Electrical Engineering 2. Lecture 2. Microelectronics 2. Dr. Peter Ewen. (Room G08, SMC; email - pjse). 10 5 10 4 10 3 10 2 10 1. GWP. Electronics. Automobiles. Global sales ($ Billions). Semi- conductors. Steel. Source: “Fundamentals of semiconductor
Electrical Engineering 2 Lecture 2 Microelectronics 2 Dr. Peter Ewen (Room G08, SMC; email - pjse)
105 104 103 102 101 GWP Electronics Automobiles Global sales ($ Billions) Semi- conductors Steel Source: “Fundamentals of semiconductor Fabrication” by G.S. May and S.M. Sze 1980 1990 2000 2010 Year Fig. 2 Gross world product (GWP) and sales volumes of various manufacturing industries from 1980 to 2000 and projected to 2010.
Gordon E. Moore, co-founder of Intel. “Moore’s Law” – The number of transistors per chip (die) doubles approximately every 18 months. Fig. 5
REASONS FOR CONTINUING SIZE REDUCTION • Higher productivity • Faster operation • Lower power consumption • Higher yield • New products
Resistance and Resistivity Cross-sectional area A A = ab A = r2 R = ρl/A A = ? a l b r l ρ is Resistivity – depends only on the material l A Fig. 8: The resistance of an object with uniform cross-sectional area A. R is Resistance – depends on the material and geometry of the object
CONDUCTANCE G = 1/R CONDUCTIVITY σ = 1/ρ
ELECTRIC FIELD + Fig. 9 E F F + - F = qEE is Electric Field F is Force on Charge q Direction of the Electric Field is defined by the direction of the force on a positive charge – i.e. if q is positive, F and E are in the same direction. V is Potential Units for E: V/m for V = kx + C
Energy acquired by a charge, q, moving through a potential difference, ΔV V1 ΔV = V2 – V1 V2 q Δx Energy (Work) = Force × Distance = qE ×Δx = q ×Δx = q ΔV ΔV Δx If q and V are both positive, the change in the energy of the particle will be positive, i.e. its energy will increase.
LECTURE 2 Useful concepts from atomic theory: the electron volt (eV) electron transitions quantum numbers electron orbits • Bonding in metals and semiconductors • Electron energy bands
The potential variation through a region of a semiconductor sample is given by • V = –2.8x3 + 0.7x • where V is in volts and x is the distance in microns from a • reference point. • What is the minimum value of the electric field in the • semiconductor and the value of x at which it occurs? • 0.289 Vμm-1 at x = 0 μm • B. 0.135 Vμm-1 at x = 0.289 μm • C. -0.7 Vμm-1 at x = 0 μm • D. Something completely different
3. Energy of a charged particle moving through a potential difference One method of producing doped regions in semiconductor wafers is to expose them to a beam of high energy dopant ions using a piece of equipment called an ion implanter. If As++ ions from an implanter are being used to create an n-type region, through what potential difference must they be accelerated if they require an energy of 3.2x10-14J to penetrate a sufficient distance into the wafer?
3. Energy of a charged particle moving through a potential difference E = 3.2x10-14J ΔV = ? As++ The arsenic ion is doubly charged in this case (As++), hence the charge q on the ion is +2e, where e is the magnitude of the charge on the electron (e = +1.610-19C):
ATOMIC THEORY • Properties of solids are governed by the properties of their atoms • Solid state processes have atomic analogues • Atomic theory can be applied directly to solids to obtain practical information Valence shell
ELECTRON ENERGY - THE ELECTRON-VOLT (eV) The ELECTRON-VOLT is defined as the energy acquired by an electron in passing through a potential difference of 1v E = q V 1eV = 1.6 x 10-19 J
ΔE = h ( = c = hc ) - frequency ΔE - wavelength ELECTRON TRANSITIONS Fig. 13 Electron energy E6 E5 E4 E3 E2 E1 nucleus electrons in allowed orbits Planck’s constant: h = 6.63 x 10-34 Js Speed of light: c = 3 x 108 ms-1 atom
The state in which an electron exists in an atom can be specified by 4 numbers: • n, l, m, s – Quantum Numbers • n – principal • l – subshell • m – magnetic moment • s – spin • PAULI EXCLUSION PRINCIPLE • No two electrons in the same system can have the same set of quantum numbers.
Fig.14: Electron orbits for selected atoms. Hydrogen Helium 1 2 +1 +2 Lithium The electrons in the outermost shell are termed valence electrons +3 2 1 Silicon Carbon +14 2 8 4 +6 2 4 Germanium Copper 2 8 18 1 +32 2 8 18 4 +29
Bonding between isolated atoms Outermost shell of valence electrons
Bonding between collections of atoms Atoms bond together to form a crystal.
METALLIC BONDING Valence electrons are free to move through solid. In monovalent metals each atom contributes one free valence electron at room temp. COVALENT BONDING Valence electrons shared with adjacent atoms. In Si & Ge each atom shares 2 valence electrons with each of 4 neighbouring atoms – i.e. there are 4 covalent bonds. +ve ion cores cloud of -ve electrons
At 0K all the valence electrons are firmly held in the bonds electrons Fig. 15: Crystal structure of silicon silicon atoms
As temperature rises, some of the bonding electrons break free electrons Fig. 15: Crystal structure of silicon silicon atoms
Fig. 16 ELECTRON ENERGY BANDS Allowed bands Forbidden band Electron energy Allowed band Allowed band 2 4 1 N Number of atoms Isolated atom
Fig. 16 ELECTRON ENERGY BANDS Conduction band Electron energy Valence electrons Valence band 1 2 4 N Number of close atoms Isolated atom
MetalSemiconductorInsulator Fig. 17 Conduction Band (CB) CB CB Valence Band (VB) Eg (~1 eV) Electron energy VB Eg The ENERGY GAP, Eg, corresponds to the energy required to break a covalent bond in the solid. VB Mainly empty energy levels Mainly occupied energy levels
Strong Bond strength Weak Fig. 18: Variation of energy gap with interatomic spacing for Group IV elements.
ELECTRON ENERGY As temperature increases, structure expands Applying pressure compresses structure Energy levels of the isolated atom Valence electrons Equilibrium spacing INTERATOMIC SPACING Fig 19: Variation of the energy bands with interatomic spacing for silicon (and also germanium and carbon).
4. Variation of energy gap with temperature Empirically the energy gap, Eg, of common semiconductors (Si, Ge, GaAs) is found to vary with temperature, T, as: (where A and B are constants and T is in degrees K). A GaAs LED is heated from room temperature to 500K. Find the change in the frequency of the light emitted if Eg(0) = 1.52 eV, A = 5.4x10-4 eV/K, and B = 204 K for GaAs.
4. Variation of energy gap with temperature C.B electron Planck’s constant frequency E = h = Eg Eg E = h energy levels V.B In atom In semiconductor A GaAs LED is heated from room temperature to 500K. Find the change in the frequency of the light emitted…
a) At room temperature (which we can take as approximately 300K): Note the conversion factor 1.610-19 to convert the 1.42eV to joules (the electron-volt is not an SI unit).
b) At 500K: Hence the change in frequency/wavelength is If this change of wavelength took place in the visible part of the spectrum it would correspond to the light changing colour from green to yellow. 60nm
I / mA If you increase the reverse voltage across a diode, eventually it will “break down” at a certain value (the breakdown voltage, VBD) and a reverse current will flow. VBD In one mechanism of reverse breakdown, carriers are accelerated to high energies by the reverse voltage and knock electrons out of bonds. In this case, how will VBD change as temperature increases? V / volts In a real device BREAKDOWN occurs: VBD – the BREAKDOWN VOLTAGE Increase Decrease
SUMMARY ELECTRONS IN ATOMS Definition of the electron volt Electron energy levels Electron transitions: DE = h Pauli exclusion principle limits the number of electrons allowed in an orbit
ELECTRONS IN SOLIDS • Bonding occurs when outermost (valence) electrons on neighbouring atoms interact. • Metallic bonding - "gas" of free electrons holds solid together. • Covalent bonding – electrons shared • with adjacent atoms. • Si and Ge atoms form 4 covalent bonds – tetrahedral structure. • Thermal energy can break covalent bonds, creating free electrons.
ELECTRON ENERGY BANDS The discrete energy levels of the isolated atom split and spread out to form BANDS of closely spaced levels in the solid. The band containing the bonding electrons is the VALENCE BAND. The band above this is the CONDUCTION BAND. The band structure determines whether the solid is a metal (no gap), semiconductor (gap 1eV), or insulator (large gap).
Energy gap, Eg - increases as bond strength increases - decreases as atomic spacing increases - decreases as temperature increases (important for diodes and LED's)