Chapter II Semiconductor Physics 半導體物理

Basic Semiconductor Physics Carrier Transport Drift Diffusion Generation and Recombination Current density equation Thermionic Emission Tunneling High Field Effects Heterojunction Quantum Well

Carrier 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 = (qnn + qpp)E

Mobility and Resistivity (Conductivity)  = -1 = [q(n n + pp)]-1 -1 = L-1 + I-1

Scattering Lattice Scattering Impurity 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: Carrier concentration scattering

Carrier 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)

Induced 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 EC EF EV x

Current Density Equations Jn = qnnE + qDn (dn/dx) Jp = qppE - qDp (dp/dx) J = Jn + Jp

Carrier Generation and Recombination Direct generation and recombination of electron-hole pairs: at thermal equilibrium. under illumination Decay of photoexcited carriers

Indirect Generation-Recombination Process Indirect G-R process at thermal equilibrium

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.

Thermionic 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

Tunneling The transmission coefficient T There is a finite probability that a particle impinging a potential barrier will penetrate the barrier.

High-field effects Saturation velocity in Si Transferred-electron effect in GaAs Avalanche Breakdown Ionization

Avalanche Breakdown Zener breakdown Avalanche 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

Transferred-electron effect

Heterojunction 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)

Quantum Well Quantum structures Quantum-sized effect 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

2DEG in Heterojunction Structure 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.

2DEG in Quantum Well Quantum Well Heterojunction