Guidelines for Class Presentation EE 235/NSE 203 Solar Cells Prof. Connie Chang-Hasnain 263M Cory Hall EECS Department Each person will give two presentations: each 7 min + 3 min Q&A. Need 17 presentations for next Monday 3/2 on solar cells. Graded by your peers 1: Excellent (i.e. I have learned something) 2: OK (i.e. clear presentation) 3: Lack of preparation or understanding By 2/25 (5 days before your presentation) email Vadim and me a paper or a set of papers you want to review. By 3/1 (1 day before presentation) Email Vadim and me your presentations 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 2 Absorption in Semiconductor Loss in Semiconductor Assuming is indepent of k; Fv=1 and fc=0 E fc =E fv =E f m r is effective reduced mass 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 3 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 4
Gain in Semicond. Outline Overview of energy demand Photovoltaic (solar cell) principles Solar concentration High efficiency multi-junction cells Summary 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 5 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 6 World Energy Production US CO 2 Emissions 2005 300 200 100 0 Millions of Barrels per Day (Oil Equivalent) Millions of tonnes per year Carbon equivalent 600 500 400 300 200 100 Natural Gas Petroleum Coal Air Trucks Buses LDVs 1860 1900 1940 1980 2020 2060 2100 Source: John F. Bookout, Two Centuries of Fossil Fuel Energy International Geological Congress, Washington DC; July 10,1985. Episodes, 12, 257-262 (1989). 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 7 0 Residential Commercial Industrial Transportation Electricity Generation Source: U.S. EPA Inventory of Greenhouse Gas Emissions, April 2007 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 8
Electric Power Generation Cost of Electricity US Electricity Generation (GWh) 10 6 10 5 10 4 10 3 source of data: Energy Information Administration TOTAL Coal Nuclear Geothermal 1992 1994 1996 1998 2000 Year Solar is microscopic. Why? Hydroelectric Wind Solar Natural Gas 2002 2004 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 9 0.35 0.3 0.25 0.2 $/KWHr (2008$s ) 0.15 0.1 0.05 0 Levelized Cost Comparison for Electric Power Generation With $100 per Ton Tax on Carbon (2008 Fuel Prices) Nuclear Coal Gas CC Gas CT Solar PV Solar Thermal Generation Technology Source: J. Weyant, Energy Modeling Forum, Stanford University 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 10 Wind Carbon Tax Fuel-2008 Variable O&M Fixed O&M Charges Capital Charges Source of Energy in US Coal-32% Natural Gas-30% Oil-18%-for transportation Nuclear-12% Hydropower-5% Renewable-1% 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 11 50 45 40 35 30 25 20 15 10 5 0 Oil Coal Source: BP & IEA The ENERGY REVOLUTION (The Terawatt Challenge) Gas Fission 2004 14.5 Terawatts 220 M BOE/day Biomass Hydroelectric Solar, wind, geothermal 0.5% The Basis of Prosperity 20 st Century = OIL 21 st Century =?? 50 45 40 35 30 25 20 15 10 5 0 Oil 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 12 Coal Gas 2050 30 -- 60 Terawatts 450 900 MBOE/day Fusion / Fission Biomass Hydroelectric Solar, wind, geothermal
Our Energy Challenge 2004 6.5 Billion People 14.5 Terawatts 2050 ~ 10 Billion People 30-60 Terawatts 165,000 TW of sunlight hit the earth Need to convert 0.025 % of incident solar energy 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 13 http://www.nd.edu/~pkamat/energyconversion.html 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 14 2006 Market Summary World wide installations reached 1.7 GW with 19% growth rate. Global industry revenues were $10.6 bn in 2006, while capital investment through the PV business chain equaling $2.8 bn. Over $4 bn in equity and debt financing, up from $1.8 bn in 2005. Primary Applications for PV Systems Grid-Connected Distributed: Off-grid nondomestic: Public and commercial buildings, The first commercial, motorway sound barriers, 1-100kW terrestrial application. PV are commercially cost competitive with other sources. Grid-connected centralized: for power stations. Off-grid Domestic: typically around 1 kw and 1-2 km from power lines. Marketbuzz 2007: ANNUAL WORLD SOLAR PHOTOVOLTAIC REPORT 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 15 TRENDS IN PHOTOVOLTAIC APPLICATIONS Survey report of selected IEA countries between 1992 and 2005; Report IEA-PVPS T1-15:2006 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 16
Cumulative Installed PV Power (International Energy Agency countries) Grid-connected is 3.7 GW or 86% of total. (IEA 2006 report) Off-grid non-domestic and domestic are 8.4% and 5.5%. Competing Technologies Flat Panel Silicon Simple arrays of large-area PV cells, fixed at latitude tilt Cost is dominated by the cost of high-quality mono-crystalline silicon Polycrystalline Si is cheaper than single-crystal, but is also less efficient Single Crystal 17-18% (SunPower) Poly Silicon 14-16% (Kyera) Thin-Film Fixed flat-panels Lowest cost per watt, but efficiency is much lower thus requiring 2-3 times larger area for same power output. CdTe Thin Film 10 % (First Solar) CIGS Thin Film 14 % (e.g. NanoSolar) Concentrator CPV Dramatically reducing the area of semiconductor through high concentration (200-1000X) Requires precise 2-axis tracking Si Single Crystal 18% (Amonix) III-V Multi-Junction 22.5% (Concentrix) 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 17 Note: Percentage figures are best estimates of module efficiency 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 18 History of PV Efficiency (Research Cells) 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 19 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 20
Current Research Directions PV system cost components CIGS Can be deposited on flexible material low cost Conversion efficiency is similar to that of silicon (~20%) Multijunction Higher power conversion efficiency Higher cost Polymer Inexpensive (disposable?) Less reliable (degrade over time) Low power conversion efficiency Nanrystalline solar cells Conversion efficiency achieved so far: 3% Still at its infancy, but there are possible solutions. 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 21 Module Half the module efficiency means double the system cost/w Support Structures for module and wiring Power conditioning and inverter (DC to AC) Design and Installation Others: land, marketing, transportation, permits 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 22 Solar Cell Operation Solar Spectrum (Space, Earth, Black Body) Due to spectral width of solar radiation, there is a tradeoff between high current (small E g semiconductor, low V ) and high voltage (large E g and low I sc ) Spectral Irradiance (Wm -2 µm -1 ) Solar Cell operation regions Wavelength (µm) 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 23 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 24
Photogeneration and Photurrent in pn Diodes Optical absorption, electric field, drift and diffusion currents Current-voltage (I-V) characteristic with increasing illumination Larger E g Solar Cell Operation Solar Cells operate in the 4th quadrant of the I-V characteristic (i.e. forward voltage and reverse current) such that power is extracted rather than input to the device. Carrier drift V Increasing V Electrons and holes outside the depletion region can diffuse the wrong direction, decreasing quantum efficiency. It is thus desirable to generate all photarriers in the depletion region 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 25 P max = V I sc FF FF = P max V I sc 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 26 Solar Cell Efficiency Multi-junction PV Optical-Electrical Energy Conversion Efficiency λ < E g Silicon Electron Energy(Output) = PhotonEnergy(Input) Energy Conversion Efficiency of Silicon Cell 1 Junction Silicon Solar Cell Efficiency (%) 30 28 26 24 22 20 18 16 Maximum 1SUN Single Junction Efficiency Ideal Diode Trap Dominated Diode Multi-junction PV cells increase efficiency by absorbing different portions of the spectrum Problems of this approach Efficiency limitations Lowest photurrent clamps others Thermal cross-talk Seasonal solar spectral shift Low yield Lattice mismatch Complex fabrication InGaP cell GaAs cell Ge cell Conc. Sunlight λ > E g Max. Theoretical Efficiency ~28% 14 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Bandgap (ev) 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 27 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 28
Market Shares 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 29 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 30 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 31 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 32
Concentrator: Motivations and Problems Motivation for concentrator solar cells is purely economic: Higher efficiencies Higher watts/material High yield/cost justifies the use of more expensive cell materials and complex solar cell schemes to maximize efficiency Problems considerable engineering tasks Concentrators can only use direct sunlight Tracking problems Loss of scattered light High temperatures at high concentration requires active cooling Series resistance loss at high concentration Recombination presses radiative, nonradiative, Auger Silicon solar cells are severely limited at high concentration factors U.C.B. Chang-Hasnain Group 33 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 33 PD PV Photodetectors vs. Photovoltaics (V=0) (V<0) (V>0) dark light Sze, Semiconductor Devices, 3 rd Ed., 2006 EE 2163/1/2009 Principles and Models of Semiconductor Prof. Chang-Hasnain Devices (Autumn 2007) EE 235/ NSE Prof. 203 J. S. Sp Harris 2009 34 34 I I ideal s PD s qdp p L qv kt ( e ) = I 1 I p no (-,-) qdnn + L n po ph PV (+,-) Solar Cell Operation Solar Cells are conceptually like detectors except they operate in the 4th quadrant of the I-V characteristic (i.e. forward voltage and reverse current) such that power is extracted rather than input to the device and typically, over a much broader spectral range. P max = V I sc FF Basic solar cell equations one sun Four main parameters: short-circuit current, open-circuit voltage, fill factor, and efficiency J J V sc dark = q bs ( E) QE( E) de qv / kt = J ( e 1) s sc J mv η = P o kt J = ln( q J J mv FF = J V m m sc o + 1) J scv FF = P s EE 2163/1/2009 Principles and Models of Semiconductor Prof. Chang-Hasnain Devices (Autumn 2007) EE 235/ NSE Prof. 203 J. S. Sp Harris 2009 35 35 36 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 36
X suns low injection 2 sin θ x X = ; θ = 0. 26 2 sun max sin θ X = 46050 J ( X ) XJ ( onesun) sc = sc sun Low injection (neglects effects on dark current) Logarithmic increase of open-circuit voltage, fill factor mkt XJ sc mkt V ( X ) = ln( + 1) V (1) + ln( X ) q J q v FF = ln( v + 0.72) ; v v + 1 V = mkt / q Power increases by factor Efficiency increases by factor o From: Jenny Nelson, The Physics of Solar Cells Martin Green, Solar cells: operating principles mkt X (1 + ln X ) qv (1) mkt (1 + ln X ) qv (1) 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 37 Experimental data Indeed, logarithmic increase at low injection, but decrease at higher injection: why? From: C Algora, A GaAs solar cell with an efficiency of 26.2% at 1000 suns and 25.0% at 2000 suns U.C.B. Chang-Hasnain Group 38 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 38 X suns high injection Resistance effect at high concentration At high injection, series resistance losses become critical Current, fill factor reduced by low shunt R, high series R q( V + JAR mkt V JAR s )/ + s J nonideal = J sc J o( e 1) R FF = FF (1 R ) o s ( v + 0.7) FFo FF = FFo 1 v Rsh U.C.B. Chang-Hasnain Group 39 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 39 sh From: Martin Wolf, Series Resistance Effects on Solar Cell Measurements U.C.B. Chang-Hasnain Group 40 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 40
Limiting recombination presses Current, voltage vs. band gap Radiative and Auger recombination nonlinear at high injection (Bn 2,Cn 3 ) Dark current term increases with generation rate V actually rises more slowly 2kT SRH press V ln X q Radiative presses Auger recombination V V kt q ln X 2kT ln X 3q If defects are high, recombination traps will severely limit solar cell performance U.C.B. Chang-Hasnain Group 41 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 41 From: Gerardo Araujo, Limiting efficiencies of GaAs solar cells U.C.B. Chang-Hasnain Group 42 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 42 Efficiency versus band gap GaAs vs. Si conversion efficiency Shape of solar cell efficiency primarily dictated by the product J L V Peak efficiency for Eg ~ 1.1eV. So why does Si show lower efficiency than GaAs? Peak ~ 1.1-1.2 ev Indirect band gap of Si means that Si solar cells are Auger-limited! Auger limit is more restrictive than the radiative recombination that limits GaAs! Ternaries such as InGaAs may take advantage of the peak efficiency at 1.1eV shown to the right U.C.B. Chang-Hasnain Group 43 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 43 U.C.B. Chang-Hasnain Group 44 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 44
Auger limit of Si solar cells Flat Panel vs Concentrator Arrays Auger limited voltage: 2kT J L V = ln 3 3q qni ( Cn C p ) W + B C, C : Auger recombination coefficients n B p W : Cell base thickness Ideality factor of Auger limited voltage is 2/3 (decreasing carrier lifetime with injection level) Note that there is a relation to thickness; can raise limit silicon solar cells imposed by intrinsic Auger presses for thinner films From: MA Green, Limits on the open-circuit voltage and efficiency of U.C.B. Chang-Hasnain Group 45 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 45 Tracking Flat Plate gives PVIII-V CPV an additional Typical 1.75x Si cell benefit is 5 x5 18% Efficient lens or mirror Concentration PV: Equivalent cell is 0.2 x 0.2 30-35% Efficient 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 46 Increased Power with Tracking Temperature Dependence of Open Circuit Voltage ~2x III-V Multi-Junction CPV (with Tracking) Tracking 40% Silicon Flat Plate Peak Consumption 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 47 Change of V is larger than change in bandgap energy 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 48
Concentrator Solar Resource Macro Concentrator Arrays Best (though not only) siting for concentrators is in the Southwest What about a big / utility-scale system? Requires long, efficient, high power grid transmission Fusing Reflective Optics 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 49 3/1/2009 Prof. Chang-Hasnain Micro Concentrator Arrays hν Fusing Refractive Optics EE 235/ NSE 203 Sp 2009 50 Limits to Cell Efficiency Conventional (single-junction) Non-Fusing Optics p n Cell, e.g. silicon Eg 0 0.5 1 Photon energy (ev) 4 photon not absorbed has unavoidable losses which put a fundamental ceiling on cell efficiency Conversion Efficiency Eg excess energy lost as heat Photon Energy when applied to the sun s broad spectrum Dramatically reduces tracking accuracy and size 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 51 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 52
High Efficiency Solar Cell Multi-junction Solar Cells Optical-Electrical Energy Conversion Efficiency PhotonEnergy(Input) = ElectronEnergy(Output) Record Efficiency 37% (Spectrolab) Energy Conversion Efficiency of Silicon Cell Energy Conversion Efficiency of MJ Cell AM 1.5 Solar Spectrum λ < E g Silicon 1 Junction Silicon Solar Cell Material 1 3 Junction Solar Cell Stack λ > E g Max. Theoretical Efficiency ~28% Material 2 Material 3 Theoretical Efficiency 45% 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 53 3/1/2009 Prof. Chang-Hasnain EE NCPV, 235/ http://www.nrel.gov/ncpv/higheff.html NSE 203 Sp 2009 54 Multijunctions: Higher Efficiencies Possible Even higher-efficiency MJ cells are being developed New materials Novel device architectures 4 5 6 7 8 9 1 2 3 4 Energy (ev) GaInP 1.8 ev GaAs 1.4 ev Ge 0.7 ev in production GaInP 1.8 ev 1.25 ev 0.7 ev GaInP 1.8 ev GaAs 1.4 ev 1.0 ev 0.7 ev future generation example structures Bandgap (ev) 2.5 2 1.5 1 0.5 0 Bandgap vs Lattice Constant for Photovoltaic Materials GaP P Ga x In 1-x N y P 1-y Si Indirect bandgaps AlAs Al x As GaAs 2 Direct bandgap Metamorphic As Ge 1 Indirect bandgap Al 1-x As InP InAs 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 Lattice Parameter (Å) 1.9eV 1.4eV 1.0eV 0.65eV 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 55 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 56
GaN 2.5 Bandgap (ev) 2 1.5 1 Wavelength Range of Alloys Lattice Matched to GaAs & InP GaP P GaAs y P 1-y GaAs AlAs Al x As InP As Al 1-x As As y P 1-y 980nm 1300nm 1550nm 0.5 GaN y As 1-y Gax In 1-x N y As 1-y InAs on GaAs InN y As 1-y 0 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 Lattice Parameter (Å) Wavelengths from 650-1600 nm accessible Telecommunications Multi-junction Solar Cells Optical Communication Wavelengths 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 57 Alloys Lattice Matched to GaAs for Multi- Bandgap Solar Cells Bandgap (ev) 2.5 2 1.5 1 0.5 GaP GaAs y P 1-y GaN y As 1-y In AlAs x P GaAs Al x As Ge As Al 1-x As As y P 1-y 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 58 InP Ga x In 1-x N y As 1-y InAs InN y As 1-y 0 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 Lattice Parameter (Å) Either 3 or 4 cell combination with optimum bandgaps can be grown lattice matched to GaAs III-V Multijunction Solar Cells In-Production Require new materials GaInNAs GaInNAsSb New 0.9 ev 38.7% 42.3% 42.8% 43.5% Theoretical power conversion efficiency (AM1.5D, low-aod, 500-suns)* Internal Quantum Efficiency 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% AM1.5D Low-AOD Spectrum GaInNAsSb GaInNAs E g GaAs (*) Friedman, D.J., Kurtz, S.R., and Geisz, J.F., 29 th IEEE PVSC, pp. 856-859, (2002). 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 59 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 60
Efficiency vs Bottom Cell Bandgaps CIGS solar cell Layout InGaP GaAs Cell E 3 =1eV Cell E 4 =0.65eV Iso-efficiency plot for variation of bottom two subcells in four-junction cell at 300K, 100 SUNs, AM1.5 illumination 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 61 CuInSe2 (CIS) is used in the absorption layer. CIS-based solar cells are becoming one of the leading technologies for solar energy generators being champions in terms of efficiency (which is about 19%) among thin-film devices. Their life-time in outer space was found to be at least 50 times as long as that of amorphous silicon solar cells. 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 62 CuInSe 2 Based Solar Cells Layout Press of CuInS 2 Solar Cell Fabrication 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 63 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 64
Press of CIGS solar cell manufacturing using roll-to-roll deposition technology CuInSe 2 Based Solar Cells pros and Cons CuInSe 2 has a bandgap of 1 ev and the devices typically have open circuit voltage (V ) less than 0.5 V. This bandgap is about 0.5 ev less than required for a single junction device to have optimal efficiency for terrestrial applications. High short circuit current (J sc ) of these devices reduces module performance because of larger active area and series resistance losses. Low V typically suffer larger fractional losses as the devices are operated under real PV module operating conditions (module operating temperatures of 50 to 60 C) as compared to operation under standard measurement conditions (25 C). Solar cells based on CuInSe 2 have been made at IEC and elsewhere with bandgaps of about 1.2 ev through the addition of Ga, leading to efficiencies greater than 15%. The CuIn 1-x Ga x Se 2 cells with record-level efficiencies have been produced by reacting the absorber layers at temperatures above 500 C. Such high pressing temperatures limit the choice of substrate materials (e.g., excluding use of lightweight flexible Kapton foil) and make pressing and substrate handling in general more difficult. Increase the bandgap to 1.4 to 1.6 ev for improved module performance can be accomplished by increasing the Ga content or by adding S as an additional alloy component. 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 65 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 66 Amorphous/Micrrystalline Thin-Film Tandem Cell Structure and Features Summary -- Responsivity of thin film solar cells 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 67 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 68
Ideal vs Trap Dominated I-V Log Forward I vs V Current (A) 1E-2 1E-4 Traps q/2kt 100 SUNs 1 SUN 1E-6 Ideal q/kt 1E-8 0 0.5 1 1.5 Forward Bias Voltage (V) Traps DECREASE Forward Voltage, particularly at 1 SUN 3/1/2009 Prof. Chang-Hasnain EE 235/ NSE 203 Sp 2009 69