Lecture 2 Basic Semiconductor Physics

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Lecture 2Basic Semiconductor PhysicsIn this lecture you will learn: What are semiconductors? Basic crystal structure of semiconductors Electrons and holes in semiconductors Intrinsic semiconductors Extrinsic semiconductorsn-doped and p-doped semiconductorsECE 315 – Spring 2005 – Farhan Rana – Cornell UniversitySemiconductors in the Periodic TableAtomic numberGroup IV semiconductorsEach element in group IV has 4electrons in its outer mostatomic shellA Silicon atom has:2 electrons in the first atomic shell8 electrons in the second atomic shell4 electrons in the third outermost atomic shellA Silicon atomECE 315 – Spring 2005 – Farhan Rana – Cornell University1

Semiconductors in the Periodic TableAtomic numberGroup IV semiconductorsEach element in group IV has 4electrons in its outer mostatomic shell The outermost electrons are called valenceelectronscore The inner electrons are called the coreelectronsA Silicon atomECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityCovalent Bonding in Silicon A Silicon atom with 4 electrons in the valence shell is drawn ina cartoon way as: Two Silicon atoms can come together to form a covalent bond by sharing twoelectrons among themselvesalso drawn asshared electronsa covalent bond Covalent bonding is energetically favorable (i.e. Silicon atoms “like” to formcovalent bonds with each other)ECE 315 – Spring 2005 – Farhan Rana – Cornell University2

A Silicon Crystal Lattice (A Cartoon View)In a Silicon crystal: Each Silicon atom is surrounded by 4 other Silicon atoms Each Silicon atom forms 4 covalent bonds with the neighboring Silicon atomsECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityActual 3D Structure of a Silicon Crystal Latticecovalent bonds Each Silicon atom is surrounded by 4 other Silicon atoms in a tetrahedralconfiguration Silicon atomic density 5x1022 cm-3ECE 315 – Spring 2005 – Farhan Rana – Cornell University3

Electrons and Holes in Semiconductors - IA perfect Silicon crystal latticeECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityElectrons and Holes in Semiconductors - IIpositively chargedhole negatively chargedfree electronA Silicon crystal lattice with one broken bond It requires energy to break a covalent bond The required energy is called the “bandgap” (bandgap of Silicon is 1.12 eV) A broken bond results in one negatively charged “free electron” and onepositively charged “hole” The “free electron” can freely move around in the crystalECE 315 – Spring 2005 – Farhan Rana – Cornell University4

Electrons and Holes in Semiconductors - IIIpositively chargedhole negatively chargedfree electronA Silicon crystal lattice with one broken bond A hole can also move through the lattice !! A hole moves when an electron from a neighboring bond jumps over to fill that“hole”ECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityElectrons and Holes in Semiconductors - IIIpositively chargedhole negatively chargedfree electronA Silicon crystal lattice with one broken bond A hole can also move through the lattice !! A hole moves when an electron from a neighboring bond jumps over to fill that“hole”ECE 315 – Spring 2005 – Farhan Rana – Cornell University5

Definitions and Notations Used in ECE 3150 The word electron will usually mean a “free electron” (and not an electronforming the covalent bond or a core electron) The electron density is denoted by: n (units: 1/cm3) The hole density is denoted by: p (units: 1/cm3) The charge of an electron is: The charge of a hole is: q qq 1.6 10 19CoulombsECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityElectrons and Holes at Near Zero TemperatureA perfect Silicon crystal lattice at temperature T 0 K There are no broken bonds and no electrons and holes( i.e. n p 0 )ECE 315 – Spring 2005 – Farhan Rana – Cornell University6

Electrons and Holes at Nonzero Temperatureholes electrons A Silicon crystal lattice at temperature T 0 K Thermal energy breaks the covalent bonds and electron-hole pairs are generated(remember it takes energy to break a covalent bond) The number of electrons and holes generated are equal - for every electrongenerated there is also a hole generated ( i.e. n p ) Question: what is the electron and hole density at room temperature?ECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityThermal EnergyThermal energy is typically measured in units of “ KT ”“K” is the Boltzmann’s constant and equals 1.38 x 10-23 Joules/KelvinTemperature “T” is measured in degrees KelvinRoom temperature corresponds to T 300 KRoom temperature corresponds to a “KT ” value of 4.14 x 10-21 Joulesor 25.8 meVEnergy in eV Energy in JoulesElectron charge in CoulombsECE 315 – Spring 2005 – Farhan Rana – Cornell University7

Generation and Recombination in Semiconductors - IGeneration:The breaking of a bond to generate an electron-hole pair is called generation Generation rate G(T ) is a function of temperature Units of G(T ) are: cm-3-s-1Recombination:An electron can also combine with a hole to form a bond. This process is calledrecombination. It is the reverse of generation. Recombination rate R(T ) is proportional to the product npR T np R T k T np(you need electrons as well as holes for recombination to happen) Units of R(T ) are also: cm-3-s-1ECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityGeneration and Recombination in Semiconductors - IICondition of Thermal Equilibrium: In thermal equilibrium a steady state exists in which the rate of electron-holegeneration is equal to the rate of electron-hole recombination,R T G T k T no po G T G T no po k T thermal equilibrium electron and holedensities are usually denoted by noand poG T 2is written as ni T k T Therefore, in thermal equilibrium, no po ni2 T By convention, the ratio Since equal number of electrons and holes are present in thermalequilibrium, we have, no po ni T ni is called the “intrinsic” carrier density. It equals the number of electrons(or holes) present in a pure semiconductor in equilibrium at a giventemperature.10-3 For Silicon, ni 1 10 cmat room temperature (i.e. at T 300K)ECE 315 – Spring 2005 – Farhan Rana – Cornell University8

Doping in SemiconductorsDoping:The introduction of certain impurity atoms in a pure semiconductor to controlits electronic properties is called doping Doping is done by two kinds of impurity atoms:a)Donor atomsb)Acceptor atomsDonors:Donor atoms are used to increase the electron density in a semiconductor Group V elements have 5 electrons intheir outermost atomic shell (one morethan group IV atoms) Group V elements can act as electron“donors” in SiliconECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityDoping by Donors in Silicon (n-doping)positively chargedfixed donor atom Asnegatively chargedfree electronDoping Silicon with Arsenic Atoms Donor atom concentration is denoted by: Nd (units: 1/cm3) Each donor atom contributes one free electron to the crystal Donor atom after giving off an electron becomes positively chargedECE 315 – Spring 2005 – Farhan Rana – Cornell University9

Doping in SemiconductorsAcceptors:Acceptor atoms are used to increase the hole density in a semiconductor Group III elements have 3 electrons intheir outermost atomic shell (one less thangroup IV atoms) Group III elements can act as electron“Acceptors” in SiliconECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityDoping by Acceptors in Silicon (p-doping)negatively chargedfixed acceptor atomB positively chargedholeDoping Silicon with Boron Atoms Acceptor atom concentration is denoted by: Na (units: 1/cm3) Each acceptor atom contributes one hole to the crystal by “accepting” oneelectron from a neighboring bond Acceptor atom after giving off a hole (or equivalently, after accepting anelectron) becomes negatively chargedECE 315 – Spring 2005 – Farhan Rana – Cornell University10

Electron-Hole Density in Doped SemiconductorsConsider a N-doped semiconductor in thermal equilibrium:Doping density Ndq Nd no po 0 Use condition of charge neutrality:2 Together with the relation: no po ni To obtain:no 2Nd N d ni22 2 po 2Nd N d ni22 2 If Nd ni , which is usually the case for N-doping, then the above relationssimplify:no Ndn-doping lets one make the electron densitymuch greater than the intrinsic value nin2po iNdECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityElectron-Hole Density in Doped SemiconductorsNow consider a P-doped semiconductor in thermal equilibrium:Doping density Naq Na no po 0 Use condition of charge neutrality:no po ni2 Together with the relation: To obtain:po no If Na nisimplify:2Na N a ni22 2 2Na N a ni22 2 , which is usually the case for P-doping, then the above relationspo Nan2no iNap-doping lets one make the hole density muchgreater than the intrinsic value niECE 315 – Spring 2005 – Farhan Rana – Cornell University11

Electron-Hole Density Vs Doping DensityN-doped semiconductors With increasing N-doping the electrondensity increases above the intrinsicvalue and the hole density decreasesbelow the intrinsic valuenoExample:SupposeNd 1017 cm- 3thenpono 1017 cm- 3andpo Ndand Sinceni 1010 cm-3Nd ni ni2 103 cm- 3noECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityElectron-Hole Density Vs Doping DensityP-doped semiconductors With increasing P-doping the holedensity increases above the intrinsicvalue and the electron densitydecreases below the intrinsic valuepoExample:SupposeNa 1017 cm- 3thennopo 1017 cm-3andno Naand Sinceni 1010 cm-3Na ni ni2 103 cm-3poECE 315 – Spring 2005 – Farhan Rana – Cornell University12

Compound SemiconductorsIII-V semiconductors:Elements in group III can be combined withelements in group V to give compoundsemiconductors (as opposed to elementalsemiconductors of group IV)*One can also have II-VI semiconductorsGa atomsCrystal lattice ofthe groups III-VcompoundsemiconductorGaAsAs atomsECE 315 – Spring 2005 – Farhan Rana – Cornell UniversityElemental and Compound SemiconductorsPSiSiInA Diamond LatticeA Zincblende Lattice(Si, C, Ge, etc)(ZnS, GaS, InP, etc)ECE 315 – Spring 2005 – Farhan Rana – Cornell University13

ECE 315 – Spring 2005 – Farhan Rana – Cornell University14

Lecture 2 Basic Semiconductor Physics In this lecture you will learn: What are semiconductors? Basic crystal structure of semiconductors Electrons and holes in semiconductors Intrinsic semiconductors Extrinsic semiconductors n-doped and p-doped semiconduct

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