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Complex Band Structures: From Parabolic to Elliptic Approximation

Complex Band Structures: From Parabolic to Elliptic Approximation,10.1109/LED.2011.2160143,IEEE Electron Device Letters,Ximeng Guan,Donghyun Kim,Krish

Complex Band Structures: From Parabolic to Elliptic Approximation   (Citations: 1)
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We show that the conventional nonparabolic approx- imation of real band structures can be modified and generalized to approximate the complex band structures of common semicon- ductors with a significant improvement of accuracy against the parabolic approximation. The improvement is due to the inherent elliptic nature of the complex band structures in the vicinity of the bandgap, which has a critical impact on the band-to-band tunneling probability. Important parameters are extracted and tabulated for Si, Ge, GaAs, and GaSb, with a maximum error of < 1.4% compared to the numerical target. Index Terms—Band-to-band tunneling (BtBT), complex band structure, nonparabolicity. In this letter, we show that the long-standing nonparabolic approximation (NPA) of real bands can be extended to de- scribe the complex band structure of common semiconductor materials in the energy region important to BtBT. Compared to the capability to describe real bands, NPA shows even more improvement in describing the complex band structures over the parabolic approximation (PA). This is due to the inherent elliptic nature of the complex bands inside a bandgap region. With the recently developed numerical technique for complex band calculation (5), we have extracted and tabulated the NPA parameters for typical semiconductors. Comparison with PA shows a significant reduction of errors in the estimation of BtBT probability. The methodology is therefore suggested to be applicable in a broad range of materials and devices.
Journal: IEEE Electron Device Letters - IEEE ELECTRON DEV LETT , vol. 32, no. 9, pp. 1296-1298, 2011
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    • ...Detailed derivation of our analytical forms and its implications are described elsewhere in [7], in which a nonparabolic two-band kp i model is generalized to the case where electrons and holes have different effective masses...
    • ...Further investigation of these complex energy branches in different semiconductors reveals the fact that they are all close to the elliptic relation implied by a simple two-band model [7][13]...
    • ... model and our non-parabolic model for the direct and indirect tunneling trajectories in Ge. While our elliptic model agrees with the numerical results well, the parabolic approximation used by the effective mass approach overestimates the action integral by 20% for direct and 30% for indirect tunneling, which, when substituted into (3), translates to an underestimation of T by 70% and 80% when a constant field of 10 6 V/cm is present [7]...
    • ...In both cases of direct and indirect tunneling, the parabolic approximation tends to overestimate the action integral and therefore underestimate the tunneling probability [7]...
    • ...VALENCE BRANCH OF Si IS ALSO FITTED FOR INDIRECT TUNNELING [7]...

    Ximeng Guanet al. Analytical approximation of complex band structures for band-to-band t...

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