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Semiconductor crystals

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Presentation on theme: "Semiconductor crystals"— Presentation transcript:

1 Semiconductor crystals
Overview The concept of hole and effective mass Intrinsic semiconductor Doped semiconductor p-n junction Refs for history: 半導體的故事, by 李雅明 矽晶之火, by M.Riordan and L.Hoddeson M.C. Chang Dept of Phys

2 Elements Compounds Bonding becomes more ionic (at 300K) Ge Si GaAs GaN
energy gap (eV) 0.67 (i) (i) (d) 3.39 (d) lattice type Diamond Diamond Zincblend Semiconductor is insulator at 0 K, but because of its smaller energy gap (diamond = 5.4 eV), electrons can be thermally excited to the conduction band more easily. Si-based device can endure higher working temperature than Ge-based (75 oC) device (Si has a larger band gap) For history of semiconductor industry, see 矽晶之火

3 Direct band gap (GaAs, GaN…)
Indirect band gap (Si, Ge…) =Eg =Eg+  Direct band gap semiconductor can emit light efficiently (1μm=1.24 eV)

4 The invention of blue-light LED
GaN can emit blue light because of its large band gap (3.4 eV) First blue-light LED: Shuji Nakamura 1989 First blue-light laser: Shuji Nakamura 1997 發明前 中村秀二 發明後 See Interview with Nakamura: Scientific American, July, 2000

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6 Overview The concept of hole and effective mass Intrinsic semiconductor Doped semiconductor p-n junction

7 A filled band does not carry current (Peierls, 1929)
Electric current density For crystals with inversion symmetry, n(k)= n(-k)  electrons with momenta ħk and -ħk have opposite velocities  no net current in equilibrium A nearly-filled band ∴ unoccupied states behave as +e charge carriers

8 The concept of holes (Peierls, 1929)
If an electron of wavevector ke is missing, then k= -ke. Alternatively speaking, a hole with wavevector kh is produced (and kh= -ke). The lower in energy the missing electron lies, the higher the energy of the whole system. If the energy of a filled valence band is set to zero, then h k The missing electron

9 The concept of effective mass
Near the bottom of a conduction band, the energy dispersion is approximately parabolic Reciprocal effective mass matrix The electron near band bottom is like a free electron (with m*). For a spherical FS, m*ij=m*δij, one m* is enough. In general, electron in a flatter band has a larger m* Negative effective mass: If E(k) is (e.g. top of valence band) then m*<0  electron (-e) with negative m* = hole (+e) with positive m*

10 For ellipsoidal FS, there can be at most three different m. s Eg
For ellipsoidal FS, there can be at most three different m*s Eg. the FS of Si is made of six identical ellipsoidal pockets L T For Si, Eg = 1.1 eV, mL = 0.9 m, mT = 0.2 m (it’s more difficult for the electron to move along the L direction because the band is flatter along that direction)

11 More band structures and Fermi surfaces
Common features Useful parameters mL /mT mHH/mLH Δ Si 0.91/ / eV GaAs / eV

12 Overview The concept of hole and effective mass Intrinsic semiconductor Doped semiconductor p-n junction

13 Density of states and carrier density
At room temperature, ε-μ >> kBT, electron density in conduction band: Top of valence band is set as E=0 hole density in valence band:

14 Carrier density and energy gap Chemical potential
In intrinsic semiconductor, the density of intrinsic carriers depends only on the energy gap. The 2nd term is very small because kBT<<EG (For Si, the atom density is 5×1022cm-3.)

15 Extrinsic carriers by doping

16 Impurity level: Bohr atom model
The ionized impurity atom has hydrogen-like potential, (m  m*, ε0  ε) Dielectric constant of Si = 11.7 (Ge=15.8, GaAs=13.13) Effective mass for Si =0.2 m Therefore, the donor ionization energy = 20 meV. Bohr radius of the donor electron, For Si, it's about 50 A (justifies the use of a constant ε)

17 Conduction band Valence band Impurity levels in Si Energy-band point of view

18 The law of mass action When the doping density >> ni, we can simply ignore ni (for majority carrier). Then the density of minority carrier is determined by the law of mass-action.

19 Change of chemical potential

20 Overview The concept of hole and effective mass Intrinsic semiconductor Doped semiconductor p-n junction (extra)

21 Equilibrium B.G. Streetman, Solid State Electronic Devices

22 Equilibrium With external bias Rectification
B.G. Streetman, Solid State Electronic Devices


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