Semiconductors and Devices

The electrical behavior of solids is explained by energy band theory, which originates from Pauli’s Exclusion Principle. In an isolated atom, electrons occupy discrete energy levels. When atoms come together to form a crystalline solid, these energy levels split and merge into continuous bands of allowed energies.

Valence Band and Conduction Band

• Valence Band (VB): The highest energy band completely or partially filled with valence electrons at absolute zero (0 K). Electrons in this band do not contribute directly to electrical conduction.
• Conduction Band (CB): The next higher permitted band above the valence band. At 0 K, it is completely empty. Electrons that gain enough energy to jump into this band become free electrons and contribute to the electric current.
• Forbidden Energy Gap (E_g): The energy separation between the top of the valence band and the bottom of the conduction band. No electron can exist in this gap.

Classification based on Energy Bands

• Conductors: The valence and conduction bands overlap (E_g = 0). A large number of free electrons are available for conduction even at room temperature.
• Insulators: The forbidden gap is exceptionally wide (E_g > 3 eV). For instance, Diamond has an E_g of approximately 5.4 eV. Electrons cannot cross this barrier.
• Semiconductors: The forbidden gap is narrow (E_g < 3 eV). At 0 K, they behave as perfect insulators. At room temperature, thermal energy allows a fraction of electrons to cross the gap into the conduction band. For Silicon, E_g = 1.1 eV, and for Germanium, E_g = 0.7 eV.

Intrinsic and Extrinsic Semiconductors

Intrinsic Semiconductors

Intrinsic semiconductors are chemically pure crystals without any deliberate foreign atoms.

• Generation of Charge Carriers: When thermal energy breaks a covalent bond, an electron is excited from the valence band to the conduction band.
• Concept of Holes: The vacancy left behind by the electron in the valence band behaves as a virtual particle with a positive charge (+e), termed a hole.
• Carrier Concentrations: The number of free electrons (n_e) in the conduction band is precisely equal to the number of holes (n_h) in the valence band. This is known as intrinsic carrier concentration (n_i).

Extrinsic Semiconductors

The intrinsic conductivity of semiconductors is too low for practical electronic applications. To enhance conductivity, precise quantities of specific impurities are introduced through a process called doping. The impurity atoms are known as dopants.

N-Type Semiconductors

• Dopant: Pentavalent elements (5 valence electrons) such as Phosphorus (P), Arsenic (As), or Antimony (Sb). These are called donor impurities because they donate an extra electron to the crystal lattice.
• Carrier Profile: The majority charge carriers are electrons, while the minority charge carriers are holes.

P-Type Semiconductors

• Dopant: Trivalent elements (3 valence electrons) such as Boron (B), Aluminum (Al), Indium (In), or Gallium (Ga). These are called acceptor impurities because they create a vacancy or hole that can accept an electron.
• Carrier Profile: The majority charge carriers are holes, while the minority charge carriers are electrons.

The Law of Mass Action

Under thermal equilibrium, the product of the free electron concentration and the hole concentration is a constant and is independent of the amount of donor and acceptor doping.

Semiconductor Junction Devices

Formation of the P-N Junction

When a P-type semiconductor crystal is brought into intimate atomic contact with an N-type semiconductor crystal, a P-N junction is formed. This forms the baseline for almost all semiconductor electronics.

Key Phenomena at the Junction

• Diffusion: Due to the concentration gradient, electrons diffuse from the N-side to the P-side, and holes diffuse from the P-side to the N-side.
• Depletion Region: Near the junction, diffusing electrons and holes recombine, leaving behind uncompensated immobile donor ions (positive) on the N-side and immobile acceptor ions (negative) on the P-side. This region devoid of mobile charge carriers is the depletion region.
• Barrier Potential (V₀): The immobile ions create an internal electric field directed from the N-region to the P-region. This field opposes further diffusion of majority carriers. The potential difference across the depletion layer is the barrier potential (approx. 0.7 V for Silicon and 0.3 V for Germanium).

Biasing a P-N Junction

Advanced Applications and Optoelectronic Devices

Semiconductor devices have been engineered to interact with light or operate in specific breakdown zones to perform highly specialized roles.

Rectifiers

Rectifiers exploit the unidirectional current property of a forward-biased diode to convert Alternating Current (AC) to Direct Current (DC).

• Half-Wave Rectifier: Conducts current only during the positive half-cycle of the AC input signal. Its maximum theoretical efficiency is 40.6%.
• Full-Wave Rectifier: Conducts current during both half-cycles of the AC input using either a center-tapped transformer or a four-diode bridge configuration. Its maximum theoretical efficiency is 81.2%.

Zener Diode

• Mechanism: Designed to operate permanently under reverse bias conditions in the Zener breakdown region. Breakdown occurs due to a strong internal electric field rupturing covalent bonds (Zener effect) or due to high-velocity carriers colliding with atoms (Avalanche effect).
• Application: Once breakdown voltage (V_z) is reached, the voltage across the Zener diode remains strictly constant even if the current through it changes significantly. This makes it ideal as a voltage regulator in power supplies.

Optoelectronic Junction Devices

1. Light Emitting Diodes (LEDs)

• Operation: Forward-biased p-n junction.
• Mechanism: Electrons from the N-side cross the junction and recombine with holes on the P-side. During recombination, energy is released in the form of photons.
• Material Fact: Standard Silicon or Germanium diodes release energy as heat (infrared range). LEDs use compound semiconductors like Gallium Arsenide Phosphide (GaAsP) or Indium Gallium Nitride (InGaN) to emit visible light.

2. Photodiodes

• Operation: Reverse-biased p-n junction equipped with a transparent window.
• Mechanism: When photons with energy greater than the bandgap (hν > E_g) strike the depletion region, electron-hole pairs are generated. The internal electric field separates them before they can recombine, causing an increase in the reverse saturation current.
• Application: Used in optical switching, CD/DVD players, and smoke detectors.

3. Solar Cells (Photovoltaic Devices)

• Operation: No external bias is applied. It generates its own Electromotive Force (EMF) when exposed to solar radiation.
• Mechanism: Operates on three basic processes: Generation of electron-hole pairs due to light absorption near the junction; Separation of electrons to the N-side and holes to the P-side by the built-in electric field; Collection of these carriers by front and back metal contacts to power an external load.

Transistors and Digital Logic

Bipolar Junction Transistors (BJTs)

A BJT is a three-terminal semiconductor device consisting of two p-n junctions formed by sandwiching a thin layer of one type of semiconductor between two thicker layers of the opposite type.

• Configuration Types: NPN and PNP. The NPN configuration is more common because electrons have higher mobility than holes, resulting in faster switching speeds.
• The Three Regions:
  • Emitter: Moderately sized, heavily doped to inject a large number of charge carriers into the base.
  • Base: Extremely thin and lightly doped to ensure most injected carriers pass through to the collector without recombining.
  • Collector: Physically largest section, moderately doped, designed to collect the charge carriers and dissipate heat.

Field Effect Transistors (FETs and MOSFETs)

Unlike BJTs, which are current-controlled and involve both majority and minority carriers, Field Effect Transistors are unipolar devices where conduction is carried out by majority carriers only.

• Control Mechanism: The voltage applied to a third terminal (Gate) creates an electric field that alters the conductivity of a conducting channel between the Source and the Drain.
• MOSFET (Metal-Oxide-Semiconductor FET): Employs an insulating layer of Silicon Dioxide (SiO₂) beneath the gate. It boasts an exceptionally high input impedance, minimizing power wastage. This property makes it the fundamental element used to build microprocessors, memory chips, and CMOS image sensors.