Quantum Dots:
Quantum Dots (QDs) are nanostructures that confine the charge carriers in three spatial dimensions leading to discrete energy levels. Typically a low bandgap semiconductor is embedded in a high bandgap semiconductor matrix to realize a QD. Figure 1 shows a single QD on left with band edges of the conduction band (CB) and valence band (VB) on the right.
Figure 1: Single QD with band edges
Due to the quantum confinement effects, the energy levels of the heavy hole (Ehh) and electron (Ee) are lifted relative to the bulk band edges. Since the heavy hole level is the lowest in VB only Ehh is considered.
In general, the quantization effects occur only when the dimensions of the confining region is comparable to de Broglie’s wavelength (λDB). In semiconductors, λDB depends on effective mass m* and temperature λDB = ℎ /√(3𝑚*𝑘𝐵𝑇) where h is the Planck's constant and KB is the Boltzmann’s constant. In semiconductors, the effective masses of electron and hole are smaller than the free electron mass m0. For example m* e, GaAs =0.067m0 and m*hh, GaAs =0.5m0. This smaller effective mass makes the de Broglie wavelength on the order of 10-100 nm at low temperatures. The quantization is responsible for the discrete energy levels in the QD. Figure 2 shows the change of density of states (DOS) with confinement in one, two, and three dimensions compared to bulk DOS.
Figure 2: The density of states as a function of energy for the bulk and different low-dimensional semiconductor systems: quantum well, quantum wire, and quantum dot.
When the electron and hole are confined in the QD, the Coulomb attraction binds them forming a quasiparticle i.e. Exciton. The annihilation of exciton by electron-hole recombination provides a single-photon emission. Due to the quantization of the energy levels, the exciton recombination in a QD produces a sharp line in emission spectra, similar to atoms, that’s why QDs are often referred to as artificial atoms. The properties of QDs are strongly influenced by QD size, shape, and composition, as well as the matrix material properties. QDs have many advantages over real atoms for potential applications. The properties of the QD can be tuned carefully by adjusting its structure and composition. The matrix in which QDs are embedded can further be functionalized using modern semiconductor processing techniques. This makes it possible to employ QDs in potential real-world applications such as semiconductor light sources i.e. lasers[1], quantum light-emitting diodes[2], single and entangled photon emitters[2], infrared photodetectors[3], solar cells[4], flash memories[5],.etc. III-V semiconductor quantum dots were most widely investigated in the last two decades due to their interesting optoelectronic properties. The III-V QDs can be easily grow in Stranski-Krastanov (SK) growth mode by molecular beam epitaxy (MBE) or metal-organic vapor phase epitaxy(MOVPE) by utilizing the strain arising from lattice mismatch. The difference in the lattice constant of the substrate and epitaxially grown layers increases the strain in the system and after reaching a critical strain, the QDs are formed as a part of strain relaxation in the system. The schematic of the SK-growth is given in Figure 3. InAs QDs in GaAs were most widely studied and optimized for various optoelectronic applications. Other III-V QD systems include InGaAs/GaAs, GaSb/GaAs, InAs/InP, InGaSb/GaAs/GaP,.etc.
Figure 3: Illustration of SK-growth of QDs. Taken from [6]
However, there is limited control over the size, shape, and composition of the QDs grown in SK-mode. There some limitations such as Indium segregation, alloy intermixing, the collapse of the QDs after capping,.etc. Many solutions were provided to optimize the QDs for better optical quality including new growth techniques such as submonolayer growth and droplet epitaxy. Droplet epitaxy (DE) was first introduced by Koguchi[7] and has attracted a lot of research interest as it can have better control over the growth of QDs and the fabrication of high-quality QDs for various optoelectronic applications including quantum technology were reported in the literature. The inhomogeneities in the size and composition of the QDs were greatly reduced by DE[8]. Droplet epitaxy involves the formation of droplets of group III element and crystallizing these droplets in group V environment to obtain the QDs. The size and composition of the quantum dots can be controlled by controlling the molar flow, substrate temperature, and crystallization conditions[9]
Figure 4: Illustration of droplet epitaxy. Taken from[9]
In general, Atomic Force Microscopy and Scanning tunneling microscopy are employed o characterize the as grown dots to determine the size, shape, density, and maybe composition. Since most of the QDs must be embedded in a matrix for real-world applications, the change in shape and size of the QDs after capping is inevitable. Therefore, techniques such as Cross-sectional scanning tunneling microscopy (X-STM), X-TEM, or Atom probe tomography are necessary to determine the final structure of the QDs after capping. X-STM is a wonderful technique to unveil the structure of buried quantum dots[10]– [13]. X-STM is similar to STM in the working principle only difference is the cleaving of the sample. III-V semiconductors have a zincblende crystal structures in which {110} are the natural cleaving planes producing atomically flat surfaces. W-tips made by electrochemical etching will be used to probe the surface. When the tip is brought close to the surface, the electrons tunnel from tip to sample or sample tip ( Quantum Tunneling effect) depending on the bias voltage. The tunneling current produced decreases exponentially with the distance between the tip and sample. Under correct operating conditions, the surface is studied with extreme atomic resolution revealing the final structure of the QDs after capping. The atomic resolution X-STM images can be used to estimate the size, shape, orientation, density, and composition of the QDs. Overall, QDs are the creamy layer of quantum research with its applications extending from semiconductor light sources to quantum technology. These are also potential candidates for quantum bits or qubits to realize a quantum computer. The current and future research on quantum dots will continue to develop and optimize the QD nanostructures with improved optoelectronic properties for different applications.
Best regards to Raj Gajjela (PhD) an acquaintance of mine who has taken his best effort to present this wonderful and concise article.
Raja Gajjela
Doctoral Candidate
Eindhoven University of Technology
“Atomic-scale characterization of III-V semiconductor Quantum dots ”
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