ECE 250

1. ECE 250 Electronic Device Modeling

2. Introduction to Semiconductor Physics • You should really take a semiconductor device physics course. • We can only cover a few basic ideas and some simple calculations.

3. Electronic Devices • Most electronic devices are made out of semiconductors, insulators, and conductors. • Semiconductors • Old Days – Germanium (Ge) • Now – Silicon (Si) • Now – Gallium Arsenide (GaAs) used for high speed and optical devices. • New – Silicon Carbide (SiC) – High voltage Schottky diodes.

4. Elements • Elements in the periodic table are grouped by the number of electrons in their valence shell (most outer shell). • Conductors – Valence shell is mostly empty (1 electron) • Insulators – Valence shell is mostly full • Semiconductors – Valence shell is half full (Or is it half empty?)

5. Semiconductors • Silicon and Germanium are group 4 elements – they have 4 electrons in their valence shell. Valence Electron Si

6. Silicon • When two silicon atoms are placed close to one another, the valence electrons are shared between the two atoms, forming a covalent bond. Covalent bond Si Si

7. Si Si Si Si Si Silicon

8. Si Si Si Si Si Silicon • An important property of the 5-atom silicon lattice structure is that valence electrons are available on the outer edge of the silicon crystal so that other silicon atoms can be added to form a large single silicon crystal.

9. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si

10. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si • At 0 ºK, each electron is in its lowest energy state so each covalent bond position is filled. • If a small electric field is applied to the material, no electrons will move because they are bound to their individual atoms. • => At 0 ºK, silicon is an insulator.

11. Silicon • As temperature increases, the valence electrons gain thermal energy. • If a valence electron gains enough energy, it may break its covalent bond and and move away from its original position. • This electron is free to move within the crystal.

12. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si + -

13. + - Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Since the net charge of a crystal is zero, if a negatively (-) charged electron breaks its bond and moves away from its original position, a positively charged “empty state” is left in its original position.

14. Semiconductors • As temperature increases, more bonds are broken creating more negative free electrons and more positively charged empty states. (Number of free electrons is a function of temperature.) • To break a covalent bond, a valence electron must gain a minimum energy Eg, called the energy band gap. (Number of free electrons is a function of Eg.)

15. Insulators • Elements that have a large energy band gap of 3 to 6 eV are insulators because at room temperature, essentially no free electrons exist. • Note: an eV is an electron volt. It is the amount of energy an electron will gain if it is accelerated through a 1 volt potential.

16. Electron Volt Also, 1 eV = 1.518 10-22 BTU, but who cares.

17. Conductors • Elements that have a small energy band gap are conductors. • These elements have a large number of free electrons at room temperature because the electrons need very little energy to escape from their covalent bonds.

18. Semiconductors • Semiconductors have a band gap energy of about 1 eV • Silicon = 1.1 eV • GaAs = 1.4 eV • Ge = 0.66 eV

19. Empty States • An electron that has sufficient energy and is adjacent to an empty state may move into the empty state, leaving an empty state behind.

20. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si + This electron can fill the empty state. Empty state originally here.

21. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si + Empty state now here.

22. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si +

23. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si +

24. Empty States • Moving empty states can give the appearance that positive charges move through the material. • This moving empty state is modeled as a positively charged particle called a hole. • In semiconductors, two types of “particles” contribute to the current: positively charged holes and negatively charged electrons.

25. Carrier Concentrations • The concentrations of holes and free electrons are important quantities in the behavior of semiconductors. • Carrier concentration is given as the number of particles per unit volume, or • Carrier concentration =

26. Intrinsic Semioconductor • Definition – An intrinsic semiconductor is a single crystal semiconductor with no other types of atoms in the crystal. • Pure silicon • Pure germanium • Pure gallium arsenide.

27. Carrier Concentration • In an intrinsic semiconductor, the number of holes and free electrons are the same because they are thermally generated. • If an electron breaks its covalent bond we have one free electron and one hole. • In an intrinsic semiconductor, the concentration of holes and free electrons are the same.

28. Intrinsic Semiconductors • = the concentration of free electrons in an intrinsic semiconductor. • = the concentration of holes in an intrinsic semiconductor.

29. Intrinsic Carrier Concentration • B and Eg are determined by the properties of the semiconductor. • Eg = band gap energy (eV) • B = material constant

30. Intrinsic Carrier Concentration • T = temperature (ºK) • K = Boltzmann’s constant = 86.2×10-6 eV/ºK

31. Material Constants

32. Important Note:Book uses a slightly different Notation!

33. Book Material Constants

34. Example • Find the intrinsic carrier concentration of free electrons and holes in a silicon semiconductor at room temperature.

35. MathCAD

36. MathCAD The concentration of silicon atoms in an intrinsic semiconductor is 51022 atoms/cm3.

37. Extrinsic Semiconductors • Since the concentrations of free electrons and holes is small in an intrinsic semiconductor, only small currents are possible. • Impurities can be added to the semiconductor to increase the concentration of free electrons and holes.

38. Extrinsic Semiconductors • An impurity would have one less or one more electron in the valance shell than silicon. • Impurities for group 4 type atoms (silicon) would come from group 3 or group 5 elements.

39. Extrinsic Semiconductors • The most common group 5 elements are phosphorous and arsenic. • Group 5 elements have 5 electrons in the valence shell. • Four of the electrons fill the covalent bonds in the silicon crystal structure. • The 5th electron is loosely bound to the impurity atom and is a free electron at room temperature.

40. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si - Si Si Si Si Si P

41. Extrinsic Semiconductors • The group 5 atom is called a donor impurity since it donates a free electron. • The group 5 atom has a net positive charge that is fixed in the crystal lattice and cannot move. • With a donor impurity, free electrons are created without adding holes.

42. Extrinsic Semiconductors • Adding impurities is called doping. • A semiconductor doped with donor impurities has excess free electron and is called an n-type semiconductor.

43. Extrinsic Semiconductors • The most common group 3 impurity is boron which has 3 valence electrons. • Since boron has only 3 valence electrons, the boron atom can only bond with three of its neighbors leaving one open bond position.

44. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si B

45. Extrinsic Semiconductors • At room temperature, silicon has free electrons that will fill the open bond position, creating a hole in the silicon atom whence it came. • The boron atom has a net negative charge because of the extra electron, but the boron atom cannot move.

46. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si + Si Si Si Si Si B

47. Extrinsic Semiconductors • Since boron accepts a valence electron, it is called an acceptor impurity. • Acceptor impurities create excess holes but do not create free electrons. • A semiconductor doped with an acceptor impurity has extra holes and is called a p-type semiconductor.

48. Carrier Concentrations • For any semiconductor in thermal equilibrium nopo=ni2, where • no = the concentration of free electrons. • po = the concentration of holes. • ni = the intrinsic carrier concentration

49. Extrinsic Carrier Concentrations • For an n-type semiconductor with donor impurities, the concentration of donor impurities is Nd with units #/cm3. • If Nd >> ni, then the concentration of free electrons in the n-type semiconductor is approximately no Nd.

50. Extrinsic Carrier Concentrations • Since nopo=ni2 for any semiconductor in thermal equilibrium, and • For an n-type semiconductor, no Nd • Where po is the concentration of holes in the n-type semiconductor.