Novel design of solar cell efficiency improvement using an embedded electron accelerator on-chip

Itsara Srithanachai; Surada Ueamanapong; Surasak Niemcharoen; Preecha P Yupapin

doi:10.1364/OE.20.012640

1. Introduction

Energy has been an important issue of the world for half a century, where the most of energies are come from coal and oil. Moreover, the pollutions are increased due to the burning process of coal and oil [1–4]. Nuclear power plant is the other way to generate energy. This technique can produce the electrical energy using the heat of nuclear reaction, instead burning of coal and oil. On the other hand, the nuclear reaction is very dangerous because the accidents in nuclear reactions are distribution of radioactivity. Green energy is the better choice more than burning of coal, oil and nuclear reaction. The green energy can generate electrical energy from many ways such as water, wind and sunlight. Although, the green energy from wind and water can be used to substitute the energy from burning energy, however, the differences of depreciation of landscapes and weather to electrical generate from wind and water are less than the sunlight.

A solar cell is the device for changing the sunlight to electrical energy. Although, the solar cells are important for green energy generation, on the other hand, the performance of the device is not high enough because there are many problems. The developments of solar cells are still continuously needed. Generally, the solar cell performance is caused by many problems such as the reflection of surface [5], silicon bulk defects [6,7]. To solve the reflection problem on the surface, there are many ways such as adjust the surface of solar cells angle to ability for obtaining most of sunlight [8,9]. Furthermore, the solar cell production is used high cost and not worth investment, where we found that the defect in silicon bulk is the important problem for solar cell performance decreasing because the electron and hole are recombined by trapping or defecting in silicon bulk. To solve this problem, several research works proposed the methods of modified bulk and heterojunction [10,11] and control hole transport in silicon bulk to contact [12]. Therefore, this work presents the use of a PANDA microring resonator to improve the solar cells performance, in which the trapped holes can be controlled and faster transport to the required destination.

However, the use of a PANDA microring resonator is a new system, which has been proposed by the Suwanpayak et al [13]. By using the optical tweezer, the solar cell efficiency can be increased. The optical tweezers are generated by a PANDA microring, which can be used to accelerate and move electron and hole via the optical waveguide to the solar cell device contact. By using this technique, hole can transport to the contact without recombination in silicon bulk, therefore, the current of solar cell is increased. Moreover, the use of a PANDA microring is also founded in many applications such as photonic microdevice [14], hybrid transistor [15], therapeutic applications [16], and telephone networks [17]. In this paper, the trapping tool generation is reviewed and the new design system for particle accelerator described. Finally, simulation results using the commercial MATLAB is demonstrated, where all parameters were used closely to the practical fabricated device.

2. Particle trapping principle

A novel system of the P-N diode using a PANDA microring resonator was proposed by the authors in reference [13]. By using a dark-bright soliton pulses propagating within a modified add/drop optical multiplexer (PANDA microring), the trapping tools can be formed, which can be used to trap molecules/atoms. Inthis work, the multiplexed signals with slightly different wavelengths of the dark solitons are controlled and amplified within the system. The dynamic behaviors of dark bright soliton interaction are also analyzed and described. Finally, the use of optical switching to form a P-N photodetector using the Gaussian control at the add port is discussed in detail.

We are looking for a stationary dark soliton pulse, which is introduced into the add/drop optical filter system as shown in Fig. 1 . The input optical field (E_in) and the add port optical field (E_add) of the dark, bright soliton or Gaussian pulses are given by [18].

E_{i n} (t) = A \tanh [\frac{T}{T_{0}}] \exp [(\frac{z}{2 L_{D}}) - i ω_{0} t],

E_{i n} (t) = A sech [\frac{T}{T_{0}}] \exp [(\frac{z}{2 L_{D}}) - i ω_{0} t],

E_{a d d} (t) = E_{0} \exp [(\frac{z}{2 L_{D}}) - i ω_{0} t],

Here $A_{0}$ and

z

are the optical field amplitude and propagation distance, respectively.

T = t - β_{1} z,

where

β_{1}

and $β_{2}$ are the coefficients of the linear and second-order terms of Taylor expansion of the propagation constant.

L_{D} = T_{0}^{2} / | B_{2} |

is the dispersion length of the soliton pulse.

T_{0}

in Eq. is a soliton pulse propagation time at initial input (or soliton pulse width), where t is the soliton phase shift time, and the frequency shift of the soliton is

ω_{0}

. The optical fields of the system within the device as shown in Fig. 1 are obtained and expressed in following forms.

n = n_{0} + n_{2} I = n_{0} = (\frac{n_{2}}{A_{e f f}}) P,

E_{1} = - j κ_{i} + τ_{1} E_{4},

E_{2} = \exp (\frac{j ω T}{2}) \exp (\frac{- α L}{4}) E_{1},

E_{3} = τ_{2} E_{2} - j κ_{2} E_{1},

E_{4} = \exp (\frac{j ω T}{2}) \exp (\frac{- α L}{4}) E_{3},

E_{t} = τ_{t} E_{i} - j κ_{1} E_{4},

E_{d} = τ_{2} E_{a} - j κ_{2} E_{2},

Here

E_{i}

is the input field,

E_{a}

is the add(control) field,

E_{t}

is the through field,

E_{d}

is the drop field,

E_{1}

…

E_{4}

are the fields in the ring at points 1…4,

κ_{1}

is the field coupling coefficient between the input bus and ring,

κ_{2}

is the field coupling coefficient between the ring and output bus,

L

is the circumference of the ring,

T

is the time taken for one round trip(roundtrip time), and

α

is the power loss in the ring per unit length. We assume that this is the lossless coupling, i.e.,

τ_{1, 2} = \sqrt{1 - κ_{1, 2}^{2}},

T = \frac{L n_{e f f}}{c}

.

Fig. 1 A PANDA microring resonator

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The output intensities at the drop and through ports are given by

{| E_{d} |}^{2} = | \frac{- κ_{1} κ_{2} A_{1, 2} Φ_{1 / 2}}{1 - τ_{1} τ_{2} A Φ} E_{i} + \frac{τ_{2} - τ_{1} A Φ}{1 - τ_{1} τ_{2} A Φ} E_{a} |,

{| E_{t} |}^{2} = | \frac{τ_{2} - τ_{1} A Φ}{1 - τ_{1} τ_{2} A Φ} E_{i} + \frac{- κ_{1} κ_{2} A_{1, 2} Φ_{1 / 2}}{1 - τ_{1} τ_{2} A Φ} E_{a} |,

Here

A_{1 / 2} = \exp (\frac{- α L}{4})

the half-round-trip amplitude),

A = A_{1, 2}^{2},

Φ_{1 / 2} \exp (\frac{j ω T}{2})

(the half-round-trip phase contribution), and

Φ = Φ_{1 / 2}^{2}

.

To form the broad soliton spectrum output, two nonlinear ring resonators are introduced. The circulated roundtrip light fields of the right ring radii, $R_{r}$ , are given in Eq. (11) and (12), respectively [19].

E_{r 1} = \frac{j \sqrt{1 - γ} \sqrt{κ_{0} E_{1}}}{1 - \sqrt{1 - γ} \sqrt{1 - κ_{0}} e^{- \frac{α}{2} L_{1} - j κ_{n} L_{1}}},

E_{r 2} = \frac{j \sqrt{1 - γ} \sqrt{κ_{0} E_{1}} e^{- \frac{α}{2} L_{1} - j κ_{n} L_{1}}}{1 - \sqrt{1 - γ} \sqrt{1 - κ_{0}} e^{- \frac{α}{2} L_{1} - j κ_{n} L_{1}}},

Thus, the output circulated light field,

E_{0}

, for the right ring is given by

E_{0} = \frac{\sqrt{1 - γ} \sqrt{(1 - κ_{0})} - (1 - γ) e^{- \frac{α}{2} L_{1} - j κ_{n} L_{1}}}{1 - \sqrt{1 - γ} \sqrt{1 - κ_{0}} e^{- \frac{α}{2} L_{1} - j κ_{n} L_{1}}},

Similarly, the output circulated light field,

E_{0 L}

, for the left ring at the left side of the add/drop optical multiplexing system is given by

E_{0 L} = E_{3} (\frac{\sqrt{1 - γ_{3}} \sqrt{(1 - κ_{3})} - (1 - γ_{3}) e^{- \frac{α}{2} L_{2} - j κ_{n} L_{2}}}{1 - \sqrt{1 - γ_{3}} \sqrt{1 - κ_{3}} e^{- \frac{α}{2} L_{2} - j κ_{n} L_{2}}}),

Where

κ_{3}

is the intensity coupling coefficient,

γ_{3}

is the fractional coupler intensity loss,

α

is the attenuation coefficient,

κ_{n} = \frac{2 π}{λ}

is the wave propagation number,

λ

is the input wavelength light field and,

L_{2} = 2 π R_{L}

,

R_{L}

is the radius of left ring.

From Eq. (11)-(14), the circulated light fields, $E_{1}$ , $E_{3}$ and $E_{4}$ are defined by given $x_{1} = {(1 - γ_{1})}^{1 / 2},$ $x_{2} = {(1 - γ_{2})}^{1 / 2},$ $y_{1} = {(1 - κ_{1})}^{1 / 2},$ and $y_{2} = {(1 - κ_{2})}^{1 / 2}$ .

E_{1} = \frac{j x_{1} \sqrt{κ_{1}} E_{i 1} + j x_{1} x_{2} y_{1} \sqrt{κ_{2}} E_{0 L} E_{i 2} e^{- \frac{α}{2} \frac{L}{2} - j κ_{n} \frac{L}{2}}}{1 - x_{1} x_{2} y_{1} y_{2} E_{0} E_{0 L} e^{- \frac{α}{2} L - j κ_{n} L}},

E_{3} = x_{2} y_{2} E_{0} E_{1} e^{- \frac{α}{2} \frac{L}{2} - j κ_{n} \frac{L}{2}} + j x_{2} \sqrt{κ_{2} E_{i 2}},

E_{4} = x_{2} y_{2} E_{0} E_{1} e^{- \frac{α}{2} \frac{L}{2} - j κ_{n} \frac{L}{2}} + j x_{2} \sqrt{κ_{2} E_{i 2}} e^{- \frac{α}{2} \frac{L}{2} - j κ_{n} \frac{L}{2}},

Thus, from Eq. (11)-(17), the output optical field of the through port

(E_{t 1})

is expressed by

E_{t 1} = x_{1} y_{1} E_{i 1} + (j x_{1} x_{2} y_{2} \sqrt{κ_{1}} E_{0} E_{0 L} E_{1} - x_{1} x_{2} \sqrt{κ_{1} κ_{2} E_{0 L} E_{i 2}}) e^{- \frac{α}{2} \frac{L}{2} - j κ_{2} \frac{L}{2}},

The power output of the through port

(P_{t 1})

is written by

P_{t 1} = (E_{t 1}) \cdot {(E_{t 1})}^{*} = {| E_{t 1} |}^{2},

Similarly, the output optical field of the drop port

(E_{t 2})

is given by

E_{t 2} = x_{2} y_{2} E_{i 2} + j x_{2} \sqrt{κ_{2}} E_{0} E_{1} e^{- \frac{α}{2} \frac{L}{2} - j κ_{n} \frac{L}{2}},

The power output of the drop port

(P_{t 2})

is expressed by

P_{t 2} = (E_{t 2}) \cdot {(E_{t 2})}^{*} = {| E_{t 1} |}^{2},

An optical tweezer is recognized as a promising tool for molecule/atom trapping, which is basically depended on the laser wavelength control, where in this work the tweezer is formed by using a PANDA microring resonator. The optical tweezer generation can be designed and embedded within the device based on silicon, in which an electron can be injected to the contact without loss, and the transport time can be controlled before reaching the contacts. The optical tweezers can be varied and adjusted via the add port of a PANDA ring.

Figure 2 shows the optical tweezer for electron and hole trapping and transportation via the optical waveguide. The trapping tool size (d) is required to tune between these two conditions, where (i) d > electron size, this case an electron can escape from the trap in the transport process to the contact, (ii) d < electron size, this case an electron cannot be trapped when the size of the trap too small. Therefore, the trap size is required to fit the electron/hole size (0.22 nm) [20].

Fig. 2 Optical tweezer for hole trapping, where (a) trapping potential well, (b) an optical tweezer for hole trapping

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3. Results and discussion

By using the proposed design, the optical tweezer can be used to trap and move the electron/hole via the optical waveguide. A PANDA microring resonator can generate the optical tweezer by add/drop, the particles in a bottle will be trapped and moved by the input tweezers, the suitable tweezers can be controlled and generated by the controlled port signals. In our application, the improvement solar cell performance by using PANDA microring is proposed. Normally, the characteristics of solar cells study by J-V characteristics, the J-V characteristics of solar cells depend on factors such as (i) series and shunt resistance, (ii) the front and back contacts and (iii) the main junction. The main junctions in the important factor for controls the current of solar cells because of P-N junction can generate the electron-hole pair. However, the diffusion of carriers to contact has a problem in silicon bulks such as the recombination of hole. This problem can be solved by increasing the trapped hole speed to the contact via optical waveguide, without trapping within a silicon bulk.

From Fig. 3 , the holes are trapped in the junction and moved to the contact via optical waveguide. The ring radii are $R_{a d d}$ = 15 µm, $R_{R}$ = 3 µm and $R_{L}$ = 3 µm, in which the evidence of the fabricated device was reported by the authors in reference [21]. $A_{e f f}$ is 300 µm², κ = κ₁ = κ₂ = κ₃ = 0.5, the waveguide losses coefficient, $α$ is 0.1 and coupling loss, $γ$ is 0.01 and n₀ is 1.37. The simulation results are obtained for four different center wavelengths of tweezers generated, where the dynamical movements are (a) ${| E_{1} |}^{2},$ (b) ${| E_{2} |}^{2},$ , (c) \ ${| E_{3} |}^{2},$ , (d) ${| E_{4} |}^{2},$ (e) through port and (f) drop port signals as shown in Fig. 4 .

Fig. 3 Solar cell model using a PANDA microring, where (a) hole trapping and moving via optical waveguide, (b) diode model with PANDA microring.

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Fig. 4 Results of dynamic optical tweezers generated at different center wavelengths, where (a) \E₁\², (b) \E₂\², (c) \E₃\², (d) \E₄\², (e) through port and (f) drop port signals.

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Figure 5 shows the optical tweezer that can be adjusted to fit the electron/hole size from 0.25 to 2 nm, which can be used for electron/hole transportation at the through port and drop port. The sizes of optical tweezers are important for trapping electron/hole moving to device contact. The current of solar cells compare between fabrication technique and using PANDA mircroring resonator for accelerator electron/hole, the current of solar cells is calculated by using Eq. (22).

Fig. 5 Trapping potential well of optical tweezers with various trapping sizes, where (a) 2 nm, (b) 1 nm, (c) 0.5 nm, and (d) 0.25 nm.

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I_{L} = q A (L_{n} + W + L_{p}) G

Where $I_{L}$ is the light current, $A$ is the area, $L_{n}$ is the diffusion length of electron, $L_{p}$ is the diffusion length of hole and $W$ is the depletion width and $G$ is the generation rate.

The current of the device after using a trapping tool and technique of a PANDA microring resonator system is increased by 5 orders [22–25], which is shown in Fig. 6 .

Fig. 6 Light current of the diode using PANDA microring resonator.

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4. Conclusions

We have proposed a new method of electron/hole accelerator, which can be used to accelerate electron/hole within the solar cell device. By using optical tweezers and optical waveguide embedded within the solar cell device, the hole/electron speed can be increased about 5 orders. Silicon is the applied material in this study, in which an electron can move to the metal contact via an optical waveguide without recombination in the silicon bulk. The obtained results have shown that the PANDA microring resonator can be used to generate the optical tweezers, which can be adjusted for electron/hole trapping. This design can also be used for the applications such as capacitor, photodetector and transistor.

Acknowledgments

The authors would like to thank Thai Microelectronics Center (TMEC), National Electronics and Computer Technology Center (NECTEC), Thailand and Thailand Graduate Institute of Science and Technology (TGIST), Institute of Nanoscale Science and Engineering Research Alliance and Hybrid Computing Research Laboratory, King Mongkut’s Institute of Technology Ladkrabang (KMITL), Bangkok 10520, Thailand.

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Novel design of solar cell efficiency improvement using an embedded electron accelerator on-chip

Abstract

1. Introduction

2. Particle trapping principle

3. Results and discussion

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (6)

Equations (24)

Optics Express