SEMICONDUCTOR DEVICES

A new method for calculation of majority carrier compensation in photovoltaics

Rumin Zhang1, 2, , Peng Liu1, 2, Dijun Liu2, 3 and Guobin Su3

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 Corresponding author: Rumin Zhang, E-mail: rm_zhang@foxmail.com

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Abstract: In thin film solar cells, the semiconductor materials usually contain multiple impurity/defect states as donor or acceptor dopants. The local charge neutrality (LCN) condition determines the equilibrium Fermi (EF) level and concentration of electrons and holes. However, the equation of LCN is a transcendental equation of EF. It is impossible to find its analytical solution and we can only solve it by graphic or numerical method. A simple approximate graphic method (GM) used for estimation of majority carrier compensation of semiconductors with multiple donors and acceptors was proposed by Chin. By introducing the concept of ranking the dopants and the wrapping step function, dopants concentration and Fermi level could be obtained easily. In this paper, we analyze the graphic method and propose a new numeric graphic method (NGM) based on GM. In addition, comparison of NGM with NM and analytics of the accuracy of GM are presented. With numerical calculation, some procedures of GM extending the application of GM are improved.

Key words: doping II-VIsemiconductorsdefect



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Fig. 1.  (Color online) A single shallow acceptor dopant without compensation in semiconductor. Red curves represent minor carrier concentration plus ionized acceptor or donor density. Curve $a$: $E_{\rm A}$ $=$ 0.10 eV, $N_{\rm A}$ $=$ 1 $\times$ 10$^{16}$ cm$^{-3}$; curve $b$: $E_{\rm A}$ $=$ 0.35 eV, $N_{\rm A}$ $=$ 1 $\times$ 10$^{16}$ cm$^{-3}$; curve $c$: $E_{\rm D}$ $=$ 1.5 eV, $N_{\rm A}$ $=$ 1 $\times$ 10$^{15}$ cm$^{-3}$; curve $d$: $E_{\rm D}$ $=$ 1.10 eV, $N_{\rm A}$ $=$ 1 $\times$ 10$^{15}$ cm$^{-3}$.

Fig. 2.  (Color online) A single donor dopant compensated by a single acceptor ($E_{\rm A}$ $=$ 0.35 eV, $N_{\rm A}$ $=$ 1 $\times$ 10$^{16}$ cm$^{-3})$. Curve $b$ depicts the ionized acceptor density; curves $a$ and $c$ are ionized donor density with two different doping concentration ($E_{\rm D}$ $=$ 1.50 eV, $N_{\rm D}$ $=$ 1 $\times$ 10$^{15}$ cm$^{-3}$ for curve $a$; $E_{\rm D}$ $=$ 1.50 eV, $N_{\rm D}$ $=$ 1 $\times$ 10$^{17}$ cm$^{-3}$ for curve $c$).

Fig. 3.  Formation of wrapping step function when $E_{\rm D'1}$ and $E_{\rm D'2}$ are far away from each other. Intervals ①, ②, ③ and ④ are used to estimate the closeness of $N_{\rm D1}$ and $N_{\rm D2}$ which determine forming the wrapping step function.

Fig. 4.  Formation of wrapping step function when $N_{\rm D'1}$ and $N_{\rm D'2}$ are far away from each other. Intervals ⑤ and ⑥ are used to estimate the closeness of $E_{\rm D1}$ and $E_{\rm D2}$ which determine formation of the wrapping step function.

Fig. 5.  (Color online) A single donor dopant compensated by two acceptor compensators whose doping concentrations are far away from each other. Blue line represents the ionized acceptor density $N_{\rm A1}^-$; green line, the ionized acceptor density $N_{\rm A2}^-$; red line, the total ionized acceptor density plus electron density and purple line, the ionized donor density $N_{\rm D}^+$. Since $N_{\rm A1}^-$ and the total ionized acceptor are almost equivalent, they overlap in the plane concentration versus $E_{\rm F}$.

Fig. 6.  (Color online) A single donor dopant compensated by two acceptor compensators whose doping concentrations are equivalent.

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Table 1.   Fermi level and majority carrier concentration calculated by NGM and NM respectively.

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    Received: 25 September 2014 Revised: Online: Published: 01 July 2015

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      Rumin Zhang, Peng Liu, Dijun Liu, Guobin Su. A new method for calculation of majority carrier compensation in photovoltaics[J]. Journal of Semiconductors, 2015, 36(7): 074004. doi: 10.1088/1674-4926/36/7/074004 R M Zhang, P Liu, D J Liu, G B Su. A new method for calculation of majority carrier compensation in photovoltaics[J]. J. Semicond., 2015, 36(7): 074004. doi: 10.1088/1674-4926/36/7/074004.Export: BibTex EndNote
      Citation:
      Rumin Zhang, Peng Liu, Dijun Liu, Guobin Su. A new method for calculation of majority carrier compensation in photovoltaics[J]. Journal of Semiconductors, 2015, 36(7): 074004. doi: 10.1088/1674-4926/36/7/074004

      R M Zhang, P Liu, D J Liu, G B Su. A new method for calculation of majority carrier compensation in photovoltaics[J]. J. Semicond., 2015, 36(7): 074004. doi: 10.1088/1674-4926/36/7/074004.
      Export: BibTex EndNote

      A new method for calculation of majority carrier compensation in photovoltaics

      doi: 10.1088/1674-4926/36/7/074004
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      • Corresponding author: E-mail: rm_zhang@foxmail.com
      • Received Date: 2014-09-25
      • Accepted Date: 2014-12-26
      • Published Date: 2015-01-25

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