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Chapter IIChapter IISemiconductor PhysicsSemiconductor Physics

半導體物理

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Basic Semiconductor PhysicsBasic Semiconductor Physics

• Carrier Transport– Drift

– Diffusion

– Generation and Recombination

– Current density equation

• Thermionic Emission

• Tunneling

• High Field Effects

• Heterojunction

• Quantum Well

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Carrier DriftCarrier Drift

Carrier Drift (飄移 )– Carrier transport in an applied electric

field

– vn = -nE

– vp = pE n (p): carrier mobility (移動率 )

(cm2/V-s)

– Drift Current Density

J = (qnn + qpp)E

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Mobility and Resistivity (Conductivity)Mobility and Resistivity (Conductivity)

-1 = L-1 + I

-1 = -1 = [q(n n + pp)]-1

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ScatteringScattering

• Lattice Scattering– Thermal vibration of lattice L ~ T-3/2

• Impurity Scattering– Carrier scattered by impurities (donors or acceptor) I ~ T3/2/NT

The main factors in influence of resistance of solid-state materials are:① Carrier concentration

② scattering

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Carrier DiffusionCarrier Diffusion

Carrier Diffusion (擴散 )– The carriers tend to move from a

region of high concentration to a region of low concentration.

– Diffusion Current Density

Jn = qDn (dn/dx)

Dn: diffusivity (diffusion coefficient)

Einstein relation: Dn = ( kT/q)n)

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Induced Electric Field (Built-in Field )in a semiconductorInduced Electric Field (Built-in Field )in a semiconductor

• For a semiconductor that is non-uniformly doped with donor impurity atoms and is in thermal equilibrium, there exists an induced electric field Ex in this semiconductor.

Built-in voltage in a p-n junction diode Accelerating field in a graded-base bipolar junction transistor

dx

xdN

xNe

kTE d

dx

1

EC

EF

EV

x

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Current Density EquationsCurrent Density Equations

• Jn = qnnE + qDn (dn/dx)

• Jp = qppE - qDp (dp/dx)

• J = Jn + Jp

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Carrier Generation and RecombinationCarrier Generation and Recombination

Direct generation and recombination of electron-hole pairs:

(a) at thermal equilibrium.

(b) under illumination

Decay of photoexcited carriers

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Indirect Generation-Recombination ProcessIndirect Generation-Recombination Process

Indirect G-R process at thermal equilibrium

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其他重要的專有名詞其他重要的專有名詞

• Carrier lifetime• Diffusion Length• Recombination center• Surface recombination• Auger recombination

– Auger process: an electron and a hole recombine, giving up the excess energy to an electron (producing a “hot” electron), and then the hot electron eventually loses its energy by emitting phonons (i.e. giving up heating)

– Auger recombination is an important non-radiative recombination, especially in materials with narrow bandgap.

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Thermionic EmissionThermionic Emission

• 當電子的能量大於 qX 時 ,它就可以被熱離子式地發射至真空能階 .

• 金屬與半導體之間主要的載子傳輸機制

• 單載子元件 (unipolar device)的電流形成模型

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TunnelingTunneling

• The transmission coefficient T

– There is a finite probability that a particle impinging a potential barrier will penetrate the barrier.

kaV

E

V

ET 2exp116

00

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High-field effectsHigh-field effects

• Saturation velocity in Si

• Transferred-electron effect in GaAs

• Avalanche Breakdown

– Ionization

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Avalanche BreakdownAvalanche Breakdown

• Zener breakdown– field ionization

– heavily doped p/n region

– VBD < 5V

– VBD has a NTC

• Avalanche breakdown– impact ionization

– Low or medium doped p/n region

– VBD > 7V

– VBD has a PTC

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Transferred-electron effectTransferred-electron effect

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HeterojunctionHeterojunction

• Junction formed by two different semiconductors (different EG)

• Under thermal equilibrium:

– Gradient of EF = 0

– Continuous vacuum level

– Specific EC and EV

EC = χ2 –χ1

EV = EG – (χ2 –χ1)

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Quantum WellQuantum Well

• Quantum structures– 2D: Quantum Well– 1D: Quantum Wire– 0D: Quantum Dot

• Quantum-sized effect• Quantum-confined effect

• Quantum Well– W-N-W heterojunction multi-layer

structure with a very thin narrow-bandgap semiconductor

– Energy band split into discrete quantized energy levels

– Red laser diode in GaAs

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2DEG in Heterojunction Structure2DEG in Heterojunction Structure

• 2DEG– Two-Dimensional Electron Gas

– Electrons will spill over the AlGaAs into the GaAs and become trapped in the potential well, called 2DEG

– Very high mobility electrons with negligible impurity scattering

• Devices in which conduction occurs parallel to the interface can be construct from 2DEG structure.

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2DEG in Quantum Well2DEG in Quantum Well

Quantum Well Heterojunction