April 4, 2009, Updated, April 16, 2012 By I. Kamiya Engineering of Energy Conversion, Summer Semester 2012

Physics of solar cells The principles of operation and fundamental physics How to understand solar cells and other

Semiconductor physics & electronics : Topics to be dealt : carrier generation, recombination, transport, … (In principle, will NOT deal with quantum structures)

Solar Cell is a “minority carrier” device. p-n junction. Most semiconductor devices are “majority carrier” devices. Basically, how to allow minority carriers to survive & transport.

Optics Fundamentals of optics such as reflection, absorption, …

If time permits, Photocatalysts, photosynthesis will also be discussed.

Lecture notes can be downloaded from http://www.toyota-ti.ac.jp/Lab/Zairyo/QIL-Website/Home-J.html

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1 Introduction

1.1. Photons In, Electrons Out : The Photovoltaic Effect – Albert Einstein 1905 Workfunction of metals : UV light into metal resulting in electron emission Actually, initially observed by Heinrich Rudolf Hertz in 1887. UV → cathode → lowering of electronic potential Vacuum pump : Otto von Guericke 1650 Langmuir @ General Electric 1920~40’s Photovoltaic (PV) effect : separation of excited carriers in semiconductors Built-in potential asymmetry p-n junction

1.2. Brief History of the (SC) Reference: Norwegian University of Science and Technology http://org.ntnu.no/solarcells/pages/history.php

Photovoltaic Effect 1839 – Alexandre-Edmund Bequerel (Fr) – “The beginning” of the solar cell technology. By illuminating two electrodes coated by light sensitive materials, AgCl or AgBr. With different types of light, and carried out in a black box surrounded by an acid solution. The electricity increased with light intensity. 1873 – Willoughby Smith (GB) – photoconductivity (PC) of Se 1876 – William Grylls Adams & Richard Evans Day (GB) – PC of Se/Pt contact by sunlight. Very poor efficiency 1894 – Charles Fritts – construction of SC Au/Se/Metal contact. Efficiency ~ 1% 1904 – Wilhelm Ludwig Franz Hallwachs – discovery of photosensitivity of Cu/CuO 1905 – Albert Einstein – paper on photoelectric effect. Claimed that light consists of “packets” or quanta of energy (now called photons). The energy varies only with its frequency

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(electromagnetic waves, or the “color of the light”). A very simple, but revolutionary theory explaining the absorption of the photons regarding to the frequency of the light. 1914 – Goldman & Brodsky – Schottky barrier & rectification 1916 – Robert Andrews Millikan (US) provided experimental proof of the photoelectric effect. 1918 – Jan Czochralski (PL) developed a way to grow single-crystal Si. This increased the efficiency of the silicon-based cells considerably. 1930s – Walter Schottky, Neville Mott et al.,development of theory of metal-semiconductor interfaces 1932 – Audobert & Stora – PV of CdS 1950s – n-type Si 1950s – Bell Labs produce solar cells for space activities. 1951 – A grown p-n junction enabled the production of a single-crystal cell of Ge. 1953 – Dan Trivich (Wayne State, US) : first theoretical calculations of the efficiencies of various materials of different band-gap widths based on the spectrum of the sun 1954 – Daryl Chapin, Calvin Fuller, & Gerald Pearson (Bell Labs) – discovery of Si SC Initially, 4% $1000/W (made by hand), later, 11%. Conversion 6%, $200/W. 1954 – p-n CdS conversion 6% 1958 – Hoffman Electronics achieved 9% efficient PV cells. 1958 – The first PV-powered satellite, Vanguard I launched. area 100cm² and delivered ~ 0.1W. The power system operated for 8 yrs, and is the world's oldest satellite still in orbit (2007). 1958 – Ted Mandelkorn (U.S. Signal Corps Laboratories) fabricates n-on-p Si PV cells. 1959 – Hoffman Electronics achieved 10% efficient commercially available PV cells and demonstrated the use of a grid contact to significantly reduce series resistance. 1959 – Explorer-6 launched with a PV array of 9600 cells, 1 cm x 2 cm each. 1960 – Hoffman Electronics achieved 14% efficient PV cells. 1961 – “Detailed Balance Limit of Efficiency of p-n Junction Solar Cells,” William Shockely and Hans J. Queisser, J. Appl. Phys. 32, 510-519 (1961). 1962 – Telstar communications satellite launched by Bell Labs, initial powered (14W) by SCs. 1963 – Sharp Corporation produces a viable PV module of Si SCs. 1970 – First highly effective GaAs heterostructure SCs by Zhores Alferov (a Russian physicist) and his team in the USSR. 1972 – The Institute of Energy Conversion established at the Univ. of Delaware to perform R&D on thin-film (TF) PV and solar thermal systems, becoming the world’s first laboratory dedicated to photovoltaic R&D. 1976 – David Carlson and Christopher Wronski (RCA Laboratories) produced the first a-Si PV cells, which could be less expensive to manufacture than crystalline Si devices.

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(Efficiency ~1.1%)

1980 – The first TF SC exceeds 10% efficiency. (Made of copper sulfide (Cu2S) and cadmium sulfide (CdS). 1981 – Paul MacCready builds the -powered aircraft, the Solar Challenger. Flies from France to England across the English Channel. The aircraft had over 16,000 solar cells mounted on its wings, which produced a power of 3kW. 1982 – Hans Tholstrup (Australian) drives the first solar-powered car, the Quiet Achiever, 4,000km between and in 20 days. That was 10 days faster than the first gasoline-powered car to do so. The max. speed was 72 km/h, and the av. was 24 km/h. 1984 – The IEEE Morris N. Liebmann Memorial Award was presented to Drs. David E. Carlson and Christopher R. Wronski at the 17th Photovoltaic Specialists Conference, "For crucial contributions to the use of a-Si in low-cost, high-performance PV SCs." 1985 – University of South Wales breaks the 20% efficiency barrier for Si SC under one sun conditions. 1989 – Reflective solar concentrators are first used with solar cells. 1991 – Efficient photoelectrochemical cells (PEC) developed. Each cell consists of a semiconducting photoanode and a metal cathode immersed in an electrolyte. The Dye-sensitized SC (DSC), also called Grätzel cells, invented. It was a new class of low-class DSC. 1992 – University of South Florida develops a 15.9% efficient TF PV cell made of CdTe, breaking the 15% barrier for the first time for this technology. 1994 – The National Renewable Energy Laboratory (NREL) develops a SC, made from GaInP and GaAs, that becomes the first one to exceed 30% conversion efficiency. 1996 – Renewable Energy Corporation (REC), a Norwegian company established. 1996 – EPFL, the Swiss Federal Institute of Technology in Lausanne, achieves 11% efficiency with the DSCs. 1999 – Spectrolab, Inc. and NREL develop a PV SC that converts 32.3% of the sunlight that hits it into electricity. The high conversion efficiency was achieved by combining three layers of PV materials into a single SC. The cell performed most efficiently when it received sunlight concentrated to 50 times normal. To use such cells in practical applications, the cell is mounted in a device that uses lenses or mirrors to concentrate sunlight onto the cell. Such “concentrator” systems are mounted on tracking systems that keep them pointed toward the sun. 1999 – NREL achieves a new efficiency record (18.8%) for TF PV SCs. 2000 – Two new TF solar modules, developed by BP Solarex, break previous performance records. The company’s 0.5-m2 module achieves 10.8% conversion efficiency — the highest in the world for TF modules of its kind. And its 0.9-m2 module achieved 10.6% conversion efficiency and a power output of 91.5W — the highest power output for any TF module in

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the world. 2001 – TerraSun LLC : use of holographic films to concentrate sunlight onto a solar cell 2003 – REC Solar started production. 2007 – Univ. of Delaware achieves a 42.8% efficiency.

Active research taking place in Australia : University of New South Wales Also in Spain. The Japanese companies used to dominate the market. Now, Chinese companies

1. 中国 Suntech 6.6% 2. 中国 Ja Solar 6.1% 3. アメリカ合衆国/ ドイツ/ マレーシア First Solar 5.9% 4. 中国 英利() 4.7% 5. 中国 4.7% 6. ドイツ/ マレーシア Q セルズ 3.9% 7. 台湾 Gintech 3.3% 8. 日本 シャープ 3.1% 9. 台湾 Motech 3.0% 10. 日本 京セラ 2.7%

By 太陽光発電情報、2011 年 5 月分、資源総合システム

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1.3. Photovoltaic Cells and Power Generation

1.3.1. Photovoltaic cells, modules and systems Solar cells – basic building block of solar photovoltaics Cells : 2 terminal devices like diodes → connected / encapsulated to modules (Fig. 1.2) 28 ~ 36 cells in series for 12V Cells → modules → arrays (generator): battery, regulator, etc. DC power → AC : inverter

1.3.2. Some important definitions Solar cell vs. battery

VOC : open circuit voltage

ISC : short circuit current

JSC : short circuit current density (per area) I(V) : current determined by current-voltage characteristic

V  IV RL

Battery Solar cell emf constant determined by phases caused by illumination power constant varies by illumination life limited unlimited character voltage generator current generator

emf : electromotive force （起電力、voltatge）

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1.4. Characteristics of the Photovoltaic Cell : A Summary 1.4.1. Photocurrent and quantum efficiency Photocurrent generated by SC under short circuit : depends on incident light

J  q b E QE E dE (1.1) SC  S    

where QEE : quantum efficiency of an incident photon of energy E delivering one electron

bS E : incident spectral photon flux density

(number of photons in E ~ E+dE incident on unit area in unit time)

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Example : GaAs vs. solar spectrum hc Remember E  (1.2)  1238 For E [eV], [nm] EeV   nm

1.4.2. Dark current and open circuit voltage Dark current : reverse current under load

qV kBT J darkV  J0 e 1 (1.3)

Photocurrent : defined as positive in SCs Net current density

qV kBT JV   J SC  J darkV   J SC  J 0 e 1 (1.4)

For ideal diode

qV kBT J  J SC  J0 e 1 (1.5)

Following the conventions used in Fig. 1.6, at VOC, J = 0. (Details in Chap. 6)

Therefore, from Eq. 1.5

qVOC kBT qVOC kBT 0  J SC  J0 e 1 ∴ J SC  J0 e 1

qV  J  J SC qVOC kBT OC SC ∴ 1 e ∴  ln 1 J 0 kBT  J 0 

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k T  J  ∴ B  SC  (1.6) VOC  ln 1 q  J 0 

Functions of a diode (non linear resistive element) V < 0 : photodetector – consuming power to generate photocurrent

0 < V < VOC : power generator (SC)

V > VOC : LED

1.4.3. Efficiency

In 0 < V < VOC : power generator (SC), Cell power density P  JV (1.7)

Maximum of P achieved at maximum power point Vm, Jm (Fig. 1.8).

V Optimum load for max power has sheet resistance m J m

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Fill factor (‘squareness’ of J-V curve) defined by J V FF  m m (1.8) J SCVOC

Efficiency  : power delivered over incident power (PS) J V J V FF   m m  SC OC (1.9) PS PS

Standard Test Condition (STC) Air Mass 1.5 (Sun @ elevation 42°), incident power density 1000 W/m2, 25℃, optical path length to Sun 1 nAirMass   cos ec  s  (2.5) optical path length if Sun directly overhead sin s

 s : angle of elevation of the sun (Fig.2.2)

Typical characterisics : Table 1.1

VOC vs JSC (Fig. 1.9)

1.4.4. Parasitic resistances Power dissipation (loss) : contact resistance, leakage currents

→ series (Rs) and parallel/shunt (Rsh) (Figs. 1.10, 1.11)

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For better cell performance

small Rs and large Rsh The diode equation 1.5 is modified to

qV kBT J  J SC  J0 e 1 (1.5)

qV JARs  kBT V  JARs J  J SC  J 0 e 1 (1.11) Rsh

1.4.5. Non-ideal diode behaviour Introduction of ideality factor m ( 1 < m < 2 )

qV mkBT J  J SC  J0 e 1 (1.12)

1.5. Summary

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