# Gain of TlBr/BrCl Quantum Dot Semiconductor Optical Amplifier

Authors: Baqer O. Al-Nashy; Buraq T. Sh. Al-Mosawi; Mushtaq Obaid Oleiwi; Amin H. Al-Khursan
Journal: Journal of Electrical and Computer Engineering
 (2023)

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## Abstract

This work studies the thallium halogenide TlBr/BrCl quantum dot (QD) semiconductor structure and specifies its optical properties. This QD structure is poorly studied. High gain is obtained, with two peaks at800 and 3000nm. Doping is shown to increase the gain by one order. Then, TlBr QD semiconductor optical amplifier (SOA) characteristics are studied. High dB gain is shown mainly at the doped structure, which can be used in various inline applications.


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## Body

## 1. Introduction

The superior characteristics of quantum dot semiconductor optical amplifiers (QDSOAs), such as high gain, ultrafast (picosecond) recovery time, wide bandwidth, low noise figure, and polarization-insensitive makes the quantum dots (QDs) in the milestone of today’s all-optical applications [1, 2]. These merits result from the complete quantization of QD and discrete energy states [3]. Other types of semiconductor optical amplifier (SOA), such as multiquantum-well SOA, vertical cavity SOA, and distributed feedback SOA, possess a lower recovery time than QDSOA due to their carrier lifetime. Their signal processing is limited to 40 Gbps, which is very low compared to the 160 Gbps of QDSOAs [4].Thallium bromide (TlBr) is a promising candidate with a highly efficient wide bandgap (2.68 eV) and strong ionic-binding semiconductor material. Their band structure is near the lead chalcogenides, not the alkali halides, as they have two more s-valence-electrons than the band structure of the filled shell of the rare gases. They are expected to work above room temperature due to their high atomic numbers (Br: 35 and Tl: 81) and high density7.56gm/cm3 [5–10]. Their simple cubic lattice (CsCI structure) gives a simple electronic structure and optical spectra, different from other halides with anisotropic structures [11].Mir et al. [12] prepared TlBr nanocrystals that suppress the defects compared to other wide-bandgap semiconductors >2.5eV. They exhibit high photoluminescence efficiency, which results from their high carrier mobility and long diffusion length. The work in our laboratory on thallium-based quantum dot (QD) structures began after investigating the well-known III–V semiconductor structures. First, it starts with InTlSb QD structures [13], InTlAsSb QDs [14], then TlGaN QDs [15], and finally, InTlSb, InTlP, InTlAs, and InTlN QDs are studied [16]. As the III–VII semiconductors are poorly studied, this work studied the thallium halogenide TlBr QD structure, which is not poorly studied. Then, the structure is examined as a semiconductor optical amplifier characteristics, with high gain obtained, mainly at a doped structure.


## 2. Inhomogeneous Gain

An inhomogeneous density of states function describes the broadening functionD (E) to cover the QD fluctuations in size and shape during the self-organization growth mode. This function locates the theory similarly to the experiment. Then, the optical linear gain per QD layer of the self-organized QDs is given by [17](1)gtrℏw=C0∑i∫dEMenv2e^.p⟶cv2DELgE,ℏwfcEc,Fc−fvEv,Fv.Note thati runs over the conduction and valence QD energy sub-bands considering all the radiative transition energies. Menv is the envelope function between the QD energy sub-bands of the electron and hole. e^.p⟶cv is the momentum matrix element of the QD that depends on the polarization of light and e^ is a unit vector along the polarization direction. Regarding the parabolic shape of bands, the QDs momentum matrices are the same as those of the quantum well near the zone center (kt = 0). They are expressed as e^.p⟶cv2=3/2Mb2 for the heavy hole band, with Mb2=Epm0/6 is the bulk momentum matrix element and Ep is the parameter of the optical matrix energy and is given by [17](2)Ep=m0me−1Eg.Eg+∆0Eg+3/2∆0,where m0,me are the free and effective electron masses, respectively; Eg is the QD bandgap energy and ∆0 spin-orbit splitting energy. In equation (1)(3)C0=πe2nbcε0m02w,where e is the electron charge, w is the angular optical frequency, nb is the background refractive index of the QD material, c is the free space light speed, and ε0 is the permittivity of the free space. The self-assembled QDs density of states, including the inhomogeneous broadening, is defined by [18](4)DE=siVdoteff12πσ2exp−E−Emaxi22σ2.Here,si is the degeneracy degree at each QD energy sub-band. In this model, si = 2 for the QD ground sub-band energy and si = 4 for the QD excited sub-band energy. Considering NQ is the surface density of QDs, and h is the average height of QDs. The QDs effective volume Vdoteff is defined as Vdoteff=h/NQ. In equation (4), Emaxi is the peak optical transition energy in the QD distribution, and σ is the spectral variance of the QD distribution. The quasi-Fermi distribution functions in the respective conduction and valence bands are represented by fc and fv. The Lorentzian function of line shape for the gain spectrum is defined by [17](5)LE,ℏw=ℏγcv/πE´−ℏw2+ℏγcv2.Withγcv is the interband relaxation. The QDs have a quantum disk shape, and the QD energy sub-bands are calculated using the quantum disk model. This model is described well in [17] and compared with the experiment [19].


## 3. Gain of TlBr QD Structure

The data used in the calculations are listed in Table1.Table 1
The parameters used in the calculations [20, 21].
ParametersTlBrBrClEnergy gap (eV)2.683.4Electron effective mass (m0)0.20.3Hole effective mass (m0)0.40.5Dielectric constant35.137.6The TlBr/BrCl QD structure is studied, where the TlBr is taken as the QDs and BrCl as the substrate. Of course, the substrate is chosen from a material of bandgap higher than the QD active region and of crystal structure similar to that of the active region to get lattice matching [22].Figure1 shows the gain spectrum of TlBr/BrCl QD with high gain. Two peaks appear; the first is near 800nm while the second is at 3000nm. These two peaks come from the first excited and ground state transitions, respectively. The first excited state transition occurs when the ground state is fully occupied, and thus, the ground state peak becomes lower than the excited. Such a result for QDs is assigned earlier [23].Figure 1
TlBr/BrCl QD gain at different carrier densities.Figure2 shows the gain spectrum for doped TlBr/BrCl QD structure where the gain is increased by one order under doping. While the increment in the ground state transition curves with doping is similar to those in the undoped curves, Figure 1, all the excited state curves are increased by a higher ratio than the undoped ones, as shown in the first peak on the left.Figure 2
The doped TlBr/BrCl QD gain at different carrier densities.The polarization phenomenon is a result of the applied fields on the TlBr. It screens the external electric field, reducing the efficiency. In addition to increasing gain, as shown here, the acceptor dopants can suppress the polarization phenomenon via binding charged vacancies and render them immobile. The acceptors used for the TlBr dopant can be Se or S. Acceptor doping in TlBr is also possible with Te [24, 25].


## 4. TlBr QD Amplifier

The rate equations are used to study the amplification characteristics of the TlBr QD structure. The dynamical system studied is shown in Figure3. In this case, the current is injected at a density J on the wetting layer (WL). The WL is a layer where the QDs are grown on it. It is in the form of the quantum well layer with only one quantized dimension. The carriers are then relaxed from WL to ES at a rate 1/τw2 and a part of these carriers can be spontaneously radiative with a rate of 1/τw2R. From the QD ES, the carriers can escape to the WL at a rate 1/τ2w. Then, the dynamics in this system can be described by the following rate equations [26](6)∂Nw∂t=JeLw−Nw1−hτw2+Nwhτ2w−Nwτw2R,∂h∂t=NwLw1−hNQτw2−NwLwhNQτ2w−1−fhτ21+f1−hτ12,∂f∂t=1−hfτ21−f1−hτ12−f2τ1R−gmaxLNQ2f−1SavcngΓ,where f and h are the ground state (GS) and excited state (ES) electron occupation probability in the QD, Nw is the WL carrier density, e is the electronic charge, t is the time, Lw is the effective thickness of the active layer, L is the SOA length, Γ is the confinement factor, gmax is the maximum optical gain, and Sav is the average density of photons [27](7)Sav=pinngℏwpAc.Figure 3
Schematic diagram of the energy band of TlBr QD.pin is the power of the input signal, gs single-pass gain, and ℏwp is the energy of the signal at the peak, A is the active region area, and c is the velocity of light in free space.


## 5. Amplifier Characteristics of TlBr QD

The optical confinement factor is defined asΓ=ζΓz with Γz is the vertical direction confinement factor and the area coverage is ζ, and its value is ζ=0.02, which corresponds to the QD density NQ that used here while Γz=0.7% [23].Figure4 shows the gain in the units of (dB) as a function of the input power for the TlBr QDSOA and doped-TlBr QDSOA. The times and SOA parameters are listed in Table 2. It is shown that the doped SOA outperforms the undoped one and can be used for inline applications. The obtained gain is higher than the counterpart InGaAs [26] and InGaSb [28] QDSOAs. Figure 5(a) shows the WL carrier density time series, and Figure 5(b) shows the time series of GS and ES of this QD structure. They show that the TlBr QD structure is at the lasing case, as shown from the red curve of GS in Figure 5(b).Figure 4
Gain (dB) versus input power (dBm) for doped (red) and undoped (blue) TlBr/BrCl QDs.Table 2
QD-SOA parameters used in the calculations [27].
ParametersValuesUnitsτw23psτ2w1nsτw2R1nsNQ3×1010cm−2τ210.16psτ121.2psτ1R0.4nsL2000μmd800μmLw0.2μmJ2.033kA/cm2Figure 5
Times series of (a) WL carrier density and (b) QD occupation of GS (red curve) and ES (blue curve).
(a)(b)


## 6. Conclusions

The thallium halogenide TlBr/BrCl quantum dot (QD) is examined in this work. A high gain with two peaks at800 and 3000nm is obtained. Doping is shown to increase the gain by one order. The peaks result from the ground state saturation, allowing the excited state transition. Examining TlBr QDSOA shows high dB gain and promises in various applications.



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