Basic Fundamentals of Solar Cell Semiconductor Physics for High School Level Physics

Review Topics

Wavelength and Frequency Period (sec) time amplitude Frequency ( ) = 1/Period [cycles/sec or Hertz] Wavelength ( ) = length of one Period [meters] For an electromagnetic wave c =,  where c is the speed of light (2.998 x 10 8 m/sec)

Spectrum Frequency ( ) Range of frequency (or wavelength, c/ ) responses or source emissions. The human eye has a response spectrum ranging from a wavelength of 0.4 microns (0.4 x meters) (purple) to 0.8 microns (red) Intensity

Energy and Power Electromagnetic waves (light, x-rays, heat) transport energy. E = h or hc/  [Joules or eV (electron-volts)] 1 eV = 1.6 x Joules h = Plank’s constant (6.625 x Joule-sec or x eV-sec) = frequency c = speed of light  = wavelength Power is the amount of energy delivered per unit time. P = E/t [Joules/sec or Watts]

Photons A light particle having energy. Sunlight is a spectrum of photons. X-rays and heat are photons also. Photon Energy E = h or hc/  [Joules or eV (electron-volts)] (higher frequency = higher energy) (lower energy)

Irradiance Amount of power over a given area, Watts/m 2 Area = 2.00 m 2 4 red photons every second Energy of 1 red photon = hc/ = (6.63 x J-s)(2.99 x 10 8 m/s)/(0.80 x meters) = 2.48 x J = 1.55 eV Irradiance = Power/Area = (4 photons/sec)(Energy of 1 photon)/2.00 m 2 = 4.96 x W/m 2 Typical sunlight irradiance is W/cm 2 = 930 W/m 2 at =.55  m

Transmission, Reflection, and Absorption air material incident light reflectance (R) transmittance (T) + absorptance (A) Incident light = T + R + A = 100% Non-transparent materials have either very high reflection or very high absorption. Absorption decreases transmission intensity with increasing depth into material.

Polarization Unpolarized light (e.g. sunlight) Linearly polarized light Polarizer Only one plane of vibration passes

Basics of Semiconductor Physics

Semiconductor Crystal Lattice Simple Cubic Structure atom covalent bond Silicon has a more complex lattice structure but a lattice structure exists nevertheless.

Si atom (Group IV) Crystalline Silicon Bonds covalent bond (electron sharing) = valance electrons

Breaking of Covalent Bond Creating Electron-Hole Pair Si atom covalent bond + e- free electron moving through lattice created hole (missing electron) Photon (light, heat) Photon hits valance electron with enough energy to create free electron

Movement of a Hole in a Semiconductor + Thermal energy causes valance electron to jump to existing hole leaving a hole behind +

Valance and Conduction Energy Bands covalent bonds + e- free electron moving in lattice structure Conduction Energy Band Valance Energy Band Band Gap Energy, E g = E c - E v Hole within valance band EcEc EvEv

Valance and Conduction Energy Bands Thermal Equalibrium covalent bonds + e- free electron within lattice structure Heat energy absorbed Energy absorbed = Energy given up Conduction Energy Band Valance Energy Band EgEg Hole created within valance band + e- Heat enery given up EcEc EvEv free electron combines with hole

Intrinsic (pure) Silicon Electron-Hole Pairs Thermal Equalibrium covalent bonds + e- n i = 1.5 x cm -3 at 300° K Number of electron-hole pairs increase with increasing temperature The thermal voltage, V t is equal to kT/e (k = 8.62 x eV/K, T = [Kelvin]) Conduction Band Valance Band E g = 1.12 eV p i = 1.5 x cm -3 at 300° K hole density = electron density number of holes per cubic centimeter = number of free electrons per cubic centimeter p i = n i = 1.5 x cm -3 EcEc EvEv

Creating a Semiconductor

Doping or Substitutional Impurities Group V Atom (Donor or N-type Doping) Si atom (Group IV) covalent bond e- The donor electron is not part of a covalent bond so less energy is required to create a free electron Phospherous (Group V) P atom

Energy Band Diagram of Phospherous Doping covalent bonds + e- N-type Semiconductor Conduction Band Valance Band EgEg n > p (more electrons in conduction band) A small amount of thermal energy (300° K) elevates the donor electron to the conduction band Donor Electron Energy e- intrinsic hole intrinsic free electrondonor free electron EcEc EvEv

Doping or Substitutional Impurities Group III Atom (Acceptor or P-type Doping) Si atom covalent bond Boron (Group III) B atom + - covalent bond created hole Boron atom attacts a momentarily free valance electron creating a hole in the Valance Band

Energy Band Diagram of Boron Doping covalent bonds + e- P-type Semicondutor Conduction Band Valance Band EgEg p > n (more holes in valance band) A small amount of thermal energy (300° K) elevates the acceptor electron to the Acceptor band Acceptor Electron Energy e- intrinsic hole intrinsic free electron acceptor electron + created hole EcEc EvEv

Charge Transport Mechanisms within a Semiconductor Drift Current Density Diffusion Current Density

y x + Current The number of holes or electrons passing through a cross sectional area, A, in one second Applied Electric Field e- I = q/t [I] = [coulombs/sec] = [amps] e- and Direction of Current holes move in Current direction electrons move in opposite direction

y x + Current Density The number of holes or electrons passing through a cross sectional area, A, in one second divided by A A (area) = xy cm Applied Electric Field e- I (amps) = coulombs/sec J (current density) = I/A [J] =[amps/cm 2 ] e- and Direction of Current

Drift Velocity The average velocity of a hole (v p ) or electon (v e ) moving through a conducting material Applied Electric Field Scattering Sites are caused by impurities and thermal lattice vibrations Electrons typically move faster than holes (v e >v p ) + e- Scattering Sites v p = d p /t 1 v e = d n /t 1 dpdp dndn

Drift Velocity and Applied Electric Field Newton’s Second Law of Motion F = ma Analogy with Electic Fields m q (mass charge) a E (accelerating field applied electric field) F = qE Without scattering sites, the charged particle would undergo a constant acceleration. Scattering sites create an average drift velocity. Similar to the terminal velocity of a falling object caused by air friction.

Drift Velocity and Applied Electric Field (cont’d) F = qE The force, F, on a charged partical is proportional to the electric field, E Scattering sites create an average drift velocity, v p or v e The average drift velocity is proportional to the applied electric field v p = μ p E v e = -μ n E (negative sign due to electrons moving in opposite direction of applied electric field) where μ p and μ n are constants of proportionality

Hole and Electron Mobility μ p is the hole mobility in the conducting material μ n is the electron mobility in the conducting material The units of mobility, μ, are v = μE [cm/sec] = [μ] [volts/cm] [μ] = [cm 2 /volt-sec] Typical mobility values in Silicon at 300° K: μ p = 480 cm 2 /volt-sec μ n = 1350 cm 2 /volt-sec

Mobility and Current Density Relation Current I = q/t q = number of charged particles passing through a cross sectional area t = time Current Density J = I/A = (q/t)/A A = cross sectional area p = number of holes per cubic centimeter (hole density [1/cm 3 ]) n = number of electrons per cubic centimeter (electron density [1/cm 3 ]) Each hole has an average velocity of v p Each electron has an average velocity of v e

++ Mobility and Current Density for Holes Each hole has traveled a distance z in a time t = z/v p The number of holes in the volume is pV (hole density x volume) The charge of each hole is e (1.6 x coulombs) I = q/t = e(pV)/(z/v p ) = ep(xyz)/(z/v p ) = ep(xy)v p = epA μ p E J p|drf = I p /A = epμ p E E x y z x y z vpvp vpvp

veve veve e- Mobility and Current Density for Electrons Replacing p with n and v p with v e gives: The charge of each electron is -e (-1.6 x coulombs) I = q/t = -epV/(z/v e ) = -ep(xyz)/(z/v e ) = -ep(xy)v e = -epA(-μ n E) I = epA(μ n E) J n |drf = I n /A = enμ n E E x y z x y z e-

Drift Current Density Expressions J p|drf = I p /A = enμ p E J n|drf = I n /A = enμ n E J p|drf and J n|drf are in same direction Total Drift Current = J p|drf + J n|drf

Diffusion Process gas filled chamberempty chamber sealed membraneAfter seal is broken Gas molecules move from high concentration region to low concentration region after membrane is broken If gas molecules are replaced by charge then a current exists during charge transport creating a Diffusion Current gas

Electron Diffusion Current distance Electron concentration, n electron flow Electron diffusion current density x slope =  n/  x electron flow is from high to low concentration (-x direction) electron diffusion current density is in positive x direction J n|dif = eD n  n/  x where D n is the electron diffusion constant

Hole Diffusion Current distance Hole concentration, p hole flow Hole diffusion current density x slope =  p/  x hole flow is from high to low concentration (-x direction) hole diffusion current density is in negative x direction J p|dif = -eD n  p/  x where D p is the hole diffusion constant

Diffusion Currents J n|dif = eD n  n/  x J p|dif = -eD n  p/  x Electron and hole diffusion currents are in opposite directions for the same direction of increasing concentration Total Diffusion Current = J n|dif - J p|dif

Formation and Basic Physics of PN Junctions

PN Junction Formation Phophorous Atom Doping Doping Atoms are accelerated towards Silicon Wafer Doping Atoms are implanted into Silicon Wafer Wafer is heated to provide necessary energy for Doping Atoms to become part of Silicon lattice structure Intrinsic Silicon Wafer Masking Barrier Boron Atom Doping

PN Junction in Thermal Equilibrium (No Applied Electric Field) metallurgical junction Free electrons from n-region diffuse to p-region leaving donor atoms behind. Holes from p-region diffuse to n-region leaving acceptor atoms behind. Internal Electric Field is created within Space Charge Region. P-type N-Type metallurgical junction E field Space Charge Region pn Initial Condition Equilibrium Condition

PN Junction in Thermal Equilibrium (No Applied Electric Field) Diffusion Forces = E Field Forces metallurgical junction E field Space Charge Region pn Diffusion force on holes Diffusion force on electrons E field force on electrons E field force on holes

Definition of Electric Potential Difference (Volts) Work (energy) per test charge required to move a positive test charge, +q, a distance x=d against an electric field, E field x=ax=b Positive test charge, +q 0  V = (V b - V a ) = W ab /q 0 = E(b - a) = Ed [volts or Joules/coulomb] d

PN Junction in Thermal Equilibrium Electric Field metallurgical junction Internal E field direction Space Charge Region pn E - x p + x n x = 0 E = 0

metallurgical junction Internal E field direction Space Charge Region pn Positive test charge, +q 0 E = 0 V - x p + x n x = 0  V = V bi PN Junction in Thermal Equilibrium Built-in Potential, V bi

Conduction and Valance Band Diagram for PN Junction in Thermal Equilibrium Built-in Potential, V bi - x p + x n x = 0 eV bi EcEc EvEv p region n region space charge region EcEc EvEv

Conduction Band Diagram for PN Junction in Thermal Equilibrium - x p + x n x = 0 eV bi EcEc p regionn regionspace charge region EcEc Work or Energy is required to move electrons from n region to p region (going uphill) Electron Energy

Applying a Voltage Across a PN Junction Non-Equilibrium Condition (external voltage applied) Reverse Bias Shown E applied is created by bias voltage source V applied. E field exists in p-region and n-region. Space Charge Region width changes. V total = V bi + V applied metallurgical junction E field Increased Space Charge Region p n E applied V applied Forward Bias Reverse Bias

Reverse Bias PN Junction Non-Equilibrium Condition (external voltage applied) E R is created by reverse bias voltage source V R. E R is in same direction as internal E field. Space Charge Region width increases. V total = V bi + V R I reverse is created from diffusion currents in the space charge region metallurgical junction E field Increased Space Charge Region p n E R VRVR I reverse

Conduction and Valance Band Diagram for PN Junction Reverse Bias Voltage Applied V total = V bi + V R - x p + x n x = 0 eV bi + eV R EcEc EvEv p regionn region space charge region EcEc EvEv

Forward Bias PN Junction (Diode) Non-Equilibrium Condition E applied is created by voltage source V a. E applied must be greater than internal E field for I Forwad to exist. When E applied = E field, V a is called the “turn on” voltage. metallurgical junction E field Space Charge Region p n E applied VaVa I Forward + -

Forward Bias PN Junction (Applied Electric Field > Internal Electric Field) Diffusion Forces > E Field Forces metallurgical junction E field Space Charge Region pn Diffusion force on holes Diffusion force on electrons Net E field force on electrons Net E field force on holes Applied E field

Forward Bias PN Junction Diffusion Forces > E Field Forces Creates Hole and Electron Injection in Space Charge Region E field p Diffusion force on holes Diffusion force on electrons Net E field force on electrons Net E field force on holes Applied E field n Hole Injection across Space charge region from Diffusion force Electron Injection across Space charge region from Diffusion force

Forward Bias PN Junction Diffusion Forces > E Field Forces Creates Hole and Electron Injection in Space Charge Region pn Hole Injection across Space charge region from Diffusion force J p|inj Electron Injection across Space charge region from Diffusion force J n|inj Current density Total Current density J total J total = J p|inj + J n|inj

Forward Bias PN Junction Electron and Hole Current Components pn hole diffusion current J p|dif electron diffusion current J n|dif Current density Total Current density J total hole drift current J p|drf electron drift current J n|drf hole injection current J p|inj electron injection current J n|inj

Forward Bias PN Junction Electron and Hole Current Components pn J p|dif J n|dif Current density J total p-region: J total = J p|drf + J n|dif n-region: J total = J n|drf + J p|dif space charge region: J total = J n|inj + J p|inj J p|drf J n|drf J p|inj J n|inj

Ideal PN Junction Current-Voltage Relationship JSJS J total J S = Reverse Bias Current Density V a = Applied Voltage J total = J S [exp(eV a /(kT) - 1] VaVa turn on voltage

Key Concepts of PN Junction Thermal Equalibrium (no voltage source applied) Internal E field created by diffusion currents Built in potential, V bi, exists Space charge region created E field is zero outside of space charge region No current flow Forward Bias Applied Hole and electron injection in space charge region Total current density is constant through out semiconductor Diffusion, injection, and drift currents exist E field is not zero outside of space charge region Reverse Bias Applied A constant reverse bias current exists for large applied voltages due to diffusion currents

PN Junction Hole and Electron Injection Reversible Process Forward biased voltage applied to a PN junction creates hole and electron injection carriers within the space charge region. External photon energy absorbed in space charge region creates hole and electron injection carriers that are swept out by the internal E field creating a voltage potential.

PN Junction Solar Cell Operation Step 1 Photon h > E g Space Charge Region E field pn e- Photons create hole-electron pairs in space charge region Created hole-electron pairs swepted out by internal E field

PN Junction Solar Cell Operation Step 2 Created hole-electron pairs are swept out by the E field. creates excess holes in p-region creates excess electrons in n-region E injected is created by excess holes and electrons Photocurrent, I L, is in reverse bias direction Photon h > E g Space Charge Region E field pn ILIL E injected e-

PN Junction Solar Cell Operation Step 3 Attaching a resistive load with wires to the PN Junction allows current flow to/from p-n regions Photocurrent, I L, is in reverse bias direction I forwad is created by E injected I cell = I L - I forward Photon h > E g Space Charge Region E field pn Resistor V cell ILIL I cell I Forwad + - E injected e-

PN Junction Solar Cell Operation Step 3 I cell = I L - I forward I cell = I L - I S [exp(eV cell /(kT) -1] I cell is always in reverse bias direction Photon h > E g Space Charge Region E field pn Resistor V cell ILIL I cell I Forwad + - E injected e- heat

Typical Silicon Solar Cell Design N-type Silicon Wafer P-type Doping Protective High Transmission Layer To load Wires 4-6 inches 0.6 mm Photons Photons transmit through thin protective layer and thin P-type doped layer and create hole-electron pairs in space charge region Typical Silicon Single Cell Voltage Output = ~ 0.5 volts

Silicon Solar Cell 6 Volt Panel Series-Parallel Design 12 cells in series = 6 volts 6 volts p to n connection - +

External Factors Influencing Solar Cell Effeciency Photon transmission, reflection, and absorption of protective layer Maximum transmission desired Minimum reflection and absorption desired Polarization of protective layer Minimum polarized transmission desired Photon Intensity Increased intensity (more photons) increases cell current, I cell Cell voltage, V cell, increases only slightly Larger cell area produces larger current (more incident photons) Theoretical Silicon Solar Cell Maximum Efficiency = 28% Typical Silicon Solar Cell Efficiency = 10-15%