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1070nm连续激光辐照三结GaInP2/GaAs/Ge太阳电池物理模型和各层尺寸如图 1所示。图中O为坐标原点,r方向表示太阳电池径向方向,z方向表示太阳电池轴向方向,a为太阳电池厚度,b为太阳电池半径。
当激光辐照到太阳电池时,经电池表面反射,透射到底电池的激光能量一部分传给光生载流子,通过电池内建场作用在底电池P-N结薄层之间产生光生伏打电动势,剩余部分则以声子形式传递给晶格转换为热能积聚在电池内部。因此通过求解光电转换模型中太阳电池转换效率,其剩余激光能量全部转换为热量作为光热转换模型中电池热源项。
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基于P-N结整流方程,太阳电池理想模型中各电学参量方程式[12]为:
$ {V_{{\rm{OC}}}} = \frac{{A{k_{\rm{B}}}T}}{q}\ln \left( {\frac{{{I_{{\rm{ph}}}}}}{{{I_{\rm{s}}}}} + 1} \right) $
(1) $ {I_{{\rm{SC}}}} = {I_{{\rm{ph}}}} $
(2) $ \eta = \frac{{{I_{{\rm{SC}}}}{V_{{\rm{OC}}}}{F_{\rm{f}}}}}{{{P_{{\rm{in}}}}}} $
(3) $ {F_{\rm{f}}} = \frac{{{V_{{\rm{OC,n}}}} - \ln \left( {{V_{{\rm{OC,n}}}} + 0.72} \right)}}{{{V_{{\rm{OC,n}}}} + 1}} $
(4) $ {V_{{\rm{OC,n}}}} = \frac{{{V_{{\rm{OC}}}}}}{{{k_{\rm{B}}}T/q}} $
(5) 式中, ISC和VOC分别为太阳电池短路电流和开路电压;Iph为光生电流,Is为反向饱和电流;Pin为入射激光功率;η为光电转换效率;A为二极管理想因子;kB为玻尔兹曼常数;q为电子电量;Ff为填充因子;VOC,n为归一化开路电压。
$ {I_{\rm{s}}} \approx Sq\left[ {{D_{\rm{n}}}n_{\rm{i}}^2/\left( {{L_{\rm{n}}}{N_{\rm{a}}}} \right) + {D_{\rm{p}}}n_{\rm{i}}^2/\left( {{L_{\rm{p}}}{N_{\rm{d}}}} \right)} \right] $
(6) $ \left\{ \begin{array}{l} {D_{\rm{n}}} = {k_{\rm{B}}}T{\mu _{\rm{n}}}/q\\ {D_{\rm{p}}} = {k_{\rm{B}}}T{\mu _{\rm{p}}}/q \end{array} \right. $
(7) $ {I_{{\rm{SC}}}} = \left( {1 - R} \right){P_{{\rm{in}}}}{Q_{\rm{e}}}\left( T \right)\frac{\lambda }{{1240}} $
(8) $ {Q_{\rm{e}}}\left( T \right) = {Q_{\rm{e}}}\left( {{T_0}} \right)\left[ {1 + {k_1}\left( {T - {T_0}} \right)} \right] $
(9) 式中, S为光斑面积;Dn和Dp分布为电子和空穴扩散系数;Ln和Lp分别为电子和空穴扩散长度;ni为Ge本征载流子浓度;Na和Nd分别为底电池P-N结两侧受主掺杂浓度和施主掺杂浓度;μn和μp分别为电子和空穴迁移率;R为电池表面反射率;λ为入射激光波长;Qe(T)为内量子效率;Qe(T0)为室温T0下内量子效率;kt为内量子效率温度系数。表 1中给出了光电转换模型中各种参量[15-16]。
Table 1. Parameters of photoelectric conversion model
parameter value the Boltzmann constant kB/(J·K-1) 1.381×10-23 unit charge q/C 1.6×10-19 diode ideal factory A 2 intrinsic carrier concentration ni/cm-3 9.15×1019 (T/300)1.5×exp[-15.2/(T/300)] internal quantum efficiency at T0 Qe(T0) 0.95 internal quantum temperature coefficient kt 8×10-4 reflectivity R 0.1 laser wavelength λ/nm 1070 electron mobility μn/(cm2·V-1·s-1) 4000×(T/300)-2.5 hole mobility μp/(cm2·V-1·s-1) 2090×(T/300)-2.33 electron diffusion length Ln/μm 1.5 hole diffusion length Lp/μm 3 acceptor doping concentration Na/cm-3 1×1017 donor doping concentration Nd/cm-3 1×1018 -
柱坐标系下热传导方程为:
$ \begin{array}{*{20}{c}} {{\rho _m}{c_m}\frac{{\partial {T_m}\left( {r,z,t} \right)}}{{\partial t}} = \frac{1}{r}\frac{\partial }{{\partial r}}\left[ {r{\kappa _m}\frac{{\partial {T_m}\left( {r,z,t} \right)}}{{\partial r}}} \right] + }\\ {\frac{\partial }{{\partial z}}\left[ {{\kappa _m}\frac{{\partial {T_m}\left( {r,z,t} \right)}}{{\partial z}}} \right] + {Q_m}\left( {T,r,z,t} \right)} \end{array} $
(10) 式中, m=1, 2, 3, …;Tm(r, z, t),ρm,cm和κm表示在t时刻的第m层温度场分布、材料密度、比热容和热导率;Qm(T, r, z, t)为在第m层材料中的激光功率体密度。
由于减反膜层、顶电池层GaInP2和中电池层GaAs对波长1070nm激光吸收系数非常小,可假设其不吸收此波长光能。在300K~400K时,Ge对1070nm波长激光吸收系数约为13600cm-1~15100cm-1[16],其穿透深度为几个微米,因此太阳电池热源可设为底电池层吸收热源Q(T, r, z, t):
$ \begin{array}{*{20}{c}} {Q\left( {T,r,z,t} \right) = {I_0}\left( {1 - R - \eta } \right)\alpha \left( T \right)f\left( r \right)g\left( t \right) \times }\\ {\exp \left[ { - \alpha \left( T \right)z} \right],\left( {0{\rm{ \mathsf{ μ} m}} < z \le 4.5{\rm{ \mathsf{ μ} m}}} \right)} \end{array} $
(11) $ \left\{ \begin{array}{l} f\left( r \right) = \left\{ \begin{array}{l} \exp \left( { - 2{r^2}/a_0^2} \right),\left( {0 < r \le {a_0}} \right)\\ 0,\left( {r > {a_0}} \right) \end{array} \right.\\ g\left( t \right) = 1,\left( {0 < t \le \infty } \right) \end{array} \right. $
(12) 式中, I0为激光功率密度;f(r)和g(t)分别是入射激光能量空间分布和时间分布;a0为入射激光光斑半径;α(T)为Ge对入射激光吸收系数。
由于实验[11]中使用的真空泵能够达到最低真空度为10-4Pa,不能使太阳电池处于绝对真空环境,因此对该物理模型加入热对流修正,则初始条件和边界条件为:
$ T\left( {r,z,t} \right)\left| {_{t = 0}} \right. = {T_0} = 300{\rm{K}} $
(13) $ - \kappa \frac{{\partial T{{\left( {r,z,t} \right)}_{t = 0}}}}{{\partial z}}\left| {_{z = a}} \right. = - \kappa \frac{{\partial T\left( {r,z,t} \right)}}{{\partial r}}\left| {_{r = b}} \right. = 0 $
(14) $ \begin{array}{*{20}{c}} { - \kappa \frac{{\partial T\left( {r,z,t} \right)}}{{\partial z}}\left| {_{z = 0}} \right. = - h\left[ {T\left( {r,z,t} \right) - {T_0}} \right] - }\\ {\sigma \varepsilon \left[ {{T^4}\left( {r,z,t} \right) - T_0^4} \right]} \end{array} $
(15) 式中, T0为环境温度;κ为Ge的热导率;σ为斯特藩常量;h为热对流系数;ε为电池上表面发射率;T(r, z, t)为电池表面温度。表 2中给出了Ge材料热学参量[16]。
Table 2. Thermal parameters of Ge
parameter value density ρ /(kg·m-3) 5323.4 thermal conductivity κ /(W·cm-1·K-1) 0.6×(T /300)-1 specific heat capacity c /(J·kg-1·K-1) 303+6.13×10-2T energy gap Eg/eV 0.803-3.9×10-4T coefficient of heat transfer h /(W·m-2·K) 10 the Stefan constant σ /(W·m-2·K-4) 5.67×10-8 thermal radiation rate ε 0.1 laser radius a0/cm 1.5 cell radius b /cm 1.5 absorption coefficient α(T)/cm-1 1.4×104exp[2.81×(1.16+0.67-Eg-1.17)]
连续激光辐照三结GaAs太阳电池温度场仿真
Simulation of three-junction GaAs solar cell temperature field by continuous wave laser irradiation
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摘要: 为了研究真空环境下1070nm连续激光辐照对三结GaAs太阳电池输出性能的影响,利用COMSOL软件构建了相应物理模型,通过数值仿真研究了激光功率密度、光斑半径、减反膜和热辐射热对流对温度场的影响。结果表明,吸收系数、热导率和光电转换效率是温度演变的3个主要因素;温升幅度随激光功率密度增大而增大;光斑半径越小使得电池表面温差越大;拥有减反膜结构可有效地提高太阳电池转换效率,但也使电池温度较高;热对流散热在电池较低温度(300K~400K)情况下占据主导作用;当入射功率密度为16.7W/cm2、光斑半径与电池半径相同时,经20s后,电池中心温度达到501.521K,导致光电转换效率为0。该数值模拟结果与实验结果基本相符,对激光损伤太阳电池机理研究提供一定的理论依据。Abstract: In order to study the effects of 1070nm continuous wave laser irradiation on output performance of three-junction GaAs solar cell, a physical model was established by software COMSOL. The influence of laser power density, spot radius, anti reflection film, thermal radiation and thermal convection on temperature field were studied by numerical simulation. The results show that, absorption coefficient, thermal conductivity and photoelectric conversion efficiency are three main factors of temperature evolution. The magnitude of temperature increases with the increasing of laser power density. The smaller the spot radius is, the greater the temperature difference of cell surface. The conversion efficiency of solar cells can be effectively improved by anti reflection film structure, but it also makes battery temperature higher. Thermal convection dominates under the lower temperature (300K~400K) of the battery. When the incident power density is 16.7W/cm2 and spot radius is the same as the cell radius, after 20s, the central temperature of battery can reach 501.521K and lead to photoelectric conversion efficiency of 0. The numerical simulation results are in good agreement with the experimental results. The study provides a theoretical basis for the research of the mechanism of laser damage solar cells.
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Key words:
- laser technique /
- continuous wave laser /
- numerical simulation /
- temperature field
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Table 1. Parameters of photoelectric conversion model
parameter value the Boltzmann constant kB/(J·K-1) 1.381×10-23 unit charge q/C 1.6×10-19 diode ideal factory A 2 intrinsic carrier concentration ni/cm-3 9.15×1019 (T/300)1.5×exp[-15.2/(T/300)] internal quantum efficiency at T0 Qe(T0) 0.95 internal quantum temperature coefficient kt 8×10-4 reflectivity R 0.1 laser wavelength λ/nm 1070 electron mobility μn/(cm2·V-1·s-1) 4000×(T/300)-2.5 hole mobility μp/(cm2·V-1·s-1) 2090×(T/300)-2.33 electron diffusion length Ln/μm 1.5 hole diffusion length Lp/μm 3 acceptor doping concentration Na/cm-3 1×1017 donor doping concentration Nd/cm-3 1×1018 Table 2. Thermal parameters of Ge
parameter value density ρ /(kg·m-3) 5323.4 thermal conductivity κ /(W·cm-1·K-1) 0.6×(T /300)-1 specific heat capacity c /(J·kg-1·K-1) 303+6.13×10-2T energy gap Eg/eV 0.803-3.9×10-4T coefficient of heat transfer h /(W·m-2·K) 10 the Stefan constant σ /(W·m-2·K-4) 5.67×10-8 thermal radiation rate ε 0.1 laser radius a0/cm 1.5 cell radius b /cm 1.5 absorption coefficient α(T)/cm-1 1.4×104exp[2.81×(1.16+0.67-Eg-1.17)] -
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