Supplementary Information Supplementary Figures

Supplementary Figure 1: Process flow diagram depicting the fabrication steps in realizing the GaN microcantilever with embedded AlGaN/GaN HFET at the base. (a) A diced sample (1.4 cm (a) (b) (c) (d) (h)

Corresponding strain values were obtained from the simulations, where 30 µm bending yielded an average strain (along XY plane of the mesa) of 1.3431 × 10 -3 .

Supplementary Figure 5:
Step bending performance of device 2 when the tip of the cantilever was bent 1 µm (downward) and released for multiple cycles (26 cycles are shown here). For each cycle, the cantilever was kept in the bent state for 5s and in the released state also for 5 s.
R int is the drain-source resistance of the intrinsic transistor. R c denotes the source and drain contact resistances (assumed to be equal). R acc is the access region resistance (resistance of the channel from the gate to the source or to the drain, which are also assumed to be equal) and is given by [1], Here, L DG is the length of the access region on the drain side and W D is the width of the channel. acc ,  acc and n acc are the sheet resistivity, mobility and 2D sheet carrier concentrations for the access regions. R int is the drain-source resistance of the intrinsic device, i.e. the resistance of the channel under the gate, and given as [1], Here, int ,  int and n int are the sheet resistivity, mobility and carrier concentrations for the intrinsic device, which can differ significantly from  acc and n acc , especially with applied gate bias.
Taking differential of both sides of eqn. (1) we get (4) Now, taking differential of both sides of eqn. 3, we have Dividing both sides with R int = int (L DG /W D ) we get, where, ʋ (= L DG / W D ) is the Poisson's ratio, and ε (= W D /W D ) is the strain. Similarly, Dividing both sides of the eqn. 4 with R DS and rearranging, we get, Near the pinch-off region (higher negative V GS ), R DS ≈ R int , and R DS >> R acc . Thus using eqn. 6, eqn. 8 can be written as Since, , taking differentials and dividing both sides by int we have the fractional change in piezoresistivity (Δρ int /ρ int ) given as From eqns. 9 and 10 we get, For gate bias near channel pinch-off, << n s,int /n s,int and  int / int , so we can write It is also evident from Eqns. (1) and (2) that as gate bias, V GS approaches to channel pinch off, GF increases significantly. However for the dynamic deflections, as the deflections are very small, HFET biasing should be optimized based on sensitivity (i.e. voltage responsivity, VR), Johnson noise, and the power consumptions. There has to be tradeoffs among these three parameters. Fig. S11 shows the relations of these three parameters with gate bias for device 1.
The bottom graph shows that VR increases as V GS becomes more negative (closer to pinch off), which supports our step bending scenario. The VR was measured as described in the main text and also in the next Supplementary Note 3. However as V GS becomes more negative, R DS increases more, which increases the power consumed by the HFET as can be seen in the middle graph. The power consumption was calculated using, , where I DS = 10 µA is the constant current supplied from SMU, and R DS was measured from the I-V characteristics of device 1 [see Fig. 2 (a)]. At the same time the Johnson noise (S J √ ) will also increase with more negative V GS , since R DS increases, as can be seen in the top graph of Fig. S11 (the Johnson noise was measured as described in the main article and also in Supplementary Thermo-mechanical noise at resonance: Thermo-mechanical noise off resonance (nm): The two important noise sources for microcantilevers with electrical readouts are Johnson noise and Thermomechanical noise, which we calculated following the same procedure as discussed in Ref.
2. For V GS = -2.2 V and V DS = 0.5 V, R DS was found from Fig. 2 (a) to be 5 kΩ and the Johnson noise using (1) , was calculated as 9.12 nV Hz -1/2 for a measurement bandwidth (Δf) of 1 Hz, and using k B T = 0.026 eV at room temperature. However the voltage noise spectral density (in the inset of Fig. 4 (b)) was 86 nV Hz -1/2 which actually incorporates other noise sources, such as, current preamplifier, dynamic signal analyzer, cables, etc., in addition to the Johnson noise.