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The authors present a review and assessment of state-of-the-art analytical models which describe the breakdown behaviour of JI and SOI RESURF power devices. The results are compared with numerical values, and a short evaluation of strengths and weaknesses specific to each model is given. A new modelling concept for the breakdown regime in RESURF power structures is introduced, and the results are assessed against numerical values. The same technique can be used to derive the breakdown voltage of RESURF devices fabricated in JI and SOI technologies, and is potentially useful for non-standard technologies, such as linearly graded SOI, partial SOI and 3-D RESURF. The model provides accurate description for punch-through, non-punch-through and volume breakdown.