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Catégorie :Category: nCreator TI-Nspire
Auteur Author: Jagrit
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 6.04 Ko KB
Mis en ligne Uploaded: 25/02/2025 - 10:32:51
Mis à jour Updated: 25/02/2025 - 10:33:02
Uploadeur Uploader: Jagrit (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4517178
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 6.04 Ko KB
Mis en ligne Uploaded: 25/02/2025 - 10:32:51
Mis à jour Updated: 25/02/2025 - 10:33:02
Uploadeur Uploader: Jagrit (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4517178
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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1. Basic Semiconductor Concepts Energy Band Diagram: The energy band structure determines a material's electrical conductivity: Metal: No band gap or overlapping conduction and valence bands High conductivity. Insulator: Large band gap (~8 eV) No free carriers at room temperature. Semiconductor: Moderate band gap (~1 eV) Conductivity increases with temperature. 1 eV = 1.6 × 10{¹y Joules. Intrinsic Silicon (Si): Group-IV element with 4 valence electrons, forms covalent bonds. At 300K (room temperature): Intrinsic carrier concentration (ni): ~1.5 × 10¹p carriers/cm³. Very low conductivity without doping. Electron-Hole Pair Generation: Thermal energy can break covalent bonds frees electrons (conduction band) and creates holes (valence band). Both carriers contribute to conduction. 2. Doped Semiconductors n-type Semiconductor: Doping intrinsic Si with Group-V elements (e.g., Phosphorus, Arsenic) adds extra electrons. Donors: Atoms that donate electrons. Electron concentration (nn): nn H ND (donor density) when ND >> ni. Minority carriers: Holes with concentration pn = ni² / ND. p-type Semiconductor: Doping intrinsic Si with Group-III elements (e.g., Boron) creates holes. Acceptors: Atoms that accept electrons. Hole concentration (pp): pp H NA (acceptor density) when NA >> ni. Minority carriers: Electrons with concentration np = ni² / NA. Mass Action Law: np = ni² Holds true under thermal equilibrium. 3. Charge Transport Mechanisms Drift Current: Movement of carriers due to an external electric field. Drift velocity: v_drift = ¼E Electron mobility (¼n): ~1350 cm²/V·s. Hole mobility (¼p): ~480 cm²/V·s. Current density: Jn = q·n·¼n·E (for electrons) Jp = q·p·¼p·E (for holes) Diffusion Current: Movement due to carrier concentration gradients. Current density: Jn = q·Dn·(dn/dx) (electrons) Jp = -q·Dp·(dp/dx) (holes) Dn, Dp: Diffusion coefficients for electrons and holes. Total Current: Jn_total = q·n·¼n·E + q·Dn·(dn/dx) Jp_total = q·p·¼p·E - q·Dp·(dp/dx) 4. The pn Junction Diode Formation of pn Junction: Joining n-type and p-type semiconductors. Depletion Region: Formed by recombination of electrons and holes near the junction. Depleted of free carriers but contains immobile ionized dopants. Built-in Potential (V): V = (kT/q) * ln((NN)/ni²) k: Boltzmann constant (~8.62 × 10{u eV/K). q: Electron charge (~1.6 × 10{¹y C). Typical V for silicon: ~0.6V to 0.8V at 300K. Depletion Width (W): W = sqrt((2µ(V + V))/(q(N + N)/(NN))) µ: Permittivity of silicon (~11.7 × µ). V: Applied voltage. Higher doping Narrower depletion width. 5. Biasing the pn Junction Open-Circuit Condition: No external voltage applied. Drift and diffusion currents are balanced. Forward Bias: p-side connected to positive terminal. Reduces the potential barrier. Increases carrier injection significant current flows. Diode equation: I = I (e^(qV/kT) - 1) I: Reverse saturation current (very small). Reverse Bias: p-side connected to negative terminal. Widens depletion region. Only minority carriers contribute to a small leakage current . Breakdown Mechanisms: Zener Breakdown: In heavily doped diodes. Strong electric fields break covalent bonds. Avalanche Breakdown: In lightly doped diodes. High-energy carriers trigger impact ionization. 6. Capacitance Effects in pn Junctions Depletion Capacitance (Cj): Acts like a voltage-dependent capacitor. Cj = Cj / (1 + V?/V)^m V?: Reverse bias voltage. m: Grading coefficient (0.5 to 0.33). Used in Varactor Diodes for tuning circuits. 7. Key Formulas & Constants Built-in Potential: V = (kT/q) * ln((NN)/ni²) Diode Current Equation: I = I (e^(qV/kT) - 1) Depletion Width: W = sqrt((2µ(V + V))/(q(N + N)/(NN))) Depletion Capacitance: Cj = Cj / (1 + V?/V)^m Constants: q = 1.6 × 10{¹y C (electron charge) k = 8.62 × 10{u eV/K (Boltzmann constant) µ = 8.854 × 10{¹t F/cm (vacuum permittivity) µ = 11.7 × µ (permittivity of silicon) 8. Practice Problems Examples 1. Calculate the built-in potential V for a silicon pn junction with N = N = 2 × 10¹v atoms/cm³ at 300K. Use V = (kT/q) * ln((NN)/ni²). 2. Determine the electron and hole concentrations in n-type silicon doped with 10¹v atoms/cm³. Use nn H ND and pn = ni² / ND. 3. Find the depletion width for a pn junction under reverse bias of 5V. Use W = sqrt((2µ(V + V?))/(q(N + N)/(NN))). Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
1. Basic Semiconductor Concepts Energy Band Diagram: The energy band structure determines a material's electrical conductivity: Metal: No band gap or overlapping conduction and valence bands High conductivity. Insulator: Large band gap (~8 eV) No free carriers at room temperature. Semiconductor: Moderate band gap (~1 eV) Conductivity increases with temperature. 1 eV = 1.6 × 10{¹y Joules. Intrinsic Silicon (Si): Group-IV element with 4 valence electrons, forms covalent bonds. At 300K (room temperature): Intrinsic carrier concentration (ni): ~1.5 × 10¹p carriers/cm³. Very low conductivity without doping. Electron-Hole Pair Generation: Thermal energy can break covalent bonds frees electrons (conduction band) and creates holes (valence band). Both carriers contribute to conduction. 2. Doped Semiconductors n-type Semiconductor: Doping intrinsic Si with Group-V elements (e.g., Phosphorus, Arsenic) adds extra electrons. Donors: Atoms that donate electrons. Electron concentration (nn): nn H ND (donor density) when ND >> ni. Minority carriers: Holes with concentration pn = ni² / ND. p-type Semiconductor: Doping intrinsic Si with Group-III elements (e.g., Boron) creates holes. Acceptors: Atoms that accept electrons. Hole concentration (pp): pp H NA (acceptor density) when NA >> ni. Minority carriers: Electrons with concentration np = ni² / NA. Mass Action Law: np = ni² Holds true under thermal equilibrium. 3. Charge Transport Mechanisms Drift Current: Movement of carriers due to an external electric field. Drift velocity: v_drift = ¼E Electron mobility (¼n): ~1350 cm²/V·s. Hole mobility (¼p): ~480 cm²/V·s. Current density: Jn = q·n·¼n·E (for electrons) Jp = q·p·¼p·E (for holes) Diffusion Current: Movement due to carrier concentration gradients. Current density: Jn = q·Dn·(dn/dx) (electrons) Jp = -q·Dp·(dp/dx) (holes) Dn, Dp: Diffusion coefficients for electrons and holes. Total Current: Jn_total = q·n·¼n·E + q·Dn·(dn/dx) Jp_total = q·p·¼p·E - q·Dp·(dp/dx) 4. The pn Junction Diode Formation of pn Junction: Joining n-type and p-type semiconductors. Depletion Region: Formed by recombination of electrons and holes near the junction. Depleted of free carriers but contains immobile ionized dopants. Built-in Potential (V): V = (kT/q) * ln((NN)/ni²) k: Boltzmann constant (~8.62 × 10{u eV/K). q: Electron charge (~1.6 × 10{¹y C). Typical V for silicon: ~0.6V to 0.8V at 300K. Depletion Width (W): W = sqrt((2µ(V + V))/(q(N + N)/(NN))) µ: Permittivity of silicon (~11.7 × µ). V: Applied voltage. Higher doping Narrower depletion width. 5. Biasing the pn Junction Open-Circuit Condition: No external voltage applied. Drift and diffusion currents are balanced. Forward Bias: p-side connected to positive terminal. Reduces the potential barrier. Increases carrier injection significant current flows. Diode equation: I = I (e^(qV/kT) - 1) I: Reverse saturation current (very small). Reverse Bias: p-side connected to negative terminal. Widens depletion region. Only minority carriers contribute to a small leakage current . Breakdown Mechanisms: Zener Breakdown: In heavily doped diodes. Strong electric fields break covalent bonds. Avalanche Breakdown: In lightly doped diodes. High-energy carriers trigger impact ionization. 6. Capacitance Effects in pn Junctions Depletion Capacitance (Cj): Acts like a voltage-dependent capacitor. Cj = Cj / (1 + V?/V)^m V?: Reverse bias voltage. m: Grading coefficient (0.5 to 0.33). Used in Varactor Diodes for tuning circuits. 7. Key Formulas & Constants Built-in Potential: V = (kT/q) * ln((NN)/ni²) Diode Current Equation: I = I (e^(qV/kT) - 1) Depletion Width: W = sqrt((2µ(V + V))/(q(N + N)/(NN))) Depletion Capacitance: Cj = Cj / (1 + V?/V)^m Constants: q = 1.6 × 10{¹y C (electron charge) k = 8.62 × 10{u eV/K (Boltzmann constant) µ = 8.854 × 10{¹t F/cm (vacuum permittivity) µ = 11.7 × µ (permittivity of silicon) 8. Practice Problems Examples 1. Calculate the built-in potential V for a silicon pn junction with N = N = 2 × 10¹v atoms/cm³ at 300K. Use V = (kT/q) * ln((NN)/ni²). 2. Determine the electron and hole concentrations in n-type silicon doped with 10¹v atoms/cm³. Use nn H ND and pn = ni² / ND. 3. Find the depletion width for a pn junction under reverse bias of 5V. Use W = sqrt((2µ(V + V?))/(q(N + N)/(NN))). Made with nCreator - tiplanet.org
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