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Theory of superfast fronts of impact ionization in semiconductor structures
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10.1063/1.2767378
/content/aip/journal/jap/102/3/10.1063/1.2767378
http://aip.metastore.ingenta.com/content/aip/journal/jap/102/3/10.1063/1.2767378
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Sketch of the electric field and total concentration of free carriers concentrations (lower panel) in the structure during the passage of the ionization front. The field corresponds to the transition from linear low-field transport to saturated drift velocities. Coordinates and correspond to stationary and comoving frames, respectively. Note relations and between the initial concentration in the depleted region, doping and plasma concentration . The relation generally holds only for and can be broken for .

Image of FIG. 2.
FIG. 2.

Dependence of total carrier concentration on electric field in the traveling ionization front. See notations and comments to Fig. 1. Path A–B–C–D corresponds to piecewise linear approximation of the field profile shown in Fig. 10.

Image of FIG. 3.
FIG. 3.

Concentration just behind the ionization zone as a function of for different values of . Thick solid lines 1, 2, 3 correspond to symmetric case . Dotted lines 1d, 2d, 3d and dashed lines 1e, 2e, 3e correspond to the two limiting asymmetric cases [immobile holes, case (d)] and [immobile electrons, case(e)], respectively. Curves of first, second, and third series correspond to , , and , respectively. Thin solid line 4 shows concentration at the point of maximum electric field for the symmetric case .

Image of FIG. 4.
FIG. 4.

Maximum electric field as a function of according to Eq. (36). Both and are normalized by . Note that when .

Image of FIG. 5.
FIG. 5.

Maximum electric field as a function of for different values of according to Eq. (36). Thick solid curves 1a, 2a, 3a correspond to the symmetric case (a) , [Eq. (37)]. Thin solid curves 1b, 2b, 3b correspond to impact ionization by electrons , [case (b), Eq. (38)]; dashed curves 1c, 2c, 3c correspond to impact ionization by holes , [case (c), Eq. (38)]. Curves of first, second, and third series correspond to , , and , respectively. The parameter corresponds to the doping level in Si.

Image of FIG. 6.
FIG. 6.

Maximum electric field as a function of for different values of according to Eq. (36). Thick solid lines 1a, 2a, 3a correspond to the symmetric case , [case (a), Eq. (37)]. Thin solid lines 1b, 2b, 3b correspond to impact ionization by electrons , [case (b), Eq. (38)]. Curves of first, second, and third series correspond to , , and , respectively; . Inset shows the Townsends’s dependence for impact ionization coefficient .

Image of FIG. 7.
FIG. 7.

Slope of electric field in the screening region normalized by the slope in the depleted region as a function of for different values of . Solid lines 1, 2, 3 correspond to the symmetric case . Dotted lines 1d, 2d, 3d and dashed lines 1e, 2e, 3e correspond to the two limiting asymmetric cases [immobile holes, case (d)] and [immobile electrons, case (e)], respectively. Curves of first, second, and third series correspond to , , and , respectively.

Image of FIG. 8.
FIG. 8.

Concentration of electron-hole plasma generated by the front passage as a function of front velocity . In panel (a) the dependence is shown for different values of . Solid curves 1, 2, 3 correspond to the case of symmetric transport , (e.g., , ). Dotted lines 1d, 2d, 3d and dashed lines 1e, 2e, 3e correspond to the limiting cases of immobile holes , [case(d)] and immobile electrons , [case (e)], and are calculated for the same values of . Curves of first, second, and third series correspond to , , and , respectively. In panel (b) the dependence is shown for different values of and and fixed value . Solid lines from 1 to 7 correspond to , , 0, 0.5, 0.8, 0.9, and 1.0, respectively. Associated dotted and dashed lines in panel (b) correspond to and , respectively, and the same value of as for the respective solid lines.

Image of FIG. 9.
FIG. 9.

Electric field in the electron-hole plasma generated by the front passage as a function of front velocity . In panel (a) the dependence is shown for different values of . Solid curves 1, 2, 3 correspond to case of symmetric transport , (e.g., , ). Dotted lines 1d, 2d, 3d and dashed lines 1e, 2e, 3e correspond to the limiting cases of immobile holes , [case(d)] and immobile electrons , [case (e)], respectively. Curves of first, second, and third series correspond to , , and , respectively. In panel (b) the dependence is shown for different values of and and fixed value . Solid lines from 1 to 7 correspond to , , 0, 0.5, 0.8, 0.9, and 1.0, respectively. Associated dotted and dashed lines correspond to and , respectively, and the same value of as for the respective solid lines.

Image of FIG. 10.
FIG. 10.

Piecewise linear approximation of the field profile used to calculate the voltage across the base (Sec. III H). The respective dependence is shown by dashed line A–B–C–D in Fig. 2.

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/content/aip/journal/jap/102/3/10.1063/1.2767378
2007-08-09
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Theory of superfast fronts of impact ionization in semiconductor structures
http://aip.metastore.ingenta.com/content/aip/journal/jap/102/3/10.1063/1.2767378
10.1063/1.2767378
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