disclosed herein are type ii resonant matched vibratory gyroscopes 10 and fabrication methods 30 relating thereto . the type ii resonant matched vibratory gyroscopes 10 are referred to as resonating star gyroscopes 10 . referring to the drawing figures , fig1 shows a conceptual illustration of an exemplary resonating star gyroscope 10 . a schematic diagram of an exemplary resonating star gyroscope 10 is illustrated in fig2 . as is illustrated in fig1 , the resonating star gyroscope 10 may be visualized as a merged superposition of two substantially identical square entities 11 that are spatially 45 ° apart . this provides for pairs of degenerate flexural vibratory modes in the resulting eight - fold star - shaped member 12 or shell 12 ( fig2 ), which is anchored to a substrate 13 comprising a central post 13 or anchor 13 , through flexural springs 14 . it is to be understood , however , that the central post 13 or anchor 13 may be located outside of the shell 12 . in the current design , eight optimally designed springs are used to maintain degeneracy of the resonant modes . furthermore the star shell or member may also be suspended at alternate points on the periphery using flexural springs or support posts connected at one or several section ( s ) of the substrate . the physical dimensions of these support structures may / may not be governed by the dimensions of the star - structural material , i . e . the thickness of the support flexures may be less than the actual star shell or member . rotation - induced coriolis acceleration causes energy to be transferred between two flexural modes of any degenerate resonant pair . the nodes of each mode are located at the anti - nodes of its degenerate counterpart . the star gyroscope 10 is a fully symmetric and balanced structure that offers differential sensing capability . as is shown in fig2 , the shell 12 is surrounded by capacitive drive , sense and tuning ( balancing ) electrodes 15 , 16 , 17 . the electrodes 15 , 16 , 17 may be separated from the shell 12 by capacitive gaps 18 , although this is not required in all devices . electrode placement schemes enable frequency matching of both primary and higher - order flexural modes . it is to be understood , however , that the electrodes need not be capacitively coupled to the shell 12 , and may be physically connected in certain embodiments . electrodes in the form of piezoelectric / piezoresistive material may be deposited along the nodal - points of the star - shaped periphery . such materials may also act as an anchoring agent to the underlying device substrate . structural features of the exemplary resonating star gyroscope 10 shown in fig2 are that the external star - shaped shell 12 is suspended using flexural springs 14 supported at a central anchor 13 , eight flexural springs 14 are used to ensure degenerate resonant flexural mode pairs , the frequency of the structure is dependent on dimensions of the flexural springs 14 , the width of the flexural springs 14 also govern mechanical quality factors of the resonant mode , the central anchor 13 also effects the overall resonant frequency and mechanical quality factor of the flexural modes , the electrodes 15 , 16 , 17 ( in this case ) are distributed around the periphery of the star - shell 12 , the electrodes are electrically isolated from an underlying substrate 20 or structural member 20 , and the resonating star shell 12 is kept at the same potential of the substrate 20 . however , it is to be understood that the resonating star gyroscope 10 need not necessarily embody a shell 12 supported by multiple flexural springs 14 coupled to the support member 13 or central post 13 . the star structure may be fabricated using a solid star - shaped member 12 a that may or may not employ the flexural springs 14 . a portion of an exemplary gyroscope 10 comprising a solid star - shaped member 12 is illustrated in fig2 a . an exemplary solid resonating star gyroscope 10 has the solid star - shaped member 12 a supported at its center of mass or coupled to and supported by the support member 13 using a plurality of flexural springs 14 . the solid star - shaped member 12 a may have perforations in formed its structure during fabrication to facilitate its release . fig3 illustrates an exemplary electrode configuration for the resonating star gyroscope 10 shown in fig2 . the electrodes include a drive electrode 15 disposed at 0 °, a sense electrode 16 disposed at − 45 °, a sense electrode 16 disposed at 45 °, a sense electrode 16 disposed at 135 °, a drive tuning electrode 15 a disposed at − 90 °, a sense tuning electrode 16 a disposed at − 135 °, a drive monitoring electrode 15 b disposed at 180 °, and two tuning ( balancing ) electrodes 17 disposed at 157 . 5 ° and − 157 . 5 °, respectively . the star - shaped shell 12 is electrostatically driven into resonance at the primary flexural mode . when the gyroscope 10 is subjected to rotation , coriolis force causes energy to be transferred to the secondary degenerate mode located 45 ° away . this consequential motion is sensed capacitively at the sense electrodes 16 . with regard to the electrode configuration shown in fig3 , for bare - minimal operation , two electrodes are required — the drive electrode 15 ( 0 °) and the sense electrode 16 ( 45 °). for optimal operation , the operating modes must have the same frequency ( mode - matching ). to achieve mode - matching quadrature cancellation must be performed . differential operation ( for improved sensitivity ) can be achieved using the extra sense - electrodes . the unused electrodes are connected to a polarization voltage ( v p ). the star - shell 12 is also maintained at v p . fig4 a and 4 b illustrate primary degenerate flexural modes of an exemplary resonating star gyroscope 10 . as is shown in fig4 a and 4 b , the mode shapes are spatially 45 ° apart . this is the preferred mode of operation . fig5 a and 5 b illustrate higher order flexural modes of an exemplary resonating star gyroscope 10 . as is shown in fig5 a and 5 b , the mode shapes are spatially 30 ° apart . this is a secondary mode of operation . fig6 is an schematic illustrating characterization electronics for use with the resonating star gyroscope 10 . more sophisticated electronics are required to ensure automatic mode - matching , quadrature cancellation , and operation in the closed - loop ( to ensure flexible operating bandwidth ). fig7 illustrates the increased electrode area of an exemplary resonating star gyroscope 10 . fig7 a shows the encircled portion of fig7 and illustrates that quadrature cancellation is provided by the resonating star gyroscope 10 . in order to increase the effective resonant mass ( and consequently decrease the mechanical noise of the gyro 10 ) multiple - shells 12 may be implemented . fig8 illustrates an exemplary multi - shell implementation of a resonating star gyroscope 10 , fig8 a shows an enlarged view of the portion of fig8 . fig9 illustrates an exemplary resonating star gyroscope 10 fabricated using a high aspect ratio and poly - and single - crystalline silicon ( harpss ) process . in the resonating star gyroscope 10 shown in fig9 , the substrate 20 is a low resistivity silicon wafer . the structural material is doped trench - refilled polysilicon . the anchor 13 is defined by an etched silicon post . electrodes 15 , 16 , 17 are isolated using a nitride passivation layer . referring to fig1 a - 10 f , they illustrate exemplary steps of a harpss fabrication process 30 that may be used to fabricate the resonating star gyroscope 10 shown in fig9 . the harpss fabrication process 30 may be used to fabricate thick polysilicon versions of the resonating star gyroscope 10 . representative processing steps are also disclosed in a paper by f . ayazi and k . najafi , entitled “ a high - aspect ratio combined poly and single - crystal silicon ( harpss ) mems technology ”, ieee / asme jmems , september 2000 , pp . 288 - 294 . as is shown in fig1 a , a nitride isolation layer 21 is formed on a substrate 20 . this layer acts as electrical isolation between the substrate and the device electrode . ( a host of other material may be used as a dielectric isolation material ). as is shown in fig1 b , trenches 22 are etched to define the geometry of the resonating star gyroscope 10 . as is shown in fig1 c , sacrificial oxide 23 is deposited ( using a low pressure chemical vapor deposition ( lpcvd ) system ) and doped . the sacrificial oxide layer may also be formed by thermal oxidation of the exposed silicon . the trenches 22 are refilled with lpcvd polysilicon 24 . as is shown in fig1 d the polysilicon layer 24 is etched back , the oxide 23 is patterned , and the polysilicon 24 is deposited , doped and patterned . as is shown in fig1 e , an anisotropic silicon etch is performed and the vibratory structure of the resonating star gyroscope 10 is undercut using an isotropic silicon etch . as is shown in fig1 f , the sacrificial oxide 23 is then etched 46 in hydrogen fluoride ( hf ) solution , for example , to release the resonating structure from the substrate 20 and form the gyroscope 10 . as is illustrated by fig1 a - 10 f , mechanical structures ( resonating star gyroscopes 10 ) are created by refilling trenches 21 with polysilicon 22 deposited over a sacrificial oxide layer 23 . the structural layer of polysilicon 22 is doped to make it conductive . silicon sense electrodes 16 as tall as the star - shaped shell 12 ( ring structure ) are released from the substrate 20 using a two - step dry release process . small high aspect ratio capacitive actuation gaps 24 ( 1 μm ) between the electrodes 15 , 16 , 17 and the star - shaped shell 12 enable low voltage operation of the gyroscope 10 . fig1 a and 11 b are graphs showing frequency response and mode matching , respectively , for the primary flexural modes of an exemplary harpss implementation of the resonating star gyroscope 10 . fig1 is a graph that illustrates sensitivity of the harpss fabricated resonating star gyroscope 10 . fig1 illustrates an exemplary ( 100 ) single crystal silicon on insulator implementation of the resonating star gyroscope 10 . the gyroscope 10 may be fabricated using deep reactive ion silicon etching . fig1 a and 14 b are graphs showing frequency response and mode matching , respectively , for the higher - order flexural modes of the single crystal silicon on insulator implementation of the resonating star gyroscope 10 . fig1 c is a graph that illustrates high - q , higher - order flexural modes of the ( 100 ) single crystal silicon on insulator implementation of the resonating star gyroscope shown in fig1 . fig1 illustrates an exemplary epitaxial - polysilicon implementation of the exemplary resonating star gyroscope 10 . the gyroscope may be fabricated using deep reactive ion silicon etching . fig1 a and 16 b are graphs showing frequency response and mode matching , respectively , for the higher - order flexural modes of an exemplary epitaxial - polysilicon implementation of the resonating star gyroscope 10 . fig1 c is a graph that illustrates high - q , higher - order flexural modes of the epitaxial - polysilicon implementation of the resonating star gyroscope 10 . a prototype polysilicon resonating star gyroscope 10 was fabricated and tested open loop under vacuum . a sinusoidal drive signal was applied at the drive electrode and output signals , monitored at the 0 ° and 45 ° electrodes , were amplified using external amplifiers . the primary flexural mode frequency of the prototype gyroscopes 10 was measured to be 39 . 6 khz which is in agreement with ansys simulations . electronic tuning allows compensation of any fabrication imperfections that may cause a frequency separation (˜ 100 - 400 hz ) between the two degenerate resonant modes . frequency splits as great as 430 hz have been matched by applying less than 11v tuning voltages to the tuning ( balancing ) electrodes 17 . fig1 a and 11 b illustrates the two modes before and after balancing , respectively . after balancing , the two peaks merge together and the sense and drive mode frequencies become equal . table 1 illustrates an exemplary specifications for 1 mm polysilicon resonating star gyroscopes 10 . rate test from the polysilicon resonating star gyroscopes 10 under matched operation yields an open - loop sensitivity of 1 . 6 mv /°/ s using discrete pcb electronics ( c parasitics ˜ 5 pf ), as shown in fig6 . the measured q of 1 mm , 65 μm - thick polysilicon resonating star gyroscopes 10 was 1500 under matched mode operation . this low q - factor is attributed to anchor and bulk ted losses ( voids inside polysilicon 22 ) such as is described in a paper by r . abdolvand , g . k . ho , a . erbil , and f . ayazi , entitled “ thermoelastic damping in trench - refilled polysilicon resonators ,” proc . transducers 2003 , pp . 324 - 327 , and can be improved by optimizing the design . an epitaxial polysilicon implementation of the resonating star gyroscope 10 also yields primary flexural mode operation . fig1 a and 16 b illustrates the two modes before and after balancing , respectively . after balancing , the two peaks merge together and the sense and drive mode frequencies become equal . rate tests from the epitaxial polysilicon implementation of the resonating star gyroscopes 10 under matched operation yields an open - loop sensitivity of 0 . 5 mv /°/ s using discrete pcb electronics , as shown in fig1 c . the above two implementations are examples of resonating star gyroscope structures fabricated using an isotropic elastic material . anisotropic ( 111 ) silicon may also be utilized to implement resonating star gyroscope 10 ( in the primary flexural mode operation ). a single crystalline silicon ( scs ) implementation of the resonating star gyroscope 10 provides for significantly improve quality factor which has been verified by an soi prototype . the pair of higher - order degenerate modes , shown in fig5 a and 5 b , may also be used to detect rotation . in this degenerate pair the nodes and antinodes are located 30 ° apart . in order to increase sensitivity and achieve better rate resolutions , it is desirable for the degenerate flexural modes to have high quality factors , greater drive amplitudes and larger mass . in an effort to achieve this , a single crystal silicon ( scs ) implementation of the resonating star gyroscope 10 was fabricated . a high q of 47 , 000 was measured for the primary flexural mode . however , due to the anisotropic nature of ( 100 ) scs substrate 20 , the primary drive and sense flexural modes occur 3 . 6 khz apart ( as predicted by ansys simulations and verified experimentally ). an interesting solution is to operate the gyroscope 10 using its higher - order degenerate flexural modes . as predicted by ansys simulations , these higher - order degenerate modes occur within close proximity of one another (& lt ; 1 khz ) and may be tuned electronically . single crystal silicon resonating star gyroscopes 10 were fabricated on 40 μm thick low resistivity soi . actuation gaps between the electrodes 15 , 16 , 17 and the vibrating shell 12 is defined through drie trench etching step and is therefore aspect ratio limited . the higher - order flexural mode frequency of the prototype gyroscope 10 was observed at 49 . 2 khz as predicted by ansys simulations . the frequency split between the two secondary flexural modes is compensated using a similar scheme described to tune the primary order flexural modes of the polysilicon resonating star gyroscope 10 . fig1 a and 14 b show the two resonant modes before and after balancing , respectively . wider capacitive gaps 24 ( 3 μm ) reduce device capacitance and consequently increases required operating voltages . polarization and balance voltages ( to compensate 330 hz frequency split ) for the scs resonating star gyroscope 10 are 20v and 26v respectively . table ii summarizes key parameters of the scs implementation of the resonating star gyroscope 10 and illustrates exemplary specifications for 1 mm single crystal silicon resonating star gyroscopes 10 . subsequent testing of other scs resonating star gyroscopes 10 have yielded quality factors in excess of 100 , 000 for these higher - order degenerate modes ( see fig9 a and 9 b ). thus , improved resonating star gyroscopes 10 have been disclosed . two modes of operation are possible using two distinct fabrication processes . the polysilicon harpss implementation of the resonating star gyroscope 10 was used to demonstrate primary degenerate mode operation . the harpss fabrication process facilitated high - aspect ratio sense and actuation gaps 24 . this increased the sensitivity and enabled operation at low voltages . the polysilicon resonating star gyroscope 10 demonstrated a sensitivity of 1 . 6 mv /°/ s and has a brownian noise floor of 0 . 03 °/ s /√ hz . the scs soi implementation of the resonating star gyroscope 10 exhibited higher - order degenerate mode operation . high - q and higher frequency resonant modes were achieved in this implementation which improves the brownian noise floor . thus , resonating star gyroscopes and fabrication methods relating thereto have been disclosed . it is to be understood that the above - described embodiments are merely illustrative of some of the many specific embodiments that represent applications of the principles discussed above . clearly , numerous and other arrangements can be readily devised by those skilled in the art without departing from the scope of the invention .