Finally, we gave atomic resolution images of surface potential measurements on a Ge (001) surface using a W-coated cantilever in HAM-KPFM. Main text Principles of potential 3-deazaneplanocin A solubility dmso sensitivities in FM- and HAM-KPFMs Firstly, we theoretically compared the performance of potential sensitivities in FM- and HAM-KPFMs. In NC-AFM, the frequency shift (∆f)

in cantilever vibration and the energy dissipation results in an amplitude variation (∆A) of the cantilever’s oscillation; these parameters are given by △f = - f 0 F c/(2kA), △A = QF d/k[16]. Here, f 0, k, Q, and A are the resonance frequency, the spring constant, the quality factor, and the amplitude of the cantilever, respectively. F c and F d are the tip-sample conservative and dissipative interactions, respectively. Therefore, the minimum detectable force EPZ5676 in vivo for conservative interaction and for dissipative interaction

are given by and . Here, δf and δA are the minimum detectable frequency and amplitude, respectively. For typical NC-AFM measurements in UHV, δf and δA are given by [11]: and , respectively. Here, B, f m, and n ds are the bandwidth of the lock-in amplifier, the modulation frequency, and the deflection sensor noise of the cantilever , respectively. Therefore, δF c and δF d are obtained as (1) (2) Under the typical conditions given in PRIMA-1MET Table 1, δF c is approximately 0.4pN and δF d, 0.075pN. Table 1 Typical values of parameters under vacuum conditions in KPFM simulation Parameter Unit Value A nm 5 k 1 N/m 40 k 2 N/m 1,600 f 1 kHz 300 f 2 kHz 300 × 6.3 Q   30,000 z0t nm 6 δzot nm 0.1 R nm 5 S μm 38 × 225 h μm 14 f m kHz 1

V ac V 1 B Hz 200 n ds fm/√Hz 100 In FM-KPFM, a bias voltage V Bias = V DC + V AC cos ω m t is applied; the electrostatic force [11] at frequency ω m is given by: (3) here, V CPD is the contact potential difference (CPD) between the tip and the sample, ε 0 and R are the dielectric constant in vacuum and the tip radius, respectively. z t0 and A are the average tip position and the selleck chemicals llc oscillation amplitude of the cantilever, respectively. Direct current (DC) component of the frequency shift induced by alternating current (AC) bias voltage is given by: (4) From the equation , the minimum detectable CPD can be described by [16] (5) Note that the minimum detectable CPD in FM-KPFM is independent of the quality factor of the cantilever. Under the typical conditions in Table 1, δV CPD-FM is approximately 15.11 mV with a V AC of 1 V. That means that if we want to obtain a potential resolution higher than 15 mV, V AC has to be higher than 1 V.