In recent years, it has been under discussion how the distribution of discrete dopant ions affects the performance of electron devices. In particular, dopant ions near the interface may not be surrounded by a sufficient number of carriers to achieve full screening. In addition, the screening effect is modeled assuming equilibrium, which cannot be validated. Therefore, the device modeling of the screening effect must be refined to cover the entire range of applied voltages. In the present work, we adequately define the length scale covering the entire voltage region in the capacitance-voltage (C-V) characteristics. Furthermore, we propose an image charge model for residual long-range potential of dopant ions near the interface. The Monte Carlo simulation of random dopant fluctuation in the C-V characteristics of 100 samples of MOS capacitors demonstrates that the main contributor to random dopant fluctuation is the location fluctuation of discrete dopant ions.