Browsing by Author "Heremans, Jean Joseph"
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- Benchmarking measurement-based quantum computation on graph statesQin, Zhangjie (Virginia Tech, 2024-08-26)Measurement-based quantum computation is a form of quantum computing that operates on a prepared entangled graph state, typically a cluster state. In this dissertation, we will detail the creation of graph states across various physical platforms using different entangling gates. We will then benchmark the quality of graph states created with error-prone interactions through quantum wire teleportation experiments. By leveraging underlying symmetry, we will design graph states as measurement-based quantum error correction codes to protect against perturbations, such as ZZ crosstalk in quantum wire teleportation. Additionally, we will explore other measurement-based algorithms used for the quantum simulation of time evolution in fermionic systems, using the Kitaev model and the Hubbard model as examples.
- Decoherence of Transverse Electronic Spin Current in Magnetic MetalsLim, Youngmin (Virginia Tech, 2022-05-31)Transport of spin angular momentum (spin currents) in magnetic thin films is important for non-volatile spin-based memory devices and other emerging information technology applications. It is especially important to understand how a spin current propagates across interfaces and how a spin current interacts with magnetic moments. The great interest in devices based on ferromagnetic metals generated intensive theoretical and experimental studies on the basic physics of spin currents for the last few decades. Of particular interest recently is the so-called "pure" electronic spin current, which is carried by electrons and yet unaccompanied by net charge flow, in part because of the prospect of transporting spin with minimal Joule heating. However, in contrast to ferromagnetic metals, spin transport in antiferromagnetic metals, which are promising materials for next-generation magnetic information technology, is not well understood yet. This dissertation addresses the mechanisms of transport by pure spin current in thin-film multilayers incorporating metals with antiferromagnetic order. We focus on two specific materials: (1) CoGd alloys with ferrimagnetic sublattices, which resemble antiferromagnets near the compensation composition, and (2) elemental antiferromagnetic Cr, which can be grown as epitaxial films and hence serve as a model system material. For both the CoGd and Cr studies, spin-valve-like structures of NiFe/Cu/CoGd and NiFe/Cu/Cr/CoFe are prepared to conduct ferromagnetic resonance spin pumping experiments. Precessing magnetization in the NiFe "spin source" pumps a transverse spin current to the adjacent layers. We measure the loss of the spin angular momentum in the "spin sink" layer by measuring the broadening of the resonance linewidth, i.e., the non-local damping enhancement, of the spin source. The antiparallel magnetic moments of Co and Gd sublattices partially cancel out the dephasing of a transverse spin current, thereby resulting in a long spin dephasing length of ≈ 5-6 nm near the magnetic compensation point. We find evidence that the spin current interacts somewhat more strongly with the itinerant transition-metal Co magnetism than the localized rare-earth-metal Gd magnetism in the CoGd alloy. We also examine spin transport via structurally clean antiferromagnetic Cr, epitaxially grown with BCC crystal order. We observe strong spin reflection at the Cu/Cr interface, which is surprising considering that thin layers of Cu and Cr individually are transparent to spin currents carried by electrons. Further, our results indicate other combinations of electrically conductive elemental metals (e.g., Cu/V) can form effective spin-reflecting interfaces. Overall, this thesis advances the basic understanding of spin transport in metallic thin films with and without magnetic order, which can aid the development of next generations of efficient spintronic devices. This work was supported in part by the National Science Foundation, Grant No. DMR-2003914.
- Fabrication and Optoelectronic Characterization of Nanoscale Resonance StructuresRieger Jr, William Theodore (Virginia Tech, 2020-05-07)Resonance structures have long been employed by RF and microwave devices ranging from antennas, to wave guides. These resonance structures have exhibited an enormous amount of control over the wavelength selectivity, polarization, and directivity of the electromagnetic radiation which couples to the structure. Traditional geometrical optics has alternatively used discrete optical components such as lenses, gratings, and polarizers to accomplish equivalent control over optical radiation. This dissertation contributes to the larger body of literature that applies lessons learned in RF and microwave resonance structures, to nanoscale resonance structures. Optoelectronic nanoscale resonance structures were fabricated and characterized using both experimental and numerical methods. Two nanoscale resonance structures were investigated: an antenna inspired Yagi-Uda array, and a metasurface inspired interdigitated structure. Experimental devices containing the nanoscale resonance structures were fabricated on semiconducting substrates forming metal-semiconductor-metal photodiodes. The spectral response of the nanoscale resonance photodiode was determined by measuring the photocurrent or photovoltage resulting from incident monochromatic light which was swept through wavelengths from 400 nm to 2000 nm. The previously mentioned Yagi-Uda based device exhibited two maxima in photoresponse at 1110 nm and 1690 nm. Effective wavelength scaling was applied to the Yagi-Uda nanoantenas, and consistency was demonstrated between the theoretical effective wavelength and experimental photoresponse maxima. The spectral response of the interdigitated structure demonstrated good qualitative agreement with the finite element modeled absorbance in an equivalent structure. Analysis of the modeled absorbance suggests that hot electron injection contributes to the photoresponse, and the spectral response of the detector device may be tuned by varying the geometrical parameters of the device. An optimized device was proposed that could improve photodetection efficiency using nanoscale resonance devices. Antenna inspired nanoscale resonance structures may be used to probe fundamental physical phenomena such as hot carrier generation, hot carrier transport, and surface plasmon resonances. Combined optical and electrical-optoelectronic devices exploiting these phenomena may be realized for a variety of applications, eliminating some or all of the discrete optical components required for optoelectronic systems and hence significantly reducing the SWaP cost of optoelectronic systems.
- Graphene Field-Effect Transistors on p-doped Semiconductors for PhotodetectionJahan, Nusrat (Virginia Tech, 2024-09-10)Recent advancements in photodetection using 2D materials suggest significant improvements in the performance of photodetectors. Among these, graphene field-effect transistors (GFETs) have demonstrated promising enhancements in photodetection, characterized by low noise, broad-spectrum response, high responsivity, and fast response [46, 126]. These photodetectors utilize graphene as the active channel, with graphene deposited on an insulating layer and semiconductor substrate. The contact of graphene with an insulator/semiconductor structure induces an interfacial potential to trap one type of photo-generated carrier at the interface. The trapped charge carriers induce opposite carriers in the graphene channel through the capacitive coupling effect. Due to a long lifetime of trapped carriers, the induced carriers in the graphene channel circulate multiple times under a given bias between the source and drain contacts, generating a photocurrent with high gain. Here, we explore GFET photodetectors fabricated on p-GaAs and p-Si wafers at room temperature. The photodetectors achieve a high gain. The photocurrent is generated due to the photogating effect. In this work, we explore GFET photodetectors fabricated on p-GaAs and p-Si wafers at room temperature. The photodetectors achieve a high gain and high responsivity of 106 (A/W) under the above bandgap excitation and can detect light below the bandgap illumination for both p-doped substrates. NEP and D* values of these detectors have been characterized along with response time characteristics. The NEP and D∗ values for both detectors are around 10−15 W/√ and 1012 Jones respectively, indicating a sensitive photodetection. The response time characterization suggests the rise and decay time depends on incident power. These results provide us with a deeper insight into the photodetection of the GFETs from the ultraviolet to near-infrared region.
- High Performance Broadband Photodetectors Based on Graphene/Semiconductor HeterostructuresWang, Yifei (Virginia Tech, 2022-04-15)Graphene, a monolayer of carbon atoms, has gained prominence to augment existing chip-scale photonic and optoelectronic applications, especially for sensing in optical radiation, owing to its distinctive electrical properties and bandgap as well as its atomically thin profile. As a building block of photodetection, graphene has been co-integrated with mature silicon technology to realize the on-chip, high-performance photo-detecting platforms with broad spectral response from the deep-ultraviolet (UV) to the mid-infrared (MIR) regime. The recent state-of-the-art graphene-based photodetectors utilizing the combination of colloidal quantum dots (QDs) and graphene have been intensively studied, where QDs function as the absorber and the role of graphene is as a fast carrier recirculating channel. With such a configuration, an ultrahigh sensitivity can be achieved on account of the photogating mechanism; however, the response time is slow and limited to the millisecond-to-second range. To achieve balance between high sensitivity and fast response time, we have demonstrated a new photodetector that is based on graphene/two-dimensional heterostructures. The homogeneous thickness and the large contact of the heterostructure give rise to fast carrier transporting between the thin absorber layer and the graphene, leading to a fast response time. This thesis carefully investigates the optimization of fabrication as well as optoelectronic characterization of photodetectors based on graphene/semiconductor heterostructures field-effect transistors (GFETs). GFETs with different architectures were demonstrated and systematically studied under optical illumination ranging from deep-UV to MIR at varying optical powers. Noise behaviors have been studied under different device parameters such as device structure, area and gate-bias. Results show that the flicker noise of graphene-based devices can be explained by the McWhorter model in which the fluctuation of carrier numbers is the dominant process of noise in low frequencies; thus, it can be scaled down by reducing the number of introduced charged carriers with optimized fabrication. Besides, the impact of absorber on top of graphene and the bottom substrate has been comprehensively explored through various experimental techniques including current-voltage (IV), photo-response dynamics, and noise characterization measurements. With our configuration, the high sensitivity and fast response time of photodetectors can be obtained at the same time. In addition to this, the study of the bottom substrate with different doping levels suggests a concept of dual-photogating effect which is induced by the top absorbent material and the photoionization of the doped silicon substrate. In summary, this thesis showcases novel device architecture and fabrication procedures of GFETs photodetectors, optimizes device structure, quantifies the performance and evaluates the effect of various absorbent materials and substrate. It provides insight into the improvement of possible routes to achieve a broadband photo-detecting system with higher sensitivity, faster response time and lower noise level.
- Hydrodynamic and ballistic transport in high-mobility GaAs/AlGaAs heterostructuresGupta, Adbhut (Virginia Tech, 2021-09-24)The understanding and study of electron transport in semiconductor systems has been the instigation behind the growth of semiconductor electronics industry which has enabled technological developments that are part of our everyday lives. However, most materials exhibit diffusive electron transport where electrons scatter off disorder (impurities, phonons, defects, etc.) inevitably present in the system, and lose their momentum. Advances in material science have led to the discovery of materials which are essentially disorder-free and exhibit exceptionally high mobilities, enabling transport physics beyond diffusive transport. In this work, we explore non-diffusive transport regimes, namely, the ballistic and hydrodynamic regimes in a high-mobility two-dimensional electron system in a GaAs quantum well in a GaAs/AlGaAs heterostructure. The hydrodynamic regime exhibits collective fluid-like behavior of electrons which leads to the formation of current vortices, attributable to the dominance of electron-electron interactions in this regime. The ballistic regime occurs at low temperatures, where electron-electron interactions are weak, constraining the electrons to scatter predominantly against the device boundaries. To study these non-diffusive regimes, we fabricate mesoscopic devices with multiple point contacts on the heterostructure, and perform variable-temperature (4.1 K to 40 K) zero-field nonlocal resistance measurements at various locations in the device to map the movement of electrons. The experiments, along with interpretation using kinetic simulations, demarcate hydrodynamic and ballistic regimes and establish the dominant role of electron-electron interactions in the hydrodynamic regime. To further understand the role of electron-electron interactions, we perform nonlocal resistance measurements in the presence of magnetic field in transverse magnetic focusing geometries under variable temperature (0.39 K to 36 K). Using our experimental results and insights from the kinetic simulations, we quantify electron-electron scattering length, while also highlighting the importance of electron-electron interactions even in ballistic transport. At a more fundamental level, we reveal the presence of current vortices in both hydrodynamic and surprisingly, ballistic regimes both in the presence and absence of magnetic field. We demonstrate that even the ballistic regime can manifest negative nonlocal resistances which should not be considered as the hallmark signature of hydrodynamic regime. The work sheds a new light on both hydrodynamic and ballistic transport in high-mobility solid-state systems, highlighting the similarities between these non-diffusive regimes and at the same time providing a way of effectively demarcating them using innovative device design, measurement schemes and one-to-one modeling. The similarities stem from total electron system momentum conservation in both the hydrodynamic and ballistic regimes. The work also presents a sensitive and precise experimental technique for measuring electron-electron scattering length, which is a fundamental quantity in solid-state physics.
- Nonlocal ballistic and hydrodynamic transport in two-dimensional electron systemsKataria, Gitansh (Virginia Tech, 2023-07-12)Electrical transport in materials is typically diffusive, due to dominant momentum-relaxing scattering of carriers with the phonons or defects. In ultraclean material systems such as GaAs/AlGaAs or graphene/hBN heterostructures, momentum-relaxing can be suppressed, leading to the onset of non-diffusive transport regimes, where Ohm's law is no longer valid. Within these non-diffusive regimes, the hydrodynamic regime occurs when momentum-conserving electron-electron scattering length scale is smaller than the device length scale (usually at intermediate temperatures). On the other hand, weak electron-electron scattering (at low temperatures) results in ballistic transport, commonly understood using the familiar single-particle framework of injected carriers travelling in straight line trajectories with intermittent reflections off device boundaries. Both the ballistic and hydrodynamic regimes can exhibit a emph{negative} nonlocal resistance, and collective behaviour such as the formation of current vortices. In this work, we study nonlocal current-voltage characteristics in mesoscopic devices fabricated from a GaAs/AlGaAs heterostructure that hosts a two-dimensional electron system in a GaAs quantum well. First, we report a quadratic non-linearity in the nonlocal current-voltage characteristics that manifests in any device where a nonlocal voltage measurement is possible. Using measurements at low temperatures ($sim$ 4 K) across multiple devices and considering various contact configurations for each device, we show that the non-linearity is universal. We apply the non-linearity to rectification and frequency multiplication. We also report on a periodic peaks in the nonlocal voltage vs. magnetic field, in an enclosed mesoscopic geometry in which transverse magnetic focusing (TMF) is typically studied. These peaks occur at weak magnetic fields, are independent of the source-detector separation and are distinct from TMF. Our experimental findings are backed by an extensive set of simulations using in both the semiclassical as well as quantum-coherent transport models.
- Optimal Control Protocols for Quantum Memory Network ApplicationsTakou, Evangelia (Virginia Tech, 2024-06-25)Quantum networks play an indispensable role in quantum information tasks such as secure communications, enhanced quantum sensing, and distributed computing. In recent years several platforms are being developed for such tasks, witnessing breakthrough technological advancement in terms of fabrication techniques, precise control methods, and information transfer. Among the most mature and promising platforms are color centers in solids. These systems provide an optically active electronic spin and long-lived nuclear spins for information storage. The first part of this dissertation is concerned with error mechanisms in the control of electronic and nuclear spins. First, I will focus on control protocols for improved electron-spin rotations tailored to specific color centers in diamond. I will then discuss how to manipulate the entanglement between the electron and the always-coupled nuclear spin register. I will describe a general formalism to quantify and control the generation of en- tanglement in an arbitrarily large nuclear spin register. This formalism incorporates exactly the dynamics with unwanted nuclei, and quantifies the performance of entangling gates in the presence of unwanted residual entanglement links. Using experimental parameters from a well-characterized multinuclear spin register, I will show that preparation of multipartite entanglement in a single-shot is possible, which drastically reduces the total gate time of conventional protocols. Then, I will present a new formalism for describing all-way entanglement and show how to design gates that prepare GHZM states. I will show how to incorporate errors such as unwanted correlations, electronic dephasing errors or pulse control errors. The second part of this thesis focuses on the preparation of all-photonic graph states from a few quantum emitters. I will introduce heuristic algorithms that exploit graph theory concepts in order to reduce the entangling gate counts, and also discuss the role of locally equivalent graphs in the optimization of the generation circuits.
- STM Study of 2D Metal Chalcogenides and HeterostructuresZhang, Fan (Virginia Tech, 2022-01-31)In recent years, two-dimensional (2D) van der Waals (vdW) materials have aroused much interest for their unique structural, thermal, optical, and electronic properties and have become a hot topic in condensed matter physics and material science. Many research methods, including scanning tunneling microscopy (STM), transmission electron microscopy (TEM), optical and transport measurements, have been used to investigate these unique properties. Among them, STM stands out as a powerful characterization tool with atomic resolution and is capable of simultaneously revealing both atomic structures and local electronic properties. This dissertation focuses on scanning tunneling microscopy and spectroscopy (STM/S) investigation of 2D metal chalcogenides and heterostructures. The first part of the dissertation focuses on the continuous interface in WS2/MoS2 heterostructures grown by the chemical vapor deposition (CVD) method. We observed a closed interface between the MoS2 monolayer and the heterobilayer with atomic resolution. Furthermore, our scanning tunneling spectroscopy (STS) results and density functional theory (DFT) calculations revealed band gaps of the heterobilayer and the MoS2 monolayer agree with previously reported values for MoS2 monolayer and MoS2/WS2 heterobilayer on SiO2 fabricated through the mechanical exfoliation method. The results could deepen our understanding of the growth mechanism, interlayer interactions and electronic structures of 2D transition metal dichalcogenides (TMD) heterostructures synthesized via CVD. The second part of the dissertation focuses on phase transformation in 2D In2Se3. We observed that 2D In2Se3 layers with thickness ranging from single to ~20 layers stabilized at the beta phase with a superstructure at room temperature. After cooling down to around 180 K, the beta phase converted to a more stable beta' phase that was distinct from previously reported phases in 2D In2Se3. The kinetics of the reversible thermally driven beta-to-beta' phase transformation was investigated by temperature dependent transmission electron microscopy and Raman spectroscopy, combined with the expected minimum-energy pathways obtained from our first-principles calculations. Furthermore, DFT calculations reveal in-plane ferroelectricity in the beta' phase. STS measurements show that the indirect bandgap of monolayer beta' In2Se3 is 2.50 eV, which is larger than that of the multilayer form with a measured value of 2.05 eV. Our results on the reversible thermally driven phase transformation in 2D In2Se3 will provide insights to tune the functionalities of 2D In2Se3 and other emerging 2D ferroelectric materials and shed light on their numerous potential applications like non-volatile memory devices. The third part of the dissertation focuses on domain boundaries in 2D ferroelectric In2Se3. The atomic structure of domain boundaries in two-dimensional (2D) ferroelectric beta' In2Se3 is visualized with scanning tunneling microscopy and spectroscopy (STM/S) combined with DFT calculations. A double-barrier energy potential across the 60° tail to tail domain boundaries in monolayer beta' In2Se3 is also revealed. The results will deepen our understanding of domain boundaries in 2D ferroelectric materials and stimulate innovative applications of these materials.
- Taking Steps Towards Superfluid-like Spin Transport in Metallic FerromagnetsSmith, David Acoya (Virginia Tech, 2022-05-12)Conventional electronics rely on the transport of electrons through a circuit to carry information. This comes with ever-present Joule heating as a result of the resistive scattering of electrons. Recent works in the field of spintronics have focused on using magnetic excitations (e.g., spin waves) instead of electrons as a means of information transport without Joule heating. However, realizing long distance information transport using conventional spin waves has proven difficult owing to their diffusive nature and the exponential decay of spin current. Theoretical studies have proposed a new form of magnetization dynamics, referred to as superfluid-like spin transport, as a way to overcome this shortfall. Instead of decaying exponentially with distance, the spin current associated with superfluid-like spin transport decays linearly with distance, potentially allowing for information transport beyond the micron-scale. In this dissertation, I discuss the work that I have done towards realizing this novel phenomenon in a metallic, ferromagnetic system. Results on a reduced damping and reduced magnetic moment Fe-based alloy, micromagnetic simulations that use established domain wall physics to explain superfluid-like spin transport, and an investigation of spin torques found in a current-in-plane spin valve structure with broken in-plane symmetry for excitation of superfluid-like spin transport dynamics are discussed. I conclude by discussing what steps remain before superfluid-like spin transport can be measured in an experimental system as well as the impacts this work could have on the wider spintronics field. This work was supported in part by National Science Foundation, Grant No. DMR-2003914.
- Tensile-Strained Ge/III-V Heterostructures for Low-Power Nanoelectronic DevicesClavel, Michael Brian (Virginia Tech, 2024-02-12)The aggressive reduction of feature size in silicon (Si)-based complimentary metal-oxide-semiconductor (CMOS) technology has resulted in an exponential increase in computing power. Stemming from increases in device density and substantial progress in materials science and transistor design, the integrated circuit has seen continual performance improvements and simultaneous reductions in operating power (VDD). Nevertheless, existing Si-based metal-oxide-semiconductor field-effect transistors (MOSFETs) are rapidly approaching the physical limits of their scaling potential. New material innovations, such as binary group IV or ternary III-V compound semiconductors, and novel device architectures, such as the tunnel field-effect transistor (TFET), are projected to continue transistor miniaturization beyond the Si CMOS era. Unlike conventional MOSFET technology, TFETs operate on the band-to-band tunneling injection of carriers from source to channel, thereby resulting in steep switching characteristics. Furthermore, narrow bandgap semiconductors, such as germanium (Ge) and InxGa1-xAs, enhance the ON-state current and improve the switching behavior of TFET devices, thus making these materials attractive candidates for further study. Moreover, epitaxial growth of Ge on InxGa1-xAs results in tensile stress (ε) within the Ge thin-film, thereby giving device engineers the ability to tune its material properties (e.g., mobility, bandgap) via strain engineering and in so doing enhance device performance. For these reasons, this research systematically investigates the material, optical, electronic transport, and heterointerfacial properties of ε-Ge/InxGa1-xAs heterostructures grown on GaAs and Si substrates. Additionally, the influence of strain on MOS interfaces with Ge is examined, with specific application toward low-defect density ε-Ge MOS device design. Finally, vertical ε-Ge/InxGa1-xAs tunneling junctions are fabricated and characterized for the first time, demonstrating their viability for the continued development of next-generation low-power nanoelectronic devices utilizing the Ge/InxGa1-xAs material system.
- Theoretical Modeling of Polymeric and Biological Nanostructured MaterialsRahmaninejad, Hadi (Virginia Tech, 2023-02-23)Polymer coatings on periodic nanostructures have facilitated advanced applications in various fields. The performance of these structures is intimately linked to their nanoscale characteristics. Smart polymer coatings responsive to environmental stimuli such as temperature, pH level, and ionic strength have found important uses in these applications. Therefore, to optimize their performance and improve their design, precise characterization techniques are essential for understanding the nanoscale properties of polymer coating, especially in response to stimuli and interactions with the surrounding medium. Due to their layered compositions, applying non-destructive measurement methods by X-ray/neutron scattering is optimal. These approaches offer unique insights into the structure, dynamics, and kinetics of polymeric coatings and interfaces. The caveat is that scattering methods require non-trivial data modeling, particularly in the case of periodic structures, which result in strong correlations between scattered beams. The dynamical theory (DT) model offers an exact model for interpreting off-specular signals from periodically structured surfaces and has been validated on substrates measured by neutron scattering. In this dissertation, we improved the model using a computational optimization approach that simultaneously fits specular and off-specular scattering signals and efficiently retrieves the three-dimensional sample profile with high precision. In addition, we extended this to the case of X-ray scattering. We applied this approach to characterize polymer brushes for nanofluidic applications and protein binding to modulated lipid membranes. This approach opens new possibilities in developing soft matter nanostructured substrates with desired properties for various applications.
- Theory of Operating Characteristics of Quantum Dot Lasers with Asymmetric Barrier LayersHammack, Cody Wade (Virginia Tech, 2023-06-27)In this work, the operating characteristics of quantum dot (QD) lasers with asymmetric barrier layers (ABLs) are studied. Several different cases are examined, in particular: 1) Effect of excited states on static and dynamic operating characteristics Within QDs, in addition to the lasing ground state, carriers can be captured into excited states, where they then decay into the ground state. This excited-state-mediated capture impacts the operating characteristics, limiting the maximum output power and modulation bandwidth. Three separate cases are considered: only indirect capture with electron-hole symmetry, both direct and indirect capture with electron-hole symmetry, and both direct and indirect capture of electrons but only indirect capture of holes. The impact of different parameters on the operating characteristics is studied, with values for maximizing the output power and modulation bandwidth being found. In addition, it is found that parasitic recombination in the active region in the space between QDs causes the output power to saturate at high injection currents for the cases of indirect capture for both electrons and holes and indirect capture for holes but direct and indirect capture for electrons, although the presence of the ABLs causes it to reach saturation at much lower currents. 2) QD laser with only a single ABL To be effective, the materials for ABLs must be carefully chosen to ensure that the band edges properly align to allow one carrier to enter the active region while preventing the other from overshooting it. Due to this requirement, it may arise that a suitable material only exists for one ABL but not the other. The performance of a QD laser with only a single ABL is considered and compared to a conventional QD laser. Specifically, the output power and characteristic temperature are calculated. While the single ABL laser only offers a negligible increase in output power compared to the conventional laser, it offers a considerable increase in characteristic temperature. 3) Analytical derivation of alpha factor in QD lasers with and without ABLs The alpha factor of a semiconductor laser describes the spectral linewidth broadening that occurs in semiconductor lasers due to changes in the refractive index due to the carrier density. While it has been studied experimentally, there has been little work done on deriving the alpha factor of QD lasers analytically. An expression for the alpha factor is found in this work using the real and imaginary parts of the complex susceptibility. For QD lasers with no inhomogeneous broadening, as well as ones with equilibrium filling of QDs with narrow line of QD size distribution, the alpha factor is independent of carrier density, and is therefore the same for any QD lasers, with or without ABLs. For QD lasers with equilibrium filling without a narrow line of QD size distribution, the alpha factor depends on carrier density, allowing for a potential difference between conventional and ABL QD lasers, however the difference between the two will be lessened.