Recombination of Mobile Carriers Across Boron Excited Levels in Silicon at Low Temperatures

T. T. Muratov

doi:10.1134/S1063782619160206

Semiconductors

December 2019, Volume 53, Issue 12, pp 1573–1577 | Cite as

Recombination of Mobile Carriers Across Boron Excited Levels in Silicon at Low Temperatures

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T. T. Muratov

ELECTRONIC PROPERTIES OF SEMICONDUCTORS

First Online: 04 December 2019

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Abstract

Carrier recombination through shallow boron-impurity centers in doped weakly compensated silicon is studied. Much attention is paid to theoretical explanation of the “empirical” temperature dependences of the carrier lifetime τ(T) in the temperature range of (1.7–4.2) K at the doping level n_B ≥ 10¹⁴ cm^–3 and compensation ≤10% (n_d + n_a ≤ 10¹³ cm^–3. It is possible to rather accurately determine that the shallow excited level with a binding energy of 5 meV (3s-state) is quasi-resonant. Approximate formulas for the trapping efficiency are obtained. The effect of “weak” magnetic field (10²–10³) G on the capture coefficient is studied; it is shown that the “weak” magnetic field slightly reduces the lifetime of carriers, thus stimulating their recombination.

Keywords:

recombination paths resonant level trapping efficiency lifetime photoconductivity classical “weak” and “strong” magnetic fields

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CONFLICT OF INTEREST

The author declares that he has no conflict of interest.

APPENDIX

Based on Eq. (6), we obtain the limit formulas:

$$\begin{gathered} \alpha _{H}^{{\max }} = \frac{{32}}{3}\frac{{{{\omega }_{H}}}}{{{{n}_{{\text{B}}}}}},\quad {{\tau }_{{\min }}} = \frac{3}{{32{{\omega }_{H}}}}{{T}_{{{\text{cr}}}}} = 64\,{\text{K}}, \\ ({{\alpha }_{H}} \leqslant \alpha _{H}^{{\max }}),\quad ({{\tau }_{H}} \geqslant {{\tau }_{{\min }}}). \\ \end{gathered} $$

To estimate the magnitude of the values, we set H = 100 G; in this case, ω_H ≈ 4 × 10⁹ rad/s. Then $\alpha _{H}^{{\max }}$ ≈ 4 × 10^–4 cm³/s and τ_min ≈ 2.7 × 10^–11 s (τ_min ≥ τ_T), from which it follows that

$$\frac{{\alpha _{H}^{{\max }}}}{{{{\alpha }_{T}}}} = \frac{{4 \times {{{10}}^{{ - 4}}}}}{{4 \times {{{10}}^{{ - 6}}}}} = {{10}^{2}}.$$

Then, taking into account Eq. (4) for the actual interval of (1.7–4.2) K (n_B = 10¹⁴ cm^–3),

$$\bar {\tau } = \frac{2}{{{{T}_{2}} - {{T}_{1}}}}\int\limits_{{{T}_{1}}}^{{{T}_{2}}} {\tau (T)dT} \approx 2.7 \times {{10}^{{ - 9}}}\,\,{\text{s}}.$$

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T. T. Muratov
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1.Tashkent State Pedagogical University named after NizamiTashkentUzbekistan

Recombination of Mobile Carriers Across Boron Excited Levels in Silicon at Low Temperatures

Abstract

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CONFLICT OF INTEREST

REFERENCES

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