Recent experimental advances highlight electron charge qubits floating above solid neon as a promising emerging platform for quantum computing, but the physical origin of single-electron lateral trapping is still not fully understood. While prior theoretical work has mainly examined electrons above bulk solid neon, experimental systems usually feature nonuniform neon layers with thicknesses of only $\lesssim 10\mathrm{nm}$, highlighting unresolved questions about how thickness influences electron trapping. Here we theoretically investigate the effect of finite thickness and nonuniformity of solid neon layers on electron trapping. For a 10-nm layer, the electron binding energy is enhanced threefold compared to the bulk. Exploiting this thickness dependence, we propose a nanopatterned-substrate mechanism in which engineered thickness variations generate lateral trapping potentials for electrons. The lateral trapping potential can be finely tuned by a perpendicular electric field. Such nonuniform-thickness-induced electron charge qubits open a viable pathway toward building multiqubit systems for quantum computation.

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• Quantum information architectures & platforms
• Quantum information with hybrid systems
• Quantum information with solid state qubits
• Qubits
• Surface states