• Semiconductor
• Semiconductor Physics Recap
  • Semiconductor Materials
    • Elemental: Diamond Cubic Structure
    • Compound: Zinc Blende Structure
  • Crystallographic Notation
  • Energy Band
  • Density of States:
  • Concentration of Carriers
    • Hole
  • Doping
  • Thermal dynamics
    • Fermi-Dirac Distribution
    • Maxwell-Boltzman Distribution:
• Summary

Semiconductor#

• crystalline 单晶硅: wafar
• amorphous 太阳能电池

Semiconductor Physics Recap#

Semiconductor Materials#

Materials with intermediate conductivity and features sensitive to physical variables.

Atomic structures:

• Crystalline: Highly ordered atomic structure, wafar
• Polycrystalline: A cluster of multiple crystalline grains.
• Amorphous: Disordered atomic structure, PV cells.

Types:

• Elemental
  • IV group: Ge at first, then Si, recently C.
• Compound
  • III+V group, pronounced three-five semiconductors: AsGa, AlP.

Elemental: Diamond Cubic Structure#

价电子 valence electrons. 共价键 covalent bound.

Each Si atom has 4 nearest neighbors. Lattice constant: 5.431$\AA$ $(10^{-10}m)$.
Number of atoms in a unit cell: $4 + 8/8 + 6/2 = 8$
Density of silicon atoms: 8 atoms / cell volumn = $5\times 10^{22}$ atoms/cm3.
Inpurity consentration: $10^{12} - 10^{19}$ atoms/cm3.

Compound: Zinc Blende Structure#

III-V compound. GaAs, GaP, GaN. High electron mobility, for high-speed ICs.

Crystallographic Notation#

• (h k l): crystal plane 晶面，截距倒数通分取分母
• {h k l}: equivalent plane 晶面族
• [h k l]: direction
• <h k l>: equivalent direction
  h: inverse x intercept. k: inverse y. l: inverse z.

立方晶系中6个等同的{100}，12个等同的{110}，8个等同的{111}晶面。

Atom density is higher viewed in <100> direction -> lower carrier speed on that plane.

Energy Band#

泡利不相容：同一状态（主量子数n+角量子数l+磁量子数m+自旋量子数s）最多被一个费米子占据。费米子：遵循费米—狄拉克统计的粒子。

电子排布$3p^2$：第三层（主量子数n=3）p亚层（角量子数l=1）有2个电子。

$Si: [Ne]\quad3s^2\quad3p^2$。自由空间独立原子，3p层所有轨道在一个能级，3s层在另一个。两个Si原子靠近，形成8个价电子的系统，3p/3s能级分别分裂成两个。N个Si原子组成晶格，3p/3s层各有2N个填充的状态（每个价电子占据一个），形成价带，也各有2N个空状态，形成导带。

• Valence Band: Highest nearly-filled band.
• Conduction Band: Lowest nearly-empty band
• $E_c$: Bottom edge of the conduction band.
• $E_v$: Top edge of the valence band.
• $E_G$: Separation between $E_c$ and $E_v$.

Band gap of common materials:

• $Si: E_G = 1.12 eV$ @ 300K\
• $SiO_2: E_G = 9 eV$\
• Metals have no band gap (conduction band is partially filled)\
• Graphene = 0\

When temp rises, the lattice transform a little bit, resulting in a changed solution of quantum mechanics, and a shrunk band gap -> temp sensors.

Measurement: minimum energy of photons that is absorbed by the semiconductor. 价带顶电子吸收能量跃迁到导带。

Density of States:#

$g(E)\rm{d}E$ = number of states per cm3 in the energy range between $E$ and $E+\rm{d}E$.

Electron effective mass 电子有效质量, $m_n^*$

Concentration of Carriers#

To change the concentration of carriers:

• Adding impurity atoms (dopants)
• Applying an electric field
• Changing the temperature
• Irradiation 辐照

Intrinsic (本征) carrier concentration of silicon: $n_i \approx 10^{10} cm^{-3}$

In a pure semiconductor,

In a doped semiconductor, at thermal equilibrium (热平衡状态) Law of Mass Action:

Hole#

Mobile positive charge associated with a half-filled covalent bond.

Holes and electrons are not necessarily in pairs. 极子器件.

Doping#

Substituting a Si atom with a special impurity atom. (Group III/V)

• Donor ionization energy: Separation between $E_c$ and donor level $E_D$
• Accepttor ionization energy: $E_A - E_v$
  大概几十个meV，随杂质原子序数增大而提高

Donor/acceptor level are close to the $E_c$ or $E_v$ so ionization is easy.

• Ionized donor concentration: $N_D$
• Ionized acceptor concentration: $N_A$
• Net dopant concentration: $N_D - N_A$

Charge neutrality condition: $N_D + p = N_A + n$

When $N_D >> N_A$

• Majority carrier: the most abundant.\
• Minority carrier: the least abundant.

Thermal dynamics#

Fermi-Dirac Distribution#

The probability that energy level E is occupied. Occupied = by electron, empty = occupied by hole.

There is only one Fermi level in a system at equilibrium (multiple with externel electrical field),

Maxwell-Boltzman Distribution:#

简并（Degenerate）半导体：必须用F-D分布，非简并可以用M-B分布。

Summary#

• Thermal equilibrium: No external forces, no electric field, no magnetic field, no mechanical stress, no light.