Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 1 Chapter I Introduction June 20, 2015June 20, 2015June 20, 2015

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 13 Introduction: Solar Cell Efficiency 1. Absorption of light: enhances absorption 1. Absorption of light: enhances absorption 2. Transformation of light energy into electron energy: depends on band gap of materials (and light spectrum of the Sun). 2. Transformation of light energy into electron energy: depends on band gap of materials (and light spectrum of the Sun). 3. Purity and perfection of crystal which does not lead to electron hole pair recombination. 3. Purity and perfection of crystal which does not lead to electron hole pair recombination. 4. Electron mobility of materials 4. Electron mobility of materials 5. Function of pn diode which can effectively collect the electrons either through diffusion or drift of electrons. 5. Function of pn diode which can effectively collect the electrons either through diffusion or drift of electrons. 6. resistance of the outside circuitry 6. resistance of the outside circuitry

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 14 Light Spectrum from the Sun Planck distribution at 5800 o K

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 15 Light Spectrum from the Sun

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 16 Blackbody Radiation from Planck’s Law where h and k are the universal Planck and Boltzmann constant.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 17 AM=air mass; AM0 = sun radiation at outerspace AM1=sun radiation normal to the earth surface AM1.5=sun radiation at a angle of 41.8 o above the horizon, or approximately an angle of incidence of solar radiation of 48 o relative to the surface normal.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 18 Solar Energy AM1.5 is the standard spectrum for measuring the efficiency of solar cells, which is a typical spectrum for moderate climates. The integral over this spectrum is 1.0 kW/m 2. For one year, the total amount of energy incident on the ground is 1000 kWh/m 2 in Germany. We speak of 1000 sun hours (with 1 kW/m 2 ) per year. Averaged over the year, the mean energy in Germany is 115 W/m 2, in Saudi Arabia is 285 W/m 2. The average value over the entire earth is 230 W/m 2. For AM0 spectrum, the average energy over the earth is 338 W/m 2. AM1.5 is the standard spectrum for measuring the efficiency of solar cells, which is a typical spectrum for moderate climates. The integral over this spectrum is 1.0 kW/m 2. For one year, the total amount of energy incident on the ground is 1000 kWh/m 2 in Germany. We speak of 1000 sun hours (with 1 kW/m 2 ) per year. Averaged over the year, the mean energy in Germany is 115 W/m 2, in Saudi Arabia is 285 W/m 2. The average value over the entire earth is 230 W/m 2. For AM0 spectrum, the average energy over the earth is 338 W/m 2.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 19 Absorption Coefficient of Some Semiconductor

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 20 Physical Means of Absorption Coefficient The inverse of the absorption coefficient is the thickness of the material where the light passing through the layer has been absorbed by 63%. For example, silicon has an α of 10 2 cm -1. Then, the inverse of α is 100 μm. That means that with a light passing through a silicon layer of 100 μm, 37% of light can penetrate through this layer. (Note: from Beer-Lambert’s Law,,, I=0.37I o ) The inverse of the absorption coefficient is the thickness of the material where the light passing through the layer has been absorbed by 63%. For example, silicon has an α of 10 2 cm -1. Then, the inverse of α is 100 μm. That means that with a light passing through a silicon layer of 100 μm, 37% of light can penetrate through this layer. (Note: from Beer-Lambert’s Law,,, I=0.37I o )

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 21 Possible Routes to Increase Photon Flux

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 22 Antireflection on Both Front and Back Surfaces

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 24 Excitation of an Electron in Metal Decay in less than s

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 25 Excitation of an Electron in Valence Band to Conduction Band Decay in less than s

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 26 Splitting of Energy Levels

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 28 Fermi Distribution Function

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 30 Band Gap

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 31 Loss of Excess Electron,Hole Kinetic Energy by Thermalisation

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 32 Effect of Band gap on the Conversion Efficiency

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 33 Effect of Band gap on the Conversion Efficiency

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 35 Band Gap Variation with Temperature

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 36 Mobilibty Variation with Dopent Concentration

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 37 Mobility Variation with Temperature

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 38 Life Time of Carriers by Recombination Process

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 39 The life time of carriers for Direct Band Gap Semiconductor In n- or p-type material, the carrier life time for holes and electrons: In n- or p-type material, the carrier life time for holes and electrons: where R ec is the recombination coefficient, N D N A is the concentration of Donor and Acceptor. where R ec is the recombination coefficient, N D N A is the concentration of Donor and Acceptor.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 40 The life time of carriers for Indirect Band Gap Semiconductor In n-type material, the carrier life time for holes: In n-type material, the carrier life time for holes: where σ p is the hole capture cross section, v th is the thermal velocity, N t is the concentration of impurity has a energy level near the mid gap. where σ p is the hole capture cross section, v th is the thermal velocity, N t is the concentration of impurity has a energy level near the mid gap.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 41 The life time of carriers for Indirect Band Gap Semiconductor In p-type material, the carrier life time for electrons: In p-type material, the carrier life time for electrons: where σ n is the electron capture cross section, v th is the thermal velocity, N t is the concentration of impurity has a energy level near the mid gap. where σ n is the electron capture cross section, v th is the thermal velocity, N t is the concentration of impurity has a energy level near the mid gap.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 42 The Total Life Time of Carrier Where the carrier life time in undoped silicon is τ o, e.g. 400 μs. Where the carrier life time in undoped silicon is τ o, e.g. 400 μs. The total life time of carrier in Silicon is

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 43 Diffusion Length of a Carrier Diffusivity of an carrier for n-type, Diffusivity of an carrier for n-type, Diffusivity of a carrier for p-type, Diffusivity of a carrier for p-type, Diffusion length of the carrier, Diffusion length of the carrier,

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 44 Diffusion Length in Different Materials In silicon, L is the order of 1 cm. In GaAs, L is the order of cm. For polymer materials, the diffusion length of the exciton is 1-10 nm or 4 – 20 nm. In silicon, L is the order of 1 cm. In GaAs, L is the order of cm. For polymer materials, the diffusion length of the exciton is 1-10 nm or 4 – 20 nm.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 45 Surface Recombination where N st is the number of surface trapping centers per unit area the boundary region.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 46 Reduction of Surface Recombination 1. For silicon, passivation with a layer of SiO 2 is used. 1. For silicon, passivation with a layer of SiO 2 is used. 2. Contact with another semiconductor layer with high band gap, e.g. the so- called window layer. 2. Contact with another semiconductor layer with high band gap, e.g. the so- called window layer.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 47 Electron and Hole Distribution in a pn Diode when illuminated with Light

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 48 I-V Curve of a Diode

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 50 Dark Current and Open Circuit Voltage For a solar in dark (which is an ideal diode) with a load applied, the current and voltage relation is For a solar in dark (which is an ideal diode) with a load applied, the current and voltage relation is (1) (1) where J o is the reverse leakage current and is constant, K B is the Boltzmann’s constant. where J o is the reverse leakage current and is constant, K B is the Boltzmann’s constant. When light is illuminated, When light is illuminated, (2) (2)

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 51 Dark Current and Open Circuit Voltage Or Or (3) (3) Re-arrange Eq (3), Re-arrange Eq (3),

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 54 Solar Cell Efficiency The power density of solar is defined as The power density of solar is defined as P=JV P=JV The fill factor is: The fill factor is: With power density from the sun, P s, the efficiency of solar cell is defined as With power density from the sun, P s, the efficiency of solar cell is defined as or or

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 55 Effect of Series and Shunt Resistance R sh much be as large as possible; R s much be as small as possible

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 56 Effect of Series and Shunt Resistance

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 57 Performance of Some PV Cells

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 58 Quantum Efficiency The quantum efficiency, QE, of a solar cell is defined as the ratio of the number of electrons in the external circuit produced by an incident photon of a given wavelength. The quantum efficiency, QE, of a solar cell is defined as the ratio of the number of electrons in the external circuit produced by an incident photon of a given wavelength. External quantum efficiency, EQE: all photons impinging on the cell surface are taken into account. External quantum efficiency, EQE: all photons impinging on the cell surface are taken into account. Internal qunatum efficiency, IQE: only photons that are not reflected are considered. Internal qunatum efficiency, IQE: only photons that are not reflected are considered.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 59 Types of Basic Device Building Blocks

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 60 For a Metal Semiconductor Contact under Thermionic Emission Condition and and Where J s is the saturation current density and A is the Richardson’s constant. Where J s is the saturation current density and A is the Richardson’s constant.

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 63 If occurs for metal/n type Si, then not for metal/p type Si When doping for Si > 6x10 19 atms/cm 3 Schottky Barrier

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 64 Pn Junction Solar Cell A electric field is established at the junction which drives minority carriers passing through the junction, but not majority carriers. However, inside each layer, the photogenerated minority carriers reach the junction by diffusion.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 65 Pn Junction Solar Cell

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 66 P-i-n Junction Solar Cell This design is for materials where the minority carrier diffusion lengths are short, and carriers photogenerated in p and n layer are very small. The diffusion length in i layer is much longer. Carrier is driven by electric field created between p and n layer.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 67 Pn Heterojunction

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 68 Junction in Organic Materials

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 69 Working Principle In some crystalline organic solids (small molecules), intermolecular forces are strong and carriers may be considered to occupy bands much like inorganic crystal. Excitons may be split spontaneously and devices can be designed using similar principles as for inorganic metal-semiconductor junctions. For amorphous organic solids or polymers, intra-molecular forces dominate and the excitons are very tightly bond. The electrostatic fields available from the difference in work functions of the junction materials is not sufficient to split the excition. Instead, the excitons drift, and only split when they approach the junction with a contact material of different work function. In some crystalline organic solids (small molecules), intermolecular forces are strong and carriers may be considered to occupy bands much like inorganic crystal. Excitons may be split spontaneously and devices can be designed using similar principles as for inorganic metal-semiconductor junctions. For amorphous organic solids or polymers, intra-molecular forces dominate and the excitons are very tightly bond. The electrostatic fields available from the difference in work functions of the junction materials is not sufficient to split the excition. Instead, the excitons drift, and only split when they approach the junction with a contact material of different work function.