CONDUCTION BAND I BANDGAP VALENCE BAND. Figure 2.1: Representation of semiconductor band theory. Black dots represents electrons

Transcription

1 2.ELECTROCHEMISTRY

2 CHAPTER-2 ELECTROCHEMISTRY 2.1: Semiconductor and Metal Theory A photoelectrochemical cell is composed primarily of a material called a semiconductor which is heart of the PEe cell. It is the semiconductor that absorbs light and turns the energy in the light into electrical energy. Figure 2.1 presents semiconductor band theory. CONDUCTION BAND E I BANDGAP VALENCE BAND Figure 2.1: Representation of semiconductor band theory. Black dots represents electrons The range of energies in the valence and conduction bands represents the allowed energies of electrons within a semiconductor. An electron will either be in the valence or conduction band, but not in the band gap. The valence band is the range of energies that the most energetic electrons in a solid typically have in their ground state. The valence band is entirely filled with electrons in a semiconductor. Because the valence band is filled, electrons are unable to move within the valence band. However, if electrons receive an input of energy larger than the band gap of the semiconductor (the energy difference between the valence band and conduction band), then electrons 26

3 can be excited into the conduction band. When this occurs, electrons can be conducted through a solid material, since there are few impediments to movement at the conduction band energy level. In a photoelectrochemical cell, electrons are excited from the valence band to the conduction band by shining light with frequencies more energetic than the band gap of the semiconductor. Semiconductors with a band gap smaller than 1.77 ev will be able to absorb the entire UV and visible spectra, since 1.77 ev correlates with a light wavelength of 700 nm. E CONDUCTION BAND I. I BANDGAP HOLES VALENCE BAND 1 ::, ::RGY LEVEL 0 Figure 2.2: Band diagram (left) and band edge diagram (right) with Fermi Energy Level. The white circle is a hole, which designates that the space was once occupied by an electron (A band edge representation of Figure 2.1) The band edge diagram in Figure 2.2 shows the highest energy level of the valence band (the valence band edge) and the lowest energy level of the conduction band (the conduction band edge). These energy levels are important because all electrons are either lower in energy than the valence band edge or higher in energy than the conduction band edge and they represent the minimum energy needed to excite an electron between bands. Also shown in Figure 2.2 is the Fermi energy level (also abbreviated cf)' The Fermi energy level is the energy level where the probability of finding an electron is one- half, and is calculated using the following formula: 27

4 /. \ _ 1 (', 11 _ l llr I C re -- C c +cl' )+ - ktln-. 2 ' ; 1 V - \.i. C / (2.1 ) where Ec and Ev are the energy levels of the conduction and valence band edges, k is the Boltzmann constant, T is the temperature, and Nv and Nc are the effective state density at the valence and conduction band edges. In Figure 2.3, the majority of the electrons are in the valence band (making Nv large), while a minority are in the conduction band (making Nc small). In this case, In(Nv/Nc) is positive, shifting the Fermi level in a positive direction. This places the Fermi energy level closer to the valence band since, as Figure 2.2 shows, the positive direction is defined as downwards (representing a lower energy) and the negative direction is upwards (representing a higher energy). Although no electrons actually exist at the Fermi energy level, the Fermi energy level is important because it is the energy level that a reference electrode "sees" when it makes measurements on a system. When a reference electrode is used to make a measurement, it compares the Fermi level of the semiconductor with its own unchanging Fermi level. In a metal, the conduction band is energetically adjacent to the valence band. Thus, electrons can be easily excited from the valence band into the conduction band by thermal energy. Because of the minimal energy difference between the valence and conduction bands, conduction occurs easily in a metal. As with semiconductors, the Fermi level in a metal is the energy level where the probability of finding an electron is one-half. In the ground state, all the electrons are in the valence band and there are no electrons in the conduction band, so the probability of finding an electron abruptly goes from 100% at the top of the valence band to 0% at the bottom of the conduction band. The Fermi energy level, then, is the energy where the valence band ends and the conduction band begins. 28

5 2.2: Conditions Needed for Splitting of Water 53,138 In order to split water, the semiconductor must meet three simultaneous conditions. The first is that the semiconductor must be stable in aqueous solution during hydrogen evolution. The second is that the conduction and valence band edges of the semiconductor overlap the water redox potentials. The third is that charge transfer from the semiconductor to the water occurs quickly. The first condition must be met because the semiconductor's performance will degrade over time if it is not stable. The second condition, that the band edges of the semiconductor must overlap the water redox potentials, is illustrated in the Figure 2.3 Figure: 2.3: EF (SeE) = Fermi level of reference electrode (a saturated calomel electrode); EeB = semiconductor conduction band edge; EVB = semiconductor valence band edge; EF= semiconductor and metal counter electrode; H 2 0/H 2 = water reduction potential; H 2 0/0 2 = water oxidation potential. The x-axis on the diagram represents the increasing depth into the semiconductor/metal. Light irradiates the front surface of the semiconductor, where electrons enter into the water and hydrogen is produced. Electrons leave the water and enter into the metal counter electrode, producing oxygen gas. The water redox potentials are based on a ph 4 solution with a 20 ma/cm 2 photocurrent 137. The semiconductor must be in "overlap conditions" so that excited electrons in the conduction band can move into the water to produce hydrogen gas. The conduction band must be higher in energy than the energy level at which hydrogen production occurs because electrons will only move from a higher 29

6 energy to lower energy. This previous statement is equivalent to saying that electrons will only move from the conduction band to the water to produce hydrogen gas if the reduction potential is at a more positive potential than the conduction band potential. If the conduction band were lower in energy (or at a more positive potential) than the hydrogen production energy (or water reduction potential), then electrons would not move into the water to produce hydrogen gas, since that would require an input of energy. Similarly, electrons in the water will move into the Fermi level of the metal counter electrode only if that movement decreases the electron's energy. If the Fermi level of the metal electrode is higher in energy than the energy level at which oxygen is produced, then electrons will not enter into the metal electrode, because the electron movement requires an input of energy. Thus, overlap conditions (the conduction band and Fermi level must overlap the water redox potentials) must be met in order to split water. A corollary to the second condition for water splitting is that the band gap of the semiconductor must be larger than the water redox potential. The water redox potential in Figure 2.3 is ev (0.849 ev ev). In a semiconductor where the Fermi level is ev above the valence band edge, the band gap of the semiconductor must be least ev (and 2.2 ev at the maximum) in order to give electrons enough energy to split water. The third condition is that charge transfer from the semiconductor to the water must occur quickly because electrons will build up on the semiconductor surface otherwise. If the electrons do not move into the water, the water can't be split and hydrogen cannot be produced. Additionally, when electrons bu ild up in the conduction band of the semiconductor, the effective state density of the conduction band,ne, increases. Equation 1 predicts that the Fermi level will shift in a negative direction when this occurs. If the Fermi level shifts far enough in a negative direction, the Fermi level will no longer overlap the water oxidation potential, 30

7 causing the second condition not to be met. 2.3: Electrochemical Measurements 138 The Mott-Schottky analysis determines the position of the band edges relative to the Fermi level of the reference electrode. In the Mott-Schottky analysis, an increasing potential is applied across the semiconductor, as illustrated in Figure 2.4. The depletion region is the area near the semiconductor surface where electrons are excited into the conduction band, and subsequently enter the water. Electrons are depleted from this region; hence its name. Figure 2. 4: Mott-Schottky analysis. ECB = semiconductor conduction band edge; EVB =semiconductor valence band edge; EF = semiconductor Fermi energy level; EF (SeE) =reference electrode Fermi level; Wd = width of depletion region. As the applied potential increases, the width of the depletion region (W d ) decreases. When the depletion region decreases in width, the valence band, conduction band, and Fermi level all begin to flatten, loosing their downward bending, or band bending, near the semiconductor surface. The position of the band edges at the surface remains constant as the bands flatten; it is the band edges within the bulk of the semiconductor that change. Eventually, when a large enough potential is applied, the depletion region width decreases to zero and the "flat band condition" is achieved - the condition in which the bands are entirely flat throughout the semiconductor. The reason for decreasing the width of the depletion region is a relationship between its 31

8 width and capacitance. The capacitance of the depletion region is proportional to W d - 1, so as the width of the depletion region approaches zero, the capacitance approaches infinity. The Mott-Schottky relationship predicts a linear relationship between E, the applied potential, and 1/C 2, the inverse square of the capacitance: (2.2) In the Mott-Schottky equation, E is the static dielectric of the semiconductor, EO is the permittivity of free space, the first e is the electronic charge, ND is the doping density, V FB is the flat band potential, k is the Boltzmann constant, T is the temperature, and the second e is The operating assumption in the Mott-Schottky equation is that the semiconductor can be modeled as a series resistor and capacitor, as shown in Figure 2.5. Semiconductor Water ECB I-... EF... J,.. Eve I... Rs esc --'VW-H Figure 2.5: Modeling a semiconductor as a series resistor and capacitor. Rs = System resistance. e sc = Semiconductor capacitance in the depletion region. If the system of interest fits this model, then a graph of the applied potential versus 1/C 2 gives a value for the applied potential where the width of the depletion region is zero, or, equivalently, the applied potential when the flat band condition occurs. The x-intercept of the measurement, then, is called the flat band potential. 32

9 The flat band potential of a semiconductor is illustrated in Figure 2.6. Figure 2.6: Measurement of the flat band potential. The flat band potential is the potential difference between the Fermi level of the semiconductor and the Fermi level of the reference saturated calomel electrode (SCE). 2.4: Potential Distribution Across The p-type Semiconductor - Electrolyte Interface 53 Consider initially a p-type semiconductor in equilibrium with a redox couple. Equilibrium is reached when the Fermi level of the semiconductor is equal to the Fermi energy associated with the redox couple (see Figure 2.7). Ec EF ~ ~ Ev q 6 vscj~ Semiconductor Solution Figure 2.7: Energy diagram of the semiconductor-electrolyte interface under equilibrium. The Fermi level energy (E F ) is equal to the redox potential energy (EOredox ), 33

10 The depletion layer, more commonly known as space charge region, produces a bending of the bands to lower energies. Under potentiostatic control the applied potential is established between the working electrode and the reference electrode. If the interface is considered as ideally polarizable (electrons cannot be exchanged with the electrolyte), the zero of potential is that at which the potential in the bulk semiconductor matches that of redox couple at the reference electrode. I XOI I I I I ~ q /1Vsc Solution T Spac e charge re gion Figure 2.8: Energy diagram of an ideally polarizable interface at zero potential. The Fermi level energy (E F ) is equal to the reference electrode energy (EOreference ). From Figure 2.8 it is apparent that the concentration of the electrons in the space charge region depends on the potential difference between the working electrode (semiconductor) and the reference. At this point it is necessary to consider the other side of the working electrode/electrolyte junction, the Helmholtz double layer. Briefly, when the supporting electrolyte is in high concentration, this region contains the nonadsorbed ions that represent the counter charge. The thickness of this layer is smaller than the space charge region (see Figure 2.9). In Figure 2.9.(a) the potential distribution across the interface is shown taking the potential of the bulk of the solution as zero. The potential drop across the space charge region (t).vsc) occurs over a larger distance than the potential drop across the Helmholtz layer ( ~VH)' this is because ~V sc results from ionisation of the acceptors in the solid, whilst ~VH is due to the ions accumulated a few angstroms away from the surface (see Figure 2.9b). 34

11 X /1Vsc V /1VH Sp ace charge region ~ +++ Helmholtz layer (a) (b) Figure 2.9: Schematic representation of the potential drop (a) and charge across the semiconductor electrolyte interface under depletion conditions. Since the charge in both regions is equal but with opposite sign, the capacitance of the space charge region is normally negligible in comparison to the Helmholtz capacitance. Under these conditions, tn H is constant and any possible change in the applied potential between working and reference electrode will appear in tn sc. Thus the potential in the bulk of the working electrodes (E) is given by: (2.3) where V fb is the flat band potential. At this potential, the surface concentration of holes is equal to the bulk. At more positive potentials than the V fb, the surface concentration of electrons is decreased creating an accumulation layer of majority carriers and the bending of the bands at the surface to higher energies. At potentials more negative than the V fb, electrons produce a depletion layer, bending downwards at the surface to lower energies (see Figure 2.10). 35

12 Ee -_/ -_/ Depletion (E < V 11» Flat band (E = V 11» A c cumulation (E > V 11» Figure 2.10: Potential dependence of the band bending for a p-type semiconductor. Nsc : free carrier concentration Under depletion conditions, charging comes from the electron affinity of the acceptors. If the density of the charge is assumed constant in the space charge region, Poisson's equation can be written as (2.4 ) After integrating twice and assuming that the electric field (dv/dx) is zero at x o, a long way from the surface and that V is zero in the bulk of the semiconductor, the Schottky relation can be obtained (2.5) where w is the width of the space charge region. 2.5: Nanostructured Semiconductors Nanostructured electrodes, used in some recently developed PEe cells, are commonly referred as porous electrode built up from interconnected semiconductor particles of nanometer size 140 The nanostructured electrodes distinguish themselves by their porosity and high surface-to-volume ratio. In 36

13 a porous semiconductor film consisting of interconnected nanometer sized semiconductor particles, the effective surface area can be enhanced fold 141. The electronic and photoelectrochemical properties of nanostructured electrodes are very different from compact electrodes. From solid state semiconductor physics it is known that defects and distorted structures in polycrystalline film electrodes normally cause low performance compared with electrodes made from highly ordered materials such as single crystals. However, the polycrystalline nanostructured electrodes have proven to be able to generate good photocurrents upon illumination 142. The reason for this and the mechanism behind the charge transport in nanostructured electrodes have lately received much attention. For very small (colloidal) semiconductor particles of radii ro, the total potential drop within the semiconductor ( L'l<!>sd is described by the following equation 141 kt ro 6 q L f) L'l<!>sc = [ ] 2 (2.6) The potential difference between the surface and the bulk of the semiconductor (the band bending) has to be at least 50 mv (2kTjq) in order to support migration of the photo generated charge carriers 141. From Equation 2.6 it is apparent that the electrical field in nanostructured semiconductor particles is usually small, unless high dopant levels are present. Besides, the porous structure of nanostructured semiconductor electrodes enables the electrolyte to fully penetrate the electrode and any existing electric field is effectively screened 143. Therefore, the concept of band bending will no longer be applicable and the driving force for charge separation cannot be a built-in electric field. Instead, it is generally accepted that the transport is mainly a diffusional random walk process 144. Thus, the driving force for the transport is the concentration gradient over the nanostructured film of photoinduced electrons

14 E (ev) Figure 2.11: Schematic representation of the possible processes in an illuminated nanostructured system in PEe cell In Figure 2.11 the bold arrows show the desired processes for an efficient water splitting PEC cell after a bandgap excitation: the transport of electrons to the back contact, the transfer of the hole to the semiconductor surface followed by the oxidation of water at Semiconductor/electrolyte interface (SEI). The three major limiting processes present here are (a) bulk recombination via bandgap states, or (b) directly electron loss to holes in the valence band (eventually followed by emission of light), and (c) surface recombination 147. If a proper electron scavenger is present (represented by oxygen in Figure 2.11), electrons can also be lost from the conduction band (process I). In addition, photocorrosion of the semiconductor itself and dissolution reactions can also occur (process II). In the absence of depletion layer the initial charge separation of photogenerated charge carriers is dependent on fast interfacial kinetics 143,148. The small particle size and the large nanostructured semiconductor/electrolyte interface (NSEI), may facilitate a fast transport of photogenerated charges to the interface, which can compete with the recombination rate. The film electrode exhibits n-type behavior if the reaction consuming holes at the interface is faster than the reaction consuming electrons. Consequently, if the electrons at the NSEI are consumed faster than the holes, the electrode will show p-type behavior. A typical feature of 38

15 nanostructured electrodes is that the most efficient charge separation takes place close to the back contact, which is contrary to the compact electrodes 144. Trapping and detrapping of electrons complicate the charge transport in nanostructured materials. Electron transport, including trappingjdetrapping mechanisms, for different nanostructured materials are discussed by several authors Most of the experimental work has, however, been carried out on nanostructured Ti02 electrodes. Defects in the crystal structure, such as vacancies, dislocations, impurities and grain boundaries, may give rise to traps. In addition, the adsorbed species at the semiconductor surface may give rise to states (surface states). Ti02 is affected by these kinds of surface states and it has been proposed that the density of trap states decreases exponentially with trap depth 149. Recent results, however, by transient current decay show a distinct peak around 0.3 V below the conduction band edge at ph The ph dependency of the trap density indicated that traps investigated were surface related. Different trap depths lead to a distribution of trapping and detrapping times. If trapping is significant, the residence time in traps will determine how fast the electrons will reach the back contact. By introducing a simple trapping function in the transport equation the affect of trappingjdetrapping can be included 153. Extended studies have revealed that the electrolyte, which fills up the nanoporous matrix, alters the pure diffusion process. This behavior is understood by a coupled diffusion of electrons in the semiconductor and ions in the solution. The so-called ambipolar diffusion model describes this. This model takes into account that diffusion of ions and electrons occurs at different speeds, therefore a weak electric field couples the processes together to preserve charge neutrality. The concept has successfully been ;:jpplied to nanostructured systems

16 2.6: Standard Electrode Potential An electrochemical cell consists of two electrodes in contact with an electrolyte and an ionic conductor (which may be a solution, a liquid or a solid). A redox reaction is a reaction in which there is a transfer of electrons from one species to another. The reducing agent is the electron donor and the oxidizing agent is the electron acceptor. Any redox reaction may be expressed in terms of two half-reactions, which describe the loss and gain of electrons. The reduced and oxidized substances in a half-reaction form a redox couple, denoted D/R, with the corresponding oxidation half-reaction as (2.7) A half-reaction takes place at one of the electrodes. The electrode at which the oxidation occurs is called the anode. The electrode at which the reduction occurs is called the cathode. A cell in which the overall cell reaction is not at chemical equilibrium can do electrical work as the reaction drives electrons through an external circuit. The work that a given transfer of electrons can accomplish depends on the potential difference between the two electrodes. This potential difference is called the cell potential and is measured in volts. The potential over one electrode has no absolute value and has to be measured with reference to another electrode. The reference chosen for this is the normal hydrogen electrode, NHE. The potential is by definition set to zero and the conditions for the corresponding half cell is described by (2.8) where all species are at standard state. The potentials of all redox couples can be given numerical values with reference to this electrode. The potential in reference to the NHE is called the standard electrode potential and is noted va. The electrode potential for a half-cell reaction that is not in the standard state can be calculated with the Nernst equation 9 40

17 (2.9) where, {R} and {O} are the activities of Rand O. The activity {R} = YR [R] and {O} = Yo [0], where [0] and [R] are the molar concentrations of 0 and R. Yo and Y/? are the activity coefficients of 0 and R. The standard electrode potential is a function of the standard Gibbs energy, i1go and the relation is described by (2.10) where n is the number of electrons transferred in the overall cell reaction and F is Faradays constant. If the components in the system are not in the standard states, then the relation will be described as in equation 2.11 i1g = -n F U (2.11) 2.7: Nanomaterial Aspects of PEC Cell The charge transfer from the semiconductor to the electrolyte results in the production of hydrogen from the electrolyte. This charge transfer takes place at the interface between the semiconductor and the electrolyte, and hence, the properties of the interface playa very important role in the operation of the cell. The interfaces at the photo-electrode as well as the counter electrode (if it is not a photo electrode) are vital in efficient operation of the cell. The properties of these interfaces are directly related to the structure of the electrode materials at the nanometer level. Since it is only the interface where the charge transfer reactions are taking place, the area of the interface is an important parameter. To maximize the efficiency, the area of the interface must be maximized. We know from geometrical arguments that smaller particle size results in higher surface area to volume ratios, so the use of smaller particles will probably increase the efficiency. However, other 41

18 properties of the electrode material also change as particle size is reduced, and these changes will not necessarily be helpful in increasing the efficiency. Electronic properties of materials show profound changes as the dimensions of materials are made smaller. These changes are a result of changes in the density of states, and size is the only important parameter that decides properties of material with dimensions smaller than about 100 nm. The band structure of semiconductors and metals, their chemical and physical reactivity are affected by the size. Following figure shows how the energy levels of a material change as the dimensions of the material are made Metals Bulk Nanocrystal, ~\ I \ Isolaled atom Unoccup'Od -+- Occupied Semiconductors A=?l Density of states ~ W _ :.:.:: [H;J " D ~ I ) _ ~ Unoccupied b.j EFermi t Occupiod Densily of slates Figure 2.12: Change in energy level of material with change in dimension smaller. A schematic diagram illustrates the changes in the energy levels of materials as their dimensions become smaller 155 For bulk materials, the energy levels are continuous, however, as the dimensions are made sufficiently small, they become discreet, due to "the 42

19 confinement of the electron wave function because of the physical dimensions of the particles,,1 55. The average spacing between successive energy levels is called Kubo gap and is given by l) = 4Ef /3n (2.12) where Ef is the Fermi energy of bulk material and n is number of electrons in the particle. Size induced metal to non-metal transition occurs for nanometer sized crystals of metals. The effect of nanostructure on semiconducting electrodes or the counter electrodes has been studied in literature, but probably not to the extent to which different electrode configurations or nature of electrolytes have been studied. It has been noted that deposition of very small particles of metals on semiconducting electrodes (silicon based semiconductors or Ti0 2 ) results in a 2 to 3 fold increase in photovoltage, while a continuous coverage of the semiconductor by metal results in smaller photo-voltage. This has been explained by size dependent injection of electrons from the semiconductor to the metals, which further reduce the electrolyte 155,156. The overpotential at the electrodes is an important issue limiting the efficiency, since higher overpotential means a significant amount of generated photovoltage is used in overcoming these potentials instead of using it for the water splitting reaction. The nanostructure of materials play an important role in determining the overpotential values, as finely dispersed, small particulate electrode materials typically exhibit smaller overpotentials. For example, as reported by Milczarek et al 158, the overpotential for hydrogen evolution on a smooth platinum electrode is about 175 mv, while that on platinized platinum is only 50 mv. This is attributed to small size and particulate nature of platinum metal in case of platinized platinum. Further, when a Nafion membrane supported on platinum is platinized, the overpotential is further reduced to 38 mv due to porous, high 43

20 surface area Nafion membrane. With the discovery of newer, surfactant templated, high surface area materials having ordered structure, the potential efficiencies could be much higher 159,160. It can be briefly summed up that apart from stability and band gap of the photoactive material there are also various factors viz. the process taking place at the interface i.e. semiconductor material and the electrolyte that are determinable for the efficient water splitting system. Not only significant is the band gap but also the overlap of the band edges of the semiconductor with that of the water redox potential so that the excited electrons of the conduction can make their way into water for hydrogen generation via splitting of water. Thus the working electrode or photoactive material engineered through nanotechnology featuring all the above required properties can lead to a water splitting system of desirable efficiency. 44