Fundamentals of Light Trapping

Transcription

1 Fundamentals of Light Trapping James R. Nagel, PhD November 16, 2017 Salt Lake City, Utah

2 About Me PhD, Electrical Engineering, University of Utah (2011) Research Associate for Dept. of Metallurgical Engineering Specialties: Applied Electromagnetics Numerical Methods Physical Modeling 1

3 Introduction: What is Light Trapping? Light enters; some scatters; some is absorbed. Light trapping efficiency (LTE); aka, Absorption Factor (AF) Energy absorbed by the thing Energy that strikes a thing 2

4 Applications for Light Trapping 3

5 Solar Energy World energy demand is growing Fossil fuels are limited Solar energy is abundant and renewable 4

6 Cost Trends in Solar Power Industry goal of 1$/W. 5

7 Anatomy of a Solar Cell Incident Photons Top Contact -e N-Type Semiconductor Electron-Hole Excitation P-Type Semiconductor +e Bottom Contact 6

8 Why Silicon Dominates Silicon is: Abundant Non-toxic Easily processed Ideal band gap Pre-established infrastructure 7

9 Solar Power in Perspective: Air Mass 0 Average spectral irradiance over one year as seen from Earth orbit looking at the sun. Total power density = kw / m 2 8

10 Solar Power in Perspective: Air Mass 1.5 Solar energy has to pass through Earth s atmosphere before reaching us in the US (37 tilt towards equator) Total power density = 1.00 kw / m 2 9

11 Solar Power in Perspective: AM 1.5 Solar cells don t capture energy; they capture photons. This places fundamental limits to solar cell efficiency. Convert units to [photons / s m 2 nm] 10

12 Solar Power in Perspective: AM 1.5 Photons below the bandgap energy are useless to us. Let s just pretend they don t exist. Total usable power density = W/m 2 11

13 Maximum Possible Efficiency Bandgap energy of silicon is 1.77 x J (1.1 ev)---the absolute maximum energy each photon can provide. Integrate over spectrum: Total usable power density = W/m 2 (48.8%) If we further apply circuit theory to power delivery by a single p-n junction, this value drops to about 32% for silicon. This is called the Shockley-Queisser limit. 12

14 High Efficiency Silicon Solar Cells 25 % lab efficiency 400 µm thickness ( µm typical) 100 cm 2 area per cell From Amazon.com: HQST 100 W c-si Solar Panel $1.8/W, ~ % efficient * Prog. Photovolt: Res. Appl, 7, pp (1999) 13

15 Causes for Low Efficiency 1. Failure to capture photons (Light trapping) Reflections/Scattering Transmission Misalignment 2. Failure to extract electron/hole pairs (quantum efficiency) Recombination losses 3. Poor Fill Factor Internal resistances and impedance matching None of this other stuff matters if we can t trap the light! 14

16 Reasons for Light Loss Surface Reflections Transmission Loss Contact Reflections/ Scattering N-Type P-Type Bottom Contact 15

17 Step 1: Minimize Surface Contact Area Surface Reflections Transmission Loss N-Type P-Type Bottom Contact 16

18 Step 2: Use Antireflective Coating (ARC) Transmission Loss ARC N-Type P-Type Bottom Contact 17

19 Step 3: Make Cell Really Thick ARC N-Type P-Type Bottom Contact 18

20 Problem: Absorption Length Photon absorption is exponential as a function of distance. Define absorption length as 1/e (63%) probability of absorption for photon with given energy. Crystalline silicon requires many tens/hundreds of microns to guarantee high absorption probability. High-quality semiconductors are expensive! Thick wafers increase recombination loss. 19

21 Thin Film Silicon Solar Cells Reduce active layer thickness to 1--2 µm for lower material cost. Can be printed on large areas almost like paper (m 2 per cell) PROBLEM: Thin films are not very efficient From Amazon.com: Uni-Solar PowerBond TM, a-si, 136 W $1.2/W, ~ 6 % efficient 20

22 Absorption Calculations Consider a 1.0 µm slab of crystalline silicon above a PEC Fraction of incident photons absorbed = 27% Call this the light trapping efficiency (LTE) 1.0 µm c-si PEC

23 Anti-reflective coating (ARC) Perfect ARC improves things significantly (LTE = 40%) Longer wavelengths still struggle. How can we do better? ARC PEC

24 Step 3b: Make Light Go Horizontal. Fixed path length this way Path length enhancement! 23

25 Lambertian/Ergotic/Yablonovitch Limit Assume perfect Lambertian scattering at back contact (LTE = 81%) Common benchmark for solar cell efficiency. ARC 81 % 40 % PEC * Yablonovitch & Cody, IEEE Trans on Elec. Dev. 29, 2 (1982) 24

26 Light Trapping in Thin Silicon Films Huge variety of ideas in literature Proc. of SPIE, 7002, (2008) Surface Texturing Distributed Bragg Reflectors Surface Plasmonics Nat. Mat, 9, 205 (2010) APL, 89, (2006) Nano Lett., 10, 4692 (2010)

27 The Model-N Slab Let α = absorption coefficient for particular material. Set (R = 0) N for No Reflections 26

28 Equivalent Path Length Solve for thickness. Any arbitrary system with some absorption factor and attenuation coefficient can be represented as an equivalent model-n slab. Call this the equivalent path length. 27

29 Slab PEC Path Lengths Fabry-Perot resonance causes peaks and valleys in EPL. 1.0 µm c-si PEC 28

30 Lambertian Limit Explained ARC ARC 29

31 Lambertian Limit Explained ARC A ray (i.e., a plane wave) strikes the surface of the solar cell and scatters into the film. Assume the scattering profile is perfectly diffuse ( Lambertian ). ARC 30

32 Lambertian Limit Explained ARC Follow the rays as they propagate from top to bottom. Calculate how much light is absorbed and add up all the rays. ARC 31

33 Lambertian Limit Explained Assume that the film is very thin and low-loss. Beware of this step! Secant goes to infinity! Assume this thing dominates close to 90-deg; then the rays contribute little to the integral 32

34 Lambertian Limit Explained Once a ray strikes the lower surface, some of that energy is scattered back into the environment. Calculate the light extraction efficiency (LEE) from Snell s law. ARC Lambertian incidence, perfectly random surface Snell s Law Solve ARC 33

35 Lambertian Limit Explained Next, calculate total reflected power. ARC Fraction of energy that arrives at bottom surface. Fraction of that energy to escape. ARC 34

36 Lambertian Limit Explained Next, calculate total reflected power. ARC This thing is approximately 1. Ignore it. ARC 35

37 Lambertian Limit Explained Add up total absorbed power over each bounce. ARC ARC 36

38 Lambertian Limit Explained Add a mirror at the back. Convert to an equivalent path length. ARC PEC n = 3.5 for crystalline silicon. That amounts to nearly 50 times the path-length enhancement! 37

39 Solar Concentration Here s an idea. Near 100 % light trapping efficiency! What could possibly go wrong? PEC 38

40 Solar Concentration Mechanical fixtures/lenses are bulky, heavy, and expensive. PEC 39

41 Solar Concentration Alignment is critical; you MUST track the sun. This is why the Lambertian limit applies only to unconcentrated light. PEC 40

42 Is it really worth it? I m already getting 81% LTE with planar structures anyway. ARC 81 % 40 % PEC 41

43 EDX QUESTIONS? 42