Physics of Semiconductors 7th 2016.5...Syllabus 1. Classical transport, Transport in pn junctions 2....
Transcript of Physics of Semiconductors 7th 2016.5...Syllabus 1. Classical transport, Transport in pn junctions 2....
Physics of Semiconductors 7th 2016.5.30
Shingo Katsumoto Institute for Solid State Physics,
University of Tokyo
Syllabus
1. Classical transport, Transport in pn junctions 2. Junction transistors, field effect transistors 3. Hetero-junctions and quantum structures Quantum wells, wires and dots 4. Coherent quantum transport Landauer-Buttiker formalism Interference devices 5. Single-electron effects Charges and spins in quantum dots 6. Quantum Hall effect 7. Spin physics, spintronics, topological insulators
Lecture notes http://kats.issp.u-tokyo.ac.jp/kats/
http://kats.issp.u-tokyo.ac.jp/kats/semicon3/
Outline today
Classical Transport Boltzmann equation Drift current, diffusion current Drude formula, Einstein relation Electromagnetic effect (Hall effect) Heat transport Thermal conductivity Thermoelectric effect Transport in pn junctions Thermal equilibrium Current-voltage characteristics Response to illumination (minority carrier injection)
Classical transport: Boltzmann equation (1)
๐
๐
(๐,๐) 6-dimensional phase space
Distribution function ๐(๐,๐, ๐ก)
๐๐
๐๐
Classical transport: Boltzmann equation (2)
Boltzmann equation:
Collision term
Relaxation time approximation:
โ 0 (stable state) around thermal equilibrium
Expansion to the first order of dt
Relaxation time
Currents: Particle flows(fluxes)
๐: Anisotropic distribution = Current
Diffusion current Drift current
Drift current:
Drift current for Fermi-degenerated system
๐(๐)
๐
๐๐ฅ
๐๐ฆ
โ๐๐น
Drude formula
Maxwell distribution: ๐0 โ ๐ดexp โ๐ธ/๐๐ต๐
: Drude formula for metals
: Drude formula
Diffusion current, Einstein relation
Relaxation time approximation:
: Diffusion constant
Einstein relation
Heat transport, thermoelectric effect Heat flux density:
Thermal conductivity:
Seebeck effect:
A B B
A B B
: Seebeck coefficient
Heat transport, thermoelectric effect (2)
A B
Peltier effect J J
Electric current J : continuous
Heating at A-B interface QAB
Heat flux Q : discontinuous
: Peltier coefficient
Thomson effect
:Thomson coefficient
A J J x
Material specific
Kelvin (Thomson) relations
A B B
๐ ๐ + ฮ๐
Quasi-static
๐๐ ๐๐
๐๐ด๐ต
:First law
:Second law
: Kelvin relations
Unit charge
Seebeck coefficient as material constant
Material specific
ฮ๐ A
B
Thermocouple
Boltzmann equation and thermoelectric constants
Replace with ๐0
Boltzmann equation and thermoelectric constants (2)
๐๐ฅ = 0 Drift current Diffusion current :balance
Peltier device
Ch.2 Transport in pn junctions
Transport in pn junctions
Equilibrium
pn junction : spatially non-uniform
Diffusion current: Entropy increase
Drift current: Internal energy decrease
Balance: Minimize Free energy
pn junction thermodynamics
Consider electrons
+ +
+ + +
donors
eโ
eโ
eโ eโ
eโ
Vacuum for electrons
diffusion
โ โ โ โ โ
+ + + + +
voltage (polarization) โ energy cost
๐น = ๐ โ ๐๐
Voltage (internal energy cost) Diffusion (entropy)
Minimization of ๐น โ Built-in (diffusion) voltage ๐๐๐
Built-in potential
Einstein relation
mobility
Rigid band model:
Current-Voltage characteristics equilibrium
External voltage V
Current-Voltage characteristics (2)
๐ ๐ฅ = ๐๐exp โ๐ธ๐ ๐ฅ โ ๐๐(๐ฅ)
๐B๐
๐๐ ๐ฅ = ๐ธ๐ ๐ฅ + ๐B๐ln๐(๐ฅ)๐๐
quasi-Fermi level
Diffusion equation
Minority carrier diffusion length
๐ฟ๐ = ๐ท๐๐๐ , ๐ฟโ = ๐ทโ๐๐
generation
๐๐ ๐ฅ = ๐ฟ๐0exp๐ฅ + ๐ค๐๐ฟ๐
+ ๐๐0
๐ธF๐ โ ๐ธF๐ = ๐๐
๐ ๐ โ ๐๐๐2๐ท๐๐ฟ๐๐๐ด
+๐ทโ๐ฟโ๐๐ท
exp๐๐๐B๐
โ 1
Response to illumination
G(x) =G constant
๐๐ ๐ฅ = ๐ฟ๐0exp๐ฅ + ๐ค๐๐ฟ๐
+ ๐๐0 + ๐บ๐๐
๐ฟ๐0 = ๐๐0 exp๐๐๐๐ต๐
โ 1 โ ๐บ๐๐
๐ = ๐0 exp๐๐๐๐ต๐
โ 1 โ ๐๐บ ๐ฟ๐ + ๐ฟโ
jm Short circuit current
Vm
fill factor ๐น๐น = ๐๐ ๐๐๐oc ๐sc
โ +
Majority carrier โ ignore increase in density Minority carrier โ huge increase in density
Spin Seebeck effect
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K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa and E. Saitoh, Nature 455, 778 (2008).
Spin Seebeck effect
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