Ab initio model of carrier transport in diamond (2024)

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  Figure 1

  The electronic structure of diamond computed using the DFT-HSE approach.

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  Figure 2

  The calculated phonon dispersion in diamond. The solid black lines represent the phonon energies computed using DFT. The dashed red and green lines represent the effective acoustic and optical phonon dispersions, respectively.

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  Figure 3

  A comparison between the total electron acoustic scattering rate computed using the full phonon dispersion from DFT HSE (solid black line) and a single acoustic effective phonon mode (solid red line).

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  Figure 4

  A comparison between the total hole acoustic scattering rate computed using the full phonon dispersion from DFT HSE (solid black line) and a single acoustic effective phonon mode (solid red line).

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  Figure 5

  A comparison between the total electron optical scattering rate computed using the full phonon dispersion and electronic structure from DFT HSE (solid black line) and a single optical effective phonon mode (solid red line).

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  Figure 6

  A comparison between the total hole optical scattering rate computed using the full phonon dispersion and electronic structure from DFT HSE (solid black line) and a single effective optical phonon mode (solid red line).

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  Figure 7

  The calculated electron impact-ionization scattering rate. The open symbols are the $k$-dependent values and the solid black line is the energy-averaged scattering rate.

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  Figure 8

  The calculated hole impact-ionization scattering rate. The open symbols are the $k$-dependent values and the solid black line is the energy-averaged scattering rate.

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  Figure 9

  The measured and computed electron drift velocity in diamond as a function of the applied electric field strength. The red square, green diamond, and blue circles are the experimental values from Ref. [14]. The solid blue, dashed red, and dash-dot green lines are the values calculated in this work.

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  Figure 10

  The red square, and blue circles are the experimental values from Ref. [15]. The black triangles are experimental values from Ref. [11]. The solid blue, dashed red, and dash-dot green lines are the values calculated in this work.

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  Figure 11

  The measured and computed electron (top row) and hole (bottom row) drift velocity in the $⟨100⟩$ (left column) and $⟨110⟩$ (right column) crystallographic directions in diamond as a function of the applied electric field. The values obtained in this work are plotted with dashed lines and experimental values are plotted with symbols. The experimental values are from Refs. [11, 14, 15].

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  Figure 12

  The theoretical and experimental impact-ionization coefficient data available in the literature. The experimental data have been extracted from Schottky-barrier-diode breakdown data [48, 49, 50, 51], while the values in data set [52] have been inferred by scaling the data for silicon and silicon-carbide using the difference in the energy gap. The theoretical data [53] and [19] have been obtained from full-band Monte Carlo models that include an empirical pseudopotential and ab initio models.

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  Figure 13

  The calculated electron and hole impact-ionization coefficients in diamond as a function of the inverse applied electric field strength at 300 K. The solid red line with circles, the dot-dash red line with diamonds, and the dashed red line with squares are the calculated values for holes when the electric fields are applied in the $⟨111⟩$, $⟨100⟩$, and $⟨110⟩$ directions, respectively. The solid blue line with circles, the dot-dash blue line with diamonds, and the dashed blue line with squares are the calculated values for electrons when the electric fields are applied in the $⟨111⟩$, $⟨100⟩$, and $⟨110⟩$ directions, respectively.

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  Figure 14

  The maximum electric field value at the breakdown as a function of the $p$-type doping density for a $p^{-}$-$n^{+}$ junction. The experimental values are from Refs. [59, 60, 61, 62, 63]. The data from Ref. [61] estimate their doping to be $<8\times {10}^{15}{\mathrm{cm}}^{-3}$ but the data point is placed at $8\times {10}^{15}{\mathrm{cm}}^{-3}$. The data in Refs.[48, 49] are obtained using ionization-coefficient values fitted to the experimental values. The values in Ref. [19] have been computed using ionization coefficients obtained from a theoretical model based on DFT GW. The dashed black line with circles represent the values calculated in this work by a direct simulation of the multiplication gain. The dashed yellow line with circles represents the values calculated by solving the ionization integral and using the ionization coefficients derived from the FBMC model. The inset of the figure shows the typical field profile of the junction, with the breakdown field, $F_{\mathrm{bd}}$, defined as the peak field.

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