Introduction to Semiconductor Physics 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India http://folk.uio.no/ravi/cmp2013
Review of Semiconductor Physics Semiconductor fundamentals Doping PN junction
Temperature dependence of Resistivity The electric resistance of all substances is found to change more or less with a change in temperature. Three types of changes are observed: 1) The resistance may increase with increasing temperature, which is true for all pure metals and most alloys. 2) The resistance may decrease with increase of temperature, which is true for semiconductors. 3) The resistance may be independent of temperature, which is approximately true for some special alloys, such as manganese (Cu 0.84; Ni 0.12; Mn 0.04) P.Ravindran, PHY075- Condensed Matter Physics, Spring 2013 16 July: Introduction to Semiconductor 3 Physics
Specific Resistivity of Metals as a Function of Temperature 4
Residual Resistivity and Defects Shown here are measured curves of the low temperature resistivity of Na with different defect concentrations The resistivity is constant for very small temperatures. In the "bend" it shows T 5 characteristics. For most of the temperature range it is proportional to T. Defects clearly do increase the residual resistance (the upper two curves are for Na with defects, the lower one for rather perfect Na); the effect can be much large in other metals or for larger defect densities. 5
What Is a Semiconductor? Many materials, such as most metals, allow electrical current to flow through them These are known as conductors Materials that do not allow electrical current to flow through them are called insulators Pure silicon, the base material of most transistors, is considered a semiconductor because its conductivity can be modulated by the introduction of impurities
Semiconductors A material whose properties are such that it is not quite a conductor, not quite an insulator Some common semiconductors elemental Si - Silicon (most common) Ge - Germanium compound GaAs - Gallium arsenide GaP - Gallium phosphide AlAs - Aluminum arsenide AlP - Aluminum phosphide InP - Indium Phosphide
Crystalline Solids In a crystalline solid, the periodic arrangement of atoms is repeated over the entire crystal Silicon crystal has a diamond lattice
Crystalline Nature of Silicon Silicon as utilized in integrated circuits is crystalline in nature As with all crystalline material, silicon consists of a repeating basic unit structure called a unit cell For silicon, the unit cell consists of an atom surrounded by four equidistant nearest neighbors which lie at the corners of the tetrahedron
What s so special about Silicon? Cheap and abundant Amazing mechanical, chemical and electronic properties The material is very well-known to mankind SiO 2 : sand, glass Si is column IV of the periodic table Similar to the carbon (C) and the germanium (Ge) Has 3s² and 3p² valence electrons
Nature of Intrinsic Silicon Silicon that is free of doping impurities is called intrinsic Silicon has a valence of 4 and forms covalent bonds with four other neighboring silicon atoms
Semiconductor Crystalline Structure Semiconductors have a regular crystalline structure for monocrystal, extends through entire structure for polycrystal, structure is interrupted at irregular boundaries Monocrystal has uniform 3- dimensional structure Atoms occupy fixed positions relative to one another, but are in constant vibration about equilibrium
Semiconductor Crystalline Structure Silicon atoms have 4 electrons (valence) in outer shell inner electrons (core) are very closely bound to atom These electrons are shared with neighbor atoms on both sides to fill the shell resulting structure is very stable electrons are fairly tightly bound no loose electrons at room temperature, if battery applied, very little electric current flows
Conduction in Crystal Lattices Semiconductors (Si and Ge) have 4 electrons in their outer shell 2 in the s subshell 2 in the p subshell As the distance between atoms decreases the discrete subshells spread out into bands As the distance decreases further, the bands overlap and then separate the subshell model doesn t hold anymore, and the electrons can be thought of as being part of the crystal, not part of the atom 4 possible electrons in the lower band (valence band) 4 possible electrons in the upper band (conduction band)
Energy Bands in Semiconductors The space between the bands is the energy gap, or forbidden band
Insulators, Semiconductors, and Metals This separation of the valence and conduction bands determines the electrical properties of the material Insulators have a large energy gap electrons can t jump from valence to conduction bands no current flows Conductors (metals) have a very small (or nonexistent) energy gap (overlapping CB and VB) electrons easily jump to conduction bands due to thermal excitation current flows easily Semiconductors have a moderate energy gap only a few electrons can jump to the conduction band leaving holes only a little current can flow
Insulators, Semiconductors, and Metals (continued) Conduction Band Valence Band Conductor Semiconductor Insulator
Hole - Electron Pairs Sometimes thermal energy is enough to cause an electron to jump from the valence band to the conduction band produces a hole - electron pair Electrons also fall back out of the conduction band into the valence band, combining with a hole pair elimination pair creation hole electron
Improving Conduction by Doping To make semiconductors better conductors, add impurities (dopants) to contribute extra electrons or extra holes elements with 5 outer electrons contribute an extra electron to the lattice (donor dopant) elements with 3 outer electrons accept an electron from the silicon (acceptor dopant)
Improving Conduction by Doping (cont.) Phosphorus and arsenic are donor dopants if phosphorus is introduced into the silicon lattice, there is an extra electron free to move around and contribute to electric current very loosely bound to atom and can easily jump to conduction band produces n type silicon sometimes use + symbol to indicate heavier doping, so n+ silicon phosphorus becomes positive ion after giving up electron
Improving Conduction by Doping (cont.) Boron has 3 electrons in its outer shell, so it contributes a hole if it displaces a silicon atom boron is an acceptor dopant yields p type silicon boron becomes negative ion after accepting an electron
Epitaxial Growth of Silicon Epitaxy grows silicon on top of existing silicon uses chemical vapor deposition new silicon has same crystal structure as original Silicon is placed in chamber at high temperature 1200 o C (2150 o F) Appropriate gases are fed into the chamber other gases add impurities to the mix Can grow n type, then switch to p type very quickly
Diffusion of Dopants It is also possible to introduce dopants into silicon by heating them so they diffuse into the silicon no new silicon is added high heat causes diffusion Can be done with constant concentration in atmosphere close to straight line concentration gradient Or with constant number of atoms per unit area predeposition bell-shaped gradient Diffusion causes spreading of doped areas top side
Diffusion of Dopants (continued) Concentration of dopant in surrounding atmosphere kept constant per unit volume Dopant deposited on surface - constant amount per unit area
Ion Implantation of Dopants One way to reduce the spreading found with diffusion is to use ion implantation also gives better uniformity of dopant yields faster devices lower temperature process Ions are accelerated from 5 KeV to 10 MeV and directed at silicon higher energy gives greater depth penetration total dose is measured by flux number of ions per cm 2 typically 10 12 per cm 2-10 16 per cm 2 Flux is over entire surface of silicon use masks to cover areas where implantation is not wanted Heat afterward to work into crystal lattice
Hole and Electron Concentrations To produce reasonable levels of conduction doesn t require much doping silicon has about 5 x 10 22 atoms/cm 3 typical dopant levels are about 10 15 atoms/cm 3 In undoped (intrinsic) silicon, the number of holes and number of free electrons is equal, and their product equals a constant actually, n i increases with increasing temperature This equation holds true for doped silicon as well, so increasing the number of free electrons decreases the number of holes np = ni 2
INTRINSIC (PURE) SILICON Higher temperatures create free charge carriers. A hole is created in the absence of an electron. At 23C there are 10¹º particles/cm³ of free carriers At 0 Kelvin Silicon density is 5*10²³ particles/cm³ Silicon has 4 valence electrons, it covalently bonds with four adjacent atoms in the crystal lattice
DOPING There are two types of doping N-type and P-type. The N in N-type stands for negative. A column V ion is inserted. The extra valence electron is free to move about the lattice The P in P-type stands for positive. A column III ion is inserted. Electrons from the surrounding Silicon move to fill the hole.
Energy-band Diagram A very important concept in the study of semiconductors is the energyband diagram It is used to represent the range of energy a valence electron can have For semiconductors the electrons can have any one value of a continuous range of energy levels while they occupy the valence shell of the atom That band of energy levels is called the valence band Within the same valence shell, but at a slightly higher energy level, is yet another band of continuously variable, allowed energy levels This is the conduction band
Band Gap Between the valence and the conduction band is a range of energy levels where there are no allowed states for an electron This is the band gap E G In silicon at room temperature [in electron volts]: EG 11. ev Electron volt is an atomic measurement unit, 1 ev energy is necessary to decrease of the potential of the electron with 1 V. 1eV 1.602 10 19 joule
Impurities Silicon crystal in pure form is good insulator - all electrons are bonded to silicon atom Replacement of Si atoms can alter electrical properties of semiconductor Group number - indicates number of electrons in valence level (Si - Group IV)
Impurities Replace Si atom in crystal with Group V atom substitution of 5 electrons for 4 electrons in outer shell extra electron not needed for crystal bonding structure can move to other areas of semiconductor current flows more easily - resistivity decreases many extra electrons --> donor or n-type material Replace Si atom with Group III atom substitution of 3 electrons for 4 electrons extra electron now needed for crystal bonding structure hole created (missing electron) hole can move to other areas of semiconductor if electrons continually fill holes again, current flows more easily - resistivity decreases electrons needed --> acceptor or p-type material
Counter Doping Insert more than one type of Ion The extra electron and the extra hole cancel out
A Little Math n= number of free electrons p=number of holes ni=number of electrons in intrinsic silicon=10¹º/cm³ pi-number of holes in intrinsic silicon= 10¹º/cm³ Mobile negative charge = -1.6*10-19 Coulombs Mobile positive charge = 1.6*10-19 Coulombs At thermal equilibrium (no applied voltage) n*p=(ni) 2 (room temperature approximation) The substrate is called n-type when it has more than 10¹º free electrons (similar for p-type)
P-N Junction Also known as a diode One of the basics of semiconductor technology - Created by placing n-type and p-type material in close contact Diffusion - mobile charges (holes) in p-type combine with mobile charges (electrons) in n-type
P-N Junction Region of charges left behind (dopants fixed in crystal lattice) Group III in p-type (one less proton than Sinegative charge) Group IV in n-type (one more proton than Si - positive charge) Region is totally depleted of mobile charges - depletion region Electric field forms due to fixed charges in the depletion region Depletion region has high resistance due to lack of mobile charges
THE P-N JUNCTION
The Junction The potential or voltage across the silicon changes in the depletion region and goes from + in the n region to in the p region
Biasing the P-N Diode THINK OF THE DIODE AS A SWITCH Forward Bias Applies - voltage to the n region and + voltage to the p region CURRENT! Reverse Bias Applies + voltage to n region and voltage to p region NO CURRENT
P-N Junction Reverse Bias positive voltage placed on n-type material electrons in n-type move closer to positive terminal, holes in p-type move closer to negative terminal width of depletion region increases allowed current is essentially zero (small drift current)
P-N Junction Forward Bias positive voltage placed on p-type material holes in p-type move away from positive terminal, electrons in n-type move further from negative terminal depletion region becomes smaller - resistance of device decreases voltage increased until critical voltage is reached, depletion region disappears, current can flow freely
P-N Junction - V-I characteristics Voltage-Current relationship for a p-n junction (diode)
Current-Voltage Characteristics THE IDEAL DIODE Positive voltage yields finite current Negative voltage yields zero current REAL DIODE
The Ideal Diode Equation qv I I0 exp 1 kt, where I 0 diode current with reverse bias q 1602. 10 coulomb, the electronic ch arg e k 19 5 ev 8. 62 10, Boltzmann' s cons tan t K