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Topic 2 Semiconductors Basics

Understand the basics of resistivity in insulators, semiconductors, and conductors. Learn about covalent bonds and energy band models for semiconductors, band gap energy, and carrier concentration. Explore electron and hole behavior in semiconductors, impurities, doping, drift, diffusion currents, mobility, and more. Discover the properties of elemental and compound semiconductors like silicon and germanium.

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Topic 2 Semiconductors Basics

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  1. ECE 271 Electronic Circuits I Topic 2Semiconductors Basics NJIT ECE-271 Dr. S. Levkov

  2. Chapter Goals • Characterize resistivity of insulators, semiconductors, and conductors. • Develop covalent bond and energy band models for semiconductors. • Understand band gap energy and intrinsic carrier concentration. • Explore the behavior of electrons and holes in semiconductors. • Discuss acceptor and donor impurities in semiconductors. • Learn to control the electron and hole populations using impurity doping. • Understand drift and diffusion currents in semiconductors. • Explore low-field mobility and velocity saturation. • Discuss the dependence of mobility on doping level. NJIT ECE-271 Dr. S. Levkov

  3. The Inventors of the Integrated Circuit Andy Grove, Robert Noyce, and Gordon Moore with Intel 8080 layout. Jack Kilby NJIT ECE-271 Dr. S. Levkov

  4. Solid-State Electronic Materials • Electronic materials fall into three categories (WRT resistivity): • Insulators  > 105-cm (diamond  = 1016 ) • Semiconductors 10-3 <  < 105 -cm • Conductors  < 10-3 -cm (copper  = 10-6 ) NJIT ECE-271 Dr. S. Levkov

  5. Solid-State Electronic Materials • Electronic materials fall into three categories (WRT resistivity): • Insulators  > 105-cm (diamond  = 1016 ) • Semiconductors 10-3 <  < 105 -cm • Conductors  < 10-3 -cm (copper  = 10-6 ) • Elemental semiconductors are formed from a single type of atom of column IV, typically Silicon. NJIT ECE-271 Dr. S. Levkov

  6. Solid-State Electronic Materials • Electronic materials fall into three categories (WRT resistivity): • Insulators  > 105-cm (diamond  = 1016 ) • Semiconductors 10-3 <  < 105 -cm • Conductors  < 10-3 -cm (copper  = 10-6 ) • Elemental semiconductors are formed from a single type of atom of column IV, typically Silicon. • Compound semiconductors are formed from combinations of elements of column III and V or columns II and VI. NJIT ECE-271 Dr. S. Levkov

  7. Solid-State Electronic Materials • Electronic materials fall into three categories (WRT resistivity): • Insulators  > 105-cm (diamond  = 1016 ) • Semiconductors 10-3 <  < 105 -cm • Conductors  < 10-3 -cm (copper  = 10-6 ) • Elemental semiconductors are formed from a single type of atom of column IV, typically Silicon. • Compound semiconductors are formed from combinations of elements of column III and V or columns II and VI. • Germanium was used in many early devices. NJIT ECE-271 Dr. S. Levkov

  8. Solid-State Electronic Materials • Electronic materials fall into three categories (WRT resistivity): • Insulators  > 105-cm (diamond  = 1016 ) • Semiconductors 10-3 <  < 105 -cm • Conductors  < 10-3 -cm (copper  = 10-6 ) • Elemental semiconductors are formed from a single type of atom of column IV, typically Silicon. • Compound semiconductors are formed from combinations of elements of column III and V or columns II and VI. • Germanium was used in many early devices. • Silicon quickly replaced germanium due to its higher bandgap energy, lower cost, and ability to be easily oxidized to form silicon-dioxide insulating layers. NJIT ECE-271 Dr. S. Levkov

  9. Solid-State Electronic Materials (cont) • Bandgap is an energy range in a solid where no electron states can exist. It refers to the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors NJIT ECE-271 Dr. S. Levkov

  10. Semiconductor Materials (cont.) NJIT ECE-271 Dr. S. Levkov

  11. Covalent Bond Model • Silicon has four electrons in the outer shell. • Single crystal material is formed by the covalent bonding of each silicon atom with its four nearest neighbors. Silicon diamond lattice unit cell. Corner of diamond lattice showing four nearest neighbor bonding. View of crystal lattice along a crystallographic axis. NJIT ECE-271 Dr. S. Levkov

  12. Silicon Covalent Bond Model (cont.) Silicon atom NJIT ECE-271 Dr. S. Levkov

  13. Silicon Covalent Bond Model (cont.) Covalent bond Silicon atom Silicon atom NJIT ECE-271 Dr. S. Levkov

  14. Silicon Covalent Bond Model (cont.) Silicon atom Covalent bonds in silicon NJIT ECE-271 Dr. S. Levkov

  15. Silicon Covalent Bond Model (cont.) • What happens as the temperature increases? • Near absolute zero, all bonds are complete • Each Si atom contributes one electron to each of the four bond pairs • The outer shell is full, no free electrons, silicon crystal is an insulator NJIT ECE-271 Dr. S. Levkov

  16. Silicon Covalent Bond Model (cont.) • Near absolute zero, all bonds are complete • Each Si atom contributes one electron to each of the four bond pairs • The outer shell is full, no free electrons, silicon crystal is an insulator • Increasing temperature adds energy to the system and breaks bonds in the lattice, generating electron-hole pairs. • The pairs move within the matter forming semiconductor • Some of the electrons can fall into the holes – recombination. NJIT ECE-271 Dr. S. Levkov

  17. Intrinsic Carrier Concentration • The density of carriers in a semiconductor as a function of temperature and material properties is: • EG = semiconductor bandgap energy in eV (electron volts) • k = Boltzmann’s constant, 8.62 x 10-5eV/K • T = absolute termperature, K • B = material-dependent parameter, 1.08 x 1031 K-3 cm-6 for Si • Bandgap energy is the minimum energy needed to free an electron by breaking a covalent bond in the semiconductor crystal. NJIT ECE-271 Dr. S. Levkov

  18. Intrinsic Carrier Concentration (cont.) • Electron density is n (electrons/cm3) and for intrinsic material n = ni. • Intrinsic refers to properties of pure materials. • ni ≈ 1010 cm-3 for Si • The density of silicon atoms is na ≈ 5x1022 cm-3 • Thus at a room temperature one bond per about 1013 is broken Intrinsic carrier density (cm-3) NJIT ECE-271 Dr. S. Levkov

  19. Electron-hole concentrations • A vacancy is left when a covalent bond is broken. • The vacancy is called a hole. NJIT ECE-271 Dr. S. Levkov

  20. Electron-hole concentrations • A vacancy is left when a covalent bond is broken. • The vacancy is called a hole. • A hole moves when the vacancy is filled by an electron from a nearby broken bond (hole current). NJIT ECE-271 Dr. S. Levkov

  21. Electron-hole concentrations • A vacancy is left when a covalent bond is broken. • The vacancy is called a hole. • A hole moves when the vacancy is filled by an electron from a nearby broken bond (hole current). • The electron density is n (ni for intrinsic material) NJIT ECE-271 Dr. S. Levkov

  22. Electron-hole concentrations • A vacancy is left when a covalent bond is broken. • The vacancy is called a hole. • A hole moves when the vacancy is filled by an electron from a nearby broken bond (hole current). • The electron density is n (ni for intrinsic material) • Hole density is represented by p. NJIT ECE-271 Dr. S. Levkov

  23. Electron-hole concentrations • A vacancy is left when a covalent bond is broken. • The vacancy is called a hole. • A hole moves when the vacancy is filled by an electron from a nearby broken bond (hole current). • The electron density is n (ni for intrinsic material) • Hole density is represented by p. • For intrinsic silicon, n = ni = p. NJIT ECE-271 Dr. S. Levkov

  24. Electron-hole concentrations • A vacancy is left when a covalent bond is broken. • The vacancy is called a hole. • A hole moves when the vacancy is filled by an electron from a nearby broken bond (hole current). • The electron density is n (ni for intrinsic material) • Hole density is represented by p. • For intrinsic silicon, n = ni = p. • The product of electron and hole concentrations is pn = ni2. • The pn product above holds when a semiconductor is in thermal equilibrium (not with an external voltage applied). NJIT ECE-271 Dr. S. Levkov

  25. Drift Current • Charged particles move or drift under the influence of the applied field. • The resulting current is called drift current. NJIT ECE-271 Dr. S. Levkov

  26. Drift Current • Charged particles move or drift under the influence of the applied field. • The resulting current is called drift current. • Electrical resistivity and its reciprocal, conductivity , characterize current flow in a material when an electric field is applied. NJIT ECE-271 Dr. S. Levkov

  27. Drift Current • Charged particles move or drift under the influence of the applied field. • The resulting current is called drift current. • Electrical resistivity and its reciprocal, conductivity , characterize current flow in a material when an electric field is applied. • Drift current density is j = Qv[(C/cm3)(cm/s) = A/cm2] NJIT ECE-271 Dr. S. Levkov

  28. Drift Current • Charged particles move or drift under the influence of the applied field. • The resulting current is called drift current. • Electrical resistivity and its reciprocal, conductivity , characterize current flow in a material when an electric field is applied. • Drift current density is j = Qv[(C/cm3)(cm/s) = A/cm2] j = current density, (Coulomb charge moving through a unit area) Q = charge density, (Charge in a unit volume) v = velocity of charge in an electric field. Note that “density” may mean area or volumetric density, depending on the context. NJIT ECE-271 Dr. S. Levkov

  29. Mobility • At low fields, carrier drift velocity v (cm/s) is proportional to electric field E (V/cm). The constant of proportionality is the mobility, : NJIT ECE-271 Dr. S. Levkov

  30. Mobility • At low fields, carrier drift velocity v (cm/s) is proportional to electric field E (V/cm). The constant of proportionality is the mobility, : • vn = - nEand vp = pE, where • vn and vp - electron and hole velocity (cm/s), • n and p - electron and hole mobility (cm2/Vs) NJIT ECE-271 Dr. S. Levkov

  31. Mobility • At low fields, carrier drift velocity v (cm/s) is proportional to electric field E (V/cm). The constant of proportionality is the mobility, : • vn = - nEandvp = pE, where • vn and vp - electron and hole velocity (cm/s), • n and p - electron and hole mobility (cm2/Vs) • n ≈ 1350 (cm2/Vs), p ≈ 500 (cm2/Vs), • Hole mobility is less than electron since hole current is the result of multiple covalent bond disruptions, while electrons can move freely about the crystal. NJIT ECE-271 Dr. S. Levkov

  32. Velocity Saturation At high fields, carrier velocity saturates and places upper limits on the speed of solid-state devices. NJIT ECE-271 Dr. S. Levkov

  33. Intrinsic Silicon Resistivity • Given drift current and mobility, we can calculate resistivity (Q is the charge density) : jndrift = Qnvn = (-qn)(- nE) = qn nEA/cm2 jpdrift = Qpvp = (+qp)(+ pE) = qp pEA/cm2 jTdrift =jn + jp = q(n n + p p)E = E This defines electrical conductivity:  = q(n n + p p) (cm)-1 Resistivity  is the reciprocal of conductivity:  = 1/ (cm) NJIT ECE-271 Dr. S. Levkov

  34. Problem: Find the resistivity of intrinsic silicon at room temperature and classify it as an insulator, semiconductor, or conductor. Solution: Known Information and Given Data: The room temperature motilities. For intrinsic silicon, the electron and hole densities are both equal to ni. Unknowns: Resistivity  and classification. Assumptions: assume “room temperature” with ni = 1010/cm3. Analysis: Charge density of electrons is Qn = -qni and for holes is Qp = +qni. Thus:  = (1.60 x 10-10)[(1010)(1350) + (1010)(500)] (C)(cm-3)(cm2/Vs) = 2.96 x 10-6(cm)-1 --->  = 1/ = 3.38 x 105cm Recalling the classification in the beginning, intrinsic silicon is near the low end of the insulator resistivity range Conclusions: Resistivity has been found, and intrinsic silicon is a poor insulator. Example: Calculate the resistivity of intrinsic silicon  = q(n n + p p) NJIT ECE-271 Dr. S. Levkov

  35. Semiconductor Doping • The interesting properties of semiconductors emerges when impurities are introduced. NJIT ECE-271 Dr. S. Levkov

  36. Semiconductor Doping • The interesting properties of semiconductors emerges when impurities are introduced. • Doping is the process of adding very small well controlled amounts of impurities into a semiconductor. NJIT ECE-271 Dr. S. Levkov

  37. Semiconductor Doping • The interesting properties of semiconductors emerges when impurities are introduced. • Doping is the process of adding very small well controlled amounts of impurities into a semiconductor. • Doping enables the control of the resistivity and other properties over a wide range of values. NJIT ECE-271 Dr. S. Levkov

  38. Semiconductor Doping • The interesting properties of semiconductors emerges when impurities are introduced. • Doping is the process of adding very small well controlled amounts of impurities into a semiconductor. • Doping enables the control of the resistivity and other properties over a wide range of values. • For silicon, impurities are from columns III and V of the periodic table. NJIT ECE-271 Dr. S. Levkov

  39. Donor Impurities in Silicon • Phosphorous (or other column V element) atom replaces silicon atom in crystal lattice. • Since phosphorous has five outer shell electrons, there is now an ‘extra’ electron in the structure. • Material is still charge neutral, but very little energy is required to free the electron for conduction since it is not participating in a bond. NJIT ECE-271 Dr. S. Levkov

  40. Donor Impurities in Silicon • Phosphorous (or other column V element) atom replaces silicon atom in crystal lattice. • Since phosphorous has five outer shell electrons, there is now an ‘extra’ electron in the structure. • Material is still charge neutral, but very little energy is required to free the electron for conduction since it is not participating in a bond. A silicon crystal doped by a pentavalent element (f. i. phosphorus). Each dopant atom donates a free electron and is thus called a donor. The doped semiconductor becomes n type. NJIT ECE-271 Dr. S. Levkov

  41. Acceptor Impurities in Silicon • Boron (column III element) has been added to silicon. • There is now an incomplete bond pair, creating a vacancy for an electron. • Little energy is required to move a nearby electron into the vacancy. • As the ‘hole’ propagates, charge is moved across the silicon. NJIT ECE-271 Dr. S. Levkov

  42. Acceptor Impurities in Silicon • Boron (column III element) has been added to silicon. • There is now an incomplete bond pair, creating a vacancy for an electron. • Little energy is required to move a nearby electron into the vacancy. • As the ‘hole’ propagates, charge is moved across the silicon. Vacancy A silicon crystal doped with a trivalent impurity (f.i. boron). Each dopant atom gives rise to a hole, and the semiconductor becomes p type. NJIT ECE-271 Dr. S. Levkov

  43. Acceptor Impurities – Hole propagation Hole is propagating through the silicon. NJIT ECE-271 Dr. S. Levkov

  44. Acceptor Impurities – Hole propagation Hole Hole is propagating through the silicon. NJIT ECE-271 Dr. S. Levkov

  45. Acceptor Impurities – Hole propagation Hole Hole is propagating through the silicon. NJIT ECE-271 Dr. S. Levkov

  46. Acceptor Impurities – Hole propagation Hole is propagating through the silicon. NJIT ECE-271 Dr. S. Levkov

  47. Doped Silicon Carrier Concentrations(how to calculate) • In doped material, the electron and hole concentrations are no longer equal. NJIT ECE-271 Dr. S. Levkov

  48. Doped Silicon Carrier Concentrations(how to calculate) • In doped material, the electron and hole concentrations are no longer equal. • If n > p, the material is n-type. If p > n, the material is p-type. NJIT ECE-271 Dr. S. Levkov

  49. Doped Silicon Carrier Concentrations(how to calculate) • In doped material, the electron and hole concentrations are no longer equal. • If n > p, the material is n-type. If p > n, the material is p-type. • The carrier with the largest concentration is the majority carrier, the smaller is the minority carrier. NJIT ECE-271 Dr. S. Levkov

  50. Doped Silicon Carrier Concentrations(how to calculate) • In doped material, the electron and hole concentrations are no longer equal. • If n > p, the material is n-type. If p > n, the material is p-type. • The carrier with the largest concentration is the majority carrier, the smaller is the minority carrier. • ND = donor impurity concentration NA = acceptor impurity concentration atoms/cm3 NJIT ECE-271 Dr. S. Levkov

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