nanostructured materials for solar energy conversion, 2006, p.615

Thereis no book that offers a comprehensive overview of the nanostructured ganic and organic materials for solar energy conversion.. This book is divided into fiveparts: fundamentals of

Nanostructured Materials for Solar Energy Conversion

Nanostructured Materials for Solar Energy Conversion

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Our society is based on coal, oil and natural gas, but these fossil fuels will

be depleted someday in the future because they are limited Carbon dioxide

is produced in the combustion of fossil fuels and the rapid increase of bon dioxide concentration has affected the consequence of climate, result-ing in the global warming effect Under these circumstances, interest inphotovoltaic (PV) solar cell is increasing rapidly as an alternative and cleanenergy source

car-Photovoltaic solar cells provide clean electrical energy because thesolar energy is directly converted into electrical energy without emittingcarbon dioxide The solar energy is not limited, free of charge and distrib-uted uniformly to all human beings Crystalline silicon solar cell has beenextensively studied and used for practical terrestrial applications However,the expensive material cost and lots of energy necessary for manufacturinghave caused high cost and long energy payback time, which have preventedthe large spread of PV power generation

Recently, thin film solar cells using silicon or compound tors have been actively studied instead of the bulk silicon solar cell But thesolar cells are still too expensive to compete with public electricity charge

semiconduc-In 2004 New Energy and semiconduc-Industrial Technology Development Organization(NEDO), Ministry of Economy, Trade and Industry, Japan, announced the

“PV Roadmap Toward 2030 (PV2030)” in which the target of productioncost for PV module is 50 yen/W in 2030 It is expected that the PV powergeneration can supply approximately 50% of residential electricity con-sumption (approximately 10% of total electricity consumption) in 2030 But it would be difficult to reach this goal only by the conventional tech-nologies One important concept to reduce the solar cell cost and to increasethe conversion efficiency is to use NANOTECHNOLOGY, i.e., to use the

nanostructured material in solar cell Nanostructured materials are largelydivided into inorganic materials and organic materials In spite of the com-mon interest and common purpose, two kinds of materials have been dis-cussed in different conferences and different communities until now There

is no book that offers a comprehensive overview of the nanostructured ganic and organic materials for solar energy conversion

inor-The aim of this book is to overview the nanostructured materials forsolar energy conversion covering a wide variety of materials and device typesfrom inorganic materials to organic materials This book is divided into fiveparts: fundamentals of nanostructured solar cells, nanostructures in conven-tional thin film solar cells, dye-sensitized solar cells, organic and carbonbased solar cells and other nanostructures Authors are all specialists in theirfields But I must apologize that the important nanostructured materials aremissing in this book because of the limit of my ability This book wasintended for researchers, scientists, engineers, graduate students and under-graduate students, majoring in electrical engineering, chemical engineering,material science, physics, etc., who are interested in the nanostructured solarcells The content of my chapter is the subject of a graduate course in ourdepartment, Department of Environmental Technology and Urban Planning,devoted for the beginner of PV I strongly hope that you will get some hintsfor the development of the solar cell from this book and contribute to theprogress of PV

Tetsuo Soga

Nagoya, Spring 2006

Tetsuo Soga

Department of Environmental Technology and Urban Planning

Nagoya Institute of Technology

Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan

Energy conversion in solar cell consists of generation of electron–hole pairs

in semiconductors by the absorption of light and separation of electrons andholes by an internal electric field Charge carriers collected by two electrodesgive rise to a photocurrent when the two terminals are connected externally.When a resistance load is connected to the two terminals, the separation ofthe charge carriers sets up a potential difference

Most of the solar cells used in the terrestrial applications are bulk-typesingle- or multi-crystalline silicon solar cells The typical cell structure is athin (less than 1␮m) n-type emitter layer on a thick (about 300 ␮m) p-typesubstrate Photo-generated electrons and holes diffuse to the space chargeregion at the interface where they are separated by the internal electric field.The effective charge separation results from long diffusion length of electronsand holes in crystalline silicon Although it is aimed to reduce the solar cellmodule manufacturing cost, the drastic reduction of cell cost and increase

of the conversion efficiency cannot be expected by using the conventionalmaterials and solar cell structures Moreover, the shortage of the feedstock

of high-purity silicon is predicted in the near future although it depends onoff-spec silicon of electronics industry Therefore, research and develop-ment of solar cells with low production cost, high conversion efficiency andlow feedstock consumption are required

An important concept to reach this goal is to use nanostructured rials instead of bulk materials The motivations to employ nanostructures insolar cells are largely divided into three categories as follows:

mate-1 To improve the performance of conventional solar cells

2 To obtain relatively high conversion efficiency from low grade(inexpensive) materials with low production cost and low-energyconsumption

3 To obtain a conversion efficiency higher than the theoretical limit

of conventional p–n junction solar cell

This book brings out an overview of the organic and inorganic structured materials for solar energy conversion The book comprises of fiveparts as follows:

nano-PART I FUNDAMENTALS OF NANOSTRUCTURED

SOLAR CELLS

The fundamental issues to deal with nanostructured solar cells are described

on device modeling, optical and electrical modeling and modeling of tive index and reflectivity of quantum solar cells The chapter on basic proper-ties of semiconductor materials and the conventional p–n junction solar cellsdeals with nanostructured solar cells

refrac-PART II NANOSTRUCTURES IN CONVENTIONAL THIN

FILM SOLAR CELLS

Nanostructures of conventional thin film solar cells such as silicon solar cells,chalcopyrite-based solar cells, CdS-based solar cells and CdTe-based solarcells are described Amorphous silicon has attracted attention to reduce themanufacturing cost compared with bulk-type crystalline silicon But therestill remains a problem of stability Recently, microcrystalline thin film siliconsolar cells made up of nano-sized crystallites with the material propertiesbetween amorphous and bulk have been studied actively It is expected toobtain very high conversion efficiency (more than 15%) by employing amor-phous silicon/microcrystalline silicon tandem solar cells It also describesthat it is possible to improve the performance and reduce the cost of thinfilm solar cells based on chalcopyrite-based materials, CdS, CdTe and Cu2S

PART III DYE-SENSITIZED SOLAR CELLS

The principle and the current status of dye-sensitized solar cells are described

In the conventional p–n junction solar cells, only the electrons and holesthat can diffuse to the space charge region can be collected as a current Inorder to get a long diffusion length, the purity of semiconductors should beincreased and the defect concentration should be decreased, resulting in theexpensive solar cell materials In a dye-sensitized solar cell, a photon absorbed

by a dye molecule gives rise to electron injection into the conduction band

of nanocrystalline oxide semiconductors such as TiO2or ZnO Because of thehigh surface area, relatively high photocurrent can be obtained in spite ofthe simple process The dye is regenerated by electron transfer from a redoxspecies in solution A chapter on solid-state dye-sensitized solar cells in whichthe liquid electrolyte is replaced by p-type semiconductor is also dealt with

PART IV ORGANIC- AND CARBON-BASED SOLAR CELLS

The principle and the current status of organic solar cell and fullerene-basedsolar cell are described Organic solar cells are attractive as solar cell materialsbecause of high throughput manufacture process, ultra-thin film, flexible,lightweight and inexpensive Organic materials differ from inorganic materi-als since the excited carriers exist as excitons, excitons are separated intoelectrons and holes at the interface, charge carrier transport is followed byhopping, etc In order to increase the efficiency bulk, heterojunction solar cellsusing conjugated polymers and small molecule organic materials such asphthalocyanine have been investigated It is important to understand theproperties of fullerenes because it is often used as an organic solar cell Thephotosynthetic materials are also studied as solar cell materials and a solidstate cell is demonstrated

PART V OTHER NANOSTRUCTURES

Solar cells using other semiconductor nanostructures are overviewed Theconcept of ETA (extremely thin absorber) is similar to that of dye-sensitizedsolar cells except that the ETA solar cell is completely made up of inorganicsemiconductors The concept of quantum structures is very important becausethere is a possibility to achieve the conversion efficiency higher than the the-oretical limit of conventional p–n junction solar cells by employing quantumwell or quantum dot structures The idea is to extend the optical absorption

to longer wavelengths by quantum wells, to use the carrier multiplicationwhich produces the quantum efficiency exceeding unity, to use intermediatebands made of quantum dots, etc It is also expected that single wall carbonnanotubes can improve the transport properties of polymer-based solar cells

Chapter 2 Device Modeling of Nano-Structured Solar Cells .45

M Burgelman, B Minnaert and C Grasso

Chapter 3 Optical and Electrical Modeling of

Nanocrystalline Solar Cells 81

Akira Usami

Chapter 4 Mathematical Modelling of the Refractive Index

and Reflectivity of the Quantum Well Solar Cell .105

Francis K Rault

PART II NANOSTRUCTURES IN CONVENTIONAL

THIN FILM SOLAR CELLS

Chapter 5 Amorphous (Protocrystalline) and Microcrystalline

Thin Film Silicon Solar Cells .131

R.E.I Schropp

Chapter 6 Thin-Film Solar Cells Based on Nanostructured

CdS, CIS, CdTe and Cu2S 167

Vijay P Singh, R.S Singh and Karen E Sampson

PART III DYE-SENSITIZED SOLAR CELLS

Chapter 7 TiO2-Based Dye-Sensitized Solar Cell .193

Shogo Mori and Shozo Yanagida

Chapter 8 Dye-Sensitized Nanostructured ZnO Electrodes

for Solar Cell Applications 227

Gerrit Boschloo, Tomas Edvinsson and Anders Hagfeldt

Chapter 9 Solid-State Dye-Sensitized Solar Cells 255

Akira Fujishima and Xin-Tong Zhang

PART IV ORGANIC- AND CARBON-BASED SOLAR CELLS

Chapter 10 Nanostructure and Nanomorphology Engineering

in Polymer Solar Cells .277

H Hoppe and N.S Sariciftci

Chapter 11 Nanostructured Organic Bulk Heterojunction

Solar Cells .319

Yoshinori Nishikitani, Soichi Uchida and Takaya Kubo

Chapter 12 The Application of Photosynthetic Materials and

Architectures to Solar Cells .335

J.K Mapel and M.A Baldo

Chapter 13 Fullerene Thin Films as Photovoltaic Material 359

E.A Katz

PART V OTHER NANOSTRUCTURES

Chapter 14 Nanostructured ETA-Solar Cells 447

Claude Lévy-Clément

Chapter 15 Quantum Structured Solar Cells .485

A.J Nozik

Chapter 16 Quantum Well Solar Cells and Quantum

Dot Concentrators .517

K.W.J Barnham, I Ballard, A Bessière, A.J Chatten, J.P Connolly, N.J Ekins-Daukes, D.C Johnson, M.C Lynch,

M Mazzer, T.N.D Tibbits, G Hill, J.S Roberts and M.A Malik

Chapter 17 Intermediate Band Solar Cells (IBSC)

Using Nanotechnology 539

A Martí, C.R Stanley and A Luque

Chapter 18 Nanostructured Photovoltaics Materials Fabrication and

Characterization 567

Ryne P Raffaelle

Index 595

PART I

FUNDAMENTALS OF NANOSTRUCTURED SOLAR CELLS

of light (photon) energy producing electron–hole pairs in a semiconductorand charge carrier separation A p–n junction is used for charge carrier sep-aration in most cases It is important to learn the basic properties of semi-conductor and the principle of conventional p–n junction solar cell tounderstand not only the conventional solar cell but also the new type of solarcell The comprehension of the p–n junction solar cell will give you hints toimprove solar cells regarding efficiency, manufacturing cost, consumingenergy for the fabrication, etc This chapter begins with the basic semicon-ductor physics, which is necessary to understand the operation of p–n junc-tion solar cell, and then describes the basic principles of p–n junction solarcell It ends with the concepts of solar cell using nanocrystalline materials.Because the solar cells based on nanocrystalline materials are complicatedcompared with the conventional p–n junction solar cell, the fundamentalphenomena are reviewed.

2 FUNDAMENTAL PROPERTIES OF SEMICONDUCTORS [1–5] 2.1 Energy Band and Carrier Concentration

The electrons of an isolated atom have discrete energy levels Whenatoms approach to form crystals, the energy levels split into separate butclosely spaced levels because of atomic interaction, which results in a con-

tinuous energy band Between the two bands – the lower called the valence

band and the upper called the conduction band – there is an energy gap called band gap, Eg, which is an important parameter in solar cell All theenergy levels in the valence band are occupied by electrons and those in theconduction band are empty at a temperature of 0 K Some bonds are broken

by the thermal vibrations at room temperature because the band gap is in therange of 0.5–3 eV This results in the creation of electrons in the conductionband and holes in the valence band The representation of energy band for

semiconductor is shown in Fig 1(a) E c and E vare designated as the bottom

of the conduction band and the top of the valence band, respectively The

kinetic energy of electron is measured upward from E c, whereas that of hole

is measured downward from E v, because a hole has a charge opposite toelectron The electrons in conduction band and holes in valence band cancontribute to the current flow On the contrary, in an insulator, the band gap

is so large (E g⬎ 5 eV) that the conduction band is empty even at room perature In a conductor, the conduction band is partially filled with electrons

tem-or overlaps the valence band Consequently, there is no band gap and theresistivity is very small

2.1.1 Intrinsic Semiconductor

When electrons and holes generated from impurities are much smallerthan thermally generated electrons and holes, they are called intrinsic semi-conductors The number of electrons in the conduction band per unit vol-ume and that of holes in the valence band per unit volume are represented

as n and p, respectively, and can be derived from the density of state and the

distribution function The electron concentration in the conduction band isexpressed by

where E ⫽ 0 means the energy of the bottom of the conduction band and Etop

is the energy of the top of the conduction band Assuming that the density

of state is equal to 4p(2m n /h2)3/2E1/2and the probability of an energy level being occupied is given by Fermi-dirac distribution function,

temperature, that is, n ⫽ p ⫽ n i , where n i is the intrinsic carrier

concentra-tion If we take a product of n and p, we get the following equation:

It is obvious that the intrinsic carrier concentration decreases if the band gapbecomes larger The Fermi level of an intrinsic semiconductor is calculated

to be

Because the second term is much smaller than the first, the Fermi level of

an intrinsic semiconductor lies close to the middle of band gap as shown inFig 1(a)

2.1.2 Extrinsic Semiconductor

When electrons and holes generated by impurity are not negligible, thesemiconductor is called extrinsic semiconductor Let us consider the carrierconcentration in the case of Si When group V atoms such as phosphorus (P)are doped as impurity, the phosphorous atom forms covalent bonds with itsfour neighboring Si atoms The fifth electron is bound with P atom veryloosely, and therefore ionized even at room temperature Consequently,

it becomes a conduction electron with negative charge In this case, Sibecomes n-type semiconductor and the phosphorous atom is called a donor.Under complete ionization condition, the electron (majority carrier) con-

centration is expressed as n ⫽ N D , where N Dis the donor concentration Thedonor is an immobile atom with positive charge Because the equation

np ⫽ n i2 is valid for extrinsic semiconductor under a thermal equilibrium,

the hole (minority carrier) concentration is expressed as p ⫽ n i2/N D TheFermi level is expressed as

The Fermi level can be controlled by the donor concentration and is close

to the bottom of the conduction band The schematic energy band tation of extrinsic semiconductor with donor is shown in Fig 1(b)

represen-Similarly, when group III atoms such as boron (B) are doped as rity into silicon (Si), the boron atom forms covalent bonds with its fourneighboring Si atoms The positively charged conduction hole is created.This is a p-type semiconductor and the boron atom is called an acceptor.Under complete ionization condition, the hole (majority carrier) concen-

impu-tration is expressed as p ⫽ N A , where N A is the acceptor concentration The acceptor is an immobile atom with negative charge The electron(minority carrier) concentration is expressed as The Fermi level

is expressed as

In this case, the Fermi level moves closer to the top of the valence band The schematic energy band representation of extrinsic semiconductor withacceptor is shown in Fig 1(c)

N

v A

2.2 Carrier Transport in Semiconductor

2.2.1 Mobility

The electrons in semiconductor move randomly in all directions by thethermal energy After a short distance, the electrons collide with a latticeatom or an impurity atom, or other scattering center This scattering processcauses the electron to lose the energy taken from the electric field Thekinetic energy is transferred to the lattice in the form of heat The average

time between collisions is called the mean free time, tc The random motion

of electrons leads to the average net displacement to be zero When a small

electric field E is applied to the semiconductor, the electron experiences a

force ⫺qE and gets accelerated toward the opposite direction of the field, where q is an electric charge (1.6⫻ 10⫺19C) The velocity component pro-

duced by the electric field is called the drift velocity, v n The change inmomentum of an electron in a mean free time is given by

Let us consider an n-type semiconductor with a cross-sectional area of

A and a carrier concentration of n as shown in Fig 2 When an electric field

E is applied to the sample, the electron current density is given by

n

m v n n ⫽⫺ t qE c

where I nis the electron current Similarly, the hole current density is given by

The total current density due to the electric field is known as drift currentdensity and given by

where s is called conductivity which is reciprocal of resistivity.

We consider the drift current using the energy band diagram When theelectric field is applied to the semiconductor, as shown in Fig 3, the gradi-ent of the conduction band and the valence band takes place and the elec-trons and holes flow to reduce the potential energy It should be noted thatthe electrons and the holes move toward opposite directions, but the direc-tion of current is the same

2.2.3 Diffusion Current

When there is a spatial variation of electron concentration in the conductor sample, the electrons move from the region of higher concentra-tion to that of lower concentration This current is called the diffusioncurrent Let us consider the electron concentration with one-dimensional

semi-gradient in x-direction as shown in Fig 4(a) The electron flows from right

to left, and the electron flow rate per unit area is given by

−

Fig 2 Semiconductor sample to consider electron current density.

where D n is called diffusion coefficient of the electron Therefore, the diffusion current density of electron is expressed by

HoleFlow

Current

Fig 4 (a) Diffusion of electrons and (b) holes.

When the electron concentration increases with x, the electrons diffuse toward the negative x-direction, resulting in the current flow toward the x-direction Similarly, when the hole concentration increases with x, the holes diffuse toward the negative x-direction It should be noted that the direction

of current is opposite compared to electron The diffusion current density byhole is given by

where D pis the diffusion coefficient of hole When both an electric field and

a concentration gradient are present, the total current density is given by

for electrons and

for holes

We treated the diffusion and the drift phenomena separately, but there

is a relationship between two phenomena The diffusion coefficient isexpressed by

which is known as Einstein relation

2.3 Optical Absorption and Recombination in Semiconductor

2.3.1 Optical Absorption

The energy of a photon is hv, where h is Planck’s constant and v is the

frequency of the light The relationship between photon energy and the

where c is the speed of light in vacuum The spectrum of the solar light

energy spreads from the ultraviolet region (0.3␮m) to the infrared region(3␮m) Let us assume that a semiconductor is illuminated with solar light.When the photon energy is less than band gap of the semiconductor, thelight is transmitted through the material, that is, the semiconductor is trans-parent to the light When the photon energy is larger than band gap, the electrons in the valence band are excited to the conduction band It meansthat a photon is absorbed to create an electron–hole pair This process is called

intrinsic transition or band-to-band transition The cutoff wavelength l0

is very important to choose the solar cell material because the light withwavelength longer than cutoff wavelength cannot be used for solar energyconversion

The transition of electron by the optical absorption is shown in Fig 5

When hv is bigger than Eg, an electron–hole pair is created, whereas the

excess energy hv – Eggives the electron, or hole, additional kinetic energythat is dissipated as heat in semiconductor

Assuming that a semiconductor is illuminated by a light with a photon

flux F0 normal to the surface in units of photons per unit area per unit

time, the number of photons absorbed within a depth of x and x ⫹ ⌬x is

where a is the absorption coefficient If the initial condition is given by F(0) ⫽ (1⫺R)F0, the flux of photons at the depth of x is

assuming that R is the reflectivity of the surface to normally incident light.

At the distance of 1/a, the photon flux that exits is 1/e of the initial value.

If the absorption coefficient is large, the photons are absorbed in a short tance, but the long distance is necessary for the photons to be absorbedwhen the absorption coefficient is small It is important to note that theabsorption coefficient is a strong function of photon energy The absorptioncoefficients are approximately expressed as

dis-for direct gap semiconductor and

for indirect gap semiconductor, where A* and A** are material dependent constants and E pis the phonon energy associated at the absorption [6] When

hv ⫺ E g is much larger than E p , and E p is much smaller than kT, E pcan beneglected and the absorption coefficient of indirect gap semiconductor is

proportional to (hv ⫺ E g)2 Generally, the absorption coefficient of an indirectgap semiconductor is much smaller than that of direct gap semiconductorbecause the absorption or the emission of phonon is involved in accompany-ing a change in momentum of electrons at the absorption of photons

2.3.2 Recombination in Semiconductor

The excess charge carriers created in a semiconductor by absorption oflight are annihilated after the source light is turned off This process iscalled recombination The recombination phenomena in bulk is classifiedinto direct recombination (Fig 6(a)), indirect recombination via localizedenergy states in the forbidden energy gap (Fig 6(b)), Auger recombination(Fig 6(c)), etc First, let us consider direct recombination, which usuallydominates in direct band gap semiconductors; this process is an inverse ofabsorption When an electron makes a transition from the conduction band

to the valence band, an electron-hole pair is annihilated, resulting in theemission of photon Under thermal equilibrium conditions, the recombina-

tion rate is bn n0 p n0for an n-type semiconductor and is equal to the tion rate (the number of electron–hole pairs generated per unit volume per

genera-unit time) by thermal vibration, where b is the proportionality constant and

n n0 and p n0 are electron and hole concentrations, respectively, in n-typesemiconductor at thermal equilibrium When excess carriers are introduced

by light illumination, the recombination rate is increased to bnp because the

recombination is proportional to the number of electrons in conductionband and that of holes is valence band In the case of low-injection level, thenet recombination rate is given by

where ⌬n and ⌬p are the excess electron and hole concentrations by light

illumination It means that the net recombination rate is proportional to

the excess minority carrier concentration t p ⫽ 1/bn n0is called the minoritycarrier (hole) lifetime Similarly, in the case of p-type semiconductor, the

net recombination rate is expressed as U ⫽ ⌬n/t n , where t nis the minority

carrier (electron) lifetime expressed by t n ⫽ 1/bp p0

Next, let us consider a semiconductor containing trap states near the

midgap (Fig 6(b)) with a concentration of N t This indirect recombination

is very likely to be for indirect band gap semiconductor For an n-type

semiconductor, the minority carrier lifetime t p and the net recombination

rate U are given by

and

where v th is the mean thermal velocity of hole and s p the capture cross section of the hole trap Similarly, for a p-type semiconductor, the minoritycarrier lifetime and the recombination rate are given by

and

In the case of indirect recombination, the minority carrier lifetime is pendent of the majority carrier concentration, and is proportional to theinverse of the trap concentration

inde-In Auger recombination (Fig 6(c)), one electron gives up its extraenergy to another electron in the conduction band or the valence band dur-ing the recombination, resulting in the excitation of an electron to a higherenergy level The excited electron will give up this excess energy as heat whenthe excited electron relaxes to the band edge Because the Auger process

involves three particles, its recombination rate is expressed as U ⫽ An2p or

U ⫽Ap2n for electron–electron–hole process and hole–hole–electron process, respectively A is the Auger constant which strongly depends on temperature.

Auger process is important when the carrier concentration is high, especially

in low band gap semiconductor

Because a semiconductor is abruptly terminated, the disruption of theperiodic potential function results in the energy states within the energy band

gap at the surface These states – surface states – enhance the recombinationnear the surface They become very important with reducing the crystal sizebecause the number of carriers recombining at the surface per unit volume

is increased

For a low-injection condition, the total number of carriers recombining

at the surface per unit area and unit time is expressed as

for an n-type semiconductor, where S is the surface recombination velocity and p s is the hole concentration at the surface When an n-type semicon-ductor is irradiated uniformly by the light to create excess carriers, the gra-dient of hole concentration yields a diffusion current, which is equal to thesurface recombination current as shown in the following equation:

2.3.3 Continuity Equation

We treated the drift current, the diffusion current, the generation, andthe recombination individually But in the real semiconductor, all theprocesses occur simultaneously In order to derive the relationship of thesephenomena in one-dimensional form, we consider an infinitesimal slice

with a thickness of dx and an area of A as shown in Fig 7 Assuming that the electron current density at x is J n (x), the net increase of the electrons per

unit time in this volume is the sum of the net flow into the slice and the netcarrier generation in the slice, that is,

where G n and R nare the generation rate and the recombination rate of trons, respectively Using the Taylor series, we obtain the following conti-nuity equation for electrons in p-type semiconductor as follows:

Similarly, the one-dimensional continuity equation for holes in n-type conductor is given by

semi-where J p is the hole current density and G p and R pare the generation and therecombination rate of holes, respectively Substituting the current expres-sions using the drift current and the diffusion current, the continuity equa-tions are expressed as

and

Let us calculate the steady state excess carrier concentration in a very simple

case Assuming that the excess generation occurs at x⫽ 0 in an n-type conductor that is homogeneous and infinite in extent, the continuity equa-tion is given by

for zero-applied electric field Because the excess carrier concentrationshould decay toward zero, the general solution is

where is called the diffusion length for holes and ⌬p(0) is the excess carrier concentration at x⫽ 0 Similarly, is called the diffusion length for electrons The distribution of the steady state excesscarrier concentration is schematically shown in Fig 8 The diffusion length

is a measure of the average distance which a minority carrier can diffusewithout recombination

2.4 Photoconductive Effect

As described in Section 2.2., the conductivity of a semiconductor isgiven by

where n and p are the electron concentration and the hole concentration,

respectively, at thermal equilibrium If the semiconductor is illuminated bylight source to create electron–hole pairs, the conductivity of the semicon-ductor increases This phenomenon is called photoconductive effect For thepractical p–n junction solar cell, the light-generated electrons and holes areseparated by the internal electric field, which will be discussed in Section3.2 Therefore, the photoconductivity gives very useful information on theperformance of solar cell

Let us calculate the photoconductivity of a semiconductor, which sists of a slab with Ohmic contacts at both ends, as shown in Fig 9 Assumingthat the slab of semiconductor is illuminated homogeneously, the conduct-ivity is given by

con-at the steady stcon-ate, where ⌬n and ⌬p are excess electron concentration and

excess hole concentration, respectively Since the generation rate is equal tothe recombination rate, the continuity equations for electrons and holes areexpressed as

The photoconductive gain is given by

where t n and t pare the transit time of an electron and a hole between twoOhmic contacts, respectively Usually, ⌬s/s is a measure of how effectively

the photogenerated electron–hole pairs are collected at the external circuit

3 BASIC PRINCIPLES OF p–n JUNCTION SOLAR CELL

3.1 Electric Properties [1–5]

3.1.1 Built-In Potential

The p–n junction is commonly used for solar cell The important role

of p–n junction is the charge separation of light-induced electrons and holes.Let us calculate the built-in potential of the p–n junction Fig 10 shows theenergy band picture and majority carriers for n-type semiconductor and p-type semiconductor When a p–n junction is formed, the large carrier con-centration gradients cause the diffusion of carriers, that is, holes diffuse fromp-type semiconductor to n-type semiconductor and electrons diffuse from n-type semiconductor to p-type semiconductor Because of the ionized impu-rity atoms, a layer without mobile charge carriers is formed when the electrons

g

n n p p

Fig 10 Energy band pictures and majority carriers of n- and p-type semiconductors.

and holes diffuse across the junction This space charge sets up an electricfield, which opposes the diffusion across the junction as shown in Fig 11(a).When the drift current due to the electric field is balanced by the diffusioncurrent because of the carrier concentration gradient for each carrier, the ther-mal equilibrium is established At this point, the Fermi levels of the p-typesemiconductor and n-type semiconductor are equal as shown in Fig 11(b).The electrostatic potential difference between the p-type semiconduc-tor and the n-type semiconductor at thermal equilibrium is called the built-

in potential V b V bis equal to the difference in the work function of p-sideand n-side and is given by

where N A and N Dare the concentrations of the acceptor and donor in p-typesemiconductor and n-type semiconductor, respectively

q

N N n

ductor of doping N A for x ⬍ 0 and n-type semiconductor of doping N D

for x ⬎ 0 as shown in Fig 12 x p and x ndenote the depletion layer width ofp- and n-side, respectively, ignoring the transition region According to

Poisson’s equation, the electrostatic potential f must obey

(a) E

where ␧ is the dielectric constant of the semiconductor By integrating these

equations the electric field E is expressed as

and

E m ⫽ qN D/␧ x n ⫽ qN A/␧ x p is the maximum electric field that exists at x⫽ 0.The total potential difference, namely built-in potential, is given by

which is equal to the area of the field triangle shown in Fig 12(b) The total

depletion width w is given by

The depletion layer width increases when either the donor concentration

or the acceptor concentration is reduced When the impurity concentration

on one side is much higher than that of the other side, for example, in thecase of p⫹–n junction, where N A ⬎⬎N D, the total depletion layer width isgiven by

3.1.3 Ideal Current–Voltage Characteristics under Dark

When a bias voltage V Fwith the positive terminal to the p-side and thenegative terminal to the n-side is applied, the applied voltage reduces theelectrostatic potential across the depletion region as shown in Fig 13(a)

This polarity is called the forward bias In this case the drift current is

reduced and the diffusion of electrons and holes increases from the n-side

to the p-side and from the p-side to the n-side, respectively Therefore, theminority carrier injection occurs, that is, electrons are injected into the p-sideand holes are injected into the n-side

At thermal equilibrium, the electron concentration in the n-side isexpressed as

Therefore, when a forward bias V F is applied to the junction, the electronconcentration at the boundary of the depletion region in the n-side isexpressed as

using the electron concentration at the boundary of the depletion region inthe p-side.

In the case of the low-injection condition (n n ⬇ n n0 ), n pis expressed as

In the n-layer, the steady state continuity equation is

The solution of this differential equation is given by

where L pis the diffusion length of holes in the n-layer Therefore, the

diffu-sion current density in n-side at x ⫽ x nis

Similarly, the diffusion current density in p-side at x ⫽ ⫺x pis

where L n is the diffusion length of electrons in the p-layer Thus the totalcurrent density is the sum of the two, as follows:

J0is called the saturation current density and is expressed as

L

qD n L

n p n

n p n

qV kT n

x x L

When a reverse bias voltage V R is applied to the p–n junction, the appliedvoltage increases the electrostatic voltage across the depletion region asshown in Fig 13(b) Therefore, the diffusion current is suppressed Similarly,the current–voltage characteristics under a reverse bias is given by

3.1.4 Effects of Generation and Recombination

It is difficult to fabricate a p–n junction with an ideal current–voltagecharacteristic In the practical p–n junction solar cell, it is necessary to con-sider the generation and the recombination of carriers in the depletionregion The electron and hole generations occur through the energy state inthe forbidden energy gap in the case of reverse bias condition At the forward bias, the carriers will recombine through the energy state at the for-bidden energy gap The recombination current is approximately given by

The forward current density of the practical p–n junction is representedempirically by

where n is called the ideality factor In the case of the ideal p–n junction, when the diffusion current dominates, n⫽ 1 and when the recombination

current dominates, n ⫽ 2, that is, n has a value between 1 and 2.

3.2 Photovoltaic Properties [7–10]

When the p–n junction is illuminated by the sunshine, electron–holepair is generated by the photons that have energy greater than the band gap.The number of electron–hole pair is proportional to the light intensity.Because of the electric field in the depletion region due to the ionized impu-rity atoms, the drift of electrons toward n-side and that of holes toward p-sideoccur in the depletion region This charge separation results in the currentflow from n- to p-side when an external wire is short-circuited as shown inFig 14 The electron–hole pairs generated within a distance of diffusionlength from the edge of the depletion region contribute to the photo currentbecause of the diffusion of excess carriers up to the space charge region