半导体基础知识

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

2 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 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.

3 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 3 The Inventors of the Integrated Circuit Jack Kilby Andy Grove, Robert Noyce, and Gordon Moore with Intel 8080 layout.

4 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 4 Solid-State Electronic Materials Electronic materials fall into three categories (WRT resistivity): Insulators  > 10 5  -cm (diamond  = 10 16 ) Semiconductors 10 -3 <  < 10 5  -cm Conductors  < 10 -3  -cm (copper  = 10 -6 )

5 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 5 Solid-State Electronic Materials Electronic materials fall into three categories (WRT resistivity): Insulators  > 10 5  -cm (diamond  = 10 16 ) Semiconductors 10 -3 <  < 10 5  -cm Conductors  < 10 -3  -cm (copper  = 10 -6 ) Elemental semiconductors are formed from a single type of atom of column IV, typically Silicon.

6 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 6 Solid-State Electronic Materials Electronic materials fall into three categories (WRT resistivity): Insulators  > 10 5  -cm (diamond  = 10 16 ) Semiconductors 10 -3 <  < 10 5  -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.

7 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 7 Solid-State Electronic Materials Electronic materials fall into three categories (WRT resistivity): Insulators  > 10 5  -cm (diamond  = 10 16 ) Semiconductors 10 -3 <  < 10 5  -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.

8 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 8 Solid-State Electronic Materials Electronic materials fall into three categories (WRT resistivity): Insulators  > 10 5  -cm (diamond  = 10 16 ) Semiconductors 10 -3 <  < 10 5  -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.

9 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 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

10 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 10 Semiconductor Materials (cont.) Semiconductor Bandgap Energy E G (eV) Carbon (diamond) 5.47 Silicon 1.12 Germanium 0.66 Tin 0.082 Gallium arsenide 1.42 Gallium nitride 3.49 Indium phosphide 1.35 Boron nitride 7.50 Silicon carbide 3.26 Cadmium selenide 1.70

11 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 11 Covalent Bond Model Silicon diamond lattice unit cell. Corner of diamond lattice showing four nearest neighbor bonding. View of crystal lattice along a crystallographic axis. 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.

12 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 12 Silicon Covalent Bond Model (cont.) Silicon atom

13 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 13 Silicon Covalent Bond Model (cont.) Silicon atom Silicon atom Covalent bond

14 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 14 Silicon Covalent Bond Model (cont.) Silicon atom Covalent bonds in silicon

15 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 15 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 What happens as the temperature increases?

16 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 16 Silicon Covalent Bond Model (cont.) 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. 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

17 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 17 Intrinsic Carrier Concentration The density of carriers in a semiconductor as a function of temperature and material properties is: E G = semiconductor bandgap energy in eV (electron volts) k = Boltzmann’s constant, 8.62 x 10 -5 eV /K T = absolute termperature , K B = material-dependent parameter, 1.08 x 10 31 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.

18 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 18 Intrinsic Carrier Concentration (cont.) Electron density is n (electrons/cm 3 ) and for intrinsic material n = n i . Intrinsic refers to properties of pure materials. n i ≈ 10 10 cm -3 for Si The density of silicon atoms is n a ≈ 5x10 22 cm -3 Thus at a room temperature one bond per about 10 13 is broken Intrinsic carrier density (cm -3 )

19 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 19 Electron-hole concentrations A vacancy is left when a covalent bond is broken. The vacancy is called a hole.

20 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 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).

21 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 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 ( n i for intrinsic material)

22 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 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 ( n i for intrinsic material) Hole density is represented by p .

23 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 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 ( n i for intrinsic material) Hole density is represented by p . For intrinsic silicon, n = n i = p .

24 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 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 ( n i for intrinsic material) Hole density is represented by p . For intrinsic silicon, n = n i = p . The product of electron and hole concentrations is pn = n i 2 . The pn product above holds when a semiconductor is in thermal equilibrium (not with an external voltage applied).

25 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 25 Drift Current Charged particles move or drift under the influence of the applied field. The resulting current is called drift current .

26 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 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.

27 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 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/cm 3 )(cm/s) = A/cm 2 ]

28 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 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/cm 3 )(cm/s) = A/cm 2 ] 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.

29 .NJIT ECE-271 Dr. S. Levkov Chap 2 - 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,  :