Design and study of a GeSn-SiGeSn single quantum well structure for infrared photodetection

Quantum well infrared photodetectors (QWIPs) offer excellent performance and have many commercial and military applications. Until now, most of the QWIPs are based on stacked InGaAs/AlGaAs and GaAs/AlGaAs multi-quantum wells. Recently, tin (Sn) based group-IV material system has attracted research attention due to the direct band gap that can be achieved for some composition of Sn. The heterodevices from those materials can overcome limitations imposed by the indirect band gap of Si and Ge. The direct band gap of Sn-based group-IV was predicted in 1991 by Soref [1]. Based on this prediction, high quality strain-relaxed buffer layers of GeSn and SiGeSn have been grown on a Silicon substrate in last decade [2]. So, some optoelectronic devices such as semiconductor lasers [3] and optical modulators [4] have been proposed and designed based on Ge
_z
Sn
_1-z
and Si
_x
Ge
_y
Sn
_1-x-y
nanostructures. In this work, the direct band gap Ge
_0.83
Sn
_0.17
/Si
_0.09
Ge
_0.8
Sn
_0.11
single quantum well (SQW) structure has been analytically simulated and proposed to develop quantum well photodetector at mid-infrared region. Using solid-model and effective mass theories, potential profile and subband energies of Ge
_0.83
Sn
_0.17
quantum well were determined, respectively. In these calculations, the strain-balanced condition was considered for layers. The achieved results showed that the proposed nanostructure has type-I quantum well structure which both electrons and holes are confined in the well. The relevance of a detector that is tuned to that wavelength is that can be used for gas detection of a hydrocarbon gas via infrared absorption. For analytical simulation, we adopted the model-solid theory to estimate the band alignment [4], and the effective mass theory to obtain the various subband energies and wave functions [6] for the Ge
_z
Sn
_1-z
/Si
_x
Ge
_y
Sn
_1-x-y
single quantum well. Previous to this, most parameters for the Ge
_z
Sn
_1-z
and Si
_x
Ge
_y
Sn
_1-x-y
material systems were obtained from linear interpolations among those of Si, Ge, and α-Sn. Table 1 shows the parameters that have been used in drawing the band structure of quantum well structure using interpolation formula. Figure 1 shows the band structure and the confined states for a 10 nm Ge
_0.83
Sn
_0.17
QW with Si
_0.09
Ge
_0.8
Sn
_0.11
barriers in the absence of an electric field. According to the band alignment calculation, both the conduction band minimum and valence band maximum are located in the well region. So, this Ge
_0.83
Sn
_0.17
/Si
_0.09
Ge
_0.8
Sn
_0.11
SQW has an important type-I alignment for the necessary interband optical transitions. From the effective mass theory calculation, the transition energy between the first states of electron (C1) and heavy hole (HH
₁
) is 386 meV (3.21 μm) and with light holes (LH
₁
) is 413 meV (3.0 μm). Mostly, the C
₁
-HH
₁
transition is more probable in interband transition in quantum wells. Figure 2 shows the direct and indirect band gap (L and Γ valley) of unstrained Ge
_x
Sn
_1-x
alloys as a function of Sn concentration, which. It can be seen that for the Sn concentration about more than 10%, the band gap of Ge
_z
Sn
_1-z
changed to direct. Finally, we have demonstrated analytically a direct band gap Ge
_0.83
Sn
_0.17
/Si
_0.09
Ge
_0.8
Sn
_0.11
single quantum well structure that could be used in the quantum well infrared photodetector. In the proposed nanostructure, the transition energy between the first states of electron and heavy hole is about 386 meV that corresponds to wavelength 3.2 μm in infrared region.