InAs/InGaAs Quantum Dot Molecules

• InAs/InGaAs quantum dot molecules are vertically stacked semiconductor nanostructures where proximate dots are coupled via tunneling through a thin GaAs barrier.
• An applied electric field tunes excitonic resonances into anticrossings, enabling controlled hybridization of carrier states for spin-qubit and optical quantum control.
• Barrier engineering, including Bi alloying, enhances hole tunneling and confines molecular states, facilitating telecom O-band emission and robust quantum-light performance.

InAs/InGaAs quantum dot molecules are coupled semiconductor nanostructures in which two proximate quantum dots support hybridized carrier states analogous to molecular orbitals. In the self-assembled implementations emphasized in the literature, the constituent dots are typically stacked vertically along the growth axis and separated by a thin GaAs barrier, so that an applied electric field can tune discrete electron or hole levels into resonance and induce tunneling-mediated hybridization. Within this platform, the same underlying coupled-dot physics supports several distinct regimes: excitonic anticrossings and excited-state spectroscopy, hole- or electron-mediated spin-qubit control, barrier-engineered enhancement of molecular hole states, and electrically tunable telecom-wavelength quantum-light emission near $1.3~\mu\text{m}$ [(Chen et al., 2014); (Avdienko et al., 30 Mar 2026); (Usman et al., 2010)].

1. Structural platform and molecular-state formation

The canonical InAs/InGaAs quantum dot molecule (QDM) is a pair of vertically stacked self-assembled dots separated by a thin barrier. In the controlled-phase-gate proposal, the structure consists of two vertically coupled self-assembled dots separated by a barrier $d$, with an intentional asymmetry in dot height: dot 1 has larger height $h_1$ and therefore lower optical transition energy, while dot 2 has smaller height $h_2$ and higher-lying levels. A positive electric field along the growth direction is then used to make the hole levels of the two dots resonant while leaving the electron levels far apart in energy, so that hole tunneling is enabled but optical addressing remains selective (Chen et al., 2014).

In telecom O-band devices, the same molecular concept is realized in a p-i-n diode containing two vertically aligned InAs/InGaAs quantum dots separated by a thin GaAs barrier. The lower dot acts as a strain-induced nucleation site for the upper dot, and both dots are overgrown with an $\mathrm{In}_{0.25}\mathrm{Ga}_{0.75}\mathrm{As}$ strain-reducing layer (SRL), which redshifts the emission into the O-band. The interdot barrier is a key control parameter; the reported samples mainly use 3 nm, 5 nm, and 10 nm GaAs barriers (Avdienko et al., 30 Mar 2026).

A complementary atomistic spectroscopy study treats a single vertically stacked double quantum dot molecule composed of two lens-shaped $\mathrm{In}_{0.5}\mathrm{Ga}_{0.5}\mathrm{As}$ quantum dots separated by a 10 nm GaAs barrier, each on a 1 nm wetting layer. There the larger upper dot hosts the lowest hole ground state $H1$ and a low electron ground state, while excited lower-dot electron states can be tuned through resonance by an external electric field, making the molecule a field-tunable probe of coherent interdot coupling (Usman et al., 2010).

Across these realizations, “molecular” behavior refers to tunnel-coupled symmetric, antisymmetric, bonding, antibonding, direct, or indirect carrier configurations formed from states that would otherwise be localized in separate dots. In the excitonic language used for O-band QDMs, the low-field spectrum separates into direct excitons $X_{\rm dir}$, where electron and hole occupy the same dot, and indirect excitons $X_{\rm ind}$, where they occupy different dots; electric-field tuning drives these branches into resonance and reveals the interdot tunnel coupling spectroscopically (Avdienko et al., 30 Mar 2026).

2. Electric-field tuning, Stark shifts, and anticrossing spectroscopy

The electric-field response of InAs/InGaAs QDMs is organized by the distinct Stark behavior of direct and indirect configurations. For the direct exciton, the Stark shift is written as

$$\Delta E_{\rm Stark} = E_{\rm dir}(F)-E_{\rm dir}(0)= -pF - BF^2,$$

with $d$0 the permanent dipole moment, $d$1 the polarizability, and

$d$2

where $d$3 and $d$4 is the intrinsic region thickness. For the indirect exciton,

$d$5

so its energy shifts almost linearly because the electron-hole separation is set by the interdot distance. When the direct and indirect branches are tuned into resonance, an avoided crossing appears, and the hybridized eigenenergies take the standard two-level form

$d$6

with minimum splitting $d$7 (Avdienko et al., 30 Mar 2026).

This anticrossing is the central experimental signature of interdot tunnel coupling in O-band InAs/InGaAs QDMs. Pronounced anticrossings are observed in the 3 nm and 5 nm barrier samples, but not in the 10 nm sample. The mean tunnel coupling extracted from hyperspectral voltage scans decreases from $d$8 meV for 3 nm to $d$9 meV for 5 nm, and the probability of observing anticrossings is about 74% for 3 nm and 32% for 5 nm. In the 3 nm sample, a typical anticrossing has $h_1$0 meV and an inferred separation $h_1$1 nm, matching the designed wetting-layer-to-wetting-layer spacing $h_1$2 nm. The absence of anticrossings in the 10 nm sample is interpreted as loss of vertical correlation between the dots (Avdienko et al., 30 Mar 2026).

Excited-state spectroscopy under electric field provides a second, more resolved view of molecular coupling. In the multi-million-atom analysis of a single InAs/InGaAs QDM, externally sweeping the field along $h_1$3 probes a ladder of lower-dot states through anticrossings with upper-dot states. In a two-level picture,

$h_1$4

so that the minimum splitting is

$h_1$5

The experimentally relevant splitting is the $h_1$6 anticrossing, which matches the measured excitonic splitting around $h_1$7–$h_1$8 meV. The same analysis shows that field slopes can be used to infer electron-hole separations and reverse-engineer dot spacing; the extracted dot spacing is $h_1$9 nm, close to the TEM-measured $h_2$0 nm separation (Usman et al., 2010).

A recurring interpretive issue is whether continuum treatments are adequate for these spectra. The atomistic work argues that they are not: effective-mass modeling overestimates the tunnel coupling, giving $h_2$1 meV where the experiment and atomistic calculation give $h_2$2 meV. It also finds that piezoelectricity is not a minor perturbation in this QDM. With piezoelectricity omitted, two anticrossings appear in the experimental field window; with both linear and quadratic piezoelectricity included, only one anticrossing falls in the measured range, matching experiment (Usman et al., 2010).

3. Optical quantum control and coherence-based functionality

A prominent use of vertically stacked InAs/InGaAs QDMs is as optically addressable two-qubit systems. In the all-optical controlled-phase-gate proposal, each qubit is the electron spin in one dot, $h_2$3 or $h_2$4, and a small magnetic field $h_2$5 in Faraday geometry Zeeman-splits the spin states. Optical selection rules allow $h_2$6 light to drive $h_2$7 and $h_2$8 light to drive $h_2$9, where the trion contains two electrons in a singlet plus a heavy hole. The target operation is

$\mathrm{In}_{0.25}\mathrm{Ga}_{0.75}\mathrm{As}$0

$\mathrm{In}_{0.25}\mathrm{Ga}_{0.75}\mathrm{As}$1

so that only $\mathrm{In}_{0.25}\mathrm{Ga}_{0.75}\mathrm{As}$2 acquires a phase of $\mathrm{In}_{0.25}\mathrm{Ga}_{0.75}\mathrm{As}$3 (Chen et al., 2014).

The gate mechanism consists of three optical steps. First, a slowly turned-on $\mathrm{In}_{0.25}\mathrm{Ga}_{0.75}\mathrm{As}$4-polarized CW laser $\mathrm{In}_{0.25}\mathrm{Ga}_{0.75}\mathrm{As}$5 drives dot 1 only when that dot is in $\mathrm{In}_{0.25}\mathrm{Ga}_{0.75}\mathrm{As}$6, and hole tunneling creates a dark state

$\mathrm{In}_{0.25}\mathrm{Ga}_{0.75}\mathrm{As}$7

When $\mathrm{In}_{0.25}\mathrm{Ga}_{0.75}\mathrm{As}$8, adiabatic following transfers population from $\mathrm{In}_{0.25}\mathrm{Ga}_{0.75}\mathrm{As}$9 to $\mathrm{In}_{0.5}\mathrm{Ga}_{0.5}\mathrm{As}$0 without significantly populating the lossy intermediate trion. Second, a $\mathrm{In}_{0.5}\mathrm{Ga}_{0.5}\mathrm{As}$1 pulse $\mathrm{In}_{0.5}\mathrm{Ga}_{0.5}\mathrm{As}$2 drives a conditional $\mathrm{In}_{0.5}\mathrm{Ga}_{0.5}\mathrm{As}$3 rotation in the $\mathrm{In}_{0.5}\mathrm{Ga}_{0.5}\mathrm{As}$4 manifold; for $\mathrm{In}_{0.5}\mathrm{Ga}_{0.5}\mathrm{As}$5 and $\mathrm{In}_{0.5}\mathrm{Ga}_{0.5}\mathrm{As}$6, one obtains approximately $\mathrm{In}_{0.5}\mathrm{Ga}_{0.5}\mathrm{As}$7. Third, $\mathrm{In}_{0.5}\mathrm{Ga}_{0.5}\mathrm{As}$8 is turned off slowly, adiabatically returning the other populated states to the computational basis. Conditionality is enforced in part because the transition $\mathrm{In}_{0.5}\mathrm{Ga}_{0.5}\mathrm{As}$9 is forbidden by the Pauli exclusion principle (Chen et al., 2014).

The dissipative dynamics are simulated with a master equation,

$H1$0

with spontaneous-emission operators $H1$1. Using $H1$2 ps, $H1$3 meV, and $H1$4, the gate is completed in about $H1$5 ps for the equal superposition initial state, with reported fidelity $H1$6. The paper further notes that $H1$7 is possible if the lifetime of the relevant trion state is increased, for example by placing the system in a cavity to reduce $H1$8 (Chen et al., 2014).

Coherence engineering also appears in optical slow-light proposals for InGaAs-based QDMs. There the objective is not a logic gate but a $H1$9-scheme in which a common bonding hole state couples optically to two electron states whose overlap is deliberately made very small. In the optimized asymmetric vertically stacked molecule, the hole ground states hybridize into a bonding state while the electron states remain spatially separated. This reduces carrier-phonon and Coulomb-induced dephasing of the $X_{\rm dir}$0 quantum coherence, and the achievable group-velocity slowdown is reported to be about an order of magnitude larger than for a deep single QD at comparable absorption (Michael et al., 2014).

Closely related InAs/GaAs QDM work shows the same broader control logic in a different confinement stack: two vertically stacked singly charged InAs quantum dots coupled by coherent electron tunneling can realize a universal set of Raman gates in Voigt geometry, with any arbitrary two-qubit unitary realizable with at most 8 Raman transitions. As a benchmark, a two-qubit quantum Fourier transform is implemented with 88.1% fidelity and duration 414 ps when helping pulses are used. This does not establish identical material behavior for InAs/InGaAs molecules, but it does show that the tunneling-induced exchange, trion selection rules, and pulse-shaped Raman control strategy extend across closely related InAs-based QDM architectures (Cohen, 2015).

4. Barrier engineering, alloy disorder, and hole-state control

A major direction in InAs QDM research is deliberate barrier modification to enhance molecular hole states relevant for optical qubit control. In atomistic studies of vertically stacked InAs QDMs, the conventional GaAs interdot spacer is replaced by random-alloy $X_{\rm dir}$1. The motivation is specific: coupled hole states in resonantly tuned QDMs underpin $X_{\rm dir}$2-system optical control schemes, and increasing tunnel coupling and spin-orbit-driven spin mixing should make these protocols more robust and easier to implement (Lin et al., 2023).

Two distinct Bi-induced mechanisms are separated in the calculations. First, an orbital or barrier-height effect lowers the effective tunnel barrier for holes because Bi lowers the barrier valence-band edge relative to the dot-confined hole states. Second, a strain effect arises because Bi atoms are larger than As atoms; the resulting asymmetric strain shifts the zero-field energy offset between the two dots and therefore changes the electric field required to reach resonance. The field is introduced as an on-site electrostatic shift,

$X_{\rm dir}$3

so the upper-dot states shift approximately linearly with field while the bottom-dot states remain nearly field-independent (Lin et al., 2023).

The central quantitative result is that a full $X_{\rm dir}$4 barrier gives the best balance between enhanced tunneling and preservation of dot-like confinement. At 7% Bi, the minimum splitting at resonance between the two lowest hole states is about three times larger than in the pure GaAs barrier case, i.e. a three-fold increase in hole tunnel coupling. The resonance also shifts to higher electric fields as Bi concentration increases, not because tunneling itself repositions resonance, but because alloy strain increases the zero-field energy mismatch between top- and bottom-dot hole states. The most favorable geometry in that study is a vertically stacked InAs QDM with a full $X_{\rm dir}$5 interdot barrier alloyed with Bi (Lin et al., 2023).

The earlier companion study clarifies why an atomistic treatment is required. It uses an atomistic nearest-neighbor $X_{\rm dir}$6 tight-binding Hamiltonian with strain relaxation from a valence-force-field model and emphasizes the valence-band anticrossing (BAC) character of GaBiAs. In large random-alloy supercells, the valence-band edge shifts upward strongly with Bi concentration, while the conduction-band edge shifts only weakly. At 7% Bi, 40 random alloy configurations produce about 50 meV spread in the valence-band edge and about 10 meV spread in the conduction-band edge. Electron states in the QDM are only weakly affected by Bi incorporation, but hole states are much more sensitive to the barrier composition and microscopic Bi arrangement (Lin et al., 2018).

The alloy-disorder problem has a practical threshold. In the tunneling study, 41 sampled 7%-Bi configurations show that only 4 have an identifiable barrier-localized state within the lowest 20 hole states, and the two lowest hole states relevant for qubit operation remain well confined to the dots up to 7% Bi. Once Bi concentration reaches about 8% and above, the wavefunctions begin to leak substantially into the barrier and increasingly localize around Bi clusters, destroying the clean dot-to-dot resonance picture (Lin et al., 2023). This suggests that barrier engineering is useful only within a restricted composition window where tunnel enhancement does not collapse molecular-state integrity.

5. Telecom O-band emission, charging sequences, and quantum-light performance

InAs/InGaAs QDMs can be engineered to operate in the telecom O-band around 1300 nm while retaining electrically tunable molecular coupling. In the reported p-i-n diode structures, the $X_{\rm dir}$7 SRL pushes the emission beyond the usual $X_{\rm dir}$8 limit of conventional InAs/GaAs dots, and the GaAs platform remains compatible with high-contrast photonic structures such as Al(Ga)As/GaAs DBRs. The combination of O-band emission and field-tunable anticrossings makes these QDMs relevant for telecom-wavelength quantum photonics on GaAs (Avdienko et al., 30 Mar 2026).

At higher reverse bias, the neutral-exciton anticrossing regime gives way to sequential charging. As the field increases, electrons tunnel out more readily while holes remain trapped, and the time-integrated emission becomes progressively dominated by positively charged exciton complexes $X_{\rm dir}$9 with $X_{\rm ind}$0 to 5. The interpretation is sequential charging of the molecule, with hole accumulation in the upper dot. The reported progression is consistent with the Coulomb ordering $X_{\rm ind}$1 and with the upper dot being slightly larger and more strongly confined than the lower one (Avdienko et al., 30 Mar 2026).

Under strong pumping, biexciton emission is also identified. In photoluminescence-versus-voltage maps, higher excitation power generates new anticrossings and discrete branches, and power-law analysis separates the main complexes: the neutral-exciton anticrossing AC1 scales with an exponent near 1, AC2 is consistent with biexciton emission, and AC3 and AC4 are associated with charged-exciton behavior, including positively charged trion features and possibly a negatively charged trion contribution in one branch. The assignments are not entirely closed; the same work explicitly notes that multiexciton shell-filling effects and different final-state couplings make a definitive assignment of every high-field anticrossing difficult (Avdienko et al., 30 Mar 2026).

The quantum-light characterization is based on the second-order correlation function under continuous-wave nonresonant excitation,

$X_{\rm ind}$2

with $X_{\rm ind}$3 in the absence of bunching. For the neutral exciton line, clear antibunching is observed with

$X_{\rm ind}$4

which is strong evidence for single-photon emission from the O-band QDM. At higher excitation powers, additional bunching appears and is attributed to charge-state fluctuations, carrier shelving, and Auger-like processes. For the biexciton line, the autocorrelation exhibits the strong bunching expected for a multi-particle emitter (Avdienko et al., 30 Mar 2026).

A common simplification is to treat telecom emission and tunnel coupling as largely independent design goals. The O-band QDM results instead present a structure-property linkage in which the SRL sets the spectral window, the GaAs barrier thickness controls tunnel coupling, the static electric field tunes direct and indirect excitons into resonance, and bias and pump power expose the higher-order charge complexes. A plausible implication is that spectral tuning, coupling engineering, and quantum-light purity cannot be fully decoupled at the device-design level.

6. Modeling frameworks, related geometries, and interpretive boundaries

The study of InAs/InGaAs QDMs is methodologically heterogeneous, but the literature converges on the need for atomistic resolution whenever excited-state ordering, alloy disorder, or piezoelectricity materially affect observables. The quantitative spectroscopy work uses NEMO 3-D with $X_{\rm ind}$5 million atoms in the strain domain and $X_{\rm ind}$6 million atoms in the electronic domain, together with a 20-band $X_{\rm ind}$7 nearest-neighbor empirical tight-binding Hamiltonian. The GaBiAs-barrier studies use atomistic nearest-neighbor $X_{\rm ind}$8 tight binding with valence-force-field relaxation and iterative diagonalization via ARPACK/Arnoldi. These approaches are explicitly contrasted with virtual-crystal and effective-mass models that miss valence-band anticrossing physics, atomistic symmetry breaking, or the correct tunnel splitting [(Usman et al., 2010); (Lin et al., 2018)].

Many-body spectroscopy in related QDM geometries sharpens the same point. In laterally coupled InGaAs quantum dots embedded in GaAs and tuned by a lateral electric field, atomistic empirical pseudopotential calculations combined with configuration interaction predict that the negative trion $X_{\rm ind}$9 shows four anticrossings and the positive trion $$\Delta E_{\rm Stark} = E_{\rm dir}(F)-E_{\rm dir}(0)= -pF - BF^2,$$0 shows two in the accessible field range. The magnitudes of these anticrossings are interpreted as signatures of many-body renormalization of tunneling rather than simple single-particle splittings (Peng et al., 2010). Although this is a lateral rather than vertical molecule, it demonstrates that QDM anticrossings are often properties of correlated few-body states, not only of isolated orbitals.

Device electrostatics also extends beyond the standard vertical diode. A three-electrode lateral-field structure for single self-assembled InAs/GaAs dots shows deterministic charging by electrically injected holes induced by lateral electric fields, and it is presented as a first step toward arbitrary 2-D electric-field profiles at a single QD or QDM. The immediate result is for a single dot rather than an InAs/InGaAs molecule, but the stated relevance to QDMs is direct: fuller vector control of the local field could be used to tune charge state, emission, and potentially interdot tunneling or spin interactions in future QDM devices (Ma et al., 2018).

Finally, the term “quantum-dot molecule” has acquired a broader conceptual range than the self-assembled InAs/InGaAs heterostructures that dominate qubit and telecom studies. STM-assembled dot chains on the InAs(111)A surface, built from six ionized indium adatoms per dot, realize alternating tunnel couplings and SSH-like boundary states. Those structures are explicitly described as conceptually related to InAs/InGaAs QDMs because dot orbitals hybridize into bonding and antibonding molecular states, but they are not self-assembled heterostructure dots. Their main interpretive lesson is that electrostatic onsite-potential variations can deform, shift, and redistribute nominally ideal molecular or topological states without destroying them (Pham et al., 2024). This suggests a broader caution for InAs/InGaAs QDMs: real-device electrostatics, disorder, and strain are often constitutive elements of the molecular physics rather than perturbative corrections.