1. Solar Cells, Sluggish Capacitance, and a Puzzling Observation Tim Gfroerer Davidson College, Davidson, NC with Mark Wanlass National Renewable Energy Lab, CO ~ Supported by Bechtel Bettis, Inc. and the American Chemical Society – Petroleum Research Fund ~

2. Experiments by... Kiril Simov (Davidson ’05) Patten Priestley (Davidson ’03) and Malu Fairley (Spelman ’03)

3. Outline Semiconductors, defects, and solar cells Diode capacitance and the DLTS experiment Our measurements and an unusual result A new model for minority carrier trapping/escape during DLTS

4. Semiconductors Periodic Potential Physlet

5. InGaAs Bandgap vs. Alloy Composition Bandgap vs. Lattice Physlet

6. Semiconductor Defects Lattice-Mismatch Applet Defect Level Physlet (from the forthcoming Physlet Quantum Physics: An Interactive Introduction to Quantum Theory by Mario Belloni et al., due out this Fall

7. Solar Cell Operation Conduction Band Valence Band PHOTON ENERGY ELECTRON E-Field E- HOLE E-Field E- ++ + + - - - - - CURRENT ABSORPTION When a photon is absorbed, an electron is excited into the conduction band, leaving a hole behind in the valence band. An internal electric field sweeps the electrons and holes away, creating electricity.

8. Defect-Related Trapping and Recombination Conduction Band Valence Band ENERGY Defect Level - + PHONONS But electrons can recombine with holes by hopping through defect levels and releasing phonons (heat). This loss mechanism reduces the efficiency of a solar cell.

9. Defect-Related Transition Probabilities P ~ 10 -3 P ~ (0.5) 10 ~ 10 -3 P ~ 10 -5 P ~ 10 -1 P ~ (0.5) 16 ~ 10 -5 P ~ (0.5) 4 ~ 10 -1 The probability P of transitions involving phonon emission depends on the number of phonons required, which is determined by the position of the defect level in the gap. - +++ --

10. p/n Junction Formation N P+ + + + + + + + + + + - - - - - ++ + + + + + + + + + + Depletion Layer + - + + - - + + + - - - + + + - - - +

11. Bias-Dependent Depletion + + - - N P+ + + + + + + + + + + - - - ++ + + + + + + + + + + Depletion Layer + - + - - + + + - - + - - With Bias

12. Diode Capacitance No bias Reverse bias d1d1 V built-in V built-in +V applied d2d2 C =  Q/  V ~  0 A/d Reverse bias increases the separation between the layers where free charge is added or taken away. ENERGY

13. Defect characterization via DLTS + + - - N P+ + + + + + + + + + + - - - ++ + + + + + + + + + + Depletion Layer With Bias + - + - - + + + - - + Temporary Reduced Bias Depletion Layer With Bias - - + + - - Temporary Reduced Bias + +

14. Typical DLTS Measurements

15. DLTS Experimental Setup Computer with LabVIEW Temp Controller Pulse Generator Cryostat with sample Digital Scope (Tektronix) (1) (2) (3) (4) (5) Oxford 77K Agilent Capacitance meter (Boonton)

16. Device Structure and Band Diagram {

17. Transient Capacitance: Escape

18. Filling Pulse Dependence: Capture

19. Proposed Model

20. Testing the Model

21. Variable-Bandgap Lattice-Mismatched Stuctures Undoped InAs y P 1-y, 30 nm Undoped In x Ga 1-x As, 1.5 μm Undoped InAs y P 1-y buffer, 1 μm Undoped InAs y P 1-y step-grade region: 0.3 μm/step (~ -0.2% LMM/step), n steps Undoped InP substrate

22. Radiative Recombination Conduction Band Valence Band PHOTON ENERGY - + light in = heat + light out radiative efficiency = light out / light in heat light in light out

23. Defect-Related Density of States Valence Band Conduction Band ENERGY The distribution of defect levels within the bandgap can be represented by a density of states (DOS) function as shown above.

24. Radiative Efficiency Measurements heat light

25. Four Conclusions 0.29eV hole trap is observed in n-type InGaAs under reverse bias Temperature-dependent capture and escape rates are symmetrical Rates level off at cold temperatures due to tunneling Device modeling points to defect states near the p+/n junction Two References T.H. Gfroerer et al., APL 80, 4570 (2003). T.H. Gfroerer et al., IPRM (2005).