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Model of phosphorus diffusion in silicon for highly doped solar cell emitter layer

Wojciech Filipowski (Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, Zabrze, Poland)

Microelectronics International

ISSN: 1356-5362

Article publication date: 1 July 2019



The purpose of this paper was the development of a model enabling precise determination of phosphorus concentration profile in the emitter layer of a silicon solar cell on the basis of diffusion doping process duration and temperature. Fick’s second law, which is fundamental for describing the diffusion process, was assumed as the basis for the model.


To establish a theoretical model of the process of phosphorus diffusion in silicon, real concentration profiles measured using the secondary ion mass spectrometry (SIMS) method were used. Samples with the phosphorus dopant source applied onto monocrystalline silicon surface were placed in the heat zone of the open quartz tube furnace, where the diffusion process took place in the temperature of 880°C-940°C. The measured real concentration profiles of these samples became template profiles for the model in development.


The model was developed based on phenomena described in the literature, such as the influence of the electric field of dopant ionized atoms and the influence of dopant atom concentration nearing the maximum concentration on the value of diffusion coefficient. It was proposed to divide the diffusion area into low and high dopant concentration region.


A model has been established which enabled obtaining a high level of consistency between the phosphorus concentration profile developed theoretically and the real profile measured using the SIMS method. A coefficient of diffusion of phosphorus in silicon dependent on dopant concentration was calculated. Additionally, a function describing the boundary between the low and high dopant concentration regions was determined.



This work was partially supported by the Ministry of Science and Higher Education funding for statutory activities of researchers of the Faculty of Automatic Control, Electronics and Computer Science.


Filipowski, W. (2019), "Model of phosphorus diffusion in silicon for highly doped solar cell emitter layer", Microelectronics International, Vol. 36 No. 3, pp. 104-108.



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