYS 375 – Spring 2008
Semi-Conductor & Diodes
• Semi-Conductor– Some Quantum mechanics refresher– Band theory in solids: Semiconductor, insulator and
conductor– Doping
• Diode– p-n junction– Diode types– applications
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P. Piot, PHYS 375 – Spring 2008
Introduction
• In the next few lessons we will discuss electronics components that are semiconductors
• A semiconductor is something between a conductor and an insulator (actually very similar to insulator)
• In Solid State Physics a useful way to illustrate the properties of solids to intro-duce the concept of “bands”
• The “bands” concept comes from Quantum Mechanics
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P. Piot, PHYS 375 – Spring 2008
Quantum Mechanics “refresher”
• A model of bounded electron in a solid consist in representing the “bounding” force by a potential.
• One simple model is to consider a square infinite potential well
• particle is trapped in the potential well• Schrodinger’s equation
Wave function
Conditions at boundaries:
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P. Piot, PHYS 375 – Spring 2008
• Let’s solve the previous equation (where )
• So the solution in view of the boundary conditions finally takes the form
• And the possible energies are
Quantum Mechanics “refresher”
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P. Piot, PHYS 375 – Spring 2008
Case of many electrons
• If we have N electrons and try to trap them in an infinite quantum well, the minimum possible energy of the electron of the “top” electron is given by the Fermi energy (assume T=0 K)
• At a given temperature, the electron distribution follow the Fermi-Dirac distribution:
Enrico Fermi (1901-1954)
Paul Dirac (1902-1984)
mLhNE f 32
2
=
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P. Piot, PHYS 375 – Spring 2008
Fermi-Dirac distribution
• F-D distribution of the form:
• Limiting values:
( ) 11
)/( += − kTf e
E µε
0lim
)1)/((11
1lim )/(0
=
>>→+
=
∞→
−→
f
kTf
E
kTe
E
ε
µεµ
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P. Piot, PHYS 375 – Spring 2008
Solids Band Theory
• Real potential in a crystal is a series of potential well (not infinite and not simple “square function”)
• The allowed energies for the electron are then arranged as a series of “bands”
• Fermi Energy?
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P. Piot, PHYS 375 – Spring 2008
Differences between conductor, semiconductor and insulator
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P. Piot, PHYS 375 – Spring 2008
Semiconductor and Fermi Energy
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P. Piot, PHYS 375 – Spring 2008
• Addition of an impurity can create additional state within an energy gap.
• Depending on the impurity type:– Can add an electron: p type– Can add a hole: n type
Semiconductor: Doping
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P. Piot, PHYS 375 – Spring 2008
pn junction
• If p- and n-type semiconductors are in contact (junction), the system behaves very differently from a p or n semiconductor
• The main characteristic is that current will flow in one direction but not the other
• Local electron/hole recombination at the junction contact is theunderlying mechanism:
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P. Piot, PHYS 375 – Spring 2008
A bipolar p-n junction: The diode
• If p- and n-type semiconductors are in contact (junction), the system behaves very differently from a p or n semiconductor
• Current can only pass in one direction
Id
Vd
Forward biasing(“Vd≥0”), the diode (ideally) actsas a short (i.e. perfect conductor)
Reversed bias (Vd<0) diode = open circuit
Id
Vd
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P. Piot, PHYS 375 – Spring 2008
A bipolar p-n junction: The diode
assume steady-state regime
Vd-2 -1.5 -1 -0.5 0 0.5 1
20
60
100
140
Id
Is
■ For Vd <0, the diode acts as a good insulator : Is ~ 1 pA - 1µA , the “inverse” current, Is , increase with temperature
Linear behavior
■ For Vd >> ~0.7, current increase quickly and linearly w.r.t. Vd”Id is not proportional to Vd: (there is a threshold voltage~ Vo)
Vo
−
≅ 1exp
T
dsd V
VIIη
■ for: Vd ∈[0,~ Vo] : exponential increase of currentVT = k • T/ek = 1,38 10-23 J/K= Boltzmann constante= 1.6 10-19Coulomb, T temperature in °KelvinIs = inverse current
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P. Piot, PHYS 375 – Spring 2008
Operational Limits
■ Maximum reverse voltage
Vmax typically 10-20 Volts
! Can lead to diode destruction!
Vmax = « P.I. V » (Peak Inverse Voltage) or « P.R.V » (Peak Reverse Voltage)
Id
Vd
Vmax
PIV
Vo
A diode can only withstand a certain power andwe should make sure VdId=Pmax
■ Power limitation
VdId=Pmax
■ Temperature can strongly influence diode operation
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P. Piot, PHYS 375 – Spring 2008
Typical values : VZ ~1-100 V , Imin ~0,01- 0,1mA
This diode is designed to operated around Vz, the reverse break down voltage (whichis a well defined value for these diodes)
-Imax
Imax : maximum possible current (due to power)
-Vz
VZ : Zener Voltage (by definition: VZ >0)
-Imin
Imin : min current (absolute value) where the I-V characteristic becomes linear (this is the ZenerDomain)
Id
Vd
Characteristics
Zener Diode
Zener from Clarence Melvin Zener(1905-1993) Bell Labs
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P. Piot, PHYS 375 – Spring 2008
Light emitting diodes (ou LED)
■ Principle : The current flow induce lgith emission
Work under direct biasing (V > Vo)
light intensity ∝ current Id
! Do not work for Si diode
Vo ≠ 0.7V ! (GaAs (red): ~1.7V; GaN (blue): 3V)
Big business! Nowdays higher light intensity makes diode suitable for lighting applications
Common diode types
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P. Piot, PHYS 375 – Spring 2008
Under reverse bias, the diode produces an electric current proportional to the light intensity
Schottky diode
Shottky diode is a diode with a very low threshold voltage Vo along with a very fast response time.
« Varicap » diode
The varicap diode is a diode with variable capacitance. It uses a variation of Ct withVd in reverse bias operation.
Photodiode
Common diode types
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P. Piot, PHYS 375 – Spring 2008
Application: Clipping
Parallel Clipping
VeVg
Circuit to be
protected
Rg
Ze
(diode // charge)
Series Clipping
Ve(t)Circuit to
be protected
ZeVg
Rg
Ve cannot be much higher than Vo
Ie cannot be negative
• The purpose of Clipping is to protect circuit either by avoiding a certain sign of current or by limiting the maximum voltage
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P. Piot, PHYS 375 – Spring 2008
How do we find V and I across a diode??
• Consider the circuit we want to compute Id and Vd
Val RLVR
Id
Id , Vd, ?Vd
Id and Vd obey Kirchhoff’s law
Id et Vd follows the diode characteristics I(V) of the other component
So the operating point has to satisfy the two aforementioned conditions
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P. Piot, PHYS 375 – Spring 2008
How do we find V and I across a diode??
■ Kirchoff’s law:L
dald R
VVI −=→L
Val/RL
Val
« load line »
Id
Vd
I(V) diode characteristics
Q= operating pointIQ
VQ
Q
knowing Id(Vd) one can graphically find the operating point of a diode (actually of any components)Can also attempt an analytical estimate but need a function to describe the I-V curve