We investigate the effects of secondary electrons (SEs), induced by electrons impinging on the electrodes, on the characteristics of low-pressure single-frequency capacitively coupled plasmas (CCPs) by particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations. In a recent PIC/MCC simulation study, that incorporated a realistic description of the electron-surface interaction, such electron-induced SEs (δ-electrons) were found to have a remarkable impact on the ionization dynamics and the plasma parameters in argon at 0.5 Pa and 6.7 cm gap between SiO 2 electrodes (Horváth et al 2017 Plasma Sources Sci. Technol. 26 124001). At such low pressure and at high voltage amplitudes, the ion-induced SEs (γ-electrons) emitted at one electrode can reach the opposite electrode with high energies, where, depending on the surface material and surface conditions, they can induce the emission of a high number of δ-electrons, which can cause significant ionization and a higher plasma density. Here, we study the influence of δ-electrons on the ionization dynamics and plasma parameters at various pressures and voltage amplitudes, assuming different SE yields for ions (γ-coefficient) in single-frequency 13.56 MHz argon discharges. The emission of SEs by electron impact is found to be an important plasma-surface process at low pressures, between 0.5 Pa and 3 Pa. Both the gas pressure and the value of the γ-coefficient are found to affect the role of δ-electrons in shaping the discharge characteristics at different voltage amplitudes. Their effect on the ionization dynamics is most striking at low pressures, high voltage amplitudes and high values of the γ-coefficient. However, in the whole parameter regime investigated here, the realistic description of the electron-surface interaction significantly alters the computed plasma parameters, compared to results obtained based on a simple model for the description of the electron-surface interaction, widely used in PIC/MCC simulations of low-pressure CCPs.