Undergraduate course on semiconductor device physics-I

Learn how silicon forms energy bands from energy levels as overlapping atoms create covalent bonds, splitting levels into bands with six states per level and two electrons per state.

Explore how discrete energy levels in silicon merge into energy bands as atomic spacing decreases, forming valence and conduction bands separated by a forbidden energy gap.

Explore how covalent bonding shapes valence and conduction bands, and how the energy gap governs electron transitions in silicon and germanium. Examine intrinsic and extrinsic semiconductors and temperature-driven electron excitation.

Explore energy bands in intrinsic semiconductors. At zero kelvin, the valence band is fully filled and the conduction band is empty; thermal energy enables electrons to cross the band gap.

Explore the electron energy–momentum relation through the E vs k diagram, showing a parabolic energy dependence with energy proportional to the square of the wave number (momentum).

Derive the hole effective mass from the valence-band parabola using E(k) curvature and the relation 1/m* = (1/ħ^2) d^2E/dk^2, with Si and GaAs values near 0.526–0.56 m0.

Explore the density of states as a measure of available energy states per unit volume in a quantum system, including its derivation and relevance to intrinsic carrier concentrations.

Derive the three-dimensional density of states per unit volume from a differential k-space volume, relate it to energy, and discuss its role in intrinsic and extrinsic carrier concentrations.

Explore how the density of states in the conduction and valence bands defines the available states per unit volume as energy rises from Ec to Ev, guiding semiconductor behavior.

Describe the Fermi distribution function as a probability function for electron occupancy of conduction states and vacancies in the valence band, based on ratio of electrons to available energy states.

Describe how at zero kelvin valence bands are filled and conduction bands are empty, governed by the fermi-dirac function with a sharp switch at EF.

Explore how the Fermi-Dirac distribution governs electron occupancy at different temperatures, with the Fermi energy occupancy fixed at 0.5 and rising temperature filling conduction and emptying valence states.

the lecture presents the maxwell-boltzmann approximation for semiconductors, valid when e - e_f ≥ 3 k_B T, using f ≈ exp(-(E - E_f)/k_B T) for electrons and holes.

Derive equilibrium electron concentration in the conduction band by integrating its density of states with the Fermi-Dirac occupation, and connect to hole concentration in the valence band.

Derive free electron concentration in the conduction band using the Maxwell-Boltzmann approximation, introducing the effective density of states and its temperature dependence via E_c, E_f, and k_B T.

Analyze electrons in the conduction band and holes in the valence band, using Nc and Nv to determine equilibrium carrier concentrations. Temperature drives Nc and Nv, both scale with T^(3/2).

Link equilibrium electron and hole concentrations to intrinsic carrier concentration, intrinsic Fermi level, and the energy gap in intrinsic semiconductors, and show how temperature and density of states affect them.

Relate the intrinsic Fermi energy level to the midpoint of the energy gap in intrinsic semiconductors, noting its possible slight shifts due to effective mass and density of states.

Derive the expressions for extrinsic semiconductor electron and hole concentrations and their Fermi levels using the law of mass action, relating them to the intrinsic Fermi level with exponential behavior.

Explore n-type carrier concentration at equilibrium, where electrons are the majority and holes the minority. Relate intrinsic to donor concentration and derive n ≈ Nd, p ≈ ni^2 / Nd.

Explore how donor impurity concentration shifts the extrinsic Fermi energy toward the conduction band minimum in n-type semiconductors, linking EFI, E_c, and intrinsic carrier concentration.

Describe how p-type semiconductors have majority holes equal to acceptor concentration, derive extrinsic Fermi level expressions, and show how rising acceptor concentration moves the Fermi level toward the valence band.

Explore freeze out and complete ionisation in semiconductors, detailing donor and acceptor energy levels, Fermi energy, and carrier behavior between conduction and valence bands at 0 K and 300 K.

Describe how donor and acceptor impurity concentrations create compensated semiconductors and how balance between donors and acceptors leads to intrinsic semiconductor behavior.

Analyze compensated semiconductors by balancing donor and acceptor impurities, deriving equilibrium electron and hole concentrations and intrinsic carrier concentration from energy band diagrams and neutrality, including complete ionization.

Summarizes density of states for conduction and valence bands, intrinsic and extrinsic carrier concentrations, Fermi levels, and Boltzmann approximations in compensated semiconductors.

Explore carrier transport in semiconductors by examining electrons and holes, drift and diffusion currents, mobility, conductivity, resistivity, and the Einstein relation, plus continuity and generation–recombination.

Explore mobility, the ease with which electrons and holes move in a semiconductor, defined as a constant that varies by material and electric field, and governs drift velocity and current.

Learn how electron drift under an external electric field leads to a mobility expression in n-type semiconductors, showing mobility depends on mean free time and the effective mass.

Examine how drift velocity responds to field intensity, showing linear growth at low fields, a sqrt inverse regime at higher fields, and saturation with decreasing mobility, relevant to mosfet operation.

Examine how temperature alters mobility in semiconductors, comparing impurity ionization scattering at low temperatures with lattice scattering at high temperatures, and show mobility's decline with increased doping.

Compute the drift velocity of minority carriers in a homogeneous semiconductor under an electric field using a 1 cm displacement in 20 μs, and derive mobility from v_d = μE.

Explore drift current density and conductivity in intrinsic, extrinsic, and compensated semiconductors, and how carrier concentration and mobility under applied electric field determine current.

This lecture analyzes two identically sized silicon samples with boron acceptor in sample A and donor impurity in sample B, using mu_n/mu_p = 3 to derive the connectivity ratio.

Calculate the ratio of the heavily doped n-type semiconductor's conductance to the intrinsic semiconductor at the same temperature. Use the given mobility and doping data to obtain 20000.

Extract electron mobility from the graph for silicon at 300 kelvin and compute conductivity using sigma = q n mu for the given doping concentration.

solve an example calculating the uniform electric field in a 1 μm silicon slab at 300 kelvin and the resulting drift current density using q, n, mobility, and E.

Calculate transit time for electrons across a 1 cm silicon bar using drift velocity μE with μ = 1000 cm^2/Vs and E = 10 V/cm, yielding t ≈ 1×10^-4 s.

Explore resistivity, the reciprocal of conductivity, and how it characterizes the conductive behavior of intrinsic and extrinsic semiconductors, linking drift current density and resistance with length and cross-sectional area.

Calculate silicon resistance from geometry and doping, using R = L/(σA) with σ = n q μ, highlighting the relationship between carrier concentration, mobility, and resistance.

Calculate the donor impurity concentration Nd in n-type silicon from rho = 0.5 ohm cm and mu_n = 1250 cm^2/Vs using sigma = 1/rho, yielding Nd = 1×10^16 cm^-3.

Explore diffusion current density in non-uniform semiconductors, where electron and hole concentrations create diffusion currents opposite to drift currents under an applied field.

Derive diffusion current densities for electrons and holes using diffusion coefficients and concentration gradients, with a negative sign indicating flow toward lower concentration.

Explore the total current density in semiconductors by combining electron and hole currents from drift and diffusion, using electric field and carrier concentration gradients to derive a complete expression.

Compute diffusion current density in silicon at 300 kelvin from a linear electron concentration gradient, no electric field, using a diffusion coefficient D, yielding J ≈ −1.12×10^3 A/cm^2.

Solve for the magnitude of the electron diffusion current density in silicon by applying the diffusion formula with the given concentration gradient, electron mobility, and charge.

Explore how non-uniform doping leads to diffusion, builds a built-in potential and internal electric field, and shapes energy bands, Fermi level positioning, and drift via Einstein's relation.

Derive the Einstein relation linking diffusion coefficient and mobility in semiconductors, showing diffusion and drift currents cancel at equilibrium under electric fields, intrinsic carrier concentration, and the Fermi energy level.

Investigate the volt-equivalent of temperature and relate diffusion coefficient units in cm^2/s to mobility units in cm^2/V·s, with silicon at room temperature showing mobility near 40.

Analyze the electron density profile to compute drift and diffusion current densities, derive the internal electric field from the concentration slope, and show the net current vanishes at X=0.

In a non-uniform doping distribution in a B-type semiconductor, diffusion eliminates the internal electric field, yielding a magnitude of about 1.19 kV/cm as the design value.

Derive and apply the continuity equation for diffusion currents in semiconductors, accounting for generation and recombination, and neglect drift to analyze transient diffusion with injected carriers.

Explain intrinsic semiconductors, electron-hole pairs, and covalent bonding in silicon and germanium. Then show how adding boron or gallium forms p-type extrinsic material and leads to pn junction formation.

Analyze diffusion and drift in a pn junction, forming a depletion region and internal field that block majority carriers while minority carriers drift, producing zero net current in open circuit.

Explain forward bias in a pn junction, where voltage lowers the potential barrier and enables drift and diffusion currents as the barrier minimizes, silicon 0.6–0.7 V and germanium 0.2–0.3 V.

Explore energy band diagrams in open-circuit conditions for intrinsic and extrinsic semiconductors. Observe how Fermi levels align at the junction, forming depletion and neutral regions under an internal field.

Derive the contact potential by balancing drift and diffusion currents, relate it to the built-in potential, and express it via donor and acceptor concentrations and intrinsic carrier concentration.

Analyze the charge density at a semiconductor junction under open conditions, showing net positive equals net negative and deriving charges from donor and acceptor impurities with complete ionization.

Derive the maximum field intensity at the junction boundary by integrating the positive ion concentration from 0 to X_p, yielding E_max = Q/(epsilon X_p).

Explore how junction width relates to the contact potential, deriving W from the electric field and showing its square-root dependence on the potential, with epsilon and donor/acceptor concentrations.

Examine how doping concentration influences junction penetration and the width of the potential barrier. Higher donor or acceptor concentration extends the barrier more into the opposite lightly doped region.

Explore how forward bias narrows the depletion width by opposing the internal field, shaping energy band diagrams and Fermi level alignment, and influencing current–voltage behavior.

Describe how reverse bias widens the depletion region and raises the potential barrier, shifting the conduction and valence band energies by qVr and relocating the Fermi levels.

Derive the junction width in the space-charge region of a p–n diode under open-circuit, forward bias, and reverse bias, and show how external potential influences the width.

Calculate the depletion widths of an abrupt p-n junction from the given doping concentrations, noting a 0.3 micrometer b-side depletion within a 3 micrometer total.

Calculate the silicon p-n junction built-in potential at room temperature using doping and intrinsic carrier concentration, yielding about 0.77 V, and estimate the maximum electric field around 0.015 MV/cm.

Analyze donor and acceptor impurity concentrations in an abrupt silicon pn junction, determine the built-in potential and depletion width from intrinsic carrier concentration and permittivity under thermal equilibrium.

Solved example 04 analyzes a p-n junction with varying doping densities, deriving the built-in potential from diffusion and the resulting electric field, with emphasis on majority and minority carriers.

Calculate the charge per unit area of a silicon pn junction depletion region from given acceptor and donor doping, built-in potential, and depletion width, yielding about -48 nanocoulombs per cm^2.

Analyze the diode under forward bias by identifying four current components: hole and electron drift currents and their corresponding diffusion currents, with junction injection of minority carriers.

Derive the diode current equation by linking applied voltage to diffusion current across the p-n junction, exploring forward and reverse bias and minority carrier diffusion length.

This lesson derives the diode current equation by linking the built-in potential with external bias, showing forward bias injects minority carriers and yields exponential current behavior.

Derive the diode current equation from diffusion currents and minority-carrier concentrations. Explain how the total diode current comprises diffusion components and the saturation current under forward and reverse bias.

Examine the diode i–v characteristics, including reverse saturation current from minority carrier drift, the space-charge region, generation–recombination factor, and the exponential forward-bias behavior.

Apply the diode equation to germanium and silicon diodes at same current, including EPA and depletion-region effects, with forward biases 0.1435 and 0.718 V, to yield a ratio near 4,000.

Analyze a forward-biased silicon pn junction diode with given p- and n-doping, compute injected electron concentration at depletion edge using intrinsic carrier concentration and 0.3 V bias at 300 K.

Solve example 09 analyzes a step junction diode with depletion width 1 μm and computes the forward voltage needed to reduce it to 0.6 μm using the depletion relation.

Solve a diode current problem by calculating the reverse bias needed to reach 75 percent of the saturation current at room temperature using the ideal diode equation and thermal voltage.

Examine how temperature drives carrier generation via intrinsic carrier concentration, raising reverse saturation current by 7% per degree C—and doubling every 10 C—while diode voltage falls 2.5 mV per degree.

Demonstrates how current in a semiconductor device changes with temperature, using a 2.5 per degree coefficient to drop from 700 million at 20°C to about 650 million at 40°C.

Examine how reverse saturation current varies with temperature, doubling every 10 degrees and computing the current at 40 C from a 20 C baseline.

Analyze diode resistance by deriving the dynamic resistance from the exponential current–voltage relation and show that forward bias yields a small dynamic resistance with rapidly increasing current. In reverse bias, neglect the reverse saturation current, treat the diode as open with infinite resistance, and relate these ideal behaviors to diffusion capacitance calculations and switching applications.

Examine diode capacitance, distinguishing transition capacitance in reverse bias from diffusion (also called charge storage) capacitance in forward bias, both arising from charge variation at the junction.

Derive the expression for the transition capacitance in a reverse-biased p-n junction, showing its inverse square-root dependence on the applied reverse bias and symmetry cases.

Derives the junction capacitance relation, showing Cj proportional to 1 over the square root of bias terms, and computes Cj1 and Cj2, concluding Cj2 equals 0.5 (option B).

Examine how doping concentrations in two regions affect depletion and transition capacitances in a diode under reverse bias, and derive the ratio C2 to C1 from the given dopings.

Derive and explain diffusion capacitance under forward bias, linking injected minority carriers, charge storage, and diffusion length to conductance and current.

Explore how a junction diode switches from forward to reverse bias, analyzing carrier concentration changes, minority carrier diffusion, and the time-dependent transition to reverse saturation current.

Analyze diode switching from forward to reverse bias, detailing storage removal time and reverse recovery time, and the associated currents and carrier dynamics.

Analyze diode switching from forward to reverse bias, quantify storage time and diode current behavior, including the constant current during storage and the zero current after transition.

Explore breakdown diodes and Zener diodes operated in reverse bias, study optoelectronic devices, and analyze generation, recombination, and non-equilibrium carrier transport, absorption, and luminescence.

Observe avalanche multiplication, where minority carriers accelerated by reverse bias undergo ionizing collisions in the transition region, triggering impact ionization and generating electron-hole pairs that dramatically increase current.

Explore the concept of the critical electric field governing breakdown in pn junctions, deriving the maximum field intensity under reverse bias and its dependence on doping and material parameters.

Show how a zener diode serves as a voltage regulator to stabilize input fluctuations in appliances, by operating in parallel with a load and accommodating a wide current range.

Investigate the reverse-bias curves of diodes D1 and D2 under a 0–100 supply, compare their breakdown voltages and currents, and conclude that D1 breaks down before D2.

Explore optical absorption in semiconductors by analyzing how photon energy relative to the conduction and valence band structure and bandgap drives absorption, electron-hole generation, and recombination lifetimes.

Analyze how the absorption coefficient and semiconductor length determine transmitted light power, with a direct expression linking the input and transmitted powers in a semiconductor.

Explore optical absorption and emission in a gallium arsenide semiconductor via a 0.46 micrometers thick sample exposed to 2 eV photons, computing absorbed power, lattice heat, and recombination emission.

Analyze optical absorption in semiconductors through the band gap and photon energy, defining the absorption wavelength range between lambda min and lambda max via E = 1.24 over lambda (μm).

Explore luminescence in semiconductors, detailing radiative and non-radiative recombination and light emission from conduction to valence band transitions. Describe excitation mechanisms—photoluminescence, catalog luminescence, and electro luminescence—and generation–recombination dynamics.

Study how external excitation and optical absorption generate excess carriers, disturb equilibrium, and establish a non-equilibrium steady state through generation and recombination dynamics.

Explore how illumination creates generation and recombination rates, reaching a steady-state excess carrier concentration under low-level injection, and relate the mean lifetimes of charge carriers to minority carrier concentration.

Examine excess hole carriers in a B-type semiconductor, deriving how generation rate and mean lifetime set the excess hole concentration under illumination and its exponential decay when illumination stops.

Examine how quasi fermi levels describe non-equilibrium conditions in semiconductor band structures under external excitation, distinguishing electron and hole quasi levels and their relation to the intrinsic Fermi energy.

Determine non-equilibrium carrier concentrations under optical excitation in silicon, compute excess holes from generation rate and lifetime, and derive the deviation of the quasi-Fermi level from the intrinsic level.

Photodetectors convert optical signals into electrical current by generating electron-hole pairs, transporting carriers, and sometimes multiplying them, with applications in optical fiber communications and infrared sensors.

Explains photo conductivity in a simple semiconductor slab, deriving how optical excitation generates excess carriers, photocurrent, and a gain determined by mean lifetime and transit time.

Explore quantum efficiency, the ratio of absorbed photons that generate electron-hole pairs to the total incident photons. Not all photons are absorbed, keeping QE below one and influencing photocurrent.

Demonstrates calculating photoconductor gain from minority carrier lifetime and transit time, then determines the photocurrent by multiplying the primary current (photons and quantum efficiency) by this gain.

Explore three limitations on steady-state generation in photodiodes: nonuniform generation, distance-dependent absorption, and current components, and describe overcoming them with a practical photodiode structure involving an intrinsic region.

Learn how quantum efficiency links photon energy to electron–hole pair generation and photocurrent in a photodiode, and how the long-wavelength cutoff and depletion-region absorption shape this efficiency.

Examine how responsivity links photocurrent to incident optical power in silicon photodiodes, expressing it via quantum efficiency and photon energy, and discuss ideal 100% absorption and wavelength dependence.

Learn how photodetector speed hinges on minority-carrier diffusion, depletion-region width, transit time, and depletion capacitance, and balance transit speed with quantum efficiency using APD photodiodes from five to fifty micrometers.

Explore the p-i-n photodiode structure with a thin intrinsic layer, depletion region dynamics under reverse bias, and absorption-driven carrier generation leading to current in the depletion and drift regions.

Compute the photocurrent of a photodiode by multiplying the given responsivity by the incident power, yielding eight microamperes.

Solar energy converts light into electricity via a solar cell, where absorbed light generates electron-hole pairs and the junction field drives current to a load, as used in satellites.

Examine the solar cell’s characteristic curve under illumination, treating it as a photodiode with light-induced current. Explore forward and reverse bias behavior, especially short-circuit current, open-circuit voltage, and fourth-quadrant operation.

Analyze a solar cell's I–V characteristics to determine short-circuit current, open-circuit voltage, and the maximum power point using a maximum power rectangle and the condition dP/dV = 0.

Differentiate the solar cell power expression with respect to voltage to locate the maximum power point and express the maximum power in terms of voltage, open-circuit voltage, and load current.

Solved example computes a solar cell's maximum efficiency under 100 mW/cm^2 on a 3 cm^2 area, using open-circuit voltage 0.5, short-circuit current 0.7, and fill factor 0.6, giving 21%.

The example shows how a fivefold drop in light intensity reduces photocurrent and short-circuit current, then uses the diode equation to estimate the open-circuit voltage around 0.61 V.

Examine how photocurrent density in silicon devices scales with incident light intensity, and compute the corresponding saturation current density and open-circuit voltage when the light increases 20-fold.

Analyze a solved example on a solar cell under uniform illumination, computing photocurrent and the generation rate per unit volume from efficiency, fill factor, area, and thickness.

Explore led applications in digital display units, televisions, and remote controls, plus optoelectronic devices for fiber communications and disc readers, while linking visible spectrum wavelengths to bandgap energies.

explain how gallium arsenide phosphide's bandgap is tuned by x to span red to green, and how nitrogen doping and indium aluminium gallium nitride boost radiative recombination.

Discusses the double heterojunction structure in light emitting diodes, showing a central gallium arsenide phosphide layer that creates a potential well, boosting radiative recombination and quantum efficiency.

Explore internal and external quantum efficiency in light-emitting diodes, defined by radiative recombination rates and external photon extraction, and how doping and optical efficiency influence LED performance.

Compute energy bandgap from green light wavelength 5490 angstroms by converting to 0.549 μm and applying Eg = 1.24 / λ, yielding about 2.26 eV.