Polysilicon resistor with continuous u-shaped polysilicon resistor elements and related method

A resistor, comprising:

• a plurality of connected polysilicon resistor elements in a semiconductor-on-insulator (SOI) substrate, each polysilicon resistor element having a continuous U-shape with a continuous lateral bottom, the plurality of polysilicon resistor elements creating a serpentine polysilicon resistor, wherein the SOI substrate includes a buried insulator layer over a base semiconductor substrate;
• a trench isolation insulator within a valley of the continuous U-shape of each polysilicon resistor element;
• and
• a dopant-including high resistivity (HR) polycrystalline layer below the buried insulator layer and below each polysilicon resistor element in the base semiconductor substrate, wherein a dopant of the dopant-including HR polycrystalline layer includes a noble gas element, wherein each polysilicon resistor element extends through the buried insulator layer and into the dopant-including HR polycrystalline layer.

A method of forming a serpentine polysilicon resistor, the method comprising:

• forming a plurality of trenches in a semiconductor-on-insulator (SOI) substrate including an active semiconductor layer over a buried insulator layer over a base semiconductor substrate, each trench extending to the base semiconductor substrate;
• filling each trench with a polysilicon member;
• forming an insulator in each polysilicon member, forming a plurality of polysilicon resistor elements each having a continuous U-shape with a continuous lateral bottom in a respective trench and with the insulator in a valley of each U-shape;
• forming a dopant-including high resistivity (HR) polycrystalline layer below the buried insulator layer and below each polysilicon resistor element in the base semiconductor substrate, wherein a dopant of the dopant-including HR polycrystalline layer includes a noble gas element, and wherein each polysilicon resistor element extends through the buried insulator layer and into the dopant-including HR polycrystalline layer;
• and
• interconnecting ends of the plurality of polysilicon resistor elements sequentially to form the serpentine polysilicon resistor.