The three-dimensional (3-D) electrostatics together with the modified Wentzel-Kramers-Brillouin tunneling model has been implemented to simulate the programming and retention characteristics of the metal nanocrystal (NC) memories. Good agreements with experimental data are first demonstrated to calibrate the transport parameters. In contrast to previous works, the 3-D electrostatic effects investigated in this paper are proven very significant in the memory operations. Therefore, new design criteria of metal NC memories are investigated. Part I presents the physical model and the NC array design optimization. A sparse and large-size NC array, which is suitable for the one-dimensional narrow-channel memories, provides higher program/erase tunneling current density due to the field-enhancement effect and lower charging energy due to the large NC capacitance. On the other hand, to achieve a sufficient memory window, fast programming speed, and long retention time in the typical two-dimensional channel memories, a dense and large-size NC array is favorable while taking the tradeoff with the NC number density into account. Based on the same theoretical model, the authors continue in Part II to consider the design optimization when high-κ dielectrics can be employed.