This paper provides an overview of modelling techniques for the simulation of electron injection and confinement in a semiconductor quantum dot array at cryogenic temperatures. We consider the industrial 22-nm FD-SOI fabrication process from Global Foundries. This is motivated by its application in scalable quantum computing systems. The injection and confinement process is broken into 3 steps; quantum point con-tact initialisation/pre-charging, cryogenic confinement potential formation, and finally readout and amplification. We show initial results for pre-charge simulations using Verilog-A and cryogenic laboratory measurements. Then we describe a COMSOL finite element model of an FD-SOI 4-gate array and report initial room temperature results. The difficulties associated with moving towards cryogenic solutions in our finite element model are then highlighted.