2.1 Growth mechanism of one-dimensional ZnO nanostructures
2.1.1 Growth Mechanism of Vapor-Liquid-Solid (VLS)
Most popular approach for forming 1-D nanostructures is the vapor-liquid-solid (VLS) method [8]. The VLS method was originally developed by Wagner and his co-workers to produce micrometer-sized whisker in 1960s [9]. Recently, this technique is re-examined by Lieber [8]. In the VLS method, the catalyst plays a key role on the growth of the nanowires or nanorods. The catalyst would form an alloy nanocluster with the reactant under the proper conditions. The growth of the nanowires results from the alloy nanoclusters are supersaturated in the reactant. The formation procedure of 1-D nanostructure in the VLS method is shown in Fig. 2-1, which demonstrates the formation of semiconductor nanowire using metal catalyst.
The reactant metal vapor which could be generated by the thermal evaporation is condensed to the catalyst metal to form a liquid alloy nanocluster as the temperature is low. Nanowires grown after the liquid metal alloys become supersaturated and continue as long as the metal nanoclusters remain in a liquid state. Growth of nanowires will be terminated as the temperature reduces to the point that the metal nanoclusters solidify. Therefore, a strong evidence of the VLS mechanism is to
observe catalytic metal at the ends of the nanowires as that observed on the formation of Ge nanowires in the report by P. Yang et al. [10], as shown in Fig. 2-2. Based on the VLS growth mechanism, ZnO nanowires had been successfully grown on silicon substrates also by P. Yang et al. [11].
metal
Fig. 2-2 In situ TEM images recorded during the process of nanowire growth. (a) Au nanoclusters in solid state at 500 C; (b) Alloying is initiated at 800 oC, at this stage Au exists mostly in solid state; (c) liquid Au/Ge alloy; (d) the nucleation of a Ge nanocrystal on the alloy surface; (e) Ge nanocrystal elongates with further Ge condensation; (f) eventually forms a wire; and (g) Au-Ge binary phase diagram. [11]
2.1.2 Growth Mechanism of Solution-Liquid-Solid (SLS)
In the SLS growth mechanism [12], crystal growth requires (1) a reversible pathway between the fluid (solution, melt or vapor) and the solid phase or (2) high surface mobility in the solid phase. These conditions let the atoms, ions, or molecules to get the correct positions developing the crystal lattices. Aqueous or organic solvants dissolve their constituent ions or molecules and condition (1) is met, so molecular or ionic solids can be crystallized from solution at low temperature.
However, covalent nonmolecular solid such as III-V semiconductors are generally insoluable and cannot be crystallized from the solution at low temperature. These materials should be synthesized from solution by condition (2) with two circumstances that support low temperature crystal growth: catalysis by protic reagents and the participation of metallic flux particles. The growth mechanism of low temperature SLS shown in Fig. 2-3 is analogous to that of high-temperature VLS.
Fig. 2-3 Solution-Liquid-Solid method
2.2 Device operation principles
Figure 2-4 illustrates the equivalent circuit of an ideal solar cell. From this diagram, one could find the photo-generated current density J can be written as:
J JSC J E V RSIT 1 , (2.1)
where n is the ideality factor of diodes (1 < n < 2, n = 1 for the Shockley equation).
JSC is the short current density and J0 is the reverse saturation current density. RS is the equivalent series resistance of the solar cell. In Fig. 2-5, the cell J-V characteristics in dark condition and under illumination are shown. The parameters used to describe the solar cell are indicated as follows:
The open-circuit voltage VOC can be derived from by Eq. (2.1) with J = 0
VOC Tln JJSC 1 . (2.2)
The fill factor FF is another parameter of solar cell, which is defined as the ratio of the maximum output power to the product of the open-circuit voltage and the short-circuit current, or equivalently
FF JJ V
SCVOC . (2.3)
The efficiency of solar cell is defined as the ratio of the maximum output power to the input power
η V P SI 100% VOC JPSC FF%, (2.4)
where Pin and S are the input power per unit area and the effective area of solar cell, respectively.
Fig. 2-4 Equivalent circuit of an ideal solar cell
Fig. 2-5 J-V curve of a solar cell in dark condition and under illumination
2.3 Scanning Electron Microscope (SEM)
The principle of SEM used for examining a solid specimen in the emissive mode is closely comparable to that of a closed circuit TV system shown in Fig. 2-6. In the TV camera, light emitted from an object forms an image on a special screen, and the signal from the screen depends on the intensity of image at the point being scanned.
The signal is used to modulate the brightness of a cathode ray tube (CRT) display, and the original image is faithfully reproduced if (a) the camera and display raster are geometrically similar and exactly in time and (b) the time for signal collection and processing is short compared with the time for the scan moving from one picture point to the next.
In the SEM the object itself is scanned with the electron beam and the electrons emitted from the surface are collected and amplified to form the video signal. The emission varies from point to point on the specimen surface, and so an image is obtained. Many different specimen properties cause variations in electron emission, thus, although information might be obtained about all these properties, the images need interpreting with care. The resolving power of the instrument can not be smaller than the diameter of the electron probe scanning across the specimen surface, and a small probe is obtained by the demagnification of the image of an electron source by means of electron lenses. The lenses are probe forming rather than image
forming, and the magnification of the SEM image is determined by the ratio of the sizes of raster scanned on the specimen surface and on the display screen.
For example, if the image on the CRT screen is 100 mm across, magnifications of 100X and 10000X are obtained by scanning areas on the specimen surface 1mm and 10μm across, respectively. One consequence is that high magnifications are easy to obtain with the SEM, while very low magnifications are difficult. This is because large angle deflections are required which imply wide bore scan coils and other problem parts, and it is more difficult to maintain scan linearity, spot focus and
efficient electron collection at the extremes of the scan.
(a) (b)
Fig.2-6 Closed circuit TV (a) and scanning electron microscope (b) [13]
2.4 The electrochemical impedance spectroscopy theory in dye-sensitized solar
cells
2.4.1 The Bisquert Equation [14]
Bisquert obtained the impedance of diffusion and recombination based on the following three assumptions: (1) electrons in the conduction band diffuse, (2) there is
no trap, and (3) an irreversible first-order reaction is assumed for the recombination.
The diffusion-recombination model for small amplitude oscillating quantities,
superimposed to a given stationary state, is written as
J kn D kn, (2.5)
where n , D, and k represent the small oscillating electron density, diffusion coefficient of an electron in the ZnO nanocrystal, and reaction rate constant for recombination, respectively.
The boundary condition is given as
0, at x L, (2.6)
where L represents the film thickness of ZnO. The impedance under boundary condition (2) is given by Bisquert as
Z RWRK coth 1 , (2.7)
where
ω LD , ω k , (2.8)
R ConDL, Con BAT , R R ConL , (2.9)
Here, Z, Rw, Rk, τ, kB, T, q, A, and ns represent the impedance, electron transport resistance in TiO2, charge-transfer resistance related to recombination of an electron, lifetime of an electron in ZnO, Boltzmann constant, absolute temperature, charge of a proton, the electrode area, and the electron density at the steady state in the
conduction band, respectively.
Equation (2.7) can be rewritten to obtain
Z R coth 1 . (2.10)
Fig. 2-7 Reaction paths in the TiO2 electrode of the DSSCs in the model of Kern et al.[15]
On the other hand, Kern et al. [15] derived the impedance of diffusion and recombination in TiO2 based on the reaction paths shown in Figure 2-7. They set the following three assumptions:
(1) Electrons are injected into the conduction band from the excited dye at the
injection rate G under illumination; (2) only a single trap level is assumed, and the rate constant, k1, for the trapping of the conduction band electrons is much faster than k2 for the detrapping of the electrons; and (3) trapped electrons are lost by the recombination with I3-, and the second-order reaction rate is assumed with respect to electrons for the recombination.
The continuity equations for the conduction band electrons and for the electrons in the trap state, which describes injection, diffusion, collection, trapping, detrapping, and recombination of electrons in the TiO2 of the DSSCs, are given as
D k n k N G, (2.11)
N k n k N k n, (2.12)
n n ∆ne , (2.13)
N N ∆Ne , (2.14)
where Dcb represents the diffusion coefficient of an electron in the conduction band and ns and Ns are the steady state electron density in the conduction band and in the trap state, respectively. ∆n and ∆N are the amplitudes of the modulated component of the conduction band and trap state electron density, respectively.
Defining
D D , (2.15) Dk 2NSk , (2.16)
γ D D . (2.17)
And using the following boundary conditions At x=L, qD ∆ ∆IA ∆J; (2.18) At x=0, ∆ 0. (2.19)
Impedance is obtained by Kern et al. [15] as
Z S
Equation (2.16) was transformed into Eq. (2.20) as follows.
Defining
ω DL , ω k , (2.22)
γL , (2.23)
and impedance can be rewritten as
Z R coth 1 , (2.24)
where
R BAT DL ConDL , R ConL . (2.25) Then, Eq. (2.24) becomes the same as Eq. (2.10)
Let us consider here the reason why the impedance by Kernet al. becomes the same as the Bisquert equation. The assumption that the trapping is much faster than
detrapping (k1 » k2) results in Ns » ns. Electrons in the trap state N detrap to the conduction band and diffuse with the diffusion coefficient Dcb for the period proportional to k2/k1. Thus, electrons in the trap state are regarded as diffusing charges with the diffusion constant Deff = Dcb(k2/k1). Electrons in the trap state also react with I3- with a pseudo-first-order reaction rate with reaction rate constant keff
=2Nskr. Therefore, the model by Kern et al. is simplified as follows:
Injected electrons become the trap electrons, diffusing with the diffusion coefficient Deff and being lost by the pseudo-first-order recombination rate with the rate constant keff. This reaction scheme is eventually the same as that of Bisquert.
2.4.2 Models of the Impedance of the Electron Transfer at the Pt Counter
Electrode and the Finite Warburg Impedance of Tri-Iodide in Electrolyte
First, the impedance of the electron transfer at the Pt counter electrode can be described approximately by the following simple RC circuit with
Z C , (2.26)
ω C , (2.27)
where rp and Cp represent the resistance at the Pt surface and the capacitance at the Pt surface, respectively.
Second, the finite Warburg impedance describes the diffusion of triiodide ions in the electrolyte as
ZN RD liquid film, respectively. The number of electrons transferred in each reaction, m, is 2 in this case. AV and C* are Avogadro’s constant and the concentration of I3- in the bulk, respectively.
2.4.4 The total impedance of the DSSC
The total impedance of the DSSC, ZS, is given as the summation of the impedance of diffusion and recombination in the ZnO electrode, Z, given by Eq.
(2.24), Z , given by Eq. (2.25??), and Zp N, given by Eq. (2.27??), and ZS Z ZP ZN. (2.31)
2.5 IPCE Measurements
The incident-photon-to-current-efficiency (IPCE), also referred to as incident-photon-to-collected-electron-efficiency, gives the spectral resolution of the photocurrent. These measurements were done in Ar-glove boxes using a homemade setup: The light coming from a Xe-lamp is optically chopped. After passing a monochromator the light is focused onto the sample using a light fibre. Each time
the lamp is turned on, the lamp spectrum is calibrated using a monocrystalline silicon diode with known sensitivity. For signal detection a lock-in amplifier is used.
After the measurement the IPCE can be calculated using
IPCE % 1240 V nm I AI W 100%. (2.32)
In this equation Ip is the light power incident on the device.