SiGe MQW QCSE electro-absorption modulator (EAM)

Attention

This tutorial is under construction.

Input files:

1D_Ge_GeSi_QCSE_Kuo2005_8kp_nnp_exciton.in 1D_Ge_GeSi_QCSE_Kuo2005_simplified_8kp_nnp_exciton.in

Scope of the tutorial:

In this tutorial, we show an approach how to model absorption spectrum for a series of quantum wells inside p-i-n junction. This tutorial reproduces experimental results from [KuoNature2005].

The most relevant keywords:

• contacts

• optics{ quantum_spectra{} }

• quantum{excitons{} kp8{}}

Relevant output files:

bias_xxxxx\bandedges.dat bias_xxxxx\Optics\absorption_quantum_region_TEy_eV.dat structure\density_acceptor.dat structure\density_donor.dat

Introduction

In this tutorial, we will explore the physics behind the quantum-confined Stark effect (QCSE) and its application in modulating light absorption in semiconductor structures. The QCSE is a phenomenon in which the absorption edge of a semiconductor is shifted when an electric field is applied perpendicular to its surface, resulting in a redshift of the exciton peak. This effect can be utilized in electro-optic devices such as modulators, switches, and tunable lasers.

We will begin by simulating the QCSE in a simplified structure consisting of only an intrinsic region. In the second example, we will simulate a more complex structure consisting of a p-i-n junction with the quantum well embedded in the intrinsic region. This will provide us with a more accurate representation of the electro-optic properties of a complete device and allow us to investigate the behavior of absorption versus bias.

This tutorial reproduces the experimental results from [KuoNature2005]. The design consists of the p-doped buffer, grown on Si substrate, bottom spacer, series of 10 quantum wells, top spacer and n-doped cap layer. The device parameters are given below

Name	Thikness, nm	Ge concentration	doping type	doping concentration, cm-3
Buffer	500	0.9	p-type	5 \(\times\) 1018
Bottom spacer	100	0.9	—	—
Barrier	16	0.85	—	—
Well	10	1.0	—	—
Top spacer	100	0.9	—	—
Cap layer	200	0.9	n-type	1 \(\times\) 1019

The modeling approach used in this tutorial is similar to the one used in our previous tutorial on SiGe excitons — “SiGe QW excitonic absorption”. Specifically, the Ge content profile is smoothed with a characteristic diffusion length of 1 nm, and a residual tensile strain of 0.1% is assumed in the strain-relaxed buffer. The electron states are computed with 8-band kp hamiltonian.

In both examples, the quantum_region consists only of 1 well. It is sufficient to model only valence and conduction states in a single quantum well, because the barrier is wide enough, so there is no overlap of wave functions between different wells.

Simulation 1: Only intrinsic region

Solvers:

• strain

• poisson

• quantum

• quantum_optics

Omitting the doped layers, the simulation regions consist of bottom spacer, MQW and top spacer. The built-in potential of the junction has to be included in the simulation. Furthermore, the diffusion of dopants from a buffer and cap layer effectively decreases the intrinsic region. Following [LeverJLT2010], the built-in is assumed to be \(0.8 V\) and the intrinsic region is shortened by \(75 nm\) (i.e. the bottom spacer region used in the simulation is \(25 nm\))

Since Simulation 1 example does not include any doped regions, the current equation is not necessary and can be omitted.

The simulated banedges at zero bias are shown in the figure Figure 2.5.12.99

Figure 2.5.12.99 Valence and conduction band edges at zero bias. The electric field is induced by 0.8V built-in potential, included in the simulation

When additional bias applied, the electric filed in the quantum well is increased (figure Figure 2.5.12.99)

Figure 2.5.12.100 Valence and conduction band edges at 2V external bias.

The absorption spectra computed at different biases is given in the figure

Figure 2.5.12.101 Absorption spectra inside the MQW region at different external bias

Simulation 2: Whole pin device

Solvers:

• strain

• current_poisson

• quantum

• quantum_optics

For a more accurate representation of the electro-optic properties of a complete device, we will consider a more detailed structure consisting of a p-i-n junction with the quantum well embedded in the intrinsic region.

In contrast to the simplified example, the second example involves the inclusion of doped regions in the simulation. This necessitates the use of current equation to model the device behavior.

As discussed above, the diffusion of dopants from the p and n regions to the intrinsic region effectively decreases the width of the intrinsic region, which increases the electric field. In order to model this phenomenon, we use a smoothed doping profile corresponding to the analytical solution of diffusion between two infinite half-spaces with a constant initial concentration \(c_{0}\) in one subspace and zero concentration in the other.

\[c= \frac{c_{0}}{2} + \frac{c_{0}}{2} erf( \pm \frac{x-x_{0}}{d})\]

Here: \(x_{0}\) is junction position, \(d\) is characteristic diffusion length, \(erf\) is error function, plus inside error function is for the case when initial nonzero concentration is at \(x>x_0\) and vice versa.

We find \(d=30 nm\) to give the closest result to experiment. In order to use the diffused doping profile, we initialize doping profile function in import

import{
...
    analytic_function{
        name     = "pdoping_profile"
        function = "$pDopingConcentration*0.5 + $pDopingConcentration*0.5*erf(-(x-$pdoping_junction_position)/$diffusion_dopants_length)"
        }
    analytic_function{
        name     = "ndoping_profile"
        function = "$nDopingConcentration*0.5 + $nDopingConcentration*0.5*erf((x-$ndoping_junction_position)/$diffusion_dopants_length)"
        }
}

These functions are used in structure to initialize doping

impurities{
    donor{
        name = "n-type"
        energy = -1000  # (= all ionized)
        degeneracy = 2  # degeneracy of energy levels, 2 for n-type, 4 for p-type
    }
    acceptor{
        name = "p-type"
        energy = -1000  # (= all ionized)
        degeneracy = 4  # degeneracy of energy levels, 2 for n-type, 4 for p-type
    }
}
...
structure{
...
    region{ # n-doping
        line{
            x = [$x_min, $x_max]
        }
        doping{
            import{
            name = "n-type"
            import_from = "ndoping_profile"
            }
        }

    }

    region{ # p-doping
        line{
            x = [$x_min, $x_max]
        }
        doping{
            import{
                name = "p-type"
                import_from = "pdoping_profile"
            }
        }
    }
...
}

The resulting doping profile is shown in the figure Figure 2.5.12.102.

Figure 2.5.12.102 The doping profile in the device

The band edges at zero bias is shown in the figure Figure 2.5.12.103

Figure 2.5.12.103 Valence and conduction band edges at zero bias

At zero bias there is no current in the system, therefor the electron and hole Fermi levels coincide. At nonzero reverse bias, the current is induced, separating electron and hole Fermi level and enhancing the electric field in the MQW region (see Figure 2.5.12.104).

Figure 2.5.12.104 Valence and conduction band edges at zero bias

The absorption spectra computed in this example are shown in the Figure 2.5.12.105.

Figure 2.5.12.105 Absorption spectra inside the MQW region at different external bias for Simulation 2

The position of exciton peaks are in a good agreement with experiment — within \(3\;meV\) error for each bias. While the relative change of absorption spectra with applied bias also agrees with experimental data, the absolute value differs by a factor \(1.5-1.8\). The nextnano software is continuously improving to meet last criteria as well.

Acknowledgment

This tutorial is based on the nextnano GmbH collaboration in the scope of the SiPho-G Project aiming at development of ultrahigh-speed optical components for next-generation photonic integrated circuits, and it is funded by the European Union’s Horizon 2020 research and innovation program under grant agreement No 101017194.

Last update: nn/nn/nnnn