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# Solid St Electr Devices ELEE 4328

University of Texas-Pan American (UTPA)

GPA 3.89

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This 20 page Class Notes was uploaded by Belle Wintheiser on Thursday October 29, 2015. The Class Notes belongs to ELEE 4328 at University of Texas-Pan American (UTPA) taught by Edward Banatoski in Fall. Since its upload, it has received 34 views. For similar materials see /class/231313/elee-4328-university-of-texas-pan-american--utpa- in Electrical Engineering at University of Texas-Pan American (UTPA).

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Chapter 6 FETHEMTMOSFET Page 1 of7 ELEE 4328 Solid State Electron Device Theory Fall 2008 Consider channel ow in resistive channel of varying width From Ohms law V IR In differential form since R is varying 7 g 1 ii If we consider that there is no recombination of electrons the current must be conserved as a function of distance that is I is a constant and dIdX 0 and therefore dV dR 7 17 dx dx We can also write the differential resistance in terms of the resistivity differential length dX and area A of the channel The area is the height of the resistive channel 2aW times the width Z W is the gate depletion region given in terms of Vgc gate to channel voltage dx 1 dx 1 dx 1 dx dR p7 A qud 22a2W Zq nNdZ CIW Zq nNdZ 251g Vcx a 9N4 qazN We then have for dRdX defining a new quantity the pinch off voltage as VP T s dR l l l 1 d V 7 Cx 1 dx 2qNZ ngg ch anNZ 1 Vg ch 1 dx a a qua2 VP Rearranging the equation with dX on the left and fVcXchX on the right we have Jailc x an nNd Z VC x WTVP P L Vd V V x 1dej2qaynNdz1 0 0 P Defining G0 anynNdZ L lejIL 0ILGOL Vd g 3 VP P P MTV Hg Chapter 6 FETHEMTMOSFET Page 2 of7 ELEE 4328 Solid State Electron Device Theory Fall 2008 62 Junction FET The JFET equation in terms of a conducting n channel width controlled by reverse biased pn junctions with channel resistance de ned by mobility u and doping Nd is 3 3 22 N V V V 3 V 3 N 2 IdquP 713 3 D G 3 7G where VPq a isthepinch L VP 3 VP 3 25 off voltage Equation 610 where VDVPVG results from setting BIDBVD0 for Max ID the saturation current should read Negative sign was positive in 5th Edition V 3 V 3 P 3 V V 3 IDsat GOVP 76E 76 1 P or if the pn junction or Schottky gate built in voltage is included 3 V V V V 3 IDsatG0VP MEM l VP 3 V 3 P IDSS the IDSat for VG 0 from 610 would be IDSSG0Vp3 so the IDSat equation could then be written 3 3V V 3 I sat1 is2 7G l D DSS V VP P As mentioned in the text measured characteristics more closely follow the squared characteristic 2 2 2 V V V V I sat2 is 1 1 1i or I 17b G D DSS VP DSS VP DSS VP with the built in voltage Vbi of the pn junction for the JFET or Schottky voltage for Schottky gate Chapter 6 FETHEMTMOSFET Page 3 of7 ELEE 4328 Solid State Electron Device Theory Fall 2008 63 The Metal Semiconductor FET 631 The GaAs MESFET The ID equation for the GaAs MESFET is the same as for the JFET except there is no factor of two for the dual gate The single gate pinches the channel against the semi insulating GaAs substrate and the dimension a is 01 to 02 microns The built in Schottky potential Vbi is included in the expression I 3 3 quDZQan V7DE Vin VG 23 VDVZ71VG 2 D L P VP 3 VP 3 V P A simpler model applicable to the MESFET and HEMT is to assume the electron velocity is entirely saturated under the gate and the mobile charge is determined by conditions at the source edge of the gate controlled only by the gate voltage For the MESFET it is just the hx at x0 determined by the gate voltage so the drain current is ID sat qnv 1 Vb VG 3 mch qnvtha l T 614 page 254 in the text P Again it is usually assumed a square law applies to the GaAs FET 1d IDSSVg Vz PSPICE model level l Bbreak For the velocity saturated case the model goes over to linear at high gate bias V V 1d 1DSS g 2 PSPICE model level 2 1 3ng V i For both models a nite slope of drain current with respect to drain voltage occurs resulting in the equations 1d IDSSVg V 2 1 lVdS PSPICE model level 1 V V 1d 1DSS g 2 1lVdS PSPICE model leve12 1 3ng Vi The Cgs for level 1 is the same as the JFET Chapter 6 FETHEMTMOSFET Page 4 of7 ELEE 4328 Solid State Electron Device Theory Fall 2008 The level 2 GaAs FET Bbreak PSPICE Cgs is ofthe form Cgs Area C gSO 1 K K 1 Vquot 2C K 1 2 V ng 3 171 1 V 7 CgSArea Cg50K1K3l V ngo kK2 171 Where the K s are functions of the voltages There are some effects due to a doping profile Ndx which may be adjusted to get a linear current and therefore constant transconductance 632 The High Electron Mobility Transistor HEMT The are two common HEMTs The first is the AlGaAsGaAs HEMT where electrons are confined in a triangular well created by the high electric field a due to the positive ionized donors in the AlGAAs The second is the pseudomorphic A1015 Ga075AsIn 02Ga08AsAlo25 Ga075 As pHEMT usually delta doped planar doped above and below the InGaAs channel in the ratio 4 top to 1 bottom for maximum at range of transconductance where the electrons are confined to the InGaAs channel potential well The electrons so confined require a solution of the Shrodinger wave equation for the triangular well in terms of Airy functions or the finite potential well for the pHEMT Solving the Shrodinger and Poisson equation self consistently and using the 2D density of states results in a curve of the equilibrium Fermi level referred to the minimum of the channel conduction band at the top of the high mobility channel versus the two dimension electron gas concentration nS electronscmz This curve is then linearly approximated and does not vary much within the restrictions required for an optimal structure The linear approximations may then be used to calculate the threshold voltage for the HEMT For the HEMT the linearized function is EF 71 EF0 a1ns 00518eV009427x10 eVcm2 Chapter 6 FETHEMTMOSFET Page 5 of7 ELEE 4328 Solid State Electron Device Theory Fall 2008 For the HEMT 2 VM Vb Vp0 EF0 AEC where VP M for the HEMT where a is the gr sup ply 50 distance from the gate to the AlGaAsGaAs heterojucntion and 5 is the spacer thickness that is the distance from where the doping ND stops to the AlGaAsGaAs heterojunction usually 30 Angstoms The EFO comes from the linear t of the Ef versus nS curve where the intercept for nzd 0 the threshold condition is the EFO 00518eV A simple approximation that EFO is just the rst energy level of a in nite quantum well for the channel well gives a value close to EFO Solving the Poisson equation for the gate voltage above threshold results in the expression qquot WUP AEC EF VG mxVP AEC EF0 a1nsVG Vbz rearranging the equation where a new quantity Aa is de ned as Aa srsupplysoalq which is about 6070 Angstroms 6070 XlO398 cm often 68A is used resulting in grsu 150 grsu 150 qnzd ap AEC EF0 VG Vbz VG Vzh Since the nzd is the sheet density electronscm2 the channel current assuming velocity saturation is then Z IDSat39 qnzdvnsatz CVg V2 W043 AEC EF0 VG Vb For the HEMT above threshold the gate capacitance is given by the change in channel charge nS with gate voltage times the area of the 2D which is the gate length multiplied by the width L zgrsu 18 g PFJ 0 ngCOX a C53 mkz a Ag 2 Chapter 6 FETHEMTMOSFET Page 6 of7 ELEE 4328 Solid State Electron Device Theory Fall 2008 For the GaN HEMT an additional complication occurs because of polarization charge at the AlGaNGaN interface so the Vth is Vth bx Vp0 EF0 AE C The polarization for AlGaNGaN is the sum of spontaneous and piezioelectric components and is given in terms of the composition X of the Alea1xN as PT PSP 13 8404x10 6x1725 gtlt10 6x2 For the pHEMT the linearization is not appropriate and the Vth can just be extracted from measurement The Cox equation is still applicable 11 MOSFET Mosfet Thresholds Ref Introduction to VLSI Circuits and Systems John Uyemura John Wiley and Sons NY 2002 ISBN 0471127043 MOSFET threshold N channel p well DI shallow implant dose for threshold control cm2 note surface charge Qi and oxide capacitance C Fcm2 are per unit area For inversion S 2 KT N KT N Q g 7lni l 7lniD V or 7 C i fn q n J fp q n J FB ms ps Car or tax 1 qD 1 qD V7H C7 2ngINA S 2 fn VFB C I Ci quSNA 2 fn 2 fn VFB C I 1 qD 1 qD VIP C7M 2ngND S 2 fp VFB C0 C7M 2ngIND 2 fp 2 fp VFB C I D1 acceptors for th and donors for th would be positive sign for acceptors for th For polysilicon gates the following equations apply N 0 N E N FS KTlnDply Elni 1m i glni 1 for p well 617 n q n 2 q 7 Ipaly ELEE4328 Fall 2008 Topic 1 SI Units Material Properties of Matter Reference Chapter 1 Solid State Electronic Devices Page 1 T11 SI Units Bold type most important italic information only and not on exams The units used in most texts for semiconductors are SISystem International same as mksmeters kiligramsseconds except that centimeters are used instead of meters For example concentrations are usually atomscm3 The formula then require that constants such as so the dielectric constant offree space be expressed as 8854x103914 Volts cm not 8854x103912 Vm Also it is good to keep in mind that in the quantum mechanics section energy calculations are usually in joules while in the semiconductor equations energy is in eV electron volts Electron volts must be multiplied by q16x10 19 to convert electron volts to joules That is 1 eV equals 16x103919joules Joules must be divided by q16x10 19 to convert joules to eV electron volts Also many statistical quantities are related to the energy E in joules divided by the average thermal energy EKBT where the average energy in joules is given by Boltzmann s constant KB Goules deg K times temperature T in degrees KKelvin room temperature 27 deg C300 deg Kelvin If E is in eV multiplying by q to get joules gives qEKBT EKBTq The quantity KBTq equals 00259 eV in Appendix II page 523 in the text You should become familiar with this constant KBTq00259 eV as it appears repeatedly in many equations While length is usually in centimeters cm other units include Angstroms A I will use the symbol A 1 A 1x108 cm 1x10 10m 01 nm microns 1 p 1x10 4 cm1x10 6 n1 nanometer 1nm1x10 7 cm 1x109 m10 A You should be able to readily convert from one unit to another T12 Material Properties of Matter Reference Chapter 1 Crystal Properties and Growth of Semiconductors Periodic chart of Elements Groups 1 to 8 4 5 6 7 8 H He Li Be B C N 0 F1 Ne Na Mg A1 Si P S C1 Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Sl Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pg Ad Cd In Sn Sb Te I Xe Cs BaLu Hf Ta W Re Os Ir Pt Au Hg Ti Pb Bi Po At Rn metals lt lsemiconductorsl gt gases and liquids 1 MetalsSemiconductorsInsulators Metals found on left side of chart outer electrons forming metallic bond are mobile free electrons that move with electric field but metal remains charge neutral during conduction Semiconductors outer electrons form pairs in covalent electron bond Covalent electron pairs are immobile rigidly locked in place valance electrons at absolute zero and semiconductor is insulator As temperature increases from absolute zero some electrons ELEE4328 Fall 2008 Topic 1 SI Units Material Properties of Matter Reference Chapter 1 Solid State Electronic Devices Page 2 become conduction free electrons and leave a hole missing electron at the valance bond site Conduction occurs by both the motion of conduction free electrons and motion of valence electron adjacent to a hole lling the hole resulting in the hole moving in the opposite direction The hole has a net unbalanced positive charge The energy required to free the immobile valence electron creating a mobile conduction electron and mobile hole pair is the bandgap energy Eg 111V Silicon text Appendix 111 page 540 Insulators outer electrons form pairs in covalent electron bond and have extremely high bandgap energy Eg 90V for Silicon Dioxide Only extremely high Electric Fields 2x105 Volts cm can break bonds in an insulator in what is called dielectric breakdown 2 Compound Semiconductors Semiconductors can be formed from two or more elements the most common of which is Gallium Arsenide GaAs GaAs is a binary compound with half the atoms the anion Gallium and half the atoms cation Arsenide Ternary compounds such as Aluminum Gallium Arsenide are made up of three elements and can contain fraction amounts of the two anions Aluminum and Gallium The amount of atoms are expressed by a quantity x which is the fraction of the anion sites of the rst element and lx the fraction of anion sites occupied by the second ion The maximum of Aluminum that can be made for AlGaAs without producing a defect called EL2 is 25 or x the composition of 025 The compound Alea1xAs would be expressed as A1015 Ga075As and 14 the anion sites would be occupied by Aluminum and 34 the anion sites by Gallium The compound semiconductors are sometimes characterized by what periodic chart groups they are formed from GaAs is referred to as a IIIV semiconductor as Gallium is from group 3 and arsenide from group 5 Usually Roman numerals are used for the groups Recently the group IV compound semiconductor SiGe is used in some HBTs and FETs and SiC in some power FETs Less common are the IIVI compound semiconductors such as Cadmium Sul de CdS 11 Semiconductor MaterialsClassi cation of materials Electrical Energy Elemental Compound Conductivity band gap mobile energy to create electronscms mobile electron Metals good1023cm3 0 volts GroupIIIIA1 A1CuSi Semiconductors Intinsic poor 1071014cm3 02 to 33 voltsGroup IV Group IIIV Doped moder10161020cm3 CSiGe GaAsGaN Insulator few0cm3 0cm3 gt5 voltsSiOz90VSi3N450V 12 Crystal lattices web sites httpjasengbuf faloeduapplets and httpcst wwwnrlnavymillattice Single Crystal made up of atoms have ordered repeated spacing over long range Polycrystalline made up of randomly oriented small regions of single crystal Amorphous atoms random oriented and spaced ELEE4328 Fall 2008 Topic 1 Page 3 Unit cell The smallest orthogonal volume of a crystal with side dimension a the lattice constant with an arrangement of atoms that is repeated throughout the crystal 121 Crystal has periodic structure Position of atoms in crystal speci ed by pqs indices with unit vectors abc r p a q b s c abc on the order of5 to 7 Angstroms 103910 In 122 Cubic Lattices Cubic lattice a b c atom locations form a cube side length a Lattice Type Abbreviation Atoms per unit cell Total Atomscomer AtomsFace Atoms in Cell 18 atom 12 atom 1 atom Simple Cubic sc 1 8X1 8 Body centered Cub bcc 2 8X1 8 1Xl Face centered Cub fcc 4 8X1 8 6X12 Diamond Zinc blend diazb 8 8X 1 8 6X 1 2 1X4 Wurtzitenon cubic wrtz 12 2X6X16 2X126X131X7 Packing factor fraction of unit cell lled by spherical atoms packed such that spheres in contact Abrev Nearest Atom Spheres x Vol sphere Fill Fractio Neighbor Radius volume ofcube or Packing Factor Simple Cubic scc a a2 14713 a23a3 716 0 52 Bodycentered Cubic bcc 13a2 a W4 24713a1343a3 m380 68 Face centered Cubic fcc max2 a 124 44u3ma 1243a3 n1260 74 Diamond ah39a 13a4 a V349 847 3a1383a3 m316034 123 Planes and directionsplanes and directions and lt gt hkl plane hkl equivalent planes hkl direction lthklgt equivalent directions hkl called the Miller indices of a plane found by 1 Find intercepts of plane with crystal axes in multiples of base vectors abc 2 Take reciprocals of integers in step 1 and multiply each by the same constant integer until three numbers are all integers 3 Label plane with hkl where hkl are the three integers hkl direction same as vector Note 111 direction perpendicular to 111 Note lt111gt equivalent to 111111111111111111111 Note 100 from inverse of plane aXis intercepts X1yoozoo note Xl not 0 That is plane is not allowed to go through origin in designating 100 Note 110 from inverse of plane with aXis intercepts X1y1zoo 124 Diamond Zinc Blend and Wurtzite Lattice Diamond fcc with extra atoms located at r14a 14 b 14c from each fcc atom Note no bonds along unit cell sides but internal tetrahedral bonds 4 from each atom Can also think of fcc unit cell with two atoms 1A way up lying on diagonal of bottom plane and two atoms 3A way up lying on diagonal of bottom plane that is perpendicular to diagonal of two atoms 1A way up Diamond lattices made from atomic Group IV elements C Si and Ge ELEE4328 Fall 2008 Topic 1 Page 4 Zinc Blend Same as diamond except the atoms inside the unit cell are different from the atoms on the corners and faces the fcc atoms of the unit cell Atoms in ZincBlend are from Atomic groups either 111 and V or II and VI Gallium Aresnide GaAs is the most common IIIV GaN may become the most common IIIV Wurtzite is a distorted Zinc Blend with a longer bond along one direction of the 4 tetrahedral bonds and the other three then in a common plane that form a hexagon pattern Wurtzite was practically unheard of in semiconductors until Gallium Nitride GaN A vast amount of research and a number of companies formed in the last three years to manufacture GaN Planes in Wurtzite are designated a1a2a3c with a s in plane rotated 60deg and c normal to that plane Wurtzite then has two parameters of the unit cell a and c Alloys Alloys have more than one atom that perform the same bond function Gallium and Aluminum are both group III elements so an alloy of Alea1xAs is formed with x being the fraction of Gallium sites occupied by Aluminum The fraction X can range from 0 which would be pure GaAs to 1 which would be pure AlAs There is also no regular pattern to the order of Al and Gallium in the alloy So if X was 13 the pattern need not be a repeating 1 Al two Ga but a random arrangement A portion of which might be AlGaGaAlGaAlGaGaAlGaGaGa so that only on the average 13 of the Gallium sights are occupied by aluminum 13 Bulk Crystal Growth 134 Starting Materials reference only not on ELEE4328 exams M GS VI etallurgical grade Silicon up to several thousand ppm parts per million impurities is madefrom reduction ofSiOz glass using carbon S102 2C Sz39 2C0 The Si is reacted with H Cl gas not acid to form trichlorsilane which is now EGSElectronic grade impurities ppbparts per billion Si 3HCl aSiHCl3 H2 Liquid SiH C l 3 is fractionally distilled to separate SiH Cl 3 from the impurities and then reacted with hydrogen to get ppb Si 2SiHCl3 2H2 2Si 6HCl 135 Growth of Single Crystal Ingots Single crystal Silicon is grown from melted Si by putting a small stationary Silicon single crystal seed in contact with the melt at a particular orientation and slowly raising it up from the rotating melt The crystal growth method is called the Czochralski method The melt is kept molten byRF heating while it is in the rotating Carbon crucible GaAs crystalline growth is a bit more complicated in that the As is volatile so to keep it from evaporating a layer of melted B 20 3 oats on top of the molten GaAs This method is called liquid encapsulated Czochralski LEC growth ELEE4328 Fall 2008 Topic 1 Page 5 136 Wafers The crystals are then ground into perfect cylinders Most Si is grown in the lt100gt direction which gives the best surface characteristics Note often designated 100 not lt100gt A at is then ground on the cylinder to identify the 110plane The circuits and scribe lines are oriented to the at to minimize damage when the individual chips on the wafer are sawed or scribed and broken apart The cylinder is then sawed into wafers The individual wafers may then have an additional grove etched into the wafer for further process orientation For Silicon presence and combinations of ats designate dopant type and crystal orientation See web site wwwmacomgaaswaferscomdata 137 Doping Two types of impurity atoms called dopants are purposely introduced into a semiconductor to control conductivity 1 Donor atoms have an extra valence electron Gourp V 5 outer electrons one of which is easily removed when the remaining 4 form tetrahedral bonds The easily removed electron becomes a mobile conduction electron at room temperature leaving behind the donor atom as an immobile ionized atom of positive charge The number of mobile conduction electrons created per unit volume the concentration n is equal to the concentration of impurity atoms 11 ND where n mobile electronscm3 and ND donor atomscm3 A semiconductor doped with donor atoms is called 11 type and electric current conduction is by mobile conduction electrons 2 Acceptor atoms have one less electron than what is needed to form 4 tetrahedral bonds The acceptor atom takes an electron from an adjoining semiconductor atom creating a hole an unoccupied valence electron site at that atom The captured electron is now a fixed negative charge at the acceptor atom sight The number of holes created is equal to the number of acceptor atoms p N A where p mobile holescm3 and N A acceptor atomscm3 Because neighboring immobile valance electrons can jump into an adjacent hole their mobility is limited to jumping into adjacent holes the quantity that is kept track of is the hole which acts as mobile positive charge A semiconductor doped with acceptor atoms is called p type and current conduction is by mobile holes the motion of a valance bond sight missing a valence electron Reference only not ELEE4328 1 mpurity atoms are added during crystal growth to the initial melt but because the solubility of atoms is different for the liquid and solid state to calculate the number ofatoms a distribution coef cient must be used wherefor C3 the concentration in the solid and C L that in the liquid the distribution coef cient kd relates the two concentrations by kd is kd 035 phosphorus 03 Arsenic in Silicon ELEE4328 Fall 2008 14 Topic 1 Page 6 Epitaxial Growth Epitaxial growth or epitaxy is the growth of single crystal semiconductor on a semiconductor wafer referred to as the substrate Dopants are introduced at the same time and are usually opposite that of the substrate wafer forming a diode which electrically isolates the epi region from the bulk wafer Lattice Matching in Epitaxial Growth Figure 113 page 19 and next page notes Except for the Alea1xAs and Alea1xN systems if the material or alloy composition changes for the epi layer being grown the spacing between the atoms characterized by a the unit cell lattice constant also changes The Alea1xAs system doesn t because AlAs and GaAs have approximately the same lattice constant 566 A versus 565 A Si a543A and Ge a565 A do not have the same lattice constant so for SixGe1x epitaxy on Si wafers the growth is pseudomorphic This means the xy spacing is 543A the same as Silicon but the vertical cell dimension will be somewhere between 565 and 543A Figure 114 page 20 Pseudomorphic growth is under strain however and this limits defect free growth to a few hundred Angstroms in the vertical direction The relationship between lattice constant a and alloy composition is usually linear and this is referred to as Vegard s law So for SixGe1x the latest constant is given by a543x565lx565565543x564022x Anstroms using the lattice constants for Silicon 543A and Germanium 565A given above The relationship between band gap and alloy composition is usually quadratically non linear Experimentally measured band gap as a function of alloy composition is usually fit with a quadratic equation with higher order terms referred to as bowing parameters Some equations for band gap versus x composition for ternarythree element alloys and xy composition for quatemary4 element alloys are please note there are a number of different equations in the literature with slight variation in the constants depending on the quality of material and method of measurement Alea1xAs EgeVl424l247x for xlt045 EgeVl424l247xll47x0452 for xgt045 In1 xGaxAs EgeV03600505x0555x2 IanAs1x EgeV036008910101x2 Gaxln1xP EgeVl3510643x0786x2 EgeVl350688x1068y0758x20078 y20069xy 0322x2y003xy2 Alea1xNZinc BlendEgeV338250x005x2 Si or GaP substrate AlealXNWu1tziteEgeV342l7lxl0x2 A1203 Sapphire or SiC substrate GaxIn1xAsyP1y ELEE4328 Fall 2008 142 Topic 1 Page 7 Vapor Phase Epitaxy In vapor phase epitaxy the wafer is heated to high temperature byRF heating of a carbon susceptor and a gas such as Silane is passed over it reacting as SiH4 Si1000degC 2H2 or a reversible reaction using H Cl can be used for etching Si removal or growth SiCl4 H2 Si1150 1250degC 4HCl or M OWE Metal organic vapor phase epitaxy or OM WE Organometallic vapor phase epitaxy can be used for example using the organomettalic compound trimethylgallium CH33Ga AsH3 gt GaAs700degC 3CH4 Vapor phase epitaxy have rapid growth rates 1 10 microns per hour Molecular Beam Epitaxy In molecular beam epitaxy the wafer is exposed to a beam of atoms or molecules of material The whole system is in a high vacuum and the atom beams come from effusion cells where atoms are thermally heated to high temperature to create a thermal beam The beams are controlled by inserting shutters between the effusion source and the wafers which are then open and closed The growth rate is low enough one atomic layer per second to allow atomic layer accuracy and single layer doping called delta doping but the growth rate lt 1 micron per hour which is slow making it costly Also for the nitrides plasma sources are required to produce N atoms which are more elaborate costly systems ELEE4328 Fall 2009 Topic 1 SI Units Material Properties of Matter Reference Chapter 1 Solid State Electronic Devices Page 1 T11 SI Units Bold type most important italic information only and not on exams The units used in most texts for semiconductors are SISystem International same as mksmeters kilograms seconds except that centimeters are used instead of meters For example concentrations are usually atomscm3 The formula then require that constants such as so the dielectric constant offree space be expressed as 8854x103914 Volts cm not 8854x103912 Vm Also it is good to keep in mind that in the quantum mechanics section energy calculations are usually in joules while in the semiconductor equations energy is in eV electron volts Electron volts must be multiplied by q16x10 19 to convert electron volts to joules That is 1 eV equals 16x103919joules Joules must be divided by q16x10 19 to convert joules to eV electron volts Also many statistical quantities are related to the energy E in joules divided by the average thermal energy EKBT where the average energy in joules is given by Boltzmann s constant KB Goules deg K times temperature T in degrees KKelvin room temperature 27 deg C300 deg Kelvin If E is in eV multiplying by q to get joules gives qEKBT EKBTq The quantity KBTq equals 00259 eV in Appendix II page 523 in the text You should become familiar with this constant KBTq00259 eV as it appears repeatedly in many equations While length is usually in centimeters cm other units include Angstroms A I will use the symbol A 1 A 1x108 cm 1x10 10m 01 nm microns 1 p 1x10 4 cm1x10 6 m nanometer 1nm1x10 7 cm 1x109 m10 A You should be able to readily convert from one unit to another T12 Material Properties of Matter Reference Chapter 1 Crystal Properties and Growth of Semiconductors Periodic chart of Elements Groups 1 to 8 4 5 6 7 8 H He Li Be B C N 0 F1 Ne Na Mg A1 Si P S C1 Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Sl Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pg Ad Cd In Sn Sb Te I Xe Cs BaLu Hf Ta W Re Os Ir Pt Au Hg Ti Pb Bi Po At Rn metals lt lsemiconductorsl gt gases and liquids 1 MetalsSemiconductorsInsulators Metals found on left side of chart outer electrons forming metallic bond are mobile free electrons that move with electric field but metal remains charge neutral during conduction Semiconductors outer electrons form pairs in covalent electron bond Covalent electron pairs are immobile rigidly locked in place valance electrons at absolute zero and semiconductor is insulator As temperature increases from absolute zero some electrons ELEE4328 Fall 2009 Topic 1 SI Units Material Properties of Matter Reference Chapter 1 Solid State Electronic Devices Page 2 become conduction free electrons and leave a hole missing electron at the valance bond site Conduction occurs by both the motion of conduction free electrons and motion of valence electron adjacent to a hole lling the hole resulting in the hole moving in the opposite direction The hole has a net unbalanced positive charge The energy required to free the immobile valence electron creating a mobile conduction electron and mobile hole pair is the bandgap energy Eg 111 eV for Silicon text Appendix 111 page 540 Insulators outer electrons form pairs in covalent electron bond and have extremely high bandgap energy Eg 90V for Silicon Dioxide Only extremely high Electric Fields 2x105 Volts cm can break bonds in an insulator in what is called dielectric breakdown 2 Compound Semiconductors Semiconductors can be formed from two or more elements the most common of which is Gallium Arsenide GaAs GaAs is a binary compound with half the atoms the anion Gallium and half the atoms cation Arsenide Ternary compounds such as Aluminum Gallium Arsenide are made up of three elements and can contain fraction amounts of the two anions Aluminum and Gallium The amount of atoms are expressed by a quantity x which is the fraction of the anion sites of the rst element and lx the fraction of anion sites occupied by the second ion The maximum of Aluminum that can be made for AlGaAs without producing a defect called EL2 is 25 or x the composition of 025 The compound Alea1xAs with x 025 would be expressed as A1025Ga075As and 14 the anion sites would be occupied by Aluminum and 34 the anion sites by Gallium The r 39 39 J are quot characterized by what periodic chart groups they are formed from GaAs is referred to as a IIIV semiconductor as Gallium is from group 3 and arsenide from group 5 Usually Roman numerals are used for the groups Recently the group IV compound semiconductor SiGe is used in some HBTs and FETs and SiC in some power FETs Less common are the IIVI compound semiconductors such as Cadmium Sul de CdS 11 Semiconductor MaterialsClassi cation of materials Electrical Energy Elemental Compound Conductivity band gap mobile energy to create electronscms mobile electron Metals good1023cm3 0 volts GroupIIIIA1 A1CuSi Semiconductors Intrinsic poor 1071014cm3 02 to 33 voltsGroup IV Group IIIV Doped moderate10161020cm3 CSiGe GaAsGaN Insulator few0cm3 0cm3 gt5 voltsSiOz90VSi3N450V 12 Crystal lattices web sites httpjasengbuf faloeduapplets and httpcst wwwnrlnavymillattice Single Crystal made up of atoms have ordered repeated spacing over long range Polycrystalline made up of randomly oriented small regions of single crystal grain Amorphous atoms random oriented and randomly spaced intertwined chains ELEE4328 Fall 2009 Topic 1 Page 3 Unit cell The smallest orthogonal volume of a crystal with side dimension a the lattice constant with an arrangement of atoms that is repeated throughout the crystal 121 Crystal has periodic structure Position of atoms in crystal speci ed by pqs indices with unit vectors abc r p a q b s c abc on the order of5 to 7 Angstroms 103910 In 122 Cubic Lattices Cubic lattice a b c atom locations form a cube side length a Lattice Type Abbreviation Atoms per unit cell Total Atomscomer AtomsFace Atoms in Cell 18 atom 12 atom 1 atom Simple Cubic sc 1 8X1 8 Body centered Cub bcc 2 8X1 8 1Xl Face centered Cub fcc 4 8X1 8 6X12 Diamond Zinc blend diazb 8 8X 1 8 6X 1 2 1X4 Wurtzitenon cubic wrtz ac 12 2X6X1 6 2X126X1 3 1X7 Packing factor fraction of unit cell lled by spherical atoms packed such that spheres in contact Abrev Nearest Atom Spheres x Vol sphere Fill Fraction Neighbor Radius volume ofcube or Packing Factor Simple Cubic scc a a2 8x184iu3 a23a3 7m 0 52 Bodycentered Cubic bcc 13a2 a W4 24713a1343a3 urnaw 68 Face centered Cubic fcc max2 a v24 447 3a1243a3 m260 74 Diamond alia 13a4 a V349 847 3a1383a3 m316034 123 Planes and directionsplanes and directions and lt gt hkl plane hkl equivalent planes hkl direction lthklgt equivalent directions hkl called the Miller indices of a plane found by 1 Find intercepts of plane with crystal axes in multiples of base vectors abc 2 Take reciprocals of integers in step 1 and multiply each by the same constant integer until three numbers are all integers 3 Label plane with hkl where hkl are the three integers hkl direction same as vector Note 111 direction perpendicular to 111 Note lt111gt equivalent to 111111111111111111111 Note 100 from inverse of plane aXis intercepts X1yoozoo note Xl not 0 In other words the is plane is not allowed to go through origin in designating 100 Note 110 from inverse of plane with aXis intercepts X1y1zoo 124 Diamond Zinc Blend and Wurtzite Lattice Diamond fcc with extra atoms located at r14a 14 b 14c from each fcc atom Note no bonds along unit cell sides but internal tetrahedral bonds 4 from each atom Can also think of fcc unit cell with two atoms 1A way up lying on diagonal of bottom plane and two atoms 3A way up lying on diagonal of bottom plane that is perpendicular to diagonal of two atoms 1A way up Diamond lattices are formed by atomic Group IV elements C Si and Ge but C to form diamond requires high pressure ELEE4328 Fall 2009 Topic 1 Page 4 Zinc Blend Same as diamond except the atoms inside the unit cell are different from the atoms on the corners and faces the fcc atoms of the unit cell Atoms in ZincBlend are from Atomic groups either 111 and V or II and VI Gallium Aresnide GaAs is the most common IIIV GaN may become the most common IIIV Wurtzite is a distorted Zinc Blend with a longer bond along one direction of the 4 tetrahedral bonds and the other three then in a common plane that form a hexagon pattern Wurtzite was practically unheard of in semiconductors until a Gallium Nitride GaN process was developed the past few years Planes in Wurtzite are designated a1a2a3c with a s in a plane at 60deg angles forming a hexagon and c normal to that plane Wurtzite there for has two parameters of the unit cell a and c Compound Semiconductors or Alloys Compound semiconductors have more than one atom that perform the same bond function Gallium and Aluminum are both group III elements so an alloy of AleaHAs is formed with x being the fraction of Gallium sites occupied by Aluminum The fraction X can range from 0 which would be pure GaAs to 1 which would be pure AlAs There is also no regular pattern to the order of Al and Gallium in the alloy So if is 13 the pattern need not be a repeating 1 Al 2 Ga but a random arrangement a portion of which might be AlGaGaAlGaGaGaAlGaAlGaGa so that only on the average 13 of the Gallium sights are occupied by aluminum This randomness does affect conduction electron motion and is called alloy scattering 13 Bulk Crystal Growth 134 Starting Materials reference only not on ELEE4328 exams M GS VI etallurgical grade Silicon up to several thousand ppm parts per million impurities is madefrom reduction ofSiOz glass using carbon S102 2C Sz39 2C0 The Si is reacted with H Cl gas not acid to form trichlorsilane which is now EGSElectronic grade impurities ppbparts per billion Si 3HCl aSiHCl3 H2 Liquid SiH C l 3 is fractionally distilled to separate SiH Cl 3 from the impurities and then reacted with hydrogen to get ppb Si 2SiHCl3 2H2 2Si 6HCl 135 Growth of Single Crystal Ingots Single crystal Silicon is grown from melted Si by putting a small stationary Silicon single crystal seed in contact with the melt at a particular orientation and slowly raising it up from the rotating melt The crystal growth method is called the Czochralski method The melt is kept molten byRF heating while it is in the rotating Carbon crucible GaAs crystalline growth is a bit more complicated in that the As is volatile so to keep it from evaporating a layer of melted B 20 3 oats on top of the molten GaAs This method is called liquid encapsulated Czochralski LEC growth ELEE4328 Fall 2009 Topic 1 Page 5 136 Wafers The crystals are then ground into perfect cylinders Most Si is grown in the lt100gt direction which gives the best surface characteristics Note often designated 100 not lt100gt A at is then ground on the cylinder to identify the 110plane The circuits and scribe lines are oriented to the at to minimize damage when the individual chips on the wafer are sawed or scribed and broken apart The cylinder is then sawed into wafers The individual wafers may then have an additional grove etched into the wafer for further process orientation For Silicon presence and combinations of ats designate dopant type and crystal orientation See web site wwwmacomgaaswaferscomdata 137 Doping Two types of impurity atoms called dopants are purposely introduced into a semiconductor to control conductivity 1 Donor atoms have an extra valence electron Gourp V 5 outer electrons one of which is easily removed when the remaining 4 form tetrahedral bonds The easily removed electron becomes a mobile conduction electron at room temperature leaving behind the donor atom as an immobile ionized atom of positive charge The number of mobile conduction electrons created per unit volume the concentration n is equal to the concentration of impurity atoms 11 ND where n mobile electronscm3 and ND donor atomscm3 A semiconductor doped with donor atoms is called 11 type and electric current conduction is by mobile conduction electrons 2 Acceptor atoms have one less electron than what is needed to form 4 tetrahedral bonds The acceptor atom takes an electron from an adjoining semiconductor atom creating a hole an unoccupied valence electron site at that atom The captured electron is now a fixed negative charge at the acceptor atom sight The number of holes created is equal to the number of acceptor atoms p N A where p mobile holescm3 and N A acceptor atomscm3 Because neighboring immobile valance electrons can jump into an adjacent hole their mobility is limited to jumping into adjacent holes the quantity that is kept track of is the hole which acts as mobile positive charge A semiconductor doped with acceptor atoms is called p type and current conduction is by mobile holes the motion of a valance bond sight missing a valence electron Reference only not ELEE4328 1 mpurity atoms are added during crystal growth to the initial melt but because the solubility of atoms is different for the liquid and solid state to calculate the number ofatoms a distribution coef cient must be used wherefor C3 the concentration in the solid and C L that in the liquid the distribution coef cient kd relates the two concentrations by kd is kd 035 phosphorus 03 Arsenic in Silicon ELEE4328 Fall 2009 14 Topic 1 Page 6 Epitaxial Growth Epitaxial growth or epitaxy is the growth of single crystal semiconductor on a semiconductor wafer referred to as the substrate Dopants are introduced at the same time and are usually opposite that of the substrate wafer forming a diode which electrically isolates the epi region from the bulk wafer Lattice Matching in Epitaxial Growth Figure 113 page 19 and next page notes Except for the Alea1xAs and Alea1xN systems if the material or alloy composition changes for the epi layer being grown the spacing between the atoms characterized by a the unit cell lattice constant also changes The Alea1xAs system doesn t because AlAs and GaAs have approximately the same lattice constant 566 A versus 565 A Si a543A and Ge a565 A do not have the same lattice constant so for SixGe1x epitaxy on Si wafers the growth is pseudomorphic This means the xy spacing is 543A the same as Silicon but the vertical cell dimension will be somewhere between 565 and 543A Figure 114 page 20 Pseudomorphic growth is under strain however and this limits defect free growth to a few hundred Angstroms in the vertical direction The relationship between lattice constant a and alloy composition is usually linear and this is referred to as Vegard s law So for SixGe1x the latest constant is given by a543x565lx565565543x564022x Anstroms using the lattice constants for Silicon 543A and Germanium 565A given above The relationship between band gap and alloy composition is usually quadratically non linear Experimentally measured band gap as a function of alloy composition is usually fit with a quadratic equation with higher order terms referred to as bowing parameters Some equations for band gap versus x composition for ternarythree element alloys and xy composition for quatemary4 element alloys are please note there are a number of different equations in the literature with slight variation in the constants depending on the quality of material and method of measurement Alea1xAs EgeVl424l247x for xlt045 EgeVl424l247xll47x0452 for xgt045 In1 xGaxAs EgeV03600505x0555x2 IanAs1x EgeV036008910101x2 Gaxln1xP EgeVl3510643x0786x2 EgeVl350688x1068y0758x20078 y20069xy 0322x2y003xy2 Alea1xNZinc BlendEgeV338250x005x2 Si or GaP substrate AlealXNWu1tziteEgeV342l7lxl0x2 A1203 Sapphire or SiC substrate GaxIn1xAsyP1y ELEE4328 Fall 2009 142 Topic 1 Page 7 Vapor Phase Epitaxy In vapor phase epitaxy the wafer is heated to high temperature byRF heating of a carbon susceptor and a gas such as Silane is passed over it reacting as SiH4 Si1000degC 2H2 or a reversible reaction using H Cl can be used for etching Si removal or growth SiCl4 H2 Si1150 1250degC 4HCl or M OWE Metal organic vapor phase epitaxy or OM WE Organometallic vapor phase epitaxy can be used for example using the organomettalic compound trimethylgallium CH33Ga AsH3 gt GaAs700degC 3CH4 Vapor phase epitaxy have rapid growth rates 1 10 microns per hour Molecular Beam Epitaxy In molecular beam epitaxy the wafer is exposed to a beam of atoms or molecules of material The whole system is in a high vacuum and the atom beams come from effusion cells where atoms are thermally heated to high temperature to create a thermal beam The beams are controlled by inserting shutters between the effusion source and the wafers which are then open and closed The growth rate is low enough one atomic layer per second to allow atomic layer accuracy and single layer doping called delta doping but the growth rate lt 1 micron per hour which is slow making it costly Also for the nitrides plasma sources are required to produce N atoms which are more elaborate costly systems

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