🔌Intro to Electrical Engineering Unit 9 – Semiconductor Basics in Electrical Engineering

What Are Semiconductors?

• Materials with electrical conductivity between conductors (metals) and insulators (ceramics)
• Conductivity can be controlled by doping, temperature, and applied electrical fields
• Most commonly used semiconductors are silicon (Si) and germanium (Ge)
• Semiconductors form the basis for modern electronics (transistors, diodes, integrated circuits)
• Unique properties arise from their atomic structure and energy band configuration
  • Valence band and conduction band separated by a small energy gap
  • Electrons can be excited from valence to conduction band, creating mobile charge carriers
• Intrinsic semiconductors are pure materials with equal numbers of electrons and holes
• Extrinsic semiconductors are doped with impurities to create excess electrons (n-type) or holes (p-type)

Atomic Structure and Band Theory

• Semiconductors have a crystal lattice structure with covalent bonding between atoms
• Energy bands form due to the periodic potential of the lattice and wave-particle duality of electrons
• Valence band is the highest occupied energy band at absolute zero temperature
• Conduction band is the lowest unoccupied energy band, separated from valence band by an energy gap ($E_g$)
• Fermi level ($E_F$) represents the energy level with a 50% probability of being occupied by an electron
  • In intrinsic semiconductors, $E_F$ lies near the middle of the bandgap
  • In n-type semiconductors, $E_F$ is closer to the conduction band
  • In p-type semiconductors, $E_F$ is closer to the valence band
• Electrons can be excited from valence to conduction band by absorbing energy greater than $E_g$
• Holes are created in the valence band when electrons are excited, acting as positive charge carriers

Types of Semiconductors

• Elemental semiconductors consist of a single element (Si, Ge)
• Compound semiconductors are formed by combining elements from groups III and V (GaAs, InP) or II and VI (CdTe, ZnO)
  • Offer unique properties such as direct bandgap, high mobility, and optoelectronic capabilities
• Organic semiconductors are carbon-based materials (polymers, small molecules) with semiconducting properties
• Wide bandgap semiconductors have $E_g$ greater than 2 eV (SiC, GaN, diamond)
  • Suitable for high-power, high-temperature, and high-frequency applications
• Narrow bandgap semiconductors have $E_g$ less than 1 eV (InSb, HgCdTe)
  • Used in infrared detectors and low-energy photonic devices
• Amorphous semiconductors lack long-range atomic order (a-Si:H)
  • Used in thin-film transistors and solar cells

Doping and Carrier Concentration

• Doping is the intentional introduction of impurities into a semiconductor to control its electrical properties
• n-type doping involves adding group V elements (donors) to create excess electrons in the conduction band
  • Donors occupy energy levels near the conduction band, easily ionized at room temperature
  • Examples: phosphorus (P), arsenic (As), and antimony (Sb) in silicon
• p-type doping involves adding group III elements (acceptors) to create excess holes in the valence band
  • Acceptors occupy energy levels near the valence band, easily accepting electrons from the valence band
  • Examples: boron (B), aluminum (Al), and gallium (Ga) in silicon
• Carrier concentration ($n$ for electrons, $p$ for holes) depends on doping levels and temperature
  • In intrinsic semiconductors, $n = p = n_i$, where $n_i$ is the intrinsic carrier concentration
  • In n-type semiconductors, $n \gg p$, and $n \approx N_D$, where $N_D$ is the donor concentration
  • In p-type semiconductors, $p \gg n$, and $p \approx N_A$, where $N_A$ is the acceptor concentration
• Law of mass action: $np = n_i^2$, holds for both intrinsic and extrinsic semiconductors at equilibrium

PN Junctions and Diodes

• A pn junction is formed when a p-type semiconductor is joined with an n-type semiconductor
• Diffusion of carriers across the junction creates a depletion region with a built-in electric field
  • Electrons diffuse from n-type to p-type, leaving behind positively charged donor ions
  • Holes diffuse from p-type to n-type, leaving behind negatively charged acceptor ions
• The built-in electric field opposes further diffusion, resulting in an equilibrium state
• Applying a forward bias (positive voltage to p-type, negative to n-type) reduces the depletion region and allows current to flow
• Applying a reverse bias increases the depletion region and allows only a small leakage current to flow
• The current-voltage (I-V) characteristic of a pn junction is described by the Shockley diode equation:
  • $I = I_s(e^{qV/nkT} - 1)$, where $I_s$ is the reverse saturation current, $q$ is the electron charge, $V$ is the applied voltage, $n$ is the ideality factor, $k$ is Boltzmann's constant, and $T$ is the absolute temperature
• Diodes are two-terminal devices that allow current to flow in one direction (forward-biased) and block current in the other (reverse-biased)
  • Rectifier diodes convert AC to DC
  • Zener diodes maintain a constant voltage when reverse-biased beyond a specific voltage
  • Light-emitting diodes (LEDs) emit light when forward-biased
  • Photodiodes generate current when exposed to light

Semiconductor Applications in Electronics

• Transistors are three-terminal devices that amplify or switch electronic signals
  • Bipolar junction transistors (BJTs) use both electrons and holes as charge carriers
  • Field-effect transistors (FETs) use an electric field to control the conductivity of a channel
    • Metal-oxide-semiconductor FETs (MOSFETs) are the most common type, used in integrated circuits
• Integrated circuits (ICs) are miniaturized electronic circuits fabricated on a single semiconductor substrate
  • Contain thousands to billions of transistors, diodes, resistors, and capacitors
  • Enable complex digital and analog functions (microprocessors, memory, amplifiers, sensors)
• Optoelectronic devices convert between electrical and optical signals
  • LEDs and laser diodes generate light from electrical current
  • Photodiodes and solar cells convert light into electrical current
  • Optocouplers provide electrical isolation between input and output signals
• Power electronic devices control and convert electrical power
  • Power diodes and thyristors are used in rectifiers and inverters
  • Insulated-gate bipolar transistors (IGBTs) and power MOSFETs are used in high-efficiency switching applications
• Sensors and actuators interface with the physical world
  • Temperature sensors (thermistors, thermocouples) change resistance or generate voltage with temperature
  • Pressure sensors (piezoresistive, capacitive) convert pressure into electrical signals
  • Accelerometers and gyroscopes measure acceleration and angular velocity using MEMS technology

Key Equations and Calculations

• Carrier concentration in intrinsic semiconductors: $n_i = \sqrt{N_c N_v} e^{-E_g/2kT}$
  • $N_c$ and $N_v$ are the effective densities of states in the conduction and valence bands, respectively
• Fermi level in intrinsic semiconductors: $E_F = \frac{E_c + E_v}{2} + \frac{kT}{2} \ln(\frac{N_v}{N_c})$
  • $E_c$ and $E_v$ are the conduction and valence band edges, respectively
• Carrier concentrations in extrinsic semiconductors (assuming complete ionization):
  • n-type: $n \approx N_D$, $p \approx \frac{n_i^2}{N_D}$
  • p-type: $p \approx N_A$, $n \approx \frac{n_i^2}{N_A}$
• Built-in potential of a pn junction: $V_{bi} = \frac{kT}{q} \ln(\frac{N_A N_D}{n_i^2})$
• Depletion region width of a pn junction: $W = \sqrt{\frac{2\varepsilon(V_{bi} - V_a)}{q}(\frac{1}{N_A} + \frac{1}{N_D})}$
  • $\varepsilon$ is the permittivity of the semiconductor, and $V_a$ is the applied voltage
• Shockley diode equation: $I = I_s(e^{qV/nkT} - 1)$
• Transistor current gain (BJT): $\beta = \frac{I_c}{I_b}$, where $I_c$ is the collector current and $I_b$ is the base current
• Transistor transconductance (FET): $g_m = \frac{\partial I_d}{\partial V_{gs}}$, where $I_d$ is the drain current and $V_{gs}$ is the gate-source voltage

Real-World Examples and Industry Uses

• Smartphones and tablets rely on advanced semiconductor technology
  • High-performance processors (Apple A-series, Qualcomm Snapdragon) built using billions of transistors
  • OLED and LCD displays use thin-film transistors (TFTs) to control individual pixels
  • CMOS image sensors capture high-resolution photos and videos
  • Flash memory (NAND) provides high-density storage for apps, media, and data
• Renewable energy systems heavily utilize power electronics
  • Solar inverters convert DC power from photovoltaic panels to AC power for the grid
  • Wind turbines use power converters to control generator speed and optimize power output
  • High-voltage DC (HVDC) transmission systems use thyristors and IGBTs for efficient long-distance power transmission
• Automotive industry is increasingly adopting semiconductor technology
  • Electric vehicles (EVs) rely on power electronics for motor control and battery management
  • Advanced driver assistance systems (ADAS) use cameras, radar, and sensors to enhance safety
  • Infotainment systems provide navigation, entertainment, and connectivity features
• Medical devices and healthcare applications benefit from semiconductor advancements
  • Wearable devices (smartwatches, fitness trackers) monitor vital signs and activity levels
  • Implantable devices (pacemakers, cochlear implants) use miniaturized electronics to improve patient outcomes
  • Medical imaging systems (X-ray, CT, MRI) rely on high-performance sensors and signal processing
• Aerospace and defense sectors require specialized semiconductor solutions
  • Satellites use solar cells and radiation-hardened electronics to operate in harsh space environments
  • Radar and communication systems employ high-frequency and high-power semiconductor devices (GaN, SiC)
  • Night vision and thermal imaging devices use infrared sensors (HgCdTe, InSb) to detect heat signatures