lecture 2 fundamentals
TRANSCRIPT
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KEEE 2224 Electronic Devices
Week 2:
Fundamentals of Electronic Devices
Lecturer : Dr. Sharifah Fatmadiana Wan Muhd Hatta
To arrange for appointments for small group discussions :
Email: [email protected]
mailto:[email protected]:[email protected] -
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Week 2: learning outcomes
By the end of this week, student should be able
to :
1. Describe the mechanism of charge carrier
mechanism
2. Describe on energy band diagrams, density
states band diagram.
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Basic Semiconductor Physics
3
Periodic Table and the Semiconductor Materials
Types of Solids
Atomic Bonding
Imperfections and Impurities
Doping
Electrical Conductions in Solids :
Electron and holes
Energy-band model
Density of States Function
Semiconductor in equilibrium
Charge carriers in Semiconductor
Position of Fermi Energy Level
Carrier Transport
Carrier drift, Carrier DiffusionConductivity, Resistivity
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Band Diagram: Potential vs Kinetic
Energy
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Electrostatic Potential
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Energy Bands
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Basic convention:
EC
Ev
Eref
K.E.
P.E.
+E
+V
Kinetic energy:
Potential Energy:
CEEEK ..
refC
refC
EEq
V
EEqVEP
1
..
Electric field:dx
dE
qdx
dVV C
1D1inor,
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Electric Field
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Examples of energy band structures:
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Si GaAs
Based on the energy band structure, semiconductors can beclassified into:
Indirect band-gap semiconductors (Si, Ge)
Direct band gap semiconductors (GaAs)
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Direct VS Indirect Bandgaps
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Photogenerationband-diagramatic description:
Momentum and energy conservation:
E
k
Eg
Phonon emission
Phonon absorption
Indirect band-gap Semics.
Virtualstates
Ec
EV
E
kDirect band-gap Semics.
Eg
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Fermi-Dirac Distribution Function
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The conduction band in a piece of semiconductor consists of many
available, allowed, empty energy levels. When calculating how many
electrons will fill these, we consider two factors:
How many energy levels are there within a given range of energy,
How likely is it that each level will be populated by an electron.
The likelihood in the second item is given by a probability function
called the Fermi-Dirac distribution function. f(E) is the probability
that a level with energy E will be filled by an electron, and the
expression is:
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Density of States
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for electrons in the conduction band
for holes in the conduction band
The integration of the product of the density of states g(E) and the Fermi-
Dirac distribution function f(E) gives the carrier distribution over the
energy range above or below the bandgap (see next slide)
g(E)gives the
distribution ofenergy levels
(states) as a
function of energy.
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Density of States
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Intrinsic semiconductor. (a) Schematic band diagram. (b) Density of
states. (c) Fermi distribution function. (d) Carrier concentration.
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or g(E)
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The energy band diagram with the position of the
Fermi level EFas a function of the doping type
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Boltzmann Approximation
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C
V
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Equilibrium Carrier Concentration
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Density of states functionin the CB. If we assume
m*n=m0, hence at T=300K,
Nc=2.8x1019cm-3
C i d E ilib i C i
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Continued Equilibrium Carrier
Concentration
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Exercise: Fermi LevelThe probability that a state is filled at the conduction band edge (Ec) is precisely
equal to the probability that a state is empty at the valence band edge (Ev). Where
is the Fermi level located?
Answer: The Fermi function,f(E), specifies the probability of electrons occupying
states at a given energy E. The probability that a state is empty (not filled) at a
given energy E is equal to 1 f(E). Here we are told
f(Ec) = 1f(Ev)
Since
And,
Hence, we can conclude
or
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Quasi Fermi Level
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Describes the population of electronsseparately in the conduction
bandand valence band, when their populationsare displaced
from equilibrium.
This displacement could be caused by the application of an external
voltage, or by exposure to light of energy, which alter the populations
of electrons in the conduction band and valence band.
The displacement from equilibrium is such that the carrier populationscan no longer be described by a single Fermi level, however it is possible
to describe using separate quasi-Fermi levels for each band.
http://en.wikipedia.org/wiki/Electronhttp://en.wikipedia.org/wiki/Conduction_bandhttp://en.wikipedia.org/wiki/Conduction_bandhttp://en.wikipedia.org/wiki/Valence_bandhttp://en.wikipedia.org/wiki/Populationshttp://en.wikipedia.org/wiki/Thermodynamic_equilibriumhttp://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Thermodynamic_equilibriumhttp://en.wikipedia.org/wiki/Populationshttp://en.wikipedia.org/wiki/Valence_bandhttp://en.wikipedia.org/wiki/Conduction_bandhttp://en.wikipedia.org/wiki/Conduction_bandhttp://en.wikipedia.org/wiki/Electron -
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Example: Quasi Fermi Level
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d h
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Basic Semiconductor Physics
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Periodic Table and the Semiconductor Materials
Types of Solids
Atomic Bonding
Imperfections and Impurities
Doping
Electrical Conductions in Solids :
Electron and holes
Energy-band model
Density of States Function
Semiconductor in equilibrium
Charge carriers in Semiconductor
Position of Fermi Energy Level
Carrier Transport
Carrier drift, Carrier Diffusion
Conductivity, ResistivityKEEE 2224 Electronics Devices
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Intrinsic Carrier Concentration, ni
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Intrinsic Fermi Level, Ei
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Charge Carrier Concentration
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For Si, ni = 1e10 cm-3
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Thermal Equilibrium
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Majority and Minority Carriers
N-type material, the electron is called majority carrier and hole the minority
carrier
P-type material, the hole is called majority carrier and electron the minority
carrier.
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Example: Extrinsic Semic
Silicon at T=300K is doped with arsenic atoms
such that the concentration of the electrons is
n0=7 x 1015 cm-3.
(a) Find Ec-EF
(b) Finc EF-Ev
(c) po
(d) Which carrier is the minority carrier?
(e)Ev-EF
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Anwers
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d) Holes
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Example A new semiconductor is to be designed. The
semiconductor is to be p-type and doped with 5 x 1015
cm-3 acceptor atoms. Assume complete ionization and
assume Nd=0. The effective density of states functions
are Nc=1.2 x 10
18
cm
-3
and Nv=1.8 x 10
19
cm
-3
at T=300Kand vary as T2. A particular semiconductor device
fabricated with this material requires the hole
concentration to be no greater than 5.08 x 1015cm-3at
T=350K. What is the minimum bandgap energyrequired in this new material?
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Answer
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B i S i d t Ph i
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Basic Semiconductor Physics
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Periodic Table and the Semiconductor Materials
Types of Solids
Atomic Bonding
Imperfections and Impurities
Doping
Electrical Conductions in Solids :
Electron and holes
Energy-band model
Density of States Function
Semiconductor in equilibrium
Charge carriers in Semiconductor
Position of Fermi Energy Level
Carrier Transport
Carrier drift, Carrier Diffusion
Conductivity, ResistivityKEEE 2224 Electronics Devices
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Free Carriers in Semiconductors
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Three primary types of carrier action occur
inside a semiconductor:
drift
diffusionrecombination-generation
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Electron as Moving Particles
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Where mn* is the electron effective mass
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Example: Kinetic Energy of ElectronThe initial velocity of an electron is 107 cm/s. If the kinetic
energy of the electron increases by E=10-12 eV, determine theincrease in velocity. Hint:
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Carrier Effective Mass
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In an electric field, , an electron or a hole accelerates:
Electron and hole conductivity effective masses:
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Carrier Scattering
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Mobile electrons and atoms in the Si lattice are
always in random thermal motion.
lattice scattering or phonon scattering
increases with increasing temperature
Average velocity of thermal motion forelectrons: ~107 cm/s @ 300K
Other scattering mechanisms:
deflection by ionized impurity atoms
deflection due to Coulombic force betweencarriers
only significant at high carrier concentrations
The net current in any direction is zero, if no electric
field is applied.KEEE 2224 Electronics Devices
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Example: Scattering Three scattering mechanisms are present in a particular
semiconductor material. If only the first scattering mechanismwere present, the mobility would be 1=2000 cm
2/V-s, is only
the second mechanism were present, the mobility would be
2=1500 cm2/V-s and if only the third mechanism were
present, the mobility would be 3=500 cm2
/V-s . What is thenet mobility?
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Carrier Drift
When an electric field (e.g. due to an externally applied voltage)
is applied to a semiconductor, mobile charge carriers will be
accelerated by the electrostatic force. This force superimposes
on the random motion of electrons:
39
Electrons driftin the direction opposite to the electric field(current flows). Hence, because of scattering, electrons in a
semiconductor do not achieve constant acceleration.
However, they can be viewed as quasi-classical particles
moving at a constant average drift velocity Vd.KEEE 2224 Electronics Devices
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Small devices=> non-stationary transport
velocity overshoot=> faster devices (smaller transit time)
0
5x106
1x107
1.5x107
2x107
2.5x107
3x107
0 0.5 1 1.5 2 2.5 3
E=1kV/cm
E=4kV/cm
E=10kV/cmE=20kV/cm
E=40kV/cm
E=100kV/cm
Drif
tvelocity
[cm
/s]
time [ps]
T = 300 K
Silicon
Velocity overshoot effect
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Diffusion
Particles diffuse from regions of higher
concentration to regions of lower concentration
region, due to random thermal motion.
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Diffusion Current
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D is the diffusion constant, or diffusivity.KEEE 2224 Electronics Devices
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Total Current = Drift + Diffusion
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Einstein Relationship between D and
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Under equilibrium conditions,JN= 0 andJP= 0
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Example : Diffusion Constant
What is the hole diffusion constant in a sample
of silicon with p= 410 cm2 / V s ?
Answer:
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WherebykT/q = 26 mV at room temperature with
boltzman constant , k = 1.3806488 10-23m2kg s-2K-1 ,
T=300K, and q= 1.6e19 C.
Basic Semiconductor Physics
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Basic Semiconductor Physics
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Periodic Table and the Semiconductor Materials
Types of Solids
Atomic Bonding
Imperfections and Impurities
Doping
Electrical Conductions in Solids :
Electron and holes
Energy-band model
Density of States Function
Semiconductor in equilibrium
Charge carriers in Semiconductor
Position of Fermi Energy Level
Carrier Transport
Carrier drift, Carrier Diffusion
Conductivity, ResistivityKEEE 2224 Electronics Devices
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Carrier Mobility (Electron Momentum)
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With every collision, the electron loses momentum
Between collisions, the electron gains momentum
where mn = average time between scattering
events
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Carrier Mobility
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if
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Drift Current
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vd t A = volume from which all holes cross plane in time t
p vd
t A = # of holes crossing plane in time t
q p vdt A = charge crossing plane in time t
q p vdA = charge crossing plane per unit time = hole current
Hole current per unit areaJ = q p vdKEEE 2224 Electronics Devices
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Conductivity
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The conductivity of
a semiconductor isdependent on
the carrier
concentrations
and mobilities
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El i l R i
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Electrical Resistance
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EXAMPLE : Resistivity
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Consider a Si sample doped with 1016/cm3 Boron. What is itsresistivity?
Answer:
And for Si, ni = 1e10 cm-3
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Example: Dopant Compensation
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Consider the same Si sample, doped additionally with1017/cm3Arsenic. What is its resistivity?
Answer:
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R i i f E ti i F d t l
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Revision of Equation in Fundamental
Electronic Physics
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Basic equations for Semic. device operation:
Maxwells equations Minority-carrier equations
Continuity equations
Poissons equation
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Relaxation to Equilibrium State
Consider a semiconductor with no current flow
in which thermal equilibrium is disturbed by the
sudden creation of excess holes and electrons.
The system will relax back to the equilibriumstate via R-G mechanism:
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Mi it C i E ti
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Minority Carrier Equation
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Consider minority hole carrier injection at x=0
C ti it E ti
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Continuity Equations
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The continuity equation describes a basic concept, namely that a change in carrier density
over time is due to the difference between the incoming and outgoing flux of carriers plus
the generation and minus the recombination.
Poisson Equation
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Poisson Equation
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Important Constants
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Important formulae that govern the conductivity of a
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p f g y f
semiconductor :
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The intrinsic carrier concentration: ii pn
(same density of free electrons and holes in an intrinsic semiconductor).
With n, prespectively the electron and hole density ; ND,Arespectively the donor
and acceptor doping density (concentration).
Withn, pthe mobility of electrons, resp. holes.
m
q
With qthe charge, tthe average time between collisions (scattering), mthe mass.
Important formulae that govern the conductivity of a
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p f g y f
semiconductor :
Ev
vthe drift velocity and Ethe electric field. Electrons and holes have
opposite velocities.
In a homogeneously doped semiconductor or a semiconductor with a constant
carrier density, applying an electric field will cause drift currents to flow.
WithAthe cross sectional area perpendicular to the current flow, Eis the
applied electric field
When carrier gradients exist in a semiconductor, diffusion currents will occur.
With Dn,pthe diffusion constant of electrons respectively holes,xis the
direction of carrier propagation.
Important formulae that govern the conductivity of a
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The Einstein equation gives the relationship between the diffusion constant and
the mobility of the carrier:
p f g y f
semiconductor :
e
kTD
with, kthe Boltzman constant, Tthe temperature in Kelvin.
In the general case where both concentration gradients and electric fields arepresent the total current is the sum of both drift and diffusion currents:
Important formulae that govern the conductivity of a
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Another basic equation in semiconductor devices is the Poisson equation
p f g y f
semiconductor :
With Vthe electrostatic potential, the charge density as a function ofx;p& n
the free hole, resp. electron density which are both a function ofxas well as of Vand N-A and N
+Dthe concentration of ionised doping atoms which are a function
ofx.