Finite element simulations of compositionally graded InGaN solar cells G.F. Brown a,b,*, J.W.AgerIIIb, W.Walukiewicz b, J.Wua, b,a Advisor: H.C. Kuo Reporter: H.W. Wang Solar Energy Materials & Solar Cells 94 (2010) 478–483 a Department of Materials Science&Engineering, University of California, Berkeley,California94720,USA b Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley,California94720,USA

1. Introduction 2. Properties of In x Ga 1-x N used in simulations 3. Simulation results 4. Conclusions

 Broad band  InN - 0.7eV  GaN eV  Cheep fabrication process  Grown on Si substrates by a low temperature process  High effiency Advantage Disadvantage  Indium composition (<30%)  P-type doping  High absorption  Large lattice mismatch between InN and GaN alloys  Valence band discontinuity

Caughey–Thomas approximation

 Absorption Coefficient

APSYS simulation tool Self-consistance  Poisson equation  Carrier drift diffusion equation InGaN - wurtzite crystal structure Fermi level at the InGaN/GaN - un-pinned No reflection and light trapping effects No surface recombination losses

P-GaN In 0.5 Ga 0.5 N 100nm 1m1m AM 1.5 Optical carrier generation rate

p-GaN n-In 0.5 Ga 0.5 N 100nm 1m1m AM 1.5 5x10 18 cm -3 1x10 17 cm -3 Band diagram I–V curve

P-GaN In X Ga 1-X N AM 1.5 Efficiency Fill factor and Short-circuit current V.S. Indium composition

p-GaN n-In 0.5 Ga 0.5 N 100nm 1m1m AM 1.5 5x10 18 cm -3 1x10 17 cm -3 50nm 1x10 17 cm -3 n-In X Ga 1-X N Band diagram Efficiency

p-GaN n-In 0.5 Ga 0.5 N 100nm 1m1m AM 1.5 5x10 18 cm -3 1x10 17 cm -3 n-In X Ga 1-X N Efficiency Band diagram

p-GaN n-In 0.5 Ga 0.5 N 100nm 1m1m AM 1.5 5x10 18 cm -3 1x10 17 cm -3 50nm 1x10 17 cm -3 n-In X Ga 1-X N Minority hole life time in InGaN layer

p-GaN n-In 0.5 Ga 0.5 N 100nm 1m1m AM 1.5 5x10 18 cm -3 1x10 17 cm -3 50nm 1x10 17 cm -3 n-In X Ga 1-X N p-Si n-Si 5x10 19 cm -3 1x10 16 cm -3 1x10 19 cm nm 495  m 5m5m Efficiency

Simulate graded p-GaN/In x Ga 1-x N heterojunction  Graded layer between hetrojunction  Improve valence band discontinuity  Doping and width  Light doping & thin layer → high efficency  Double junction – InGaN/Si  28.9% → high efficiency & low cost substrate