Semiconductors and Atomic Models

• Semiconductors form the basis of most modern electronic systems like computers, communication networks, and control systems.
• The ability to control the movement of electrons in solids underlies semiconductor device engineering.

Atomic Models

• Democritus (~460-370 BC): Proposed early atomic ideas.
• Dalton (1805): Developed a modern atomic theory.
• Thomson (1904): Introduced the Plum Pudding Model.
• Rutherford (1911): Developed a model with a central nucleus.
• Bohr (1913): Added quantized energy levels to the atomic model.
• Chadwick (1932): Experimentally proved the existence of neutrons.
• Late 1920s: The Modern Atom Theory (Quantum Theory of Atoms) arose with contributions from Heisenberg and Schrödinger.

Bohr Model for Hydrogen Atom

• The force between two charges is given by F=(Q1*Q2)/(4πε₀r²), which simplifies to F = -q²/(4πε₀r²) for the hydrogen atom.
• Potential energy is related to force by F = -∇Ep = -dEp/dr.
• The change in potential energy is dEp = dEp(r) = -Fdr = (q² dr)/(4πε₀r²).
• The definition of potential states that Ep(r = ∞) = Evac.
• The integral of potential energy is ∫(Evac to Ep) dEp = ∫(r to ∞) (q² dr)/(4πε₀r²).

Potential Energy Diagram

• The potential energy is given by Ep = Evac - q²/(4πε₀r).
• The potential energy diagram represents the potential energy of an electron near a positive point charge and it looks likes there is a drop to 0 when r = 0.
• Quantization and Bohr Radius

Bohr Radius

• The velocity is expressed as vn = q² / (4πε₀ħn).
• Kinetic energy equals EKₙ = (1/2)mvₙ² = mq⁴ / (2(4πε₀)²n²ħ²).
• Potential energy equals EPₙ = Evac - mq⁴ / ((4πε₀)²n²ħ²).
• Total energy is En = EKₙ + EPₙ = Evac - mq⁴ / (2(4πε₀)²n²ħ²).
• Energy is quantized, meaning it has discrete values related to the quantum number n.
• The value n = 1 indicates the smallest radius and energy in the Bohr model.

Quantized Energy States

• First four Bohr energies and orbital radii for hydrogen atom:
• E1 = Evac - 13.6 eV, r1 = 0.0526 nm
• E2 = Evac - 3.40 eV, r2 = 0.212 nm
• E3 = Evac - 1.51 eV, r3 = 0.477 nm
• E4 = Evac - 0.850 eV, r4 = 0.848 nm
• Energy of a state must always be an energy difference between the energy of the state and a known reference point like Evac - E.

Calculation Example:

• Total energy equals En = Evac - (1/n²) * (13.6 eV)
• Electron volts, a unit of energy, is the energy gained by an electron accelerating through 1 volt of electric potential, where 1 eV = 1.60 × 10⁻¹⁹ joules.
• The Bohr radius equals rₙ = 0.0526n² nm.

Covalent Bonding

• Two-dimensional covalent bonding in a crystalline solid shows the surface crystal showing direction C.
• Potential energy for an electron in that crystal illustrates Ep between the rows of atoms.

Ionic Bonding

• Silicon forms covalent bonds and other elements in column IV of the periodic table are expected to do the same.
• Compound semiconductors, like Gallium Arsenide (GaAs), have arrangements of elements.
• Gallium is in column III with three outer shell electrons, while Arsenic is in column V with five; As and AS are shown.

Semiconductor Properties

• Electronic properties defined are the vacuum energy Evac, electron affinity X, ionization energy Y, and the energy gap Eg.
• Electron affinity and band gap differ different materials at 300 K:
• Eg for Si at is at 1.12 (eV)
• Eg for GaAs is at 1.43 (eV)
• At absolute zero (0 K), electrons occupy the lowest possible energy state, and valence band states are filled in a perfect semiconductor.

Electron Movement

• Movement of many electrons is regarded as the movement of one positively charged "hole."
• Holes arise from empty states in the valence band at nonzero temperatures.

Material Types

• Energy band diagrams illustrate insulators, semiconductors, and metals. Insulators have a large forbidden gap, semiconductors have a smaller gap, and metals have overlapping bands.

Crystal Structures

• Crystallographic planes and directions are indicated as (001) or [100].
• Cubic crystals may be simple, face-centered, or body-centered.