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SCIENCE CHINA Information Sciences, Volume 62, Issue 6: 062406(2019) https://doi.org/10.1007/s11432-017-9472-x

Systematic calibration of drift diffusion model for InGaAs MOSFETs in quasi-ballistic regime

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  • ReceivedFeb 12, 2018
  • AcceptedMay 29, 2018
  • PublishedMar 1, 2019

Abstract

This paper proposes a systematic procedure to calibrate the parameters of the drift-diffusion (DD) model for a performance evaluation of InGaAs MOSFETs in the quasi-ballistic regime. The simulation results of a deterministic multi-subband Boltzmann transport equation (BTE) solver serve as the standard. The DD model is calibrated both under low and high electric fields. The electrostatic characteristics, low field mobility model, and high field saturation model are calibrated in proper sequence, and a good agreement among the drive current, carrier distribution, and velocity distribution are achieved between the results of the calibrated DD model and the BTE solver. The proposed calibration procedure can also be employed in devices made of other materials.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61674008, 61421005, 61404005).


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  • Figure 1

    (Color online) Schematic of the simulated device structure.

  • Figure 2

    (Color online) Flow chart of the calibration procedure. The procedure consists of three parts, electrostatic characteristics, low field mobility, and high field saturation.

  • Figure 3

    (Color online) Relative error of the calibrated DG model vs. $\gamma$ parameter under various gate voltages. The drain voltage is set to be zero. The relative error is calculated using the carrier density at the middle of the channel.

  • Figure 4

    (Color online) Calibration results of the DG model with different gate voltages and $V_D$=0. The parameter barrier is set to 0.03 to compensate the carrier density variation caused by the DG model.

  • Figure 5

    (Color online) Calibration results of the electrostatic characteristics. The relationship between the carrier density in the middle of the channel and the gate voltage is shown in logarithm and linear coordinates, respectively.

  • Figure 6

    (Color online) Transfer characteristic curve of the device simulated using calibrated low field mobility model and Enormal model. The inset shows the velocity calibration under a small $V_D$.

  • Figure 7

    (Color online) Velocity distribution simulated using TCAD and the BTE solver with $V_D=0.05$ and 0.6 V. A high field saturation model is not involved in the TCAD simulation.

  • Figure 8

    (Color online) The relative error of the injection velocity with various parameters $\beta$$_0$.

  • Figure 9

    (Color online) Calibration of velocity along the channel under $V_G=0.6$ V. The injection velocity is the key point.

  • Figure 10

    (Color online) Calibration results of output characteristics curves with calibrated high field saturation model.

  • Figure 11

    (Color online) (a) Transfer characteristic curve in logarithm and linear coordinates and (b) relative error of the current under various biases after the Enormal model is involved.

  • Table 1   Structural parameters of the sample
    Parameter Value
    Channel length 20 nm
    S/D length 10 nm
    Effective oxide thickness (EOT) 1 nm
    Film thickness 5 nm
    Channel doping 10$^{17}$ cm$^{-3}$
    S/D doping 5$\times$10$^{19}$ cm$^{-3}$
  • Table 2   Relative error of every step of the calibration procedure
    Procedure Relative error
    $V_G=0.4$ V $V_G=0.5$ V $V_G=0.6$ V
    DG model 44.2% 11.7% 19.1 %
    Low field $v_{\rm~inj}$ 0.69% and 0.012% with $V_D=0.1$ and 0.5 mV
    Low field current 51.2% 18.9% 10.1 %
    Low field Enormal 39% 6.9% 3.1 %
    High field $v_{\rm~inj}$ 2.7% with $V_D=0.6$ V
    High field current 43.7% 12.5% 12.3 %
    High field Enormal 29.4% 1.2% 19.7 %

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