Electrochemistry MAE-212 Dr. Marc Madou, UCI, Winter 2016 Class IX Liquid-Junction Solar Cells

Table of Content Overview Interface Solids/Solutions Semiconductors Fermi-Dirac Electron Distribution: Fermi Level Concept Semiconductor/Liquid Contact: Liquid-Junction Solar Cells Gratzel’s Biomimetic Solution 11/22/2018

Electrodes (materials) in Solution Charge carriers in electrode materials: Metals (e.g. Pt) : electrons Semiconductors (e.g. n-Si) : electrons and holes Solid electrolytes (e.g. LaF3 ) : ions Insulators (e.g. SiO2):no charge carriers Double layer-(in case of a metal 10-40 µF cm-2) Inner Helmholtz plane (IHP) Outer Helmholtz plane (OHP) Gouy-Chapman layer (GCL)

Metals in Solution In order for current to pass the interface Me/solution an electochemical reaction must occur: an Oxidant O (say Fe 3+) gets reduced in a cathodic reaction (on the cathode, also the working electrode in this case (WE)) to become a reductant R (say Fe 2+) For a complete circuit a counter electrode must also be present in the cell for the reverse or anodic reaction on the anode (Counter electrode (CE)) Without applied bias the potential drop across the Helmholtz layer on the WE (e.g. a Pt electrode) is determined by the redox species with the largest exchange current density i0,e 107-10 8 V cm-1 Metal (working electrode, sensing electrode, detector electrode) Electrolyte Anode also CE (in this case) Cathode also WE (in this case)

Metals in Solution The fastest electron-exchange reaction (the rate of electrons going back and forth between redox species and electrode in equilibrium i.e. at zero current) determines the potential of the electrode ---zero external current and no net reaction Often there are different redox species involved in establishing the equilibrium potential in which case we speak about a mixed potential---zero external current but with a net reaction (e.g. corrosion) A working electrode (e.g. Pt) that changes potential with the redox couple present is called an electrode of the first kind An electrode that does not change it’s potential with solution composition is an electrode of the second kind i.e. a reference electrode

Semiconductors in Solution In this case most of the potential drop is in the semiconductor instead of in the solution Transport of charges to and from solution is limited to those redox systems that have states that overlap with the semiconductor bands Electrolyte Semiconductor e.g. TiO2

Semiconductors in Solution When the semiconductor is in contact with the solution a band bending results just as in the case of a conductive solution contacting a metal The flat-band potential (V FB) is that potential one needs to apply to make the bands flat in the semiconductor all the way to the surface (it can be deduced from a capacitance measurement of the interface) For a semiconductor covered with an oxide (e.g. Si with SiO2 , TiO2) the flat band potential is a function of pH (ionization of the surface OH groups changes with pH) and is often independent of redox systems (depending on their overlap with the semiconductor bands) Solution V FB

Solid electrolytes in Solution No electrons exchange at the surface just ions exchange with the solid often with very high selectively The fastest ion-exchange reaction determines the potential i.e. i0,i in the case of LaF3 that is F- (also glass for H+) This is a third type of sensor we encounter here i.e. an ion selective sensor Solution F- Solid electrolyte e.g. LaF3 Electrolyte

Insulators in Solution Electrolyte No electron exchange and no ion exchange If it is an oxide insulator it will exhibit pH sensitivity like an oxide semiconductor But how do you measure such a high impedance, the voltmeter will just show an overload ? Use an ISFET !!

Semiconductors: Quantization concept In 1901, Max Planck showed that the energy distribution of black body radiation can only be explained by assuming that this radiation (i.e. electromagnetic waves) is emitted and absorbed as discrete energy quanta - photons. The energy of each photon is related to the wavelength of the radiation: E = h  = h c /  where h = Planck’s constant (h = 6.63  1034 Js)  = frequency (Hz = s1) c = speed of light (3  108 m/s)  = wavelength (m)

Semiconductors: Example Our eye is very sensitive to green light. The corresponding wavelength is 0.555 m or 5550 Å or 555 nm. What is the energy of each photon? E = h = = 3.57  10–19 J ≡ of GaP These energies are very small and hence are usually measured using a new energy unit called electron Volts 1 eV = 1.6  1019 CV = 1.6  1019 J

Semiconductors: A new unit of energy Since the energies related to atoms and photons are very small, (EGREEN LIGHT = 3.57  1019 J), we have defined a new unit of energy called “electron Volt” or “eV” One eV is the energy acquired by an electron when accelerated by a 1.0 V potential difference.  + 1V 1 eV = 1.6 10–19 J Energy acquired by the electron is qV. Since q is 1.6  1019 C, the energy is 1.6  1019 J. Define this as 1 eV. Therefore, EGREEN LIGHT = 2.23eV 1 eV = 1 1.610–19 CV = 1.610–19 J

Semiconductors: Atomic configuration of Si An important idea we got from the Bohr model is that the energy of electrons in atomic systems is restricted to a limited set of values. The energy level scheme in multi-electron atom like Si is more complex, but intuitively similar. Ten of the 14 Si-atom electrons occupy very deep lying energy levels and are tightly bound to the nucleus The remaining 4 electrons, called valence electrons are not very strongly bound and occupy 4 of the 8 allowed slots. Configuration for Ge is identical to that of Si, except that the core has 28 electrons.

Semiconductor: Bond model Consider a semiconductor Ge, Si, or C Ge, Si, and C have four nearest neighbors, each has 4 electrons in outer shell Each atom shares its electrons with its nearest neighbor. This is called a covalent bonding No electrons are available for conduction in this covalent structure, so the material is and should be an insulator at 0 K

Semiconductors: (2D) semiconductor bonding model No electrons are available for conduction. Therefore, Si is an insulator at T = 0 K.

Semiconductors: Silicon Covalent Bond (2D) Each Si atom has 4 nearest neighbors Si atom: 4 valence elec and 4+ ion core 8 bond sites / atom All bond sites filled Bonding electrons shared 50/50 _ = Bonding electron

Semiconductors: Si Bond Model Above Zero Kelvin Enough thermal energy ~kT(k=8.62E-5 eV/K) to break some bonds Free electron and broken bond separate One electron for every “hole” (absent electron of broken bond)

Semiconductors: (a) Point defect (b) Electron generation At higher temperatures (e.g. 300 K), some bonds get broken, releasing electrons for conduction. A broken bond is a deficient electron of a hole. At the same time, the broken bond can move about the crystal by accepting electrons from other bonds thereby creating a hole.

Semiconductors: Energy band model An isolated atom has its own electronic structure with n = 1, 2, 3 ... shells. When atoms come together, their shells overlap. Consider Silicon: Si has 4 electrons in its outermost shell, but there are 8 possible states. When atoms come together to form a crystal, these shells overlap and form bands. We do not consider the inner shell electrons since they are too tightly coupled to the inner core atom, and do not participate in anything.

Semiconductors: Development of the energy-band model

Metal, Semiconductor, Insulator Figure 2.19. Schematic energy band representations of (a) a conductor with two possibilities (either the partially filled conduction band shown at the upper portion or the overlapping bands shown at the lower portion), (b) a semiconductor, and (c) an insulator.

Semiconductors: Energy band model At T = 0K No conduction can take place since there are no carriers in the conduction band. Valence band does not contribute to currents since it is full. Both bond model and band model shows us that semiconductors behave like insulators at 0K.

Semiconductors: Visualization of carriers using energy bands

Si Energy Band Structure at 0 K Every valence site is occupied by an electron No electrons allowed in band gap No electrons with enough energy to populate the conduction band

Insulators, semiconductors, and metals

Band Model for thermal carriers Thermal energy ~kT generates electron-hole pairs At 300K Eg(Si) = 1.124 eV >> kT = 25.86 meV,

Donor: cond. electr. due to phosphorous P atom: 5 valence elec and 5+ ion core 5th valence electr has no avail bond Each extra free el, -q, has one +q ion # P atoms = # free elect, so neutral

Band Model for donor electrons Ionization energy of donor Ei = Ec-Ed ~ 40 meV Since Ec-Ed ~ kT, all donors are ionized, so ND ~ n Electron “freeze-out” when kT is too small

Acceptor: Hole due to boron B atom: 3 valence elec and 3+ ion core 4th bond site has no avail el (=> hole) Each hole, adds --q, has one -q ion #B atoms = #holes, so neutral

Hole orbits and acceptor states Similar to free electrons and donor sites, there are hole orbits at acceptor sites The ionization energy of these states is EA - EV ~ 40 meV, so NA ~ p and there is a hole “freeze-out” at low temperatures

Impurity Levels in Si: EG = 1,124 meV Phosphorous, P: EC - ED = 44 meV Arsenic, As: EC - ED = 49 meV Boron, B: EA - EV = 45 meV Aluminum, Al: EA - EV = 57 meV Gallium, Ga: EA - EV = 65meV

Fermi-Dirac distribution function The probability of an electron having an energy, E, is given by the F-D distr fF(E) = {1+exp[(E-EF)/kT]}-1 Note: fF (EF) = 1/2 EF is the equilibrium energy of the system (it is directly connected to the electrochemical potential!!) The sum of the hole probability and the electron probability is 1

Fermi-Dirac probability function At T=0 all states below EF are occupied, above EF are free When T increases some electrons get enough energy to get above EF Fermi function – smoothened step

Fermi-Dirac DF (continued) So the probability of a hole having energy E is 1 - fF(E) At T = 0 K, fF (E) becomes a step function and 0 probability of E > EF At T >> 0 K, there is a finite probability of E >> EF

Maxwell-Boltzman Approximation fF(E) = {1+exp[(E-EF)/kT]}-1 For E - EF > 3 kT, the exp > 20, so within a 5% error, fF(E) ~ exp[-(E-EF)/kT] This is the MB distribution function MB used when E-EF>75 meV (T=300K) For electrons when Ec - EF > 75 meV and for holes when EF - Ev > 75 meV

Density of occupied states g(E) – density of available states f(E)- probability to find electron with a certain value of E Number of occupied states per unit volume

Electron Density of States: Free Electrons g(E) – density of available states

Electron Conc. in the MB approx. Assuming the MB approx., the equilibrium electron concentration is

Electron and Hole Conc in MB approx Similarly, the equilibrium hole concentration is po = Nv exp[-(EF-Ev)/kT] So that nopo = NcNv exp[-Eg/kT] Nc = 2.8E19/cm3, Nv = 1.04E19/cm3

Position of the Fermi Level Efi is the Fermi level when no = po Ef shown is a Fermi level for no > po Ef < Efi when no < po Efi < (Ec + Ev)/2, which is the mid-band

metals do not absorb solar radiation. Semiconductors in Solar Cells metals do not absorb solar radiation. insulators also cannot absorb as the band gap is so high (> 5 eV), the energy of the solar radiation is not sufficient to excite electron from valence band (VB) to the conduction band (CB). Semiconductors have the band gap not as large,  promotion of electron is possible with the solar radiation.

- Charge carriers in Semiconductor can be altered by doping. Schematic diagram of the energy levels of an a) intrinsic semiconductor, b) an n-type semiconductor and c) a p-type semiconductor (a) - Charge carriers in Semiconductor can be altered by doping. Addition of Group V element (P. As) into Group IV element (Si, Ge) introduces occupied energy levels into the band gap close to the lower edge of CB, thereby allowing facile promotion of electrons into the CB (n-type Si, or n-type Ge; majority charge carriers - e). (b) - Addition of Group III elements (Al. Ga) into Group IV elements introduces vacant energy levels into the band gap close to the upper edge of the VB, which allows the facile promotion of e from the VB (p-type Si, or p-type Ge; majarity charge carrier - holes). (c)

Fermi level is defined as the energy level at which the probability of occupation by an electron is ½; for an instrinsic semiconductor the Fermi level lies at the mid-point of the band gap. Doping changes the distribution of electrons within the solid, and hence changes the Fermi level. For a n-type semiconductor, the Fermi level lies just below the conduction band, whereas for a p-type semiconductor it lies just above the valence band. In addition to doping, as with metal electrodes, the Fermi level of a semiconductor electrode varies with the applied potential; for example, moving to more negative potentials will raise the Fermi level.

Idealized interface between a semiconductor electrode / electrolyte solution. If the redox potential of the solution and the Fermi level do not lie at the same energy, movement of charge between the semiconductor and the solution takes place in order to equilibrate the two phases. Excess charge located on the semiconductor does not lie at the surface as it would for a metallic electrode, but extends into the electrode for a significant distance (100-10,000 Å) - space charge region. Hence, there are two double layers to consider: the interfacial (electrode/electrolyte) double layer, and the space charge double layer.

For this n-type semiconductor electrode at open circuit, the Fermi level is higher than the redox potential of the electrolyte, hence electrons will be transferred from the electrode into the solution  positive charge associated with the space charge region, and is reflected in an upward bending of the band edges  as majority charge carrier is removed from this region, this region is referred to as a depletion layer. For this p-type semiconductor, the Fermi layer is lower than the redox potential, hence electrons must transfer from the solution to the electrode  generates negative charge in the space charge region, causes a downward bending in the band edges. Since the holes in the space charge region are removed by this process, this region is again a depletion layer. Band bending for an n-type emiconductor (a) and a p-type semiconductor b) in equilibrium with an electrolyte

Mechanism of production of photocurrent by an p-type photocathode

Mechanism of production of photocurrent by an n-type photoanode

Intensity of Solar Energy Absorbtion by Semiconductors of different band gaps energies - low band gap materials absorb more of solar radiation, but are easily photodegradable.

Nature does it another way Jean Manca

Grätzel’s Biomimetic Cell Separate charge generation and charge separation                                                                                                                    Jean Manca

Grätzel’s Biomimetic Solar Cell ITO <10W/sq Nanocrystalline TiO2 Film : 10-20 mm Deeltjes : 10-30 nm Jean Manca

Grätzel’s Biomimetic Solar Cell Jean Manca