Semiconductor Devices ECE 3080
Popular in Course
verified elite notetaker
Popular in ELECTRICAL AND COMPUTER ENGINEERING
This 0 page Class Notes was uploaded by Cassidy Effertz on Monday November 2, 2015. The Class Notes belongs to ECE 3080 at Georgia Institute of Technology - Main Campus taught by William Doolittle in Fall. Since its upload, it has received 13 views. For similar materials see /class/233888/ece-3080-georgia-institute-of-technology-main-campus in ELECTRICAL AND COMPUTER ENGINEERING at Georgia Institute of Technology - Main Campus.
Reviews for Semiconductor Devices
Report this Material
What is Karma?
Karma is the currency of StudySoup.
Date Created: 11/02/15
Lecture 3 Quantum Mechanics and relationship to electron motion in crystals Reading Notes Georgia Tech ECE 3080 Dr Alan Doolittle Recall Carrier Movement Within the Crystal Fz qEzm FqEm2 F 2 force v E velocity t 2 time F E fOFCe V E velocity t E time 6 2 electronic clz arg e 6 2 electronic clz arg e m E electron effective mass m E llOle effective mass Table 21 Density of States Effective Masses at 300 K Material mj jm0 m gjm0 Si 118 081 Ge 055 036 GaAs 0066 05 2 Ge and GaAs have lighter electrons than Si which results in faster devices Georgia Tech ECE 3080 Dr Alan Doolittle Introduction to Quantum Mechanics notes only People RARELY get quantum mechanics of their first exposure Many aspects of quantum mechanics are counter intuitive and thus visual learners will likely have more trouble than those that tend to think in the abstract We will introduce it now in hopes it will be easier the more you are exposed to it Parts of this discussion are taken from Solymar and Walsh Electrical Properties of Materials Neudeck and Pierret Advanced Semiconductor Fundamentals Dimitrijev Understanding Semiconductor Devices Mayer and Lau Electronic Materials Science Colclaser and DiehlNagle Materials and Devices for electrical engineers and physicists Tipler Physics for scientists and engineers V4 Georgia Tech ECE 3080 Dr Alan Doolittle Introduction to Quantum Mechanics notes only To fully understand the origin of the energy bandgap and effective mass concepts as well as future topics of energy states in quantum wells and tunneling currents one must have at least a basic understanding of electron motion in free space and in the presence of other sources of electrostatic potential atomic cores for example This requires an understanding of the dual waveparticle nature of electrons and in turn quantum mechanics Consider the electron microscope Eectrons have a charge and thus can be focused but also have a phase and thus can interfere with each other destructively or 00n3trUCtiVely Electron Source U 2 h quotM 6 6 10 34J 39u X S 091 lo k 10711 725gtlt107ms Deflection Plates t 1 39 X g X meters voltage used to focus electrons 1 I 39 KE 2 m02 qV Thin sample 39 2 7 2 spatially varied charge creates multiple 91X10 31725 X107ms 215000 V phase delayed electron paths 2 X1 6 X 1019C Phosphor Screen converts electron energy to visible light waves It 15KV glves SUb atomlc constructively and destructiver interfere to get light resolution Georgia Tech and dark rlegions ECE 3080 Dr Alan Doolittle Introduction to Quantum Mechanics notes only What is the wavelength of macroscopic particles Consider a bullet 1 kms 1 gram e34 lOOOms M 1 66 x10 34m 1x 10 3kg gtlt xi Though it acts as a wave it s wavelength is too small to ever measureobserve So an electron or every particle acts as a wave AND a particle simultaneously How can we describe this Other useful properties of energyparticle waves E hf ha mc2 7239 Or the momentum of the photon is h h p this is known as the de Broglie hypothesis Where scalar k is known as the wave number If momentum p is expressed as a vector k is know as the wave vector ECE 3080 Dr Alan Doolittle Georgia Tech Introduction to Quantum Mechanics notes only Why do we use k or k instead of p or p k27ct is independent of mass Classically pmv However we will show that the mass will change with crystalline direction allowing two parameters m and v to change the momentum Thus k is simpler to consider actually the effective mass is what changes with crystalline direction Georgia Tech ECE 3080 Dr Alan Doolittle Introduction to Quantum Mechanics notes only So how do we account for the wavelike nature of small particles like electrons Schrodenger Equation n Electrical Properties of Materials Solymar and Walsh point out that there are NO physical assumptions available to derive the Schrodenger Equation Just like Newton s law of motion Fma and Maxwell s equations the Schrodenger Equation was proposed to explain several observations in physics that were previously unexplained These include the atomic spectrum of hydrogen the energy levels of the Planck oscillator nonradiation of electronic currents in atoms and the shift in energy levels in a strong electric field FE Kinetic energy operator Other operators exist Potential electron moves through Energy operator Table 11 Dynamic VariableOperator Correspondence Dynamic Variable a Mathematical Operator aup Expectation Value a x y z 8 Jay 2 x Af ll x l c f X 9 Z fx y 2 h a h a f a h N V 1 H 7 i T39 p p 6 iaylaz A Agni axd v Neudeck and Pierret Table 21 E 9 z 1 Georgia Tech ECE 3080 Dr Alan Doolittle Introduction to Quantum Mechanics notes only Pxyzt is called the electron wave function It is related to the probability of finding an electron at time t in a volume dxdydz Specifically this probability is I Px yz l 2 dxdydz or P dexdydz But since 1 is a probability J J EOILPQ yzt 2dxdydz 1 or in 1D Wm 1 05 04 03 i 0392 Introducing the concept ofth wave function WZId1 proportional to 0quot the probability that the electron may 0 G be found in the interval d at the Z0 Z1 Z2 33 4 Z poim V Solymar and Walsh figure 31 Georgia Tech ECE 3080 Dr Alan Doolittle Introduction to Quantum Mechanics notes only To solve the Schrddinger equation one must make an assumption about the wave function Lets assume the wave function has separate spatial and temporal Plugging this into the Schrddinger equation and dividing both sides by we arrive at 712 v21 l 1 aw V fl w at K2m l j Since the left hand side varies only with position and the right hand side varies only with time the only way these two sides can equate is if they are equal to a constant we will call this constant total energy E Thus we can break this equation into two equations 2 2 U V P w at K 2m 1 VWE 1 Consider first the time variable version left side then later we will examine the spatially variable portion This will give us time variable solutions and a separate spatially variable solution Georgia Tech ECE 3080 Dr Alan Doolittle Introduction to Quantum Mechanics notes only Consider the time variable solution Jamie W war 6w E z w at h W0 eigjlj OI WU e iat where E 2 ha This equation expresses the periodic time nature of the wave equation Georgia Tech ECE 3080 Dr Alan Doolittle Introduction to Quantum Mechanics notes only Consider the space variable solution 712 WW 2m 1 The combined operator is called LP 2 ET the Hamiltonian momentum 1 2 operator w V LPZELP ell Kinetic Potential Total Energy Energy Energy VJE Classically momentum pmv and kinetic energy is mv22 p22m Georgia Tech ECE 3080 Dr Alan Doolittle Introduction to Quantum Mechanics notes only Consider a specific solution for the free space no electrostatic potential VO wave solution electron traveling in the x direction in 1D only l 2v2VlPELP K 2quot J 722 62 11 2 0 2m 6x LPx Ae kx 36qu 2 2 Wherek2 sz orE h k 7 2m the x direction B0 Classically momentum pmv and kinetic energy is mv22 p22m Since we have to add our time dependent portion see previous our total solution is 39 kx 39 kx LP 2 Pxwt Ae 4 gt Be W gt This is a standard wave equation with one wave traveling in the x direction and one wave traveling in the x direction Since our problem stated that the electron was only traveling in ECE 3080 Dr Alan Doolittle Georgia Tech Introduction to Quantum Mechanics notes only An interesting aside What is the value of A Since 1 is a probability m If Tde1 0 Aeiker ikxdx l 0 AZez39kxiikxdx 1 I Azdx 1 This requires A to be vanishingly small unless we restrict our universe to finite size and is the same probability for all x and t More importantly it brings out a quantum phenomena If we know the electrons momentum p or k we can not know it s position This is a restatement of the uncertainty principle Aprzh Where Ap is the uncertainty in momentum and Ax is the uncertainty in position Georgia Tech ECE 3080 Dr Alan Doolittle Introduction to Quantum Mechanics notes only The solution to this free particle example brings out several important observations about the dual waveparticle nature of our universe L11 L11xwr Ae W kx While particles act as waves their charge is carried as a particle e you can only say that there is a probability of finding an electron in a particular region of space but if you find it there it will have all of it s charge there notjust a fraction Energy of moving particles follows a square law relationship 2 2 2 h k p Neudeck and Pierret Fig 23 2m 2m E E ltpgt k Energy momentum relationship for a free particle Energy momentum relationship for a free particle Classically momentum pmv and kinetic energy is mv22 p22m Georgia Tech ECE 3080 Dr Alan Doolittle Introduction to Quantum Mechanics notes only What effect does this Ek square law relationship have on electron velocity and mass The group velocity rate of energy delivery of a wave is CE 1 CE vg dp h dk So the speed of an electron in the direction defined by p is found from the slope of the Ek diagram flsz imilarl since E S y 1 2 2 d E m 2h 2 4 m dk k gtk SO the effective mass Of an Ek diagram for a free electron with massm solid line and a 39 smaller mass m39 The parabolic E k diagram leads to a linear v versus k relation electron is related to the local and a constant mass inverse curvature of the Ek diagram Georgia Tech After Mayer and La F39g 12392 ECE 3080 Dr Alan Doolittle What effect does an electrostatic potential have on an electron Consider the electron moving in an electrostatic potential V0 The wave solution electron traveling in the x direction in 1D only l 2v2VlPELP K 2quot J E W 2m 8x2 LPx Ae kx 36quot 2 2 Wherek2 1MOIEhk V0 xi 7 2m Since we have to add our time dependent portion see previous our total solution is 39 kx 39 kx LP 2 LPxwr A6 w gt Be W gt This is again a standard wave equation with one wave traveling in the x direction and one wave traveling in the x direction Since our problem stated that the electron was only traveling in the x direction B0 E V0LP0 When the electron moves through an electrostatic potential for the same energy as in free space the only thing that changes is the wavelengt of the electron Georgia Tech ECE 3080 Dr Alan Doolittle What about an electrostatic potential step Consider the electron moving incident on an electrostatic potential V0 The wave solution 1D only Vxlt00 Xgt0o 0 V O A 7 Region XO Region II We have already solved these in regions I and II The total solution is LP 2 LP Xw t Aeiw k1x BIe iatk1x LPN I LPN DOWN t Aeiwtk11xBHe ialk x whereklzzl and knle w A llh 2 ll 72 Georgia Tech ECE 3080 Dr Alan Doolittle What about an electrostatic potential step 0 V O cont d 7 Region XO Region II LP 2 LP Xw t Aeiwlk1xBIe iwtk1x LPH I LPN DOMH t Aeia lk11x BHe iwtka WherekIJ u 2m and A h I h When the wave is incident on the barrier some of it is reflected some of it is transmitted However since there is nothing at x to reflect the wave back B0 Since p is a wave both p and it s first derivative must be continuous across the boundary at x0 for all time t Thus L1113520LPH3 O AIBIZAH and and 6Tx 0 6 11Hx 0 z kA 3 z kHAH 6x 6x Georgia Tech ECE 3080 Dr Alan Doolittle What about an electrostatic potential step 0 V cont d A L 7 Region XO Region II We can de ne a reflection coefficient as the amplitude of the reflected wave relative to the incident wave B 2 k1 k1 A k k1 And likewise we can define a transmission coefficient as the amplitude of the transmitted wave relative to the incident wave RE T E i 2 i A k k1 The probability of a reflection is RR while the probability of transmission is TT I 11 Georgia Tech ECE 3080 Dr Alan Doolittle What about an electrostatic potential step cont d Consider2 cases Case 1 EgtV Both kl and k are real and thus the particle moves with a wave of different wavelength in the two regions However RR is finite Thus even thought the electron has an energy E greaterthan V it will have a finite probability of being reflected by the potential barrier f EgtgtV this probability of reflection reduces to 0 kl 9 k 4 4 R E k kH W A k kH T 2k H V A k k klzzl 2sz and kllzzl w Regionl XO Region H X it h 2 V h Georgia Tech ECE 3080 Dr Alan Doolittle What about an electrostatic potential step cont d Case 2 EltV kl is real but k is imaginary When an imaginary k is placed inside our exponential expiknx a decaying function of the form exp ax results in region However TT is now finite so even thought the electron has an energy E less than V it will have a finite probability of being found within the potential barrier The probability of finding the electron deep inside the potential barrier is 0 due to the rapid decay of lJ W R EI k1 k11 A kIkH T 2k H V A kk klzzl 2sz and kllzzl w Regionl XO Region H X it h 2 V h Georgia Tech ECE 3080 Dr Alan Doolittle What about an electrostatic potential step Without proof see homework consider the following potential profile with an electron of energy EltVo l V0 l Regionl XO Xa X Region II The electron has a finite probability to tunnel through the barrier and will do so if the barrier is thin enough Once through it will continue traveling on it s way Georgia Tech ECE 3080 Dr Alan Doolittle Now consider an periodic potential in 1D KronigPenney Model l quot l w Consider what potentials an electron would see as it moves 0 Armcmnzrqi through the lattice limited to 1D for now The electrostatic potential VX is periodic such that VXLVx X x The Bloch theorem states that since the potential repeats every L lengths the magnitude of the wavefunction but not necessarily the phase must also repeat every L lengths This is true because the probability of finding an electron at a given point in the crystal must be the same as found in the X same location In any other unIt cell The wavefunction in one unit cell is Since VX L VX merely a phase shifted version of the wavefunction in an adjacent Px L eikL PX 4 unit cell I X L I X L e39ikL Ifk XeikL I X I X I X We MUST have standing waves in the crystal that have a period equal to a multiple ofthe period of the crystal s electrostatic potential Similar to a multilayer antireflection coating in optics It is important to note that since the wavefunction repeats A A A f A each unit cell we only have to consider what happens in one unit cell to describe the entire Crystal Thus We can restrict a Onedimensional crystalline lattice b d Potential energy ofan electron inside the lattice considering b only the atomic core at r O c the atomic cores at both x 0 and ourselv2es to vagues of k such that na to na Implying ka x y and dmeenmmimhm s or nQtas Georgia Tech After Neudeck and Peirret Fig 31 ECE 3080 Dr Alan Doolittle lJfJ Jl Now consider an periodic potential in 1D KronigPenney Model Assumptions of KronigPenney Model Simpifying the potential to that shown here 1 D only oAssume electron is a simple plane wave of the form eikx moduated by the periodic crystalline potential Ux The crystalline potential is periodic UxUxL Thus the wave function is a simple plain wave modulated by the periodic crystalline potential wdpuaw Georgia Tech Ux Ux U0 mm 0 t t t gt 1 0 a b Figure 32 Kronig Penney idealization of the potential energy associated with a one dimensional crystalline lattice a Onedimensional periodic potential b Kronig Pennev model 39 Neudeck and Peirret Fig 32 ECE 3080 Dr Alan Doolittle Resonant reflectancetransmission creates standing waves in the crystal Only certain wavelengths energies can pass through the 1D crystal By analogy a multiple layer optical coating has similar reflectiontransmission characteristics The result is the same only certain wavelengths energies are transmitted through the optical stack In a since we have an optical bandgap Transmittance 90 l 200 400 000 8 0 1000 1200 1400 Wavelength nm ECE 3080 Dr Alan Doolittle Georgia Tech KronigPenney Model For 0ltxlta LPa x A sin00c B cos00c Georgia Tech For bltxlt0 2 j VZ w qu m 6qu 8x2 6 2 2LP0 2m E U0 hZ 2mU0 E Tf0r0ltEltUo 1 L113x C sin x D cos2 x forE gt U0 ECE 3080 Dr Alan Doolittle KronigPenney Model For 0ltxlta For bltxlt0 LPa x A sin00c B cos00c L113x C sin6x D cos2 x Applying the following boundary conditions TAX LPN WAX d 1 bx dx dx BC for continuous wave function at the boundary x0 x0 LPa x a eikabLPb x b dLPaOC eikltabgt dLPbOC dx dx BC for periodic wave function at the boundary x b Georgia Tech ECE 3080 Dr Alan Doolittle KronigPenney Model Applying the boundary conditions we get B D 05A 2 BC A sinora B cosaa e Ww C sinBb D cosBb aA cosaa 05B sinora eikabLBC cosBb BD sinBb Eliminating the variables C and D using the above equations we get Asinaa eikab sinBb Bcosora e uwb cos b 0 Aor cosora aeikltabgt cos2 b B or sinora Beikquotb sinBb o This equation set forms a matrix of the form w x A 0 y z B 0 A and B are only nonzero nontrivial solution when the determinate of the above set is equal to zero Georgia Tech ECE 3080 Dr Alan Doolittle KronigPenney Model Taking the determinate and simplifying we get 2056 Plugging in the definitions for 0c and B we get 1 U sina1 2m Pjsin 14 5 1 cosa12m chos lupin 5 1 coskab forEgtU0 2 1 h UH h UH h UH h U0 U0 U0 1 25 U 7 sinaquot2mf0 Psinhbquot2mgg r1 cosaquot2mg 7 Pcoshbquot2mg 7 r1 Wcoskab for0ltEltUo E h U0 h ilk U0 h U0 h ilk U0 2 11l 0K U0 The right hand side is constrained to a range of 1 and is a function of k only The limits of the right hand side 1 occurs at k0 and nab where ab is the period of the crystal potential Sin06a sin3b 005W 005 b coska b 23 Elm The left hand side is NOT constrained to 1 and is a function of energy only ECE 3080 Dr Alan Doolittle Georgia Tech KronigPenney Model The right hand side is constrained to a range of 1 and is a function of k only The limits of the right hand side 1 occurs at k0 to nab The left hand side is NOT constrained to 1 and is a function of energy only Within these forbidden energy ranges no solution can exist ie electrons can not propagate Various Bands or allowed energy exist where the energy E is a function of the choice of k see solution equation Left or Right hand side of KronigPenney Solution 0 Graphical determination of allowed electron energies The lefthand side of the Eqs 318 Kronig Penney model solution is plotted as a function of E EUo The shaded regions where 1 s f lt 1 identify the allowed energy states for the speci c case where 2mUL7 2mUL7 Georgia Tech ECE 3080 Dr Alan Doolittle KronigPenney Model Replotting the previous result in another form recognizing the lower k limit is shared by and nab while the upper limit is for k0 There are at most 2 k values for each allowed energy E The slope dEdK is zero at the k zone boundaries at k0 k nab and k TEab Thus we see that the velocity of the electrons approaches zero at the zone boundaries This means that the electron trajectorymomentum are confined to stay within the allowable kzones E y Band 4 r2quot l MN l VJ lluml 1 l n n 777 k ll l2 u h Figure 35 Reduced mnc rvprtscmntiun of allowed Iz39vA slain in a nmwdimunxiunnl cnxlul Georgia Tech After New and Peirret Fig 3395 ECE 3080 Dr Alan Doolittle Now consider an periodic potential in 1D KronigPenney Model Visualization of a conduction band elecnon moving in a crystal After Neudeok and Peirret Fig 41 Georgla Tech ECE 3080 Dr Alan Doollttle Now consider the 3D periodic potential in a cubic crystal oDifferent potentials exist in different directions Eectron wavelength and crystal momentum k2nk differs with direction Many different parabolic Ek relationships exist depending on our crystalline momentum ltlt y I f I z x A Z lt 5 r 4 Crystal MomentumSpace elrwI f1 httpbritneyspearsacphysicsdosdoshtm Georgia Tech Zinc bleude Xvalleys 300 K Eg 32 eV Ex 46 eV Cubic GaN Ex lt1oogt i t lt100gt Splitoff band Real Space ECE 3080 Dr Alan Dt olittle Now consider the 3D periodic potential in a cubic crystal Zinc blende Ex Xvalleys Cubic GaN 5 s K Ge Si GaAs L valleys E EV cV l l M e I l m G hm l PL Ef EV l Ev l a 300 K l 7 a 5g 32 eV Fvvalley EL Ex 46 eV 2 l 7 EL24851eV 73 E50 002 eV 4 0 L 111 I 100 X L 111 l 100 X L 111 I 100 X kwve vector i lt100gt A equivalent directions give redundant information and i Heavyholes lt111gt Splitoff band thus are not repeated Most important k space points F point is the center of crystal momentum space k space at k0 Xpoint is the edge ofthe first Brillouin zone TEL edge of crystal momentum space kspace in the lt100gt direction edge of crystal momentum space kspace in this 3amp13 lt111gt direction Georgia Tech 3 b or Light holes T300K E EY EV Splitvo 39 band V3 A X k wave vector Lpoint is the edge of the first Brillouin zone TEL a 100111Ek diagrams characterizing the conduction and valence bands of b Si and c d GaAs 2Hz after Szem d from Blakemoral Reprinted with Pe m ss39m39l Neudeck and Peirret Fig 313 ECE 3080 Dr Alan Doolittle Now consider the 3D periodic potential in a hexagonal crystal Wurtzite m G N 1 2V 0 i n Lmoz f z E17 4553 eV Full Band Diagram 39 quot1 EA 4755eV wo as Eso 0008 N V 5 a J E 004 eV 2 i a i k 39 E9 1 Heavy holes kx quot 2 U Light holes 5 3 114A 3 S Splitoffhand l a ll A A TEnergy an I A vallcy MLvalleys Crystal Momentum Space Suzuki M T Uenoyama A Yanase Firstprinciples calculations of effectivemass parameters of AIM and GaN Georgia Tech ECE 3080 Dr Alan Doolittle Lecture 11d Light Emitting Diodes and Laser Diodes Reading Cont d Notes and Anderson2 Chapter 1131145 Some images from Anderson and Anderson text Georgia Tech ECE 3080 Dr Alan Doolittle Optical Design Choices PhSnSc PbSnTc IO quot n H 7 39 CngTe 5 ll39lASSh Pbssc 5 4 quot lnGaAsSh 1 InAsP I A39P E 2 V AlGulnAs Qpr n s 2 55 E I z lnGaAs 1 Z l GAP g AIGaAsSb IGaMSquot I Q 5 quot AlGaAs 7 AlGalnPI PM 3 0 CdSSe s 39SiC gt 4 cans InGaN I AlGaN 01 Some semiconductor materials and their wavelength ranges Based on data from References 3 to 5 Georgia Tech ECE 3080 Dr Alan Doolittle Pn Junction IV Characteristics In Equilibrium the Total current balances due to the sum of the individual components Electron Drift Electron Diffusion Current Current n VS E 4 Cr O C O O E c x 39 Ei Q Q O gt O O gt E llole Drift V O O Turrent Hole Diffusion Current a Equilibrium VA 0 Georgia Tech ECE 3080 Dr Alan Doolittle Review pn Junction IV Characteristics Electron Diffusion I ElectmnNDrift harem n vs E Current ow Current is proportional to ewwref due to the exponential decay of carriers into the majority O O 0 carrier bands H I Hole Drift 0 e 83991 Current Current ow is Current dominated by majority carriers owing across the junction and I becoming minority 1 carriers VA gt 0 OU ckTime Movie b Forward bias VA gt 0 Georgla Tech Review pn Junction IV Characteristics Electron Drift 39urrcn is constant lt IN due to thermally Electron Diffusion Current negligible due generated quot to large encrg barrier carriers swept O 0111 E gt eldsinthe O O O S depletion O O t I E region Q S E Hole Diffusion Current negligible E due to large energy barrier 1 Current ow is E dominated by minority O H I D J V carriers owing across IP T rtren39t39 the junction and becoming majority carriers c Reverse bias VA lt O Ouick me Movie Georgia Tech ECE 3080 Dr Alan Doolittle Review p n Junction IV Characteristics Where does the reverse bias current come from Generation near the depletion region edges replenishes the current source Georgia Tech ECE 3080 Dr Alan Doolittle Review pn Junction IV Characteristics Putting it all together 1 It Forward Bias Current ow is proportional to eVaVref due to the exponential decay of carriers into the majority carrier bands lt Exponential Reverse Bias Current ow is constant due to thermally generated carriers swept out by E elds in the depletion region V quot quot A Current ow is zero at no applied voltage Constant IIOeVaVref 1 Georgia Tech ECE 3080 Dr Alan Doolittle Light Emitting Devices Basics Emission of photons by recombination of electrons and holes in direct bandgap materials Photoluminescense excess electrons and holes required for the radiative recombination are generated by photon absorption Electroluminescense excess electrons and holes required for the radiative recombination are result of an electrical current wwwosramcom Georgia Tech Slide Credit to Dr Oliver Brandt Ga Tech ECE 3080 Dr Alan Doolittle LED Applications LED Displays LED Traffic Signal LED Text LED Brake Lights LED Head Lights Georgia Tech Slide Credit to Dr Oliver Brandt Ga Tech ECE 3080 Dr Alan Doolittle and at Georgia Tech I i r a g i m quot quotquot Georgia Tech Slide credited to Dr Oliver Brandt Ga Tech ECE 3080 DR Alan Doolittle V9V Ptype A105Ga05As 39qVA Hole Current Georgia Tech Diode Applications LED or a Laser Diode 1 VFIR Light Emission W under forward Bias R1000 ohms II T Z VA gt Diode made from a direct bandgap semiconductor Note These devices may not be a simple pn type diode but behave electrically identical to a pn Quantum well made from smaller bandgap material Electron Current b junction diode quot N type A105Ga05As FN Majority Carriers that are injected to the opposite side of the diode under forward bias become minority carriers and recombine In a direct bandgap material this recombination can result in the creation of photons In a real device special areas are used to trap electrons and holes to increase the rate at which they recombine These areas are called quantum wells ECE 3080 Dr Alan Doolittle MQW LED Design Considerations Quantum well made from smaller bandgap material Ptype A10 5Ga0 5As Electron Current Hole Current Number of wells is limited to 35 due to inef cient lling of injected carriers across in last few wells Light wavelength can be tuned by quantum con ned energy state effect discussed earlier only useful for very narrow wells Georgia Tech ECE 3080 Dr Alan Doolittle MQW LED Design Considerations peleclvode pGaN p Alt 15630 BEN n lnDoeGao94N n AIOJEGRQBEIN 63 My W COLORED 39 39 A EPOXY LENS Sapphire SUDEIra39Ie METAL CAN l The shape of the die chip can greatly aid light extraction by minimizing internal Nakamura S et 11 Highipower InGaN singleiquantumiwellistructure blue and violet lightremit ng diodes Appl Phys Lett 67 1868 1995 re ectl on S Georgia Tech ECE 3080 Dr Alan Doolittle Homojunction LED Design Considerations 0 Ptype GaP FN 39qVA P N type GaP x Hole Current Eff1cient light generation results from DonorAcceptor pair transition requires high doping level so Donor and acceptor are close to each other Table 51 CHARACTERISTICS OF VISIBLE UGHT EMITI39ING DIODES from M G Craford LEDS Challenge the Incandescentsquot IEEE Circuits and Devices Magazine September 1992 Bandgap Peakwavelength Typical performance lmW Structure Material type nm color Homojunction GaAsP Direct 650 red 015 GaP Zn 0 Indirect 700 red 04 GaAsP N Indirect 630 red I 585 yellow GaP N Indirect 565 yellowgreen 26 GaP Indirect 555 green 06 SiC Indirect 480 blue 004 Single heterojunction AIGaAs Direct 650 red 2 Double hetemjunction AlGaAs Direct 650 red 4 AlGaP Direct 620 omnge 20 AlInGaP Direct 595 amber 20 AllnGaP Direct 570 yellowgreen 6 GaN Direct 450 blue 06 Double hetemjunction with AIGaAs Direct 650 red 8 transparent substrate Georgia Tech ECE 3080 Dr Alan Doolittle Blue LED based on AlGaInN p qul electrode Light transmitting pclcctrode tMA LOAN Ni A11 p Al Ca 7N l I39l CIGCtl OdP a111 N undoped Ti A1 mum n AlN Sapphire substrate Sze Figure 910 AlGaInN direct bandgap ranging from 065 eV to 62 eV corresponding to wavelength from 19 pm to 02 pm 0 Challenge nd latticematched substrate Solution sapphire substrate with AlN buffer layer Because sapphire is nonconducting both contacts are from the surface 0 Blue light originates from radiative recombination in the GaXIn1XN layer Georgia Tech Slide Credit to Dr Oliver Brandt Ga Tech ECE 3080 Dr Alan Doolittle The LED Development Beet Fluorescent Lamp Shawl Gum ma Dmicc Rlil IIil I l I n AlGnInI l Ial39 I l RLl I39I NIH quot Unfiltered Incandescent Lamp MW hm WHITE E Yeuow Filtered Rlil RII I I I H Alum muni 5 I S I s E 1 man Red Filtered V I Illl Alba 1s 1 mm x R H IIIID ORANGE I I I 0 g I 21139 ERILI A 5 a 2002 National E 1 mm Gaping Medal of Technology 2 mm quot10X W for R Dupuis g Increase Decade 39139 School of ECE L ink quot l oJ Rlil 1960 I970 I975 I980 Georgia Tech Slide Credit to Dr Oliver Brandt Ga Tech I990 I995 I985 2000 2005 ECE 3080 Dr Alan Doolittle HOW to Make White LEDS Red Green Blue LEDs UV LED RGB Phosphor Binary Complimentary i39 l39V LIED C l d Spu 39lrum gm quotm IAN lug lpc39tmm Blur l cuk L i m J M I Cumhinud V il IHgt hr I nnsl hul Speclrum hruu39 I39ma I H MHW I l11UH Blue 131 Spuulmm 410 4743 535 500 MU um V 470 515 SWIM mm 47H gt23 rmlhsll um RG13 LEDS UV LED RGB phosphor 31 LED Yellow phosphor Georgia Tech Slide Credit to Dr Oliver Brandt Ga Tech ECE 3080 Dr Alan Doolittle Photodiode ooooooo o ooooooo Reversed Bias Diode with no light Reversed Bias Diode WITH light illuminatiml illumination results in extra drift current due to photogenerated ehp s that can reach the junction Georgia Tech ECE 3080 Dr Alan Doolittle PhOtOdiOdC Every EHP created within the depletion region W and within a diffusion I total I dark I Due to Light length away from the VJ depletion region is total 0 e T 1 1Duet0Light collected inept across the llCll0ll f a bv the electric field I VTj I AXL W L G a photoeurrent oe 0 q N P current resulting from light All other I I total nght EHP39s recombine NOLight before they can be A collected 1 NoLight V gt Bias Point Georgia Tech ECE 3080 Dr Alan Doolittle Semiconductor LED vs LASER Light Emitting Diode Light is mostly monochromatic narrow energy spread comparable to the distribution of electronshole populations in the band edges Light is from spontaneous emission random events in time and thus phase Light diverges signi cantly 1 M osl LCSS 1 probable probable K it Wavelenglh lnlcnsily probability of uniwon LASER I Light is essentially single wavelength highly monochromatic 1 Light is from stimulated emission timed to be in phase with other photons Light has signi cantly lower divergence Semiconductor versions have more than gas lasers though Georgia Tech ECE 3080 Dr Alan Doolittle LED History IOU 39e AlGalnPGaP 3 Huoresccnt lump r orange AlnGuPGuP I crudorange quot nGuN A v AIInGuPGuAs quot39 green 4 Unllltered n an Iequotnt Ian 39 E I L 39L I p redorange r J 73 1 0 AlGaAsAIGzIAs I 2 red 3939 r 5 39 AlGuAszGaAs kl lnGnN 3 39 GaAsPN red blue 2 Thonms Edison s md39 yellow rst bulb Gal 2N green polymers 5 E GaPZnO red GaAsium SiC red bluell I 1 L 0 H 1 1 LL Llr11 1 14 1 I 1411 1quot1JJ 1 114 1 11J J 1 360 1970 1975 1980 l985 1990 1995 2000 Time t years Present LED technology is more efficient than even uorescent lamps However it will take some time before the cost comes down enough to replace light bulbs Georgia Tech ECE 3080 Dr Alan Doolittle LED kl a 1 A pn junction in a direct bandgap material will produce light when forward biased However reabsorption photon recycling is likely and thus should be avoided Use of quantum wells in the active region region where minority carriers are injected and recombine from the majority carrier anode source of holes and cathode source of electrons results in minimal reabsorption since the emitted light is below the bandgap of the cladding layers higher bandgap regions The quantum well also strongly con nes the electrons and holes to the same region of the material enhancing the probability of recombination and thus enhancing the radiation ef ciency light power outelectrical power in Georgia Tech ECE 3080 Dr Alan Doolittle LED ub25v O I rlllllllll Energy eV lll ll lll illllllll lllllll 5 ub34v j18AIcm2 2915eV 1 0 Energy bands and wavefunctions I l 1 600 650 700 750 Distance nm 800 660 680 700 720 740 760 780 800 850 Distance nm Often Multiple QWs are used to insure radiation efficiency Typically 35 QWs maximize the light output since holes are injected from the pside and electrons from the nside and thus would get trapped in different wells if we had too many QWs Some real effects to consider Some semiconductors N itrides and Carbides are polar materials Thus heterojunctions must contend with polarization discontinuities changes in polarization at the interfaces This leads to spikes in the band diagramsand strong electric fields in the QW that can partially separate the electron wave function from the hole wave function lowering radiation efficiency Often an electron blocking layer is introduced via a wide bandgap layer near the anode pside This prevents electrons which have higher diffusivity than holes from entering the anode pside thus limiting recombination at the wrong wavelength enhancing color purity and desired light power efficiency Georgia Tech ECE 3080 Dr Alan Doolittle Light Scattering in an LED Aclivc layer A generic surfaceemitting LED Some photons are lost by reabsorption in the bulk Fresnel re ection from the surface and total internal re ection Georgia Tech ECE 3080 Dr Alan Doolittle A fiber coupled LED LED or laser diode Lens L Spliccs Opicul fiber lt dBkm L05 1 3 06 08 12 l l 1 I1 L I In 15511quot I holodiodc Wavelength Wm H 1b A Burrustype LED This one uses a double heterostructure to con ne the carriers making recombination mg more ef cient The etched opening in the LED helps align and couple an optical ber Typically InGaAs active layers are used to produce the IR light necessary to transmit in a ber with minimal loss in the ber n AlG AS p GaAs cup Georgia Tech ECE 3080 Dr Alan Doolittle Light Channeling Waveguiding in a LED n AlGaAS p Cams active layer p AIGZIAH quot1 In an edgeemitting LED the higher refractive index active layer acts as a waveguide for photons traveling at less than the critical angle Why is reabsorption not a huge concern Georgia Tech ECE 3080 Dr Alan Doolittle LED Waveguides edge emitting LED lilndmncnlal mo c n Cladding l irsl higher order mode chl highest order mode Direction of propagal ion n AlGaAs l K nl H9 uclivc chrl C0 gt F r p AlGaAs II Cladding Electric eld oplicall gt b u gt113 The edgeemitting LED s waveguide a supports only certain transverse modes whose eld distributions are shown in b In practice only the first mode is allowed It is not completely confined to the active layer thus its absorption is reduced Georgia Tech ECE 3080 Dr Alan Doolittle Spontaneous Light Emission A W 812 k W BZI L L Ll Spontaneous Absorplion Stimulach emission emission 0 We can add to our understanding of absorption and spontaneous radiation due to random recombination another form of radiation Stimulated emission Stimulated emission can occur when we have a population inversion ie when we have injected so many minority carriers that in some regions there are more excited carriers electrons than ground state carriers holes Given an incident photon of the bandgap energy a second photon will be stimulated by the rst photon resulting in two photons with the same energy wavelength m phase This phase coherence results in minimal divergence of the optical beam resulting in a directed light source Georgia Tech ECE 3080 Dr Alan Doolittle Spontaneous vs Stimulated Light Emission Laser region Optical power LED region In Diode C U l39l39Clll The powercurrent curve of a laser diode Below threshold the diode is an LED Above threshold the population is inverted and the light output increases rapidly Georgia Tech ECE 3080 Dr Alan Doolittle Using Mirrors and Optical Gain through Stimulated emission to Amplify the Light Leaves gain region I The ends of the chip form partially re ective mirrors which allows the photons to be reflected back and forth and thus be exposed to gain for a longer period of time Georgia Tech ECE 3080 Dr Alan Doolittle Cavity Modes used in Wavelength Selection Constructive N Resonant Resonant Amiresonanl Destructive Wavelengths that are integer multiples of half the cavity s length can resonate interfering constructively Other wavelengths die out eventually Georgia Tech ECE 3080 Dr Alan Doolittle Cavity Modes used in Wavelength Selection 10 I I I 1 I I I I I I I I I I 08 I I I I I I I I I I I I I 39 I quot I quot I l I R7 I I I 33 06 I I II I I 39 quotE I I 39 I 39 I 39 3 I RO9 I I I 5 04 I I I l I I l I I I I I I I I I I I I I I I 039 I I I I I I l 00 D A The resonances of a FabryPerot cavity The Width of the resonances depends on the re ectivity R of the mirrors ECE 3080 Dr Alan Doolittle Georgia Tech Cavity Modes Gain Result in Wavelength Selection Gain curve Cavilymodcs I I l I h A t Increasing lime b Development of lasing a The gain distribution is the same as the spontaneous emission spectrum h Only the photons at the resonance will amplify The ones near the center of the gain curve will amplify the fastest Georgia Tech ECE 3080 Dr Alan Doolittle LASER Wavelength Design Electron wave functions Hole wave functions Optical eld distribution Adjusting the depth and width of quantum wells to select the wavelength of emission is one form of bandgap engineering The shaded areas indicate the width of the well to illustrate the degree of confinement of the mode Georgia Tech ECE 3080 Dr Alan Doolittle Stripline or Edge Emitting LASER The output pattern of a simple stripline edgeemitting laser is elliptical and Widely divergent Georgia Tech ECE 3080 Dr Alan Doolittle Advanced LASER Wavelength Design 1 Quantum Energy well slate band diagram L39 Quunlum Energy well stale band diagram El Exlcm of well showing overlap ol optlcul mode Rer lClIW R y H Lll dLlWL Wllh gain region Inc ex 0 tin 39 39 ro lc p L Index OpllLlll mode I mom pro le u b a A GRINSCH structure helps funnel the carriers into the wells to improve the probability of recombination Additionally the graded refractive index helps confine the optical mode in the near well region Requires very precise control over layers due to grading Almost always implemented via MBE b A multiple quantum well structure has improves carrier capture Sometimes the two are combined to give a digitally graded device where only two compositions are used but the well thicknesses are varied to implement an effective index grade Georgia Tech ECE 3080 Dr Alan Doolittle Vertical Cavity Surface Emitting Laser VECSEL Light oul Metal Top DBR Insulator 3 active layer Bollom DBR Subs rate A vertical cavity surfaceemitting laser After Ueki et al IEEE Photonics Technology Letters 11 no 12 pp 1539 1541 1999 IEEE Distributed Bragg Reflectors DBR mirrors require very precise growth control Refreactive index is varied as much as possible While still remaining electrically conductive and must be a precise fraction of a wavelength Georgia Tech ECE 3080 Dr Alan Doolittle Lecture 12b Advanced Field Effect Transistor FET Devices Reading Cont d Notes and Anderson2 Chapter 811 Some images from Anderson and Anderson text Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices High Electron Mobility Transistor HEMT diagram along this line D S 11 AIGuAs region Channel p GaAs Semiinsulating GuAs Ill E 39 Channel Tunncl V Metal n39 AlGalAs p GaAs Umlopcd AlGaAs bl Georgia Tech Semiinsulating G dAs The crosssectional schematic a of a GaAs based Heterostructure Field Effect Transistor HFET or High Electron Mobility Transistor HEMT and b the energy band diagram normal to the gate The Schottky barriers at the metalAlGaAs and metalGaAs interfaces are thin enough to be of low resistance because of tunneling Doping is removed from the channel increasing mobility significantly ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices High Electron Mobility Transistor HEMT Vacuum Level Eloctron aimmy i W EC i i 7 7 Doom 1 E 15000 F g l levels charge 39 r r Twanalor Nb Wide handgun Navraw bandmp E 10000 malarial material E a 5000 x quotx 0013 I Wquot I39llquot 1 x HIquot I IUan 1039 l quotU 100 200 aao T Kl The channel is a 2D electron gas contained in the triangular quantum well created by the AEc of the AlGaAs GaAs heterojunction Also known as a MODFET HFET TEGFET SDHT Advantages The mobility is not degraded by surfaces or interfaces like in a MOSFET The AlGaAsGaAs interface is lattice matched and thus has ZERO interface states In a 2D electron gas channel the electron scattering is reduced by a factor of approximately xz 3 making the mobility higher than in bulk Some of this increase is due to separation of the dopants from the channel modulation doping and a small additional enhancement is due to the quantum 2D nature of the channel Example Bulk GaN u10001200 cmzVSec but in an AlNGaN channel u2000 cmZVSec The device is very fast because the channel thickness can be very precisely controlled minimized making the channel easy to deplete with a small gate voltage Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices F ET Devices Pseudomorphic High Electron Mobility Transistor PHEMT Gate Source Drain I l Doped GaAs Doped AlGaAs mGaAs channel Superlamce bum3r The channel is a a strained lattice 2D electron gas contained in the triangular quantum well created by the AEc the AlGaAsInGaAs heterojunction Advantages Higher channel charge higher conductivity due to a higher AEc for InGaAs vs GaAs Channels Higher saturation velocity of InGaAs results in higher frequency operation Lower Noise Higher mobility of InGaAs results in smaller parasitic resistances and higher low field electron velocity InGaAs u12000 cmzVSec In is typically 1520 and Channels are typically 1115 nm The device is very fast because the channel thickness can be very precisely controlled minimized making the channel easy to deplete with a small gate voltage Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices F ET Devices Pseudomorphic High Electron Mobility Transistor PHEMT Single Heterostructure Double Heterostructure and Advanced InP based HEMTS offer increased performance gains due to engineering the channel mmjumon mm HEMTMW HEMTmnnP dlfferently PHEMT m WENT W 39 Primarily One tries 30 minimize the SHPHEMT on an 7 7 DHPHEMT on em mumr mm mm on In channel sheet resistance Rch by channel chmI 1 Channel increasing electron density and mlelp ll y 82015 In lwu y no2 IIIVGIMM y 2053 mobility uh um I 19mm mtg aw Having larger Dec as found in the higher Incontent InGaAS on InP 39 lives 51E f helps with noise and linearity since A 39L quot j 39 5c I the channel charge 1s confined m m d h an m d i n m d11nm GelHum deszcmn PHEMT betten a c 0 nm LMHEMT AE 02 0V AEE a 028 W 4Ee 2 062 all u 5900 le cmi39Nh u momo WW an I 9550712m ulnle nI B tidalnm cml n I 239Bl3olll cml n 39 4uox1nlicml R women39s mag a ammo mu R a 1wm mu Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices High Electron Mobility Transistor HEMT Georgia Tech Heavily doped low resistance Metal nquot n n i 39 Semi GaAs 5 AlGuAs GzlAs p GaAs msumung GaAs Undopcd AlGuAs j The energy band diagram for an HFET perpendicular to the source showing the ohmic contact through tunnel junctions ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices MESFET The ability to have semiinsulating material p 10 Qcm in compound semiconductors facilitates the construction of shallow channel easy to deplete thus fast due to being highly responsive to voltage changes Advantages The mobility is not degraded by surfaces or interfaces like in a MOSFET The device is very fast because the channel thickness can be very precisely controlled minimized making the channel easy to deplete with a small gate voltage Cheaper than HEMT since only a thin homojunction epitaxial material is needed on a semiinsulating substrate Processing is cheap requiring standard ion implantation and simple metallization Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices 1 ESFETiCross Sectional View Cross section of a MESFET E Depletion region L1 l7 at equilibrium indicating the quot quotquotJc39h39al i39ci quotquotquot quotquot quot 39 depletion regions b the Semiinsulaling substrate energy boand dlagram perpendlcular to the gate a The channel thickness is t Depletion region 0 The Gate is a Schottky i g barrier creating the SChO ky 39 Channcl depletion region that thins down the channel F 0 Adding a reverse bias to the gate will pinch off the M61211 1 n GuAs Semiinsulating GziAs 1 channel b Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices MESFET with no Drain Voltage 11 channel Energy band diagram along his line itquot F4uilibrium u n channel Energy band diagram along this 7 7 lmc EB E Negative gate voltage applied In Georgia Tech MESFET energy band diagram and depletion region a at equilibrium and b for an applied gate voltage that depletes the channel In the second case the channel is still 11 type but it is empty of carriers because of the increased barrier height ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices MESFET in LinearTriQJde Mode gig 12 5 Metal 11 GaAs Ev Semiinsulating GaAs Semiinsulating GaAs Cross section of a MESFET under small VDS bias and the corresponding energy band diagrams at the source end and drain end of the gate Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices MESFET 3D Energy Band Diagram Source end Gale Substrate Drain cnd Schottky Subslmte dcplclion region depletion region I I I I I I I I l I I I i l I l K I I The electron potential energy EC along the channel of a MESFET for VDS lt VDSsat The channel thickness decreases with increasing distance along the channel Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices MESFET in Pinch off J 0 7 i l l I l 39 L 1 I l I l L I J Semivinsulming GaAs Semi insulating GaAs The same MESFET VDS gt VDSsat At the source the diagram is the same as before At the drain however the two depletion regions overlap pinching off the channel Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices Junction FET JFET S The energy band diagram EC for VDS 0 JFET The yellow shaded areas represent the depletion regions When VDS gt 0 but not yet in saturation the depletion region at the drain end increases narrowing the channel and increasing the channel resistance Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices Junction FET JFET G D JFET For higher Gate voltages the channel can be pinched off In some JFETs there is a symmetric gatechannel region even creating a ring and cylindrical channel 5 G D Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices Vertical Power MOSFET Since large electric elds high voltages must be supported thick low doped regions must be used Thus most power mosfets use a substantial portion of the substrate as a drift region Green N region separate from the channel region that controls current ow Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices Insulated Gate Bipolar Junction Transistor Gate Emitter Collector The IGBT is very similar to a nchannel vertical power MO SFET except the n drain is replaced with a p collector creating a vertical PNP bipolar junction transistor The IGBT is used in primarily applications above 600 V blocking rating whereas power MOSFETS are used below 600V IGBTs can handle thousands of volts off state with minimal leakage currents and conduct 1000s of amps on state with typically a few volts to 103 of volts forward voltage drop on state Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices Insulated Gate Bipolar Junction Transistor Gate Emitter Collector The additional p region creates a cascaded connection of a PNP bipolar junction transistor with the surface n channel MOSFET This connection results in a significantly lower forward voltage drop compared to a conventional MOSFET By injecting minority carriers holes from the collector p region into the n drift region during forward conduction the resistance of the n drift region is considerably reduced This minority carrier injection in power devices is called conductivity modulation When in the off state this conductivity modulation does not occur allowing the low doped drift region to support very high voltages in the off state Since this is a minority carrier device this results in longer switching time slower speed and hence higher switching losses compared to a power MO SFET Georgia Tech ECE 3080 Dr Alan Doolittle Advanced Devices FET Devices Insulated Gate Bipolar Junction Transistor Gate Transistor Two Transistor Thyrister Model Model Collector Tliick COHEN n I Region V Resistance Emitter Thick n Drifl Region Resistance Gate V39 Emitt3 quot quot Emit Collector CathodeEmitter of IGBTSource of MOSFETBJT Collector This connects to negative smallest voltage Drain of MOSFETBase of BJTInterna1 Connection to 10W doped thick drift region AnodeCollector of IGBTEmitter of B T connects to PositiveLargest voltage Gate turns on BaseEmitter junction turning on emitter collector current There is actually a buried npn BJT that forces the IGBT to act like a Thyristor Georgia Tech ECE 3080 Dr Alan Doolittle Lecture 3b Bonding Model and Dopants Reading Cont d Notes and Anderson2 sections 2327 Georgia Tech ECE 3080 Dr Alan Doolittle The need for more control over carrier concentration Without help the total number of carriers electrons and holes is limited to 2ni For most materials this is not that much and leads to very high resistance and few useful applications We need to add carriers by modifying the crystal This process is known as doping the crystal Georgia Tech ECE 3080 Dr Alan Doolittle Regarding Doping MSESi JVJ MIDl must VJer no mam mummy I E 3939Iquotquotquot3939lquot39quotl39 I ll Illlll Ww i m Example P As Sb in Si Georgia Tech ECE 3080 Dr Alan Doolittle Concept of a Donor adding extra electrons Use the Hydrogen Atomic Energy levels to approximate the energy required to free an electron on a donor Replace dielectric constant with that of the semiconductor Replace mass with that of the semiconductor 4 m q 136 eV Ener E a ngydrogen electron H 47280 h n2 n2 where m0 electron mass it planks cons tant 27 h 2 q electron charge and n 2123 N 4 m m 1 Binding for electron N n q2 n 2EH E 6V f0quot 71 1 247reReohn m 8R Georgia Tech ECE 3080 Dr Alan Doolittle Georgia Tech IIIIe lll Iilililil lalil I l l l l l i l ECE 3080 Dr Alan Doolittle Concept of a Donor adding extra electrons Band diagram equivalent view 7 A J E1 sooooooo ooLooclo amp E Equot T if 0 K Increasing T Room temperature Georgia Tech ECE 3080 Dr Alan Doolittle gic 0 dopgd ma teria e ddi e All regions of I material QI III IncIrag neoo 22221 Example B Al In in Si Georgia Tech ECE 3080 Dr Alan Doolittle Concept of an Acceptor adding extra hole Band diagram equivalent view 7 Eu o f 9000 EA 1 1 Ev O O O O O O O O O O T l K Increasing T Room temperature Georgia Tech ECE 3080 Dr Alan Doolittle Georgia Tech All regions of material are neutrally charged Empty state is located next to the Acceptor ECE 3080 Dr Alan Doolittle Another valence electron can ll the empty state located next to the Acceptor leaving behind a positively charged hole Georgia Tech ECE 3080 Dr Alan Doolittle The positively charged hole can move throughout the crystal really it is the valance electrons jumping from atom to atom that creates the hole motion Georgia Tech ECE 3080 Dr Alan Doolittle The positively charged hole can move throughout the crystal really it is the valance electrons jumping from atom to atom that creates the hole motion Georgia Tech ECE 3080 Dr Alan Doolittle The positively charged hole can move throughout the crystal really it is the valance electrons jumping from atom to atom that creates the hole motion Georgia Tech ECE 3080 Dr Alan Doolittle Region around the acceptor has one extra electron and thus is negatively charged Region around the hole has one less electron and thus is positively charged The positively charged hole can move throughout the crystal really it is the valance electrons jumping from atom to atom that creates the hole motion Georgia Tech ECE 3080 Dr Alan Doolittle