[en] Highlights: • A quantum dot is represented by a helium atom in a finite oscillator potential. • Electron localization in QD is examined via Shannon entropy. • The best dot width for localizing the electron density is determined. • This method provides deeper understanding of quantum confined systems. Quantifying electron localization in quantum confined systems remains challenging, especially for excited states. A quantum dot (QD) is represented by a helium atom in a finite oscillator potential. The effect of dot width variation on the electron localization in QD is systematically examined via Shannon entropy for low-lying doubly excited states (2s^{2 1}S^e, 2p^{2 1}S^e, 2s3s ¹S^e) obtained using highly correlated Hylleraas functions. In particular, the most effective dot width where the electron density is the most localized is determined successfully and justified by the electron density plot for all three states.