Toward a 1D Device Model Part 2: Material Fundamentals

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1 Toward a 1D Device Model Part 2: Material Fundamentals Lecture 8 10/4/2011 MIT Fundamentals of Photovoltaics 2.626/2.627 Fall 2011 Prof. Tonio Buonassisi 1

2 2.626/2.627 Roadmap You Are Here 2

Spectrum Light Absorption Charge Excitation Charge

3 2.626/2.627: Fundamentals Every photovoltaic device must obey: Conversion Efficiency Output Energy Input Energy For most solar cells, this breaks down into: Inputs Outputs Solar Spectrum Light Absorption Charge Excitation Charge Drift/Diff usion Charge Separation Charge Collection total absorption excitation drift/diffusion separation collection 3

Liebig s Law of the Minimum S. Glunz, Advances in Optoelectronics 97370 (2007) Image by S. W. Glunz. License: CC-BY.

4 Liebig s Law of the Minimum S. Glunz, Advances in Optoelectronics (2007) Image by S. W. Glunz. License: CC-BY. Source: "High-Efficiency Crystalline Silicon Solar Cells." Advances in OptoElectronics (2007). total absorption excitation drift/diffusion separation collection 4

5 Rough Depiction of Interrelated Materials & Device Effects Devices Solar Cell Efficiency ( ) J sc V oc FF Open Circuit Voltage (V oc ) Materials Jsc q Short Circuit Current (J sc ) IQE p d Internal Quantum Efficiency (IQE) Shunt Resistance (R sh ) IQE 1 1 L eff 1 Fill Factor (FF) to N A,D,i Series Resistance (R s ) Built In Voltage (V o ) Surface Fermi Level Pinning Absorption Coefficient ( ) Diffusion Length (L eff ) V o kt q ln N AN D 2 n i to R s L diff D bulk Carrier Concentration (N A, N D, n i ) Surface Density Of States Im[Dielectric Constant] ( 2 ) Lifetime ( ) Mobility (µ) Source: T. Buonassisi, unpublished. 5

6 Learning Objectives: Toward a 1D Device Model 1. Describe what minority carrier diffusion length is, and calculate its impact on J sc, V oc. Describe how minority carrier diffusion length is affected by minority carrier lifetime and minority carrier mobility. 2. Describe how minority carrier diffusion length is measured. 3. Lifetime: Describe basic recombination mechanisms in semiconductor materials. Calculate excess carrier concentration as a function of carrier lifetime and generation rate. Compare to background (intrinsic + dopant) carrier concentrations. 4. Mobility: Describe common mobility-limiting mechanisms (dopants, temperature, ionic semiconductors). 6

7 Minority Carrier Diffusion Length Definition: Minority carrier diffusion length is the average distance a minority carrier moves before recombining. Importance to a Solar Cell: Photoexcited carriers must be able to move from their point of generation to where they can be collected. Longer diffusion lengths generally result in better performance. 7

8 Minority Carrier Diffusion Length Definition: The average distance a minority carrier moves before recombining. Importance to a Solar Cell: Carriers must be able to move from their point of generation to where they can be collected. Cross section of solar cell made of high-quality material Minority carrier diffusion length (L diff ) is LARGE. Solar cell current output (J sc ) is large. Most electrons diffuse through the solar cell uninhibited, contributing to high photon-toelectron (quantum) efficiencies. 8

9 Minority Carrier Diffusion Length Definition: The average distance a minority carrier moves before recombining. Importance to a Solar Cell: Carriers must be able to move from their point of generation to where they can be collected. Cross section of solar cell made of defect-ridden material Minority carrier diffusion length (L diff ) is small. Solar cell current output (J sc ) is small. Electrons generated closer to the surface make it to the contacts, but those in the bulk are likely to recombine (lose their energy, e.g., at bulk defects, and not contribute to the solar cell output current). 9

10 Mathematical Formalism Recall that the current produced in an illumianted pn-junction device, is limited by the minority carrier flux at the edge of the space-charge region. J sc qgl diff 10 PC1D Simulation for 300um thick Si Solar Cell J sc L diff From Eq in Green. J sc = illuminated current = J L G = carrier generation rate Short Circtui Current [ma/cm2] Diffusion Length [microns] 10

11 Mathematical Formalism Note that the voltage is also affected by L diff. V oc k T B q ln J sc 1 J o From Eq in Green. V oc = open-circuit voltage J o = saturation current density J o qdn 2 i L diff N From Eq in Green. D = minority carrier diffusivity N = majority carrier dopant concentration n i = intrinsic carrier concentration V oc ln 2 L diff 2ln L diff ln L diff 11

12 Mathematical Formalism Assuming a weak dependence of FF on L diff, we have the following relationship: J sc V oc L diff ln L diff 12

13 Mathematical Formalism Assuming a weak dependence of FF on L diff, we have the following relationship: J sc V oc L diff ln L diff L diff << device thickness. L diff >> device thickness. 13

14 Minority Carrier Diffusion Length When your material has short minority carrier diffusion length relative to absorber thickness, two engineering options: Reduce absorber layer thickness (if light management permits) or increase diffusion length. 14

15 Learning Objectives: Toward a 1D Device Model 1. Describe what minority carrier diffusion length is, and calculate its impact on J sc, V oc. Describe how minority carrier diffusion length is affected by minority carrier lifetime and minority carrier mobility. 2. Describe how minority carrier diffusion length is measured. 3. Lifetime: Describe basic recombination mechanisms in semiconductor materials. Calculate excess carrier concentration as a function of carrier lifetime and generation rate. Compare to background (intrinsic + dopant) carrier concentrations. 4. Mobility: Describe common mobility-limiting mechanisms (dopants, temperature, ionic semiconductors). 15

16 Collection Probability Courtesy of Christiana Honsberg. Used with permission. 16

17 Collection Probability n-type p-type Courtesy of Christiana Honsberg. Used with permission. From PV CDROM 17

18 Collection Probability Courtesy of Christiana Honsberg. Used with permission. From PV CDROM 18

19 Spectral Response (Quantum Efficiency) Courtesy of PVCDROM. Used with permission. from PVCDROM 19 Standards: IEC and

20 Minority Carrier Diffusion Length At each point Mapped over an entire sample Graph and photo source unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see See: P. A. Basore, IEEE Trans. Electron. Dev. 37, 337 (1990). 20

21 What Limits Diffusion Length? 21

22 What Limits the Minority Carrier Diffusion Length? Quick answer: Recombination-active defects, intrinsic mobility limitations, or absence of percolation pathways. Thin films: Effect of bulk defects (GBs) on. Nanostructured: Effect of morphology on. Please see lecture video for visuals. R.B. Bergmann, Appl. Phys. A 69, 187 (1999) F. Yang et al., ACS Nano 2, 1022 (2008) 22

23 Mathematical Formalism Diffusion length is governed by lifetime and mobility L diff Dt bulk L diff = bulk diffusion length D = diffusivity t bulk = bulk lifetime D k BT q For carriers in an electric field k B = Boltzmann coefficient T = temperature q = charge µ = mobility Definition of bulk lifetime : The average time an excited carrier exists before recombining. (I.e., temporal analogy to diffusion length.) Units = time. t bulk of µs to ms is typical for indirect bandgap semiconductors, while t bulk of ns to µs is typical of direct bandgap semiconductors. Definition of mobility : How easily a carrier moves under an applied field.(i.e., ratio of drift velocity to the electric field magnitude.) Expressed in units of cm 2 /(V*s). Mobilities of s cm 2 /Vs typical for most crystalline semiconductors. Can be orders of magnitude lower for organic, amorphous, and ionic materials. 23

Mathematical Formalism Diffusion length is governed by lifetime and mobility L diff Dt bulk L diff = bulk diffusion length D = diffusivity t bulk = bulk lifetime D k BT q Carrier Lifetime For

24 Mathematical Formalism Diffusion length is governed by lifetime and mobility L diff Dt bulk L diff = bulk diffusion length D = diffusivity t bulk = bulk lifetime D k BT q Carrier Lifetime For carriers in an electric field k B = Boltzmann coefficient T = temperature q = charge µ = mobility Carrier Mobility Definition of bulk lifetime : The average time an excited carrier exists before recombining. (I.e., temporal analogy to diffusion length.) Units = time. t bulk of µs to ms is typical for indirect bandgap semiconductors, while t bulk of ns to µs is typical of direct bandgap semiconductors. Definition of mobility : How easily a carrier moves under an applied field.(i.e., ratio of drift velocity to the electric field magnitude.) Expressed in units of cm 2 /(V*s). Mobilities of s cm 2 /Vs typical for most crystalline semiconductors. Can be orders of magnitude lower for organic, amorphous, and ionic materials. 24

25 Learning Objectives: Toward a 1D Device Model 1. Describe what minority carrier diffusion length is, and calculate its impact on J sc, V oc. Describe how minority carrier diffusion length is affected by minority carrier lifetime and minority carrier mobility. 2. Describe how minority carrier diffusion length is measured. 3. Lifetime: Describe basic recombination mechanisms in semiconductor materials. Calculate excess carrier concentration as a function of carrier lifetime and generation rate. Compare to background (intrinsic + dopant) carrier concentrations. 4. Mobility: Describe common mobility-limiting mechanisms (dopants, temperature, ionic semiconductors). 25

26 Excess Electron Carrier Concentration Generally equal to doping concentration n n 0 n n Gt Excess Electron Carrier Density carriers cm 3 Generation rate carriers cm 3 sec 26 Excited Carrier Lifetime [sec]

5G ~ 10 16 carriers cm 3 sec n p 10 11 cm 3 n i 10 10 cm

27 Minority, Majority Carriers in Silicon Under AM1.5G n Gt cm 3 AM1.5G ~ carriers cm 3 sec n p cm 3 n i cm 3 n p n i 27 Excited Carrier Lifetime if : ~10μs N D cm 3 then : p p 0 n 2 i N D N D n 10 4 cm 3

Carrier Lifetime and Recombination Minorit y Carrier Majority Carrier Bulk Minority Carrier Lifetime: t n R n = Excess minority carrier concentration R = Recombination rate First approximation of

28 Carrier Lifetime and Recombination Minorit y Carrier Majority Carrier Bulk Minority Carrier Lifetime: t n R n = Excess minority carrier concentration R = Recombination rate First approximation of minority carrier lifetime, for low injection (e.g., illumination) conditions. h + h + e - h + h + More Detailed Calculation: 1 1 t bulk t rad p-type silicon Radiative recombination, can be derived from thermodynamics: [ε=α] 28

Recombination rate First approximation of

injection (e.g., illumination) conditions.

29 Carrier Lifetime and Recombination Minorit y Carrier Majority Carrier Bulk Minority Carrier Lifetime: t n R n = Excess minority carrier concentration R = Recombination rate First approximation of minority carrier lifetime, for low injection (e.g., illumination) conditions. h + h + e - h + h + More Detailed Calculation: 1 1 t bulk t rad 1 t Auger p-type silicon Dominant under very high injection conditions t Auger 1 CN A 2 29

minority carrier lifetime, for low injection (e.g., illumination) conditions.

30 Carrier Lifetime and Recombination Minorit y Carrier Majority Carrier Bulk Minority Carrier Lifetime: t n R n = Excess minority carrier concentration R = Recombination rate First approximation of minority carrier lifetime, for low injection (e.g., illumination) conditions. h + h + e - h + h + More Detailed Calculation: 1 1 t bulk t rad 1 t Auger 1 t SRH p-type silicon Defect levelmediated recombination 30

Recombination non-equilibrium = R-G equilibrium t rad t rad

31 Radiative Recombination R G Bnp Bn i 2 Under equilibrium dark conditions hν R B 2 np n i n n 0 n p p 0 p Net Recombination non-equilibrium = R-G equilibrium t rad t rad 1 B N A n 1 B N D p n-type ( where n 0 =N D ) p-type ( where p 0 =N A ) 31

32 Radiative Recombination hν t rad, Si ms B n Radiative recombination is very slow in silicon, and is rarely the limiting lifetime in silicon-based solar cells. However, radiative recombination is often the lifetimelimiting recombination pathway for high-quality thinfilm materials, including GaAs. 32

Midgap states are characterized by their energy level(s) (E D ) and capture cross sections for electrons and holes (s e, s h ) Interstitial Iron (Fe i )

33 Defects and Carrier Recombination: τ SRH Defects can form in semiconductors. Defect formation energy ( E A ) determines equilibrium concentration at a given temperature. Defects can introduce midgap stages. Midgap states are characterized by their energy level(s) (E D ) and capture cross sections for electrons and holes (s e, s h ) Interstitial Iron (Fe i ) Calculated midgap states for Fe complexes in Si Substitutional Iron (Fe s ) S.K. Estreicher et al., Phys. Rev. B 77, (2008). APS. All rights reserved. This content is excluded from our Creative Commons license. For more information, see 33

34 Defects and Carrier Recombination: τ SRH Trap State (introduced by defect) t SRH t n n0 p n 0 1 t p0 p 0 n 1 n n 0 p 0 n n 1 N c e E T E c kt E c E v E T p 1 N v e t p 0 1 Nv th s p E v E T kt e - capture e - emission h + capture h + emission t n 0 1 Nv th s n N trap density s capture crosssection 34

35 Defects and Carrier Recombination: τ SRH Trap State (introduced by defect) E c E v E T With deep traps (i.e. mid-gap) and low-injection conditions: t SRH, n type t p 0 t SRH, p type t n 0 1 Nv th s p 1 Nv th s n e - capture e - emission h + capture h + emission Deep traps and high-injection conditions: t SRH t n0 t p0 35

36 Localized Defects Create Efficient Recombination Pathway Direct Bandgap Semiconductor Indirect Bandgap Semiconductor E E Recombination efficient (no phonon required) t ~ ns to µs E g hv = E g k k Recombination inefficient (phonon required) t ~ ms (a) Direct (b) Indirect Image by MIT OpenCourseWare. 36

37 Localized Defects Create Efficient Recombination Pathway Direct Bandgap Semiconductor E Indirect Bandgap Semiconductor E Recombination efficient (no phonon required) t ~ ns to µs E g hv = E g k k Efficient recombination via defect level! t < µs with high defect concentrations (a) Direct (b) Indirect Image by MIT OpenCourseWare. 37

38 Defects Impact Minority Carrier Lifetime Impurity Point Defects (c-si) Dislocations (c-si) Courtesy of Elsevier, Inc., Used with permission. American Institute of Physics. All rights reserved. This content is excluded from our Creative Commons license. For more information, see A.A. Istratov, Materials Science & Engineering B, 134, 282 (2006) C. Donolato, Journal of Applied Physics 84, 2656 (1998) 38

Effect of Defects on Minority Carrier t, L diff The distribution of defects matters as much as their total concentration! Reprinted by permission from Macmillan Publishers Ltd: Nature Materials.

39 Effect of Defects on Minority Carrier t, L diff The distribution of defects matters as much as their total concentration! Reprinted by permission from Macmillan Publishers Ltd: Nature Materials. Source: Buonassisi, T., et al. "Engineering Metal-Impurity Nanodefects for Low- Cost Solar Cells." Nature Materials 4, no. 9 (2005): T. Buonassisi et al., Nature Mater. 4, 676 (2005) 39

trap trap Sample thickness t W surf 2S 1 W

40 Surfaces Introduce Many Mid-Gap States Surface mid-gap surface states provide additional pathway for recombination. They are often formed by dangling bonds on the surface. Si Si Si Si Si Si Si Si Si Si Si Si trap trap trap Sample thickness t W surf 2S 1 W D 2 Ref: Horányi et al., Appl. Surf. Sci. 63, 306 (1993) Si Si Si Si trap Surface recombination velocity 40 Carrier diffusivity

41 Proper Passivation Reduces Surface Recombination Surface Proper surface passivation ties up dangling bonds, reduces density of trap states. Si Si Si Si Si Si Si Si H H Perfect passivation yields: S 0, t surf Practically, S approaching 1 cm/s have been achieved on silicon. Si Si Si Si H Si Si Si Si H 41

Measuring Surface Recombination Velocity 1.

measurement will reveal an effective lifetime, or t eff.) 2.

42 Measuring Surface Recombination Velocity 1. Measure lifetime of samples of varying thickness, but with same bulk and surface properties. (The lifetime will be affected by both bulk and surface conditions, thus measurement will reveal an effective lifetime, or t eff.) 2. Any variation in lifetime should be due to a changing t surf, per below: Ref: Horányi et al., Appl. Surf. Sci. 63, 306 (1993) 3. With >2 lifetime measurements (sample thicknesses), can solve for t surf! 42

43 Auger Recombination, τ Auger R n type ~ pn 2 t n type 1 Cn 2 R p type ~ np 2 t p type 1 Cp 2 *Above equations true at sufficiently high doping densities ( cm -3 in silicon) 43

44 Auger Recombination in n-type silicon R n type ~ pn 2 t n type 1 Cn 2 AIP. All rights reserved. This content is excluded from our Creative Commons license. For more information, see J. Dziewior, W. Shmid, Appl. Phys. Lett., 31, p346 (1977) 44

45 Auger Recombination in n-type silicon Courtesy of Daniel Macdonald. Used with permission t bulk t band t Auger t SRH Daniel MacDonald thesis Recombination and Trapping in Multicrystalline Silicon Solar Cells, The Australian National University (May 2011) 45

46 Measuring Minority Carrier Lifetime Recall that t bulk t rad t Auger t SRH If defect-mitigated recombination is dominant, band-to-band radiative recombination will be suppressed: 1 1 t rad t SRH In fact, band-to-band (radiative recombination) and defect-mitigated (non-radiative recombination) are inversely proportional. or t rad t SRH By imaging the band-to-band (radiative) recombination using a very sensitive CCD camera, we are able to quantitatively extract the minority carrier lifetime. 46

Photoluminescence Imaging (PLI) Experimental Setup Measurement of Wafer Chuck with d. contacts Luminescence/heat radiation CCD Camera Laser Image by MIT OpenCourseWare. M. Kasemann et al., Proc.

47 Photoluminescence Imaging (PLI) Experimental Setup Measurement of Wafer Chuck with d. contacts Luminescence/heat radiation CCD Camera Laser Image by MIT OpenCourseWare. M. Kasemann et al., Proc. IEEE PVSC, San Diego, CA (2008). AIP. All rights reserved. This content is excluded from our Creative Commons license. For more information, see T. Trupke et al., Appl. Phys. Lett. 89, (2006). 47

48 Temperature Changes σ 0 e - emission E c E v Springer-Verlag. All rights reserved. This content is excluded from our Creative Commons license. For more information, see S. Rein, Lifetime spectroscopy. Springer-Verlag (Berlin, 2005). p Trapped carriers are more likely to be (re-)emitted at higher thermal energies (k b T). At lower T, trapped carriers reside in traps longer, facilitating recombination.

49 Learning Objectives: Toward a 1D Device Model 1. Describe what minority carrier diffusion length is, and calculate its impact on J sc, V oc. Describe how minority carrier diffusion length is affected by minority carrier lifetime and minority carrier mobility. 2. Describe how minority carrier diffusion length is measured. 3. Lifetime: Describe basic recombination mechanisms in semiconductor materials. Calculate excess carrier concentration as a function of carrier lifetime and generation rate. Compare to background (intrinsic + dopant) carrier concentrations. 4. Mobility: Describe common mobility-limiting mechanisms (dopants, temperature, ionic semiconductors). 49

) American Physical Society. All rights reserved.

50 Effect of Reduced Mobility on Solar Cell Performance Low carrier mobility can reduce device efficiency by several tens of percent relative (as big of an impact as lifetime!) American Physical Society. All rights reserved. This content is excluded from our Creative Commons license. For more information, see J. Mattheis et al., Phys. Rev. B. 77, (2008) 50

51 What Limits Mobility? 1. Defect Scattering 2. Trapping at stretched bonds 3. Incomplete percolation pathways 4. Phonon Scattering Example of carrier trapping L. Wagner et al., PRL 101, (2008) Example of complex percolation pathway F. Yang et al., ACS Nano 2, 1022 (2008) Diagrams removed due to copyright restrictions. See lecture video. 51

52 Mobility and Carrier Concentration in Semiconductor Increased concentration of ionized dopant atoms increases conductivity, but can reduce carrier mobility (due to scattering). 52

53 Percolation Pathways Both µ and t play a role in determining L diff, and hence efficiency, for various device architectures. Table removed due to copyright restrictions. See lecture video. F. Yang et al., ACS Nano 2, 1022 (2008) 53

54 Simple Example 1. Well-behaved inorganic semiconductor (no effect of trapping at stretched bonds and incomplete percolation pathways). 2. Defect scattering dominant ionized dopants inside sample scatter carriers. 54

55 Demo: Conductivity of Heated Intrinsic and Doped Silicon A silicon HEAT 55

56 Demo Explained n n 0 n N D n For intrinsic Si, n >> N D. For highly doped Si, n << N D. s 1 q n Conductivity is the product of µ and n. 1.E Carrier Concentration [cm^-3] 1.E+14 1.E+12 1.E+10 1.E+08 1.E+06 1.E+04 "Intrinsic Carriers" "Carriers Doped Na=1e16" Mobility [cm^2/sec] E Temp [K] Temp [K] 56

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Charge Excitation. Lecture 4 9/20/2011 MIT Fundamentals of Photovoltaics 2.626/2.627 Fall 2011 Prof. Tonio Buonassisi

Charge Excitation. Lecture 4 9/20/2011 MIT Fundamentals of Photovoltaics 2.626/2.627 Fall 2011 Prof. Tonio Buonassisi Charge Excitation Lecture 4 9/20/2011 MIT Fundamentals of Photovoltaics 2.626/2.627 Fall 2011 Prof. Tonio Buonassisi 1 2.626/2.627 Roadmap You Are Here 2 2.626/2.627: Fundamentals Every photovoltaic device