Calculations are made of the nonlinearity coefficient, γ and the dynamic quality factor Q, of abrupt junctions, hyper-abrupt junctions, and varactors with a pagoda structure which is proposed in this report. The quantities γ and Q are defined by Kurokawa and Uenohara as

and

, respectively, where R
s, is the series resistance and C
0and C
1are the coefficients of the Fourier expansion of the time-dependent junction capacitance

, i.e.,

Compared with abrupt junctions having γ between 0.5 (for 8 volts breakdown) and 1.0 (for 150 volts breakdown) hyper-abrupt junctions improve γ by about 50%. With the pagoda structure, γ can be made around 1.8 with little dependence on breakdown voltage. The theoretical upper limit of γ is two. Improvement in γ is always accompanied by an increase in the product

, also increased fabrication difficulties, and the net effect is usually a decrease in Q. Only when the negative gradient region of a hyper-abrupt junction is made very narrow, γ can be improved without sacrificing Q. Measurements on epitaxial hyper-abrupt junctions and pagoda varactors are discussed.