recombination{}

This section specifies the coefficients related to recombination processes. These are used when the current equation is solved. In nextnano++, the following recombination processes are included:

• Shockley-Read-Hall (SRH) recombination

• Auger recombination

• Radiative recombination

Example

binary_zb {
    name    = Si                        # material name, e.g. Si, GaAs, InP, ...

        ...

    recombination{
                                        # Shockley-Read-Hall recombination
        SRH{        tau_n  = 1.0e-9     # [s]    zero doping scattering time for electrons
                    nref_n = 1.0e19     # [cm^-3] reference doping concentration for electrons
                    tau_p  = 1.0e-9     # [s]    zero doping scattering time for holes
                    nref_p = 1.0e18     # [cm^-3] reference doping concentration for holes
        }

                                        # Auger recombination
        Auger{      c_n    = 2.8e-31    # [cm^6/s]
                    c_p    = 9.9e-31    # [cm^6/s]
        }

                                        # direct recombination
        radiative{  c = = 2.0e-10   }   # [cm^3/s]
                                        # 2.0e-10 for GaAs, 0 for Si (indirect semiconductor)

    }

}

Shockley-Read-Hall (SRH) recombination

                                # Shockley-Read-Hall recombination
SRH{        tau_n  = 1.0e-9     # [s]    zero doping scattering time for electrons
            nref_n = 1.0e19     # [cm^-3] reference doping concentration for electrons
            tau_p  = 1.0e-9     # [s]    zero doping scattering time for holes
            nref_p = 1.0e18     # [cm^-3] reference doping concentration for holes
}

SRH model models the generation/recombination process that is assisted by impurities. The recombination/generation rates depend on the deviation of the carrier concentration from the equilibrium value and the scattering rates depend on the doping concentration.

\[ \begin{align}\begin{aligned}R_{SRH} &= \frac{p\cdot n - n_i^2}{\tau_p(n+n_i)+\tau_n(p+p_i)}\\\tau_{p/n}&=\frac{\tau_{p0/n0}}{1+\frac{N_D+N_A}{N_n/p,ref}}\end{aligned}\end{align} \]

\(\tau_{n0}\)	tau_n (zero doping scattering time for electrons in [\(\mathrm{s}\)])
\(N_{n,ref}\)	nref_n (reference doping concentration for electrons in [\(\mathrm{cm}^{-3}\)])
\(\tau_{p0}\)	tau_p (zero doping scattering time for holes in [\(\mathrm{s}\)])
\(N_{p,ref}\)	nref_p (reference doping concentration for holes in [\(\mathrm{cm}^{-3}\)])

Auger recombination

                                # Auger recombination
Auger{      c_n    = 2.8e-31    # [cm^6/s]
            c_p    = 9.9e-31    # [cm^6/s]
}

More imformation on physics: Auger recombination processes in semiconductor heterostructures.

For devices with an extremely high carrier concentration the Auger process is the dominant recombination channel. The process involves three particles and therefore scales with the third power of the carrier densities.

The phonon-assisted Auger recombination rate, which plays an important role especially at high carrier injection, respectively high doping levels, will be modeled in the program by the following equation:

\[R_{Auger} = (C_n n + C_p p)\cdot(np-n_i^2)\]

\(C_n\)	c_n (in [\(\mathrm{cm}^6/\mathrm{s}\)])
\(C_p\)	c_p (in [\(\mathrm{cm}^6/\mathrm{s}\)])

Radiative recombination

                                # direct recombination
radiative{  c = = 2.0e-10   }   # [cm^3/s]
                                # 2.0e-10 for GaAs, 0 for Si (indirect semiconductor)

The simplest process for the generation and recombination of electron-hole pairs is the direct process via the emission or absorption of a photon (radiative recombination). This is important for light emitting devices.

\[R_{radiative} = C(np-n_i^2)\]

\(C\)

c (in [\(\mathrm{cm}^3/\mathrm{s}\)])