ME 432 Fundamentals of Modern Photovoltaics. Discussion 11: Light AbsorpAon and Carrier ExcitaAon/ThermalizaAon 21 September PDF Free Download

ME 432 Fundamentals of Modern Photovoltaics Discussion 11: Light AbsorpAon and Carrier ExcitaAon/ThermalizaAon 21 September 2018

Fundamental concepts underlying PV conversion input solar spectrum light absorpaon carrier excitaaon & thermalizaaon charge transport charge separaaon charge collecaon output You Are Here Courtesy: Yosuke Kanai, University of North Carolina

Learning Objec2ves: Light Absorp2on 1. Describe what is meant by spectrum overlap. 2. Describe what a semiconductor is, and why semiconductors are used for photovoltaics. 3. Describe opacal absorpaon in semiconductors as transiaons of charge carriers on an energy band diagram. 4. Describe how light absorpaon is characterized in real materials in terms of the Beer-Lambert Law and the absorpaon coefficient a

Achieving Spectrum Overlap h8p://www.rfcafe.com/references/electrical/astm%20g173-03%20reference%20spectra.htm Any part of this spectrum that is not absorbed is wasted. Ideally, our solar cell would absorb all of the incident sunlight that strikes it. Such an ideal solar cell would be a black body absorber and has a theoreacal limiang efficiency of around 86% (called the Blackbody Limit ) Of course, no material is a perfect absorber. We want to choose our material so that it absorbs best near the peak of the solar spectrum.

Why do materials absorb light? There are a number of possible reasons. ONen, the absorpoon of light in a parocular range of wavelengths couples to different excitaoons that occur in materials. Excita2on Electronic TransiAons VibraAons of Atoms Dipolar TransiAons Ionic ConducAon Wavelength 300 nm 3-300 mm 300 mm 300 m Given where the solar spectrum peaks, we want to take advantage of electronic transiaons to absorb light in a photovoltaic l E e - ΔE AbsorpAon can take place if ΔE=hc/λ E e - ΔE

Why Semiconductors have Electronic Transi2ons Near the Peak of the Solar Spectrum conducaon band conducaon band Energy E E g E g valence band valence band Metal Semiconductor Gap: 0 < E g < 3 ev Insulator Gap: > 3 ev A semiconductor has a band gap E g (typically) between 0.5 ev and 3.0 ev separaang the filled and the unfilled electron levels. Note that this is right where we want it that is, right where the solar spectrum peaks at 2.23 ev. In a semiconductor: The filled electron levels live in a band of states known as the valence band. The unfilled electron levels live in a band of states known as the conduc2on band.

Learning Objec2ves: Light Absorp2on 1. Describe what is meant by spectrum overlap. 2. Describe what a semiconductor is, and why semiconductors are used for photovoltaics. 3. Describe op2cal absorp2on in semiconductors as transi2ons of charge carriers on an energy band diagram. 4. Describe how light absorpaon is characterized in real materials in terms of the Beer-Lambert law and the absorpaon coefficient a

Light AbsorpAon in Semiconductors courtesy: Tonio Buonassisi, MIT

Light Non-AbsorpAon in Semiconductors courtesy: Tonio Buonassisi, MIT

Our first source of loss in a PV cell: h8p://www.rfcafe.com/references/electrical/astm%20g173-03%20reference%20spectra.htm absorbed Not absorbed (wasted) E gap

Learning Objec2ves: Light Absorp2on 1. Describe what is meant by spectrum overlap. 2. Describe what a semiconductor is, and why semiconductors are used for photovoltaics. 3. Describe opacal absorpaon in semiconductors as transiaons of charge carriers on an energy band diagram. 4. Describe how light absorp2on is characterized in real materials in terms of the Beer-Lambert law and the absorp2on coefficient α

Beer-Lambert Law t I = I o exp αt ( ) Due to the absorpaon that takes place, the intensity of a light wave propagaang through a material decays exponenaally as it travels. The parameter a describes how quickly the exponenaal decay occurs. a is known as the absorp2on coefficient, and is a material property that also depends on the wavelength.

OpAcal AbsorpAon in Semiconductors Ager: hhp://pveducaaon.org/pvcdrom/pn-juncaon/absorpaon-coefficient Shallow AbsorpAon Edge Steep AbsorpAon Edge

Typical Semiconductor

Typical Semiconductor above-band transiaons excitons Lajce vibraaons (IR) band edge Free-carrier absorpaon impuriaes

OpAcal AbsorpAon in Insulators 1.0 Transmission 0.0 AbsorpAon in the UV from opacal transiaons across the gap. 100 1000 10000 Wavelength (nm) AbsorpAon in the IR from lajce vibraaonal modes (phonons) Ager: Mark Fox, OpAcal ProperAes of Solids, 2 nd Ed. Al 2 O 3, pure corundrum Gap: 7-8 ev

Aside: OpAcal AbsorpAon in Insulators Al 2 O 3 with impurioes Corundrum with ImpuriAes Sapphire: Ti and Fe impuriaes Ager: Mark Fox, OpAcal ProperAes of Solids, 2 nd Ed. Ruby: Cr ImpuriAes

OpAcal AbsorpAon in Semiconductors Example: CdSe, 1.73 ev band gap Conceptually, similar to insulators, but the transmission window shigs Fundamental absorpaon edge is shiged to longer wavelengths (smaller band gap); semiconductors thus are not all transparent to visible light VibraAonal modes are also shiged to longer wavelengths (lajce is a lihle soger) Ager: Mark Fox, OpAcal ProperAes of Solids, 2 nd Ed.

OpAcal AbsorpAon in Semiconductors Courtesy: Tonio Buonassisi, ager ChrisAana Honsberg and Stuart Bowden. Note how some are steep and others are shallow

OpAcal AbsorpAon in Metals Ager: Mark Fox, OpAcal ProperAes of Solids, 2 nd Ed. VIS Reflects most everything for wavelengths larger than UV Becomes transparent around UV (beyond the plasma frequency) 10000 1000 Wavelength (nm) 100

Typical Metals

Let s play a game

HOMO-LUMO gap IR -- vibraaonal modes Hints: It s a molecule Fundamental edge is around 7 ev It is transparent Microwave -- dipole rearrangement

Summary: Light Absorp2on & Thermaliza2on input solar spectrum light absorpaon carrier excitaaon charge transport charge separaaon charge collecaon output η total = η absorption η excitation η transport η separation η collection Let s consider the opamal band gap solar cell: E gap ~ 1.2-1.3 ev So how does the energy loss break down for this opamal band gap system? AbsorpAon: 18% of incoming energy is not absorbed ThermalizaAon: 47% of the incoming energy is lost as heat Transport, SeparaAon, CollecAon: 2% of the incoming energy must be lost through recombinaaon (thermodynamics we haven t gohen there yet) Leaving us with 33%

Learning Objec2ves: Carrier Excita2on & Thermaliza2on 1. Describe opacal absorpaon in semiconductors as transiaons of charge carriers on an energy band diagram. 2. Describe what phonons are. 3. Calculate the fracaon of incident solar energy lost to thermalizaaon. 4. Considering the effects of light absorpaon and thermalizaaon, plot efficiency vs. bandgap, and denote specific materials on the figure (homework). 5. What is meant by direct and indirect semiconductor? What are the implicaaons of direct and indirect absorpaon for PV cells? 6. Explain, using E vs. k diagrams, why direct absorbers are more efficient absorbers of sunlight. 7. Describe some implicaaons of the use of direct vs. indirect semiconductors on solar cells

Learning Objec2ves: Carrier Excita2on & Thermaliza2on 1. Describe op2cal absorp2on in semiconductors as transi2ons of charge carriers on an energy band diagram. 2. Describe what phonons are. 3. Calculate the fracaon of incident solar energy lost to thermalizaaon. 4. Considering the effects of light absorpaon and thermalizaaon, plot efficiency vs. bandgap, and denote specific materials on the figure (homework). 5. What is meant by direct and indirect semiconductor? What are the implicaaons of direct and indirect absorpaon for PV cells? 6. Explain, using E vs. k diagrams, why direct absorbers are more efficient absorbers of sunlight. 7. Describe some implicaaons of the use of direct vs. indirect semiconductors on solar cells

Light AbsorpAon in Semiconductors courtesy: Tonio Buonassisi, MIT

Light Non-AbsorpAon in Semiconductors courtesy: Tonio Buonassisi, MIT

Non-AbsorpAon: our first big source of loss in a PV cell h8p://www.rfcafe.com/references/electrical/astm%20g173-03%20reference%20spectra.htm absorbed Not absorbed (wasted) E gap

What are phonons? Phonons are the quanta of crystal lajce vibraaons (paracle picture) A paracular crystalline solid possesses a characterisac set of normal vibraaonal modes: phonons of different wavelengths and direcaons (wave picture) one-dimensional analogy two-dimensional analogy

What are phonons? At any finite temperature T>0K, there is an equilibrium populaaon of phonons living in a crystal As temperature increases, the phonon populaaon increases As the crystal vibrates, it is dissipaang heat to the environment Whereas we said that photons (light waves) have large energy and small momentum, phonons are the opposite: small energies, large momentum

Learning Objec2ves: Carrier Excita2on & Thermaliza2on 1. Describe opacal absorpaon in semiconductors as transiaons of charge carriers on an energy band diagram. 2. Describe what phonons are. 3. Calculate the frac2on of incident solar energy lost to thermaliza2on. 4. Considering the effects of light absorpaon and thermalizaaon, plot efficiency vs. bandgap, and denote specific materials on the figure (homework). 5. What is meant by direct and indirect semiconductor? What are the implicaaons of direct and indirect absorpaon for PV cells? 6. Explain, using E vs. k diagrams, why direct absorbers are more efficient absorbers of sunlight. 7. Describe some implicaaons of the use of direct vs. indirect semiconductors on solar cells

Thermaliza2on: Our Second Big Source of Loss in a PV cell E ConducAon band Valence band

Thermaliza2on: Our Second Big Source of Loss in a PV cell E ConducAon band E ph > E g Valence band e - 1. A photon of energy larger than the band gap strikes an electron in a semiconductor.

Thermaliza2on: Our Second Big Source of Loss in a PV cell E ConducAon band Valence band e - h + stored energy: E ph 2. AbsorpAon of the photon results in promoaon of the electron from the valence band to the conducaon band, creaang two free carriers (a hole in the valence band and an electron in the conducaon band)

Thermaliza2on: Our Second Big Source of Loss in a PV cell E ConducAon band e - stored energy: 3. ThermalizaAon: Within picoseconds, the crystal vibraaons result in the scahering of the free carrier electron and hole to the conducaon and valence band edges Valence band h + E g Consequently, for the photon of energy E ph provided by the sun: a. only E g ends up stored in the semiconductor b. E ph -E g is dissipated as heat to the environment

Thermaliza2on Losses E ConducAon band e - stored energy: E g Valence band h + QuesAon: Why does the hole go up during thermalizaaon? Answer: A hole going up in the valence band corresponds exactly to an electron going down in the valence band, and hence represents an energy loss.

Thermaliza2on Losses Punch Line In a semiconductor of band gap E g, for every photon of energy E ph that is absorbed, thanks to thermalizaaon losses: only a fracaon (E g /E ph ) of the photon s energy is stored in the semiconductor and can be converted to useful energy (electricity) the rest of the photon s energy is dissipated to the environment through lajce vibraaons To minimize thermalizaaon losses, we want to use as large gap a semiconductor as possible

Timescale of Thermaliza2on Key concept: There is virtually nothing we can do about it. ThermalizaOon happens too fast.

Learning Objec2ves: Carrier Excita2on & Thermaliza2on 1. Describe opacal absorpaon in semiconductors as transiaons of charge carriers on an energy band diagram. 2. Describe what phonons are. 3. Calculate the fracaon of incident solar energy lost to thermalizaaon. 4. Considering the effects of light absorp2on and thermaliza2on, plot efficiency vs. bandgap, and denote specific materials on the figure (homework). 5. What is meant by direct and indirect semiconductor? What are the implicaaons of direct and indirect absorpaon for PV cells? 6. Explain, using E vs. k diagrams, why direct absorbers are more efficient absorbers of sunlight. 7. Describe some implicaaons of the use of direct vs. indirect semiconductors on solar cells

Theore2cal Efficiency vs. Band Gap The figure below shows that maximum theoreacal efficiency of a solar cell as a funcaon of its band gap You will calculate this as part of your homework assignment. For small band gaps, efficiency is limited by thermalizaaon losses For large band gaps, efficiency is limited by losses due to nonabsorpaon of the solar spectrum The tradeoff between thermalizaaon and non-absorpaon losses results in the opamal band gap of a semiconductor of approximately 1.2 ev, and a maximum theoreacal efficiency of close to 30%.

Learning Objec2ves: Carrier Excita2on & Thermaliza2on 1. Describe opacal absorpaon in semiconductors as transiaons of charge carriers on an energy band diagram. 2. Describe what phonons are. 3. Calculate the fracaon of incident solar energy lost to thermalizaaon. 4. Considering the effects of light absorpaon and thermalizaaon, plot efficiency vs. bandgap, and denote specific materials on the figure (homework). 5. What is meant by direct and indirect semiconductor? What are the implica2ons of direct and indirect absorp2on for PV cells? 6. Explain, using E vs. k diagrams, why direct absorbers are more efficient absorbers of sunlight. 7. Describe some implicaaons of the use of direct vs. indirect semiconductors on solar cells

Beer-Lambert Law Due to the absorpaon that takes place, the intensity of a light wave propagaang through a material decays exponenaally as it travels. The parameter a describes how quickly the exponenaal decay occurs. a is known as the absorp2on coefficient, and is a material property that also depends on the wavelength.

OpAcal AbsorpAon in Semiconductors Ager: hhp://pveducaaon.org/pvcdrom/pn-juncaon/absorpaon-coefficient Steep AbsorpAon Edge: Direct Semiconductors Shallow AbsorpAon Edge: Indirect Semiconductors

Direct vs. Indirect Semiconductors Depending on how sharp the transiaon in the absorpaon coefficient is, we categorize our semiconductors into two categories: Direct semiconductors: sharp onset of absorpaon Indirect semiconductors: shallow onset of absorpaon Whether a semiconductor is direct or indirect has serious implicaaons for how thick a solar cell made from that semiconductor must be Example: photovoltaics made of indirect semiconductors like silicon must be quite thick (100 s of mm) to absorb sufficient quanaaes of the solar spectrum On the other hand, direct gap semiconductors (GaAs, CdTe, etc) will generally absorb 99% of an incident AM1.5 spectrum within a few mm. Typical silicon solar cell thickness: 300mm, typical CdTe solar cell thickness: 2 mm.

Silicon : Not a Great Absorber cross-secaon of solar cell: 300 mm Si absorber layer Image Credit: Q-Cells

Silicon : Not a Great Absorber cross-secaon of solar cell: 300 mm Si absorber layer Image Credit: Q-Cells e-- h+

Silicon : Not a Great Absorber cross-secaon of solar cell: 300 mm Si absorber layer Image Credit: Q-Cells h+ e-

Silicon : Not a Great Absorber cross-secaon of solar cell: h+ 300 mm Si absorber layer e- Image Credit: Q-Cells

Silicon : Not a Great Absorber cross-secaon of solar cell: h+ 300 mm Si absorber layer Image Credit: Q-Cells e- Key concept: The thicker the absorber layer is, the farther the electron and hole have to travel before they reach the top/bohom metal contacts and can be extracted into an external circuit. The thicker the absorber layer is, the more opportunity that something will go wrong (recombinaaon) before the electron and hole can be extracted.

What determines whether a semiconductor is a direct or indirect absorber? To answer this quesaon, we need to become familiar with something called E vs. k diagrams, or electronic band structure diagrams These are simply diagrams showing the available states for electrons to occupy now including energy and momentum E stands for energy of the electron and k stands for crystal momentum of the electron Let s look at a few examples P.S. CongratulaAons. This is as deep into quantum mechanics as we are going to get in the class. If you ve made it this far, you re good to go!

Electronic Band Structure of Silicon ConducAon Band (empty) E gap Valence Band (filled)

Electronic Band Structure of Silicon conducaon band minimum (CBM) valence band maximum (VBM) Based on the plot, the energy difference between the VBM and the CBM is around 1.1 ev This number does, indeed, correspond to the band gap of Silicon NoAce that the VBM and the CBM occur at different values of k Because of this, silicon is known as an indirect gap semiconductor

Electronic Band Structure of GaAs ConducAon Band (empty) E gap Valence Band (filled)

Electronic Band Structure of GaAs conducaon band minimum (CBM) valence band maximum (VBM) Based on the plot, the energy difference between the VBM and the CBM is around 1.4 ev This number does, indeed, correspond to the band gap of GaAs NoAce that, unlike Si, the VBM and the CBM occur at the same value of k Because of this, GaAs is known as a direct gap semiconductor

Electronic Band Structure of Ge conducaon band minimum (CBM) conducaon band Ge is an indirect gap semiconductor E gap = 0.66 ev valence band valence band maximum (VBM)

Electronic Band Structure of InP conducaon band conducaon band minimum (CBM) E gap valence band InP is a direct gap semiconductor valence band maximum (VBM)

What are these E vs. k diagrams? E n,k k every single point corresponds to a electronic state (y) that can be occupied by two electrons each electronic state (y) is differenaated from the others by two parameters: k,n k is the k-vector, n is the number of the band, counang up from the bohom An electron occupying the state y n,k has an energy E There is also a charge distribuaon associated with each state y n,k

Example: Electronic States in Silicon The total charge distribuaon associated with all of the electronic states y below the VBM calculated via DFT (density funcaonal theory)

Direct vs. Indirect Semiconductors generally, semiconductors are classified into two categories: examples: InP, GaAs Si, Ge

So why does the absorp2on coefficient a vary so much for a direct or indirect absorber? We ve talked about two types of paracles that can scaher electrons: Photons quanta of electromagneac radiaaon Have high energy E Have small momentum k Phonons quanta of crystal vibraaons Have low energy E Have large momentum k During a scahering process, both energy and momentum must be conserved Thus, light absorpaon in a direct semiconductor requires only photons And, light absorpaon in an indirect semiconductor requires a photon and a phonon, and is staasacally less likely to occur

So why does the absorp2on coefficient a vary so much for a direct or indirect absorber? A direct transiaon requires only a change in energy DE, and a photon is sufficient to do the job An indirect transiaon requires a change in energy DE and momentum Dk, and thus a photon and a phonon must be involved

So why does the absorp2on coefficient a vary so much for a direct or indirect absorber? Now we know why direct gap semiconductors are much beher absorbers of light. Only a photon is needed to provide the DE for the transiaon from the VBM to the CBM to take place. For any photon with energy exceeding the gap, absorpaon can place very efficiently (a is large) On the other hand, indirect semiconductors need a photon to provide the DE and a phonon to provide the Dk for a transiaon from the VBM to the CBM to occur. Since the process requires two paracles, it is much less likely to occur. AbsorpAon may or may not take place, even for photons with energy exceeding the gap (a is small) Thus, solar cells made from indirect semiconductors need to be thicker because we need to provide more opportuniaes for the transiaon to take place. QuesAon. For which type of semiconductor direct or indirect is absorpaon more temperature dependent? Why?

Temperature Dependence of Absortpion Coefficient in Indirect Semiconductors Ager Grosso and Pastori- Parravicini, Solid State Physics Answer. AbsorpAon in indirect semiconductors is temperature-dependent, because phonons are needed and phonon populaaon depends on temperature.

Example: Silicon Show where absorpaon occurs due to indirect transiaons; show where absorpaon occurs due to direct transiaons. hhp://www.ioffe.ru/sva/nsm/ Semicond/Si/Figs/145.gif

Learning Objec2ves: Carrier Excita2on & Thermaliza2on 1. Describe opacal absorpaon in semiconductors as transiaons of charge carriers on an energy band diagram. 2. Describe what phonons are. 3. Calculate the fracaon of incident solar energy lost to thermalizaaon. 4. Considering the effects of light absorpaon and thermalizaaon, plot efficiency vs. bandgap, and denote specific materials on the figure (homework). 5. What is meant by direct and indirect semiconductor? What are the implicaaons of direct and indirect absorpaon for PV cells? 6. Explain, using E vs. k diagrams, why direct absorbers are more efficient absorbers of sunlight. 7. Describe some implica2ons of the use of direct vs. indirect semiconductors on solar cells.

ImplicaAons - Summary Direct gap materials can be thinner and sall absorb most of the incident light. They are good candidates for thin films. Because crystalline Silicon has an indirect gap, the absorbing layer needs to be thicker (e.g. 300 mm thick Si wafers) RadiaAve recombinaaon is 10 3-10 4 Ames faster in direct gap materials than indirect. (However, it is typically non-radiaave, rather than radiaave, recombinaaon that is limits real device performance) AbsorpAon coefficient a(l) is more strongly dependent on temperature for indirect gap semiconductors (since phonon populaaon is strongly dependent on temperature) ThermalizaAon happens whether direct or indirect. Since it takes place through the emission (rather than absorpaon) of phonons, direct/indirect doesn t maher.

ME 432 Fundamentals of Modern Photovoltaics. Discussion 11: Light AbsorpAon and Carrier ExcitaAon/ThermalizaAon 21 September 2018