Patent Application: US-201213484560-A

Abstract:
the invention provides methods , and related devices and device components , for detecting , sensing and analyzing analytes in samples . in some aspects , the invention provides methods , and related devices and device components , useful in combination with a mass analyzer for the mass spectrometric analysis of analytes derived from biomolecules in biological samples including biological fluids cell extracts , and cell lysates . methods of some aspects of the invention utilize a thin membrane - based detector as a transducer for converting the kinetic energies of analytes into a field emission signal via excitation of mechanical vibrations in an electromechanically biased membrane by generation of a thermal gradient .

Description:
referring to the drawings , like numerals indicate like elements and the same number appearing in more than one drawing refers to the same element . in addition , hereinafter , the following definitions apply : “ molecule ” refers to a collection of chemically bound atoms with a characteristic composition . as used herein , a molecule refers to neutral molecules or electrically charged molecules ( i . e ., ions ). molecules may refer to singly charged molecules and multiply charged molecules . the term molecule includes biomolecules , which are molecules that are produced by an organism or are important to a living organism , including , but not limited to , proteins , peptides , lipids , dna molecules , rna molecules , oligonucleotides , carbohydrates , polysaccharides ; glycoproteins , lipoproteins , sugars and derivatives , variants and complexes of these . analytes of the present invention may be one or more molecules . “ ion ” refers generally to multiply or singly charged atoms , molecules , and macromolecules having either positive or negative electric charge and to complexes , aggregates and clusters of atoms , molecules and macromolecules having either positive or negative electric charge . ion includes cations and anions . analytes of the present invention may be one or more molecules . “ membrane ” refers to a device component , such as a thin , optionally flat or planar structural element . membranes of the present invention include semiconductor , metal and dielectric membranes able to emit electrons when molecules contact the receiving side of the membrane . membranes useful in the present invention may comprise a wide range of additional materials including dielectric materials , ceramics , polymeric materials , glasses and metals . “ field emission ” ( fe ) or “ field electron emission ” ( fee ) is the discharge of electrons from the surface of a condensed material ( such as a metal or semiconductor ) subjected to a electric field into vacuum , low pressure region or into another material . “ secondary emission ” or “ secondary electron emission ” ( see ) is a phenomenon where primary incident particles of sufficient energy , when hitting a surface or passing through some material , induce the emission of secondary particles , such as electrons . “ active area ” refers to an area of a detector of the present invention that is capable of receiving molecules and generating a response signal , such as a response signal comprising emitted electrons . “ phonon ” refers to a unit of vibrational energy that arises from oscillating atoms within a crystal lattice . “ semiconductor ” refers to any material that is a material that is an insulator at a very low temperature , but which has an appreciable electrical conductivity at a temperature of about 300 kelvin . in the present description , use of the term semiconductor is intended to be consistent with use of this term in the art of microelectronics and electrical devices . semiconductors useful in the present invention may comprise element semiconductors , such as silicon , germanium and doped diamond , and compound semiconductors , such as group iv compound semiconductors such as sic and sige , group iii - v semiconductors such as alsb , alas , aln , alp , bn , gasb , gaas , gan , gap , insb , inas , inn , and inp , group iii - v ternary semiconductors alloys such as alxga1 - xas , group ii - vi semiconductors such as csse , cds , cdte , zno , znse , zns , and znte , group i - vii semiconductors cuci , group iv - vi semiconductors such as pbs , pbte and sns , layer semiconductors such as pbi 2 , mos2 and gase , oxide semiconductors such as cuo and cu 2 o . the term semiconductor includes intrinsic semiconductors and extrinsic semiconductors that are doped with one or more selected materials , including semiconductor having p - type doping materials and n - type doping materials , to provide beneficial electrical properties useful for a given application or device . the term semiconductor includes composite materials comprising a mixture of semiconductors and / or dopants . in the following description , numerous specific details of the devices , device components and methods of the present invention are set forth in order to provide a thorough explanation of the precise nature of the invention . it will be apparent , however , to those of skill in the art that the invention can be practiced without these specific details . fig1 provides a flow diagram illustrating an example of a method for detecting analytes , such as ions derived from biomolecules , using a nano - membrane detector of the present invention . as shown in fig1 , provided is a detector of the invention having a nano - membrane that is electromechanically biased , for example , using a combination of a holder for holding the membrane at one or more contact points and an extraction electrode positioned to provide a selected electric field on the internal surface of the nano - membrane or an emitting layer provided thereon . in some embodiments , the electrical biasing provided by the extraction electrode is sufficient to generate an electrostatic force providing for continuous fowler - nordheim field emission from the nano - membrane or emitting layer provided on the nanomembrane . the field emission from the nano - membrane or emitting layer is detected via an electron detector position to receive the field emission . optionally , the detected field emission is characterized as a field emission current as function of time . as also shown in fig1 a , ions having a characteristic average kinetic energy are directed at the detector so as to impact the receiving surface of the membrane or layer provide thereon . contact with the receiving surface converts at least portion of the kinetic energy of the ions in thermal energy , thereby generating a non - uniform temperature distribution across and / or within at least a portion of the nanomembrane . the non - uniform temperature distribution generates a thermomechanical force ( s ) that excites one or more vibrations in the nanomembrane . the resulting vibrations modulate the distance between the nanomembrane and the extraction electrode , thereby achieving an oscillation of the observed field emission current . accordingly , monitoring changes in the field emission current provides a means of detecting and characterizing the analytes interacting with the receiving surface of the nano - membrane detector . in some embodiments , in the absence of the analyte , the nanomembrane is stationary , but it emits electrons from its internal surface by field emission and , optionally , is deformed toward the extraction gate due to the applied electric field . when the analytes , such as ions having a preselected average kinetic energy , contact the receiving surface of the membrane or an absorber layer provided thereon , the kinetic energy of the analytes is transferred mostly into thermal energy . this raises the temperature in the vicinity of the impact site causing a non - uniform temperature distribution across , or within , at least a portion the nanomembrane . this thermal gradient leads to thermomechnical forces , resulting in mechanical deformation and vibration of the nanomembrane . since the intensity of field emission is strongly dependent on the electric field , which in turn is determined by the distance between the nanomembrane and the extraction gate electrode , mechanical vibrations of the nanomembrane translate into corresponding oscillations in the field emission current . the intensities of the field emission in some embodiments does not highly depend upon the m / z of the impinging ions . it rather depends on the shape of ion packet , which translates into a corresponding thermal gradient . the steeper the slope of the leading edge of the ion packet , the higher thermal gradient and the force induced . the shape of ion packet is mainly determined by mass broadening caused by the isotope distribution and instrument resolution . mass broadening caused by the isotope distribution of bsa and igg are 30 and 46 da ( 10 %- valley criteria ), respectively . this leads to a broadening in the time - of - flight of 49 . 8 ns and 50 . 8 ns , respectively . a broader ion packet at higher masses translates into a lower slope of the leading edge of the ion packet , which results in a lower force induced by ion bombardment . in time of flight ( tof ) mass spectrometry applications of the present methods , ions are first accelerated in an electric field , and directed into a field - free drift tube where they separate by mass - to charge ratio ( m / z ) before impinging on the nano - membrane detector . in some embodiments , the time when the ions are impinging on the membrane is measured , corresponding to the time of modulated field emission current induced . based on these time of flight of ions , the mass of the ions is determined . absolute mass determination may be provided by the mass analyzer , time - of - flight ( tof ) analyzer . in an embodiment , the membrane is an overdamped oscillator , such as an overdamped harmonic oscillator . mechanical overdamping is achieved in some embodiments by integration of the membrane and the holder component of the detector . in some embodiments , for example , the holder includes one or more clamps provided at contact points on the membrane , wherein upon excitation of the membrane the clamps provide a means of removing energy , thereby providing damping the membrane . overdamped membranes of some embodiments are able to mechanically deform upon impact of an ion packet with the receiving surface and undergo relaxation to the original state without undergoing subsequent mechanical deformation or vibration as a result of the initial impact of the ion packet . in this manner , the deformation of the overdamped membrane results in a detectable modulation of the electron emission followed by a return of the detector to a state ready for another measurement . use of overdamped membranes in the present methods and systems is useful to minimize “ dead time ” of the detector in which the detector is ringing down from an earlier detection event . in this manner , detectors of the invention allowing independent detector conditions for measurements closely spaced in time . in some embodiments , the vibration modes of the nanomembrane , ζ m , n ( t ), can be described by harmonic oscillators with the characteristic frequencies ω m , n , damping factor k m , n , and external force f ( t ): ⁢ ⁢ + 2 ⁢ k m , n ⁢ ω m , n ⁢ y ζ m , n + ω m , n 2 ⁢ ζ = f ⁡ ( t ) , ( 1 ) f m , n = 1 2 ⁢ l ⁢ t ⁡ ( m 2 + n 2 ) ρ ⁢ ⁢ h , ( 2 ) where t is tension per unit length , ρ is density , h is thickness , and m and n are integer values . the five different mode frequencies obtained from the fft spectrum are : f 1 , 1 = 1 . 825 mhz , f 2 , 2 = 3 . 65 mhz , f 4 , 4 = 7 . 52 mhz , f 5 , 5 = 8 . 94 , and f 7 , 7 = 12 . 05 mhz . we consider the force induced by ion bombardments with normalized gaussian function , which can be expressed by : f ⁡ ( t ) = 1 σ ⁢ 2 ⁢ π ⁢ exp ( - ( t - μ ) 2 2 ⁢ σ 2 ) , ( 3 ) solving equation ( 1 ) with three dominant mode frequencies , ω 1 , 1 *, ω 4 , 4 , and ω 7 , 7 , separately using matlab simulink yields results for ζ 1 , 1 *( t ), ζ 4 , 4 ( t ), and ζ 7 , 7 ( t ). (* indicates overdamped oscillations ). mixing of these three modes yields not only superposition of modes but also superposition of the product of each mode with different weights . therefore , ζ ( t ) can be given by : ζ ( t )= aζ 1 , 1 *( t )+ bζ 4 , 4 ( t )+ cζ 1 , 1 *( t ) ζ 4 , 4 ( t )+ dζ 7 , 7 ( t )+ eζ 1 , 1 *( t ) ζ 7 , 7 ( t )+ fζ 4 , 4 ( t ) ζ 7 , 7 ( t )+ g ( 4 ) where a , b , c , d , e and f are numerical constants and g is the dc component . it should be noted that ƒ 7 , 7 ( t ) and ζ 1 , 1 *( t ) ζ 7 , 7 ( t ) as well as ζ 4 , 4 ( t ) and ζ 1 , 1 *( t ) ζ 4 , 4 ( t ) cannot be distinguished due to the phase noise and low value of f 1 , 1 *. fig2 shows the calculated ζ ( t ) ( blue line ) and the overdamped fundamental mode ( red dots ) ζ 1 , 1 *( t ). a main feature of the overdamped fundamental mode is that the system returns to equilibrium exponentially without subsequent oscillation . for example , fig8 shows a plot of calculated dynamic displacement of the membrane as a function of time wherein the overdamped membrane is shown as red dots ( see , also “ overdamped ” label in fig8 ) and the non - overdamped system is shown as the blue lines . fig9 illustrates an example of a method of the invention for the determination of the time - of - flight of the detected ion packet . red circles and black circles represents the ion packet and overdamped fundamental mode , respectively ( see , figure labels ). the blue square represents the second derivative of the overdamped fundamental mode ( see , figure label ). as shown in fig9 , the overdamped fundamental mode is excited when the leading edge of the ion packet arrives at the nanomembrane ( see time scale of red and black circles ). in addition to the time - of - flight of the leading edge of the ion packet , the second derivative of the overdamped fundamental mode reveals the time of flight of maximum intensity of the ion packet ( see time scale of red circles and blue squares ). the invention is further detailed in the following examples , which are offered by way of illustration and are not intended to limit the scope of the invention in any manner . a mass spectrometer is a system comprised of three major parts : an ionization source , which converts molecules to ions ; a mass analyzer , which separates ions by their mass to charge ratio ; and an ion detector . mass spectrometry was revolutionized in the late 1980s by the invention of electrospray ionization ( esi ) 1 and matrix - assisted laser desorption / ionization ( maldi ) 2 , 3 , which jointly provided means of generating ions from previously inaccessible large molecules such as proteins and peptides . mass analyzer designs have since evolved to accommodate the large ions that are produced , providing dramatic improvements in performance . however , little has changed in the area of ion detection , where ions continue to be detected by one of three basic principles 4 : direct charge detection ( as in the faraday cup detector ), image charge detection ( as in the inductive detector ), or secondary electron generation ( as in the electron multiplier ( em ) or microchannel plate ( mcp ) detector ). we describe here a new principle for ion detection in time - of - flight ( tof ) 5 mass spectrometry , in which an impinging ion packet excites mechanical vibrations in a silicon nitride ( si 3 n 4 ) nanomembrane . the nanomembrane oscillations are detected by means of time - varying field emission of electrons from the mechanically oscillating nanomembrane . ion detection is demonstrated in the maldi - tof analysis of proteins varying in mass from 5 , 729 ( insulin ) to 150 , 000 ( immunoglobulin g ) daltons . the detector response agrees well with the predictions of a thermomechanical model in which the impinging ion packet causes a non - uniform temperature distribution in the nanomembrane , exciting both fundamental and higher order oscillations . in tof mass spectrometry , ions are accelerated in an electric field , and directed into a field - free drift tube where they separate by mass - to charge ratio ( m / z ) before impinging upon a detector . tof mass spectrometry is particularly important for the mass analysis of large ions in low charge states , such as those produced in the matrix - assisted laser desorption / ionization ( maldi ) process as it is the only mass analyzer design known with an essentially unlimited m / z range . the ideal tof detector would have a large area , as the ion packets can have considerable spatial extent by the time they reach the end of the drift tube ; it would be fast , in order to provide the necessary timing resolution between successive ion packets ; and it would be sensitive , so that as few ions as possible could be detected . the detectors that have best met these requirements to date are the electron multipliers ( em ) or microchannel plate ( mcp ) detectors . in these detectors the incident ions generate secondary electrons , which are then amplified in a sequential cascade process to yield a magnified output signal . the detectors have large active areas and rapid response times , thereby meeting two of the three essential criteria ; in addition , for smaller , fast - moving ions , the conversion efficiency of incident ions to secondary electrons is quite high , making the detectors highly sensitive 6 - 8 . thus , for the time - of - flight analysis of relatively low m / z ions ( e . g . & lt ;˜ 1000 daltons ), existing detectors are highly effective . however , it has been known for many decades that these detectors suffer from a severe shortcoming for the analysis of large m / z ions such as the singly charged proteins produced in the maldi process . the secondary electron generation efficiency , γ e , decreases as v 4 . 4 where v is the velocity of the incident ion 6 . since in tof , the heavier the ion , the more slowly it moves down the flight tube , this leads to a marked decrease in ion detection efficiency for larger ions 6 - 11 . this limitation in ion detection is further exacerbated in the analysis of protein mixtures , where detector saturation effects also come into play 6 . these issues in ion detection efficiency are one of the central reasons that modern mass spectrometry remains predominantly restricted to the analysis of lower molecular weight species ( e . g . tryptic peptides rather than intact proteins ). one interesting approach to addressing this problem , the cryogenic microcalorimeter , was described in the literature about a decade ago 12 - 16 . these devices , which are operated at a temperature of 4k , exhibit very high detection efficiency approaching 100 %, along with low noise levels , enabling both single ion counting capability and the ability to discriminate singly charged from doubly charged ions by providing a measure of the amount of kinetic energy deposited in the detector by the ion impact . however , their utility is compromised by their necessarily small size ( e . g . 200 μm × 200 μm ) 12 and the requirement for a cumbersome and expensive cryogenic cooling system . more recently , several reports have appeared describing nanomechanical resonators whose resonance frequency is perturbed by surface adsorption of an ion 17 - 24 . although this approach has demonstrated exceptional mass sensitivity , the devices suffer as well from extremely low active areas and slow response times and are thus far from being suitable for practical use in tof mass spectrometry at present . we describe in this example a new approach to tof ion detection , based upon the mechanical deformation and vibration of a nanomembrane . as shown in fig2 , the nanomembrane detector consists of four parts , a nanomembrane , an extraction gate , a microchannel plate , and an anode , and in the present work is placed at the end of the flight tube in a commercial maldi - tof mass spectrometer ( perseptive biosystems voyager - de str ). the square ( 5 mm × 5 mm ) nanomembrane consists of a suspended tri - layer of al / si 3 n 4 / al . the metal layers on top and below the si 3 n 4 act as a cathode for electron emission and absorber of incident ions , respectively . the principle of operation of the detector is illustrated graphically in fig2 b , and is as follows . in the absence of ion bombardment , the nanomembrane is stationary , but it emits electrons from its cathode by field emission 25 and is deformed toward the extraction gate due to the applied electric field ( see supplementary information ). since the intensity of field emission is strongly dependent on the electric field , which in turn is determined by the distance between the nanomembrane and the extraction gate electrode , mechanical vibrations of the nanomembrane excited by ion bombardment translate into corresponding oscillations in the field emission current . the modulated field emission current is superimposed on the dc field emission current , which is then amplified by the microchannel plate ( mcp ) and collected by the anode . a capacitor connected between the anode and oscilloscope provides ac coupling , allowing the time - varying field emission current to pass through but blocking the dc field emission current . consequently , only the modulated field emission current is recorded by the oscilloscope in real time . the potentiometer connected between the oscilloscope and the ground provides the impedance matching between the oscilloscope and the rest of the detector circuitry , providing better signal responses . fig3 a shows a maldi mass spectrum obtained using the nanomembrane detector for an equimolar protein mixture ( 3 . 3 μm each ) of insulin ( 5 , 729 dalton ( da )), bovine serum albumin ( bsa , 66 , 429 da ), and immunoglobulin g ( igg , ˜ 150 , 000 da ) in a sinapinic acid matrix . the time - of - flight measured by the detector corresponds roughly to the time - of - flight of the leading edge of the ion packet , as this is what initiates the membrane oscillation . in addition to the three singly charged insulin , bsa , and igg peaks , a fourth peak , corresponding to a heavy chain of igg , is also observed at a time of flight of ˜ 190 μs . in fig3 b , a magnified view of the insulin peak is given , which clearly shows a mechanical vibration of the nanomembrane with a resonance frequency of ˜ 12 . 05 mhz . fig3 c shows a superposition of the signal obtained for each of the three proteins , and illustrates that the first peak height ( labeled as ♦) and the frequency of the membrane oscillation , once initiated by the impact of the ion packet , do not depend strongly upon the m / z of the impinging ions . the maximum and minimum amplitudes of the insulin peak are 21 . 7 mv and − 18 . 7 mv , respectively , which correspond to a maximum of 40 pa and a minimum of 19 . 8 pa of the field emission current . the corresponding average displacements to yield this level of field emission current were found to be + 6 . 5 μm and − 7 . 7 μm with respect to the average static displacement of 39 . 5 μm ( with voltage and distance between the nanomembrane and the extraction gate set to 1 . 25 kv and 127 μm , respectively ). the transduction of ion kinetic energy into membrane oscillation is described well by a thermomechanical model 26 . in this model , when accelerated ions propagate through the flight tube and bombard the absorber , the kinetic energy ( in maldi - tof , typically 25 kev ) is transformed mostly into thermal energy . this raises the temperature in the vicinity of the impact site causing a non - uniform temperature distribution across the nanomembrane . this thermal gradient leads to thermomechanical forces , resulting in mechanical deformation and vibrations of the nanomembrane . the deformation and vibrations of the nanomembrane due to the thermal force and the applied dc - voltage onto the nanomembrane can be expressed by 27 where ζ is the vertical displacement , ρ is the density , h is thickness of the nanomembrane , d = eh 3 / 12 ( 1 − σ 2 ) is the flexure rigidity , e is young &# 39 ; s modulus , σ is the poisson ratio , f is the stretching force per unit length of the edge of the nanomembrane , α is the thermal expansion coefficient , t is the temperature increase above a uniform ambient level , v is the extraction gate voltage , and c is the capacitance between the nanomembrane and the extraction gate . the first and second terms on the right correspond to the forces generated by the thermal gradient and the electrostatic voltage , respectively . the evolution of the mechanical vibration can be divided into two major time regimes , ( i ) a transient , and ( ii ) a relaxation . the transient is initiated by the leading edge of the ion packet , which causes the thermal gradient and thus initiates the membrane excitation . in the subsequent relaxation process , the non - uniform temperature distribution established by the leading edge of the ion packet becomes uniform by thermal conduction while the rest of the ions in the ion packet continue to impinge upon the nanomembrane . these ions do cause additional temperature changes , but the gradient they produce is not steep enough to reinitiate the vibration . thus , the vibration ceases , the nanomembrane relaxes back to thermal equilibrium , and is ready to sense the arrival of any subsequent ion packets . a fourier transformation of the trace in fig3 a , shown in fig3 d , reveals the mechanical modes excited by ion bombardment and their contributions to the overall power spectrum . the characteristic frequencies for the vibration of the nanomembrane , f i , j , can be expressed by 27 where l is the side length of the nanomembrane , i and j are integer values , ρ is the density , h is thickness of the nanomembrane , and f is the stretching force per unit length of the edge of the nanomembrane . the dominant feature in the power spectrum is the central mode f 7 , 7 = 12 . 05 mhz ( θ ), with sidebands on both sides due to its mixing with other frequencies . the three other dominant modal frequencies found from the power spectrum are : f 2 , 2 = 3 . 65 mhz ( β ), f 4 , 4 = 7 . 52 mhz ( γ ), and f 5 , 5 = 8 . 94 mhz ( δ ). these modes are mixed with the most dominant mode , f 7 , 7 = 12 . 05 mhz ( θ ), due to the nonlinearity of fowler - nordheim field emission 25 , yielding multiple sets of two sidebands , θ − f i , j and θ + f i , j . in addition to the four dominant modes , the fundamental mode with the characteristic frequency , f 1 , 1 = 1 . 825 mhz , can be derived from equation [ 2 ]. the mechanical vibration shape corresponding to each mode is shown in fig3 f . in the time domain , the mixing of each mode results in modulation of their amplitudes . it should be noted that the fundamental mode , f 1 , 1 , does not appear at the frequencies of θ − f 1 , 1 and θ + f 1 , 1 in the power spectrum and there is a peak near dc , labeled as α *. this is due to overdamping of the fundamental mode by the applied electrostatic force . the coefficient α * is the sinusoidal decomposition of the overdamped fundamental mode ( see supplementary information ). a numerical calculation for the mixing of the overdamped fundamental mode f 1 , 1 with f 4 , 4 ( γ ), and f 7 , 7 ( θ ), yields an oscillation profile that closely resembles the experimental data as shown in fig3 e . the envelope of the most dominant mode , θ , decays exponentially without oscillating due to modulation by the overdamped fundamental mode ( red dashed line ) ( see supplementary information ). fig6 a in the upper sequence of plots gives the individual traces of the nanomembrane detector response for four different proteins . as seen the first peak of the nanomembrane &# 39 ; s response to proteins show almost identical amplitudes . plotting these first peaks &# 39 ; amplitudes and widths vs . the mass range ( proportional to the flight time ) indicates that the amplitude is almost constant . this enables operation of the nanomechanical detector independently of the protein mass . the width increases for larger masses mainly due to the broader isotope distribution at higher masses . b , taking the width of the first resonance peak as the lower limit of the temporal resolution , consequently the mass resolution increases towards higher masses . the oscillations can be divided into two major time regimes , ( i ) a transient , and ( ii ) a relaxation . the transient corresponds to the leading edge of the ion packet , which excites the first peak of the vibration . in the relaxation regime , the temperature distribution becomes uniform , by thermal conduction , and the vibration has ceased . fig6 a shows height and width of the first peak for each protein , which falls into the transient regime . as seen , the height is reduced only slightly and the width increases slightly at higher masses . this is mainly due to the shape of the ion packets , which is smaller in height but broader in width at higher masses due to the mass broadening caused by isotope distribution . fig6 b shows a resolution over the mass range . we used the width of the first peak as the time resolution of the detector . with the time resolution being fixed for all masses , the mass resolution ( m / δm ) increases with increasing molecule mass . fig7 a shows a comparison of the nanomembrane detector and a commercial multi - channel - plate ( mcp ) detector for the bsa spectrum . the molar concentration of the bsa is 10 μm . both spectrums are calibrated to have a standard mass of bsa . the nanomembrane detector reveals many more resonances than the mcp under the same conditions , such as laser power and mcp bias . the additional resonances detected by the nanomembrane detector are attributed to fragment ions generated by the laser irradiation . the height and the width of the first peak of the resonances over the entire mass range remain constant with only small variations . fig7 c shows good separation between molecular ion and matrix adduct ion with a temporal difference corresponding to 241 da , which is close to the mass of the sinapinic acid matrix ( mass 224 da ). the nanomembrane detector can resolve two ion packets as long as they are separated by the width of the first peak even though the second ion packet arrives before the mechanical vibration excited by the first ion packet has ceased . therefore , the time resolution of the nanomembrane detector can be defined by the width of the first peak through the paper . we estimate to achieve a lower concentration limit of any given analyte of below 100 - fm , since the effective detector area can be maximized to larger than 6 ″ and may be limited by the mcps active cross section of typically 1 . 5 ″. in fig7 b , the normalized value of the first oscillation peak of the resonances is plotted over the mass range . as seen the amplitude variation is within the error , indicating as well that the nanomembrane detector is not limited in range by the mass . in fig7 c , provide results for the separation of molecule ion and matrix adduct ion . absolute resolution : two ions arrive at the detector with a temporal difference shorter than the ring - down time of the nanomembrane resonator was separated fig7 d shows a mass resolution with the widths of the first peak being the time resolution . with the width of the first peak of the oscillations defining the minimal temporal resolution , the mass resolution apparently increases towards higher masses . fig1 provides a mass spectrum of angiotensin obtained using the detection methods and detectors of the present invention . the operating conditions for this measurement include : ( 1 ) voltage between the nanomembrane and the extraction gate : 1 . 6 kv , ( 2 ) acceleration voltage : 20 kv , ( 3 ) matrix : α - cyano - 4 - hydroxycinnamic acid , ( 4 ) nanomembrane thickness : 42 nm , ( 5 ) thickness of the metal on both sides of the nanomembrane : 13 nm . this measurement further illustrates the dynamic range of the detectors and detection methods of the invention . in conclusion , the present example provides new methods and systems for ion detection in time of flight mass spectrometry , based upon the thermomechanical response of a nanomembrane to an impinging ion packet . the results of this example suggest that this mode of ion detection offers improved sensitivity in the mass analysis of large ions and complex protein mixtures . a thin layer of silicon nitride ( si 3 n 4 , ˜ 46 nm ) is deposited on both sides of a silicon wafer ( 100 ) using low - pressure chemical vapor deposition ( lpcvd ). the membrane area is defined by optical lithography and reactive ion etching of si 3 n 4 on the backside of the silicon wafer . finally , a square ( 25 mm 2 ) triple layer of al / si 3 n 4 / al is formed by anisotropic etching of the silicon wafer by potassium hydroxide ( koh ) solution followed by metal sputtering (˜ 13 nm ) on both sides of the si 3 n 4 membrane . the nanomembrane was mounted in the voyager de str and the measurements were carried out in delayed extraction mode . the proteins and matrix were purchased from sigma aldrich . the mixing of the modes was calculated using matlab simulink . the mode shapes of the nanomembrane were calculated using comsol v3 . 3 . the electrostatic force applied by the extraction gate voltage causes two important consequences : first , it bulges the nanomembrane towards the extraction gate . second , it supports emission of electrons from the nanomembrane , which is governed by fowler - nordheim field electron emission . the displacement of the nanomembrane under uniform load can be expressed by [ 1 ]: where p is the pressure , ζ max is the displacement at the center of the nanomembrane , e is young &# 39 ; s modulus , σ is the residual stress , v is the poisson &# 39 ; s ratio , t is the thickness of the nanomembrane , a is one half of the nanomembrane &# 39 ; s length , and c 1 and c 2 ( v ) are numerical constants . for small deformations , as described in the first term on right side , the displacement is proportional to the force and highly dependent upon the residual stress of the nanomembrane . however , for large deformations , as described in the second term on the right side , the displacement is proportional to the cube - root of the force and dominated by young &# 39 ; s modulus . young &# 39 ; s modulus of the al / si 3 n 4 / al tri - layer can be found by using the rule of mixtures : e tri - layer = e al υ al + e si 3 n 4 ( 1 − υ a1 ) ( s2 ) fig4 a shows a maximum ( red circles ) and an averaged ( blue squares ) displacement of the nanomembrane as a function of pressure . the pressure induced by the electrostatic force applied between the nanomembrane and the extraction gate can be given by : where ∈ 0 is the vacuum permittivity , a is the area , and v gm and d are the voltage and the distance between the nanomembrane and the extraction gate , respectively . in our particular case , as the nanomembrane deforms its shape , the displacement between the nanomembrane and the extraction gate changes continuously . once the nanomembrane is deformed , the distance between the nanomembrane and the extraction gate becomes a function of position , ζ ( x , y , v gm ). the shape function of the deformed nanomembrane can be given by [ 1 ]: where ζ max is the displacement at the center of the nanomembrane , and a is one half of the nanomembrane &# 39 ; s length . the average displacement over the nanomembrane &# 39 ; s surface can be given by : the ratio of averaged and maximum displacement for a given pressure , α , can be found by : d ( v gm )= d 0 = ζ ave ( v gm )= d 0 − αζ max ( v gm ), ( s7 ) where d 0 = 127 μm is the initial distance between the nanomembrane and the extraction gate . substituting equation ( s7 ) into equation ( s3 ) yields an equation for the pressure as a function of voltage applied between the nanomembrane and the extraction gate : therefore , the pressure can be converted into the voltage applied between the nanomembrane and the extraction gate , v gm , as shown in fig . s 1 b . the maximum static displacement ( red circles ) of 81 . 7 μm and the averaged static displacement ( blue squares ) of 39 . 5 μm were calculated for v gm at 1 . 25 kv . a modified fowler - nordheim ( fn ) equation [ 2 ], which takes this shape function into account , can be found by substituting equation ( s7 ) into the fn equation and expressed by : fig5 a shows a measured field emission current from the deformed nanomembrane plotted in fowler - nordheim representation ( red dots ). the blue line represents the calculated field emission current according to the modified fn equation given in equation ( s9 ) and shows good agreement with the measured field emission current . the field emission current of 29 . 15 pa was observed for v gm of 1 . 25 kv . the maximum and minimum of the insulin peak in fig3 a are 21 . 7 mv and − 18 . 7 mv , respectively . the field emission current to yield this level of voltage across the load resistor with the mcp gain can be found by where i fn is the field emission current , v is the voltage measured , r load is the load resistance , and gain mcp is the gain of the mcp . these result in a maximum of 40 pa and a minimum of 19 . 8 pa for the field emission current with the potentiometer resistance of 2 kω , the input impedance of the oscilloscope of 1 mω , and the mcps gain of 10 6 . the distance between the nanomembrane and the extraction gate yielding this level of field emission current can be found by using equation ( s9 ) with a v gm set at 1 . 25 kv . the averaged dynamic displacements of the nanomembrane were found to be + 6 . 5 μm and − 7 . 7 μm with respect to the averaged static displacement of 39 . 5 μm , as shown in fig5 b . the vibration modes of the nanomembrane , ζ i , j ( t ), can be described by harmonic oscillators with the characteristic frequencies ω i , j , damping factor k i , j , and external force f ( t ): where t is tension per unit length , ρ is density , h is thickness , and i and j are integer values . the four dominant mode frequencies obtained from the fft spectrum are : f 2 , 2 = 3 . 65 mhz , f 4 , 4 = 7 . 52 mhz , f 5 , 5 = 8 . 94 , and f 7 , 7 = 12 . 05 mhz . the fundamental mode with the characteristic frequency , f 1 , 1 = 1 . 825 mhz , can be derived from equation [ 2 ]. this fundamental mode is overdamped due to the applied electrostatic force . the indications for the overdamped fundamental mode can be found in the time domain traces of fig3 b and 3 c . in fig3 c , the second peak amplitude , labeled as ▾, is higher when compared to the first peak amplitude , labeled as ♦, indicating that the amplitudes are modulated by a lower frequency mode . however , the envelope of the peaks then decays to equilibrium without oscillating as shown in fig3 b . the overall envelope shape resembles a typical response of overdamped harmonic oscillators . we consider the force induced by ion bombardments with normalized gaussian function , which can be expressed by : solving equation ( s11 ) with three dominant mode frequencies , ω 1 , 1 *, ω 4 , 4 , and ω 7 , 7 , separately using matlab simulink yields results for ζ 1 , 1 *( t ), ζ 4 , 4 ( t ), and ζ 7 , 7 ( t ). (* indicates overdamped oscillations ). mixing of these three modes yields not only superposition of modes but also superposition of the product of each mode with different weights . therefore , ζ ( t ) can be given by : ζ ( t )= aζ 1 , 1 *( t )+ bζ 4 , 4 ( t )+ cζ 1 , 1 *( t ) ζ 4 , 4 ( t )+ dζ 7 , 7 ( t )+ eζ 1 , 1 *( t ) ζ 7 , 7 ( t )+ fζ 4 , 4 ( t ) ζ 7 , 7 ( t )+ g ( s14 ) where a , b , c , d , e and f are numerical constants and g is the dc component . it should be noted that ζ 7 , 7 ( t ) and ζ 1 , 1 *( t ) ζ t , t ( t ) as well as ζ 4 , 4 ( t ) and ζ 1 , 1 *( t ) ζ 4 , 4 ( t ) cannot be distinguished due to the phase noise and low value of f 1 , 1 *. as shown in fig3 e , the maximum amplitude of the overdamped fundamental mode coincides with the second peak of the most dominant mode , θ , resulting in a higher second peak amplitude , labeled as ∇, when compared to the first peak amplitude , labeled as ⋄, the envelope of the most dominant mode , θ , decays exponentially without oscillating due to modulation by the overdamped fundamental mode . fenn , j . b ., mann , m ., meng , c . k ., wong , s . f . & amp ; whitehouse , c . m . electrospray ionization for mass spectrometry of large biomolecules . science 246 , 64 - 71 ( 1989 ). tanaka , k . et al . protein and polymer analyses up to m / z 100 , 000 by laser ionization time - of - flight mass spectrometry . rapid commun . mass spectrom . 2 , 151 - 153 ( 1988 ). karas , m . & amp ; hillenkamp , f . laser desorption ionization of protein with molecular masses exceeding 10 , 000 daltons . anal . chem . 60 , 2299 - 2301 ( 1988 ). geno , p . w . ion detection in ms . in : mass spectrometry in the biological sciences : a tutorial . kluwer academic publ ., netherlands , ( 1992 ). wiley , w . c . & amp ; mclaren , i . h . time - of - flight mass spectrometry with improved resolution . rev . sci . instrum . 26 , 1150 - 1157 ( 1955 ). chen , x ., westphall , m . s . & amp ; smith , l . m . mass spectrometric analysis of dna mixtures : instrumental effects responsible for decreased sensitivity with increasing mass . anal . chem . 75 , 5944 - 5952 ( 2003 ). geno , p . w . & amp ; macfarlane , r . d . secondary electron emission induced by impact of low - velocity molecular ions on a microchannel plate . int . j . mass spectrom . ion processes 92 , 195 - 210 ( 1989 ). westmacott , g ., frank , m ., labov , s . e . & amp ; benner , w . h . using a superconducting tunnel junction detector to measure the secondary electron emission efficiency for a microchannel plate detector bombarded by large molecular ions . rapid commun . mass spectrom . 14 , 1854 - 1861 ( 2000 ). westmacott , g ., ens , w . & amp ; standing , k . g . secondary ion and electron yield measurements for surfaces bombarded with large molecular ions . nucl . instrum methods phys . res . b 108 , 282 - 289 ( 1996 ). beuhler , r . j . & amp ; friedman , l . threshold studies of secondary electron emission induced by macro - ion impact on solid surfaces . nucl . instrum . methods 170 , 309 - 315 ( 1980 ). meier , r . & amp ; eberhardt , p . velocity and ion species dependence of the gain of microchannel plates . int . j . mass spectrom . ion processes 123 , 19 - 27 ( 1993 ). hilton , g . c . et al . impact energy measurement in time - of - flight mass spectrometry with cryogenic microcalorimeters . nature 391 , 672 - 675 ( 1998 ). twerenbold , d . et al . single molecule detector for mass spectrometry with mass independent detection efficiency . proteomics 1 , 66 - 69 ( 2001 ). esposito , e ., cristiano , r ., pagano , s ., perez de lara , d . & amp ; twerenbold , d . fast josephson cryodetector for time of flight mass spectrometry . physica c ( the netherlands ) 372 / 376 , 423 - 426 ( 2002 ). gervasio , g . et al . aluminum junctions as macromolecule detectors and comparision with ionizing detectors . nucl . instrum . methods phys . res . a 444 , 389 - 394 ( 2000 ). frank , m ., labov , s . e ., westmacott , g . & amp ; benner , w . h . energy - sensitive cryogenic detectors for high - mass biomolecule mass spectrometry . mass spectrom . rev . 18 , 155 - 186 ( 1999 ). ekinci , k . l ., huang , x . m . h . & amp ; roukes , m . l . ultrasensitive nanoelectromechanical mass detection . appl . phys . lett . 84 , 4469 - 4471 ( 2004 ). yang , y . t ., callegari , c ., feng , x . l ., ekinci , k . l . & amp ; roukes , m . l . a self - sustaining ultrahigh - frequency nanoelectromechanical oscillator . nature nanotech . 3 , 342 - 346 ( 2008 ). cleland , a . n . thermomechanical noise limits on parametric sensing with nanomechanical resonators . new j . phys . 7 , 235 ( 2005 ). ekinci , k . l ., yang , y . t . & amp ; roukes , m . l . ultimate limits to inertial mass sensing based upon nanoelectromechanical systems . j . appl . phys . 95 , 2682 - 2689 ( 2004 ). lassagne , b ., garcia - sanchez , d ., aguasca , a . & amp ; bachtold , a . ultrasensitive mass sensing with a nanotube electromechanical resonator . nano lett . 8 , 3735 - 3783 ( 2008 ). jensen , k ., kim , k . & amp ; zettl , a . an atomic - resolution nanomechanical mass sensor . nature nanotech . 3 , 533 - 537 ( 2008 ). chiu , h .- y ., hung , p ., postma , h . w . c . & amp ; bockrath , m . atomic - scale mass sensing using carbon nanotube resonators . nano lett . 8 , 4342 - 4346 ( 2008 ). naik , a . k ., hanay , m . s ., hiebert , w . k . feng , x . l . & amp ; roukes , m . l . towards single - molecule nanomechanical mass spectrometry . nature nanotech . 4 , 445 - 450 ( 2009 ). fowler , r . h . & amp ; nordhein , l . electron emission in intense electric fields . proc . r . soc . london , ser . a 119 , 173 ( 1928 ). sato , t ., ochiai , i ., kato , y . & amp ; murayama , s . vibration of beryllium foil window caused by plasma particle bombardment in plasma focus x - ray source . jpn . j . appl . phys . 30 , 385 - 391 ( 1991 ). landau , l . d . & amp ; lifshitz , e . m . theory of elasticity . 3 rd edition . pergamon press , new york ( 1986 ). maier - schneider , d ., maibach , j . & amp ; obermeier , e ., a new analytical solution for the load - deflection of square membranes . j . mems . 4 , 238 - 241 , ( 1995 ). fowler , r . h . & amp ; nordhein , l ., electron emission in intense electric fields , proc . r . soc . london , ser . a 119 , 173 ( 1928 ). mechanical resonators realized on the nano - scale by now offer applications in mass - sensing of biomolecules with extraordinary sensitivity . the general idea is that perfect mechanical biosensors should be of extremely small size to achieve zepto - gram sensitivity in weighing single molecules similar to a balance . however , the small scale and long response time of weighing biomolecules with a cantilever restricts their usefulness as a high - throughput method . commercial mass spectrometry ( ms ), such as electro - spray ionization ( esi )- ms and matrix - assisted laser desorption / ionization ( maldi )- time of flight ( tof )- ms are the gold standards to which nanomechanical resonators have to live up . these two methods rely on the ionization and acceleration of biomolecules and the following ion detection after a mass selection step , such as time - of - flight ( tof ). hence , the spectrum is typically represented in m / z , i . e . the mass to ionization charge ratio . in this example , we demonstrate the feasibility and mass range of detection of a new mechanical approach for ion detection in time - of - flight mass spectrometry . the principle of which is that the impinging ion packets excite mechanical oscillations in a silicon nitride nanomembrane . these mechanical oscillations are henceforth detected via field emission of electrons from the nanomembrane . ion detection is demonstrated in maldi - tof analysis over a broad range with angiotensin , bovine serum albumin ( bsa ), and an equimolar protein mixture of insulin , bsa , and immunoglobulin g ( igg ). the results show unprecedented mass range of operation of the nanomembrane detector . mass spectrometry is a system comprised of three major parts : an ionization source , which converts molecules to ions , a mass analyzer , which separates ions by their mass to charge ratio , and an ion detector . mass spectrometry was revolutionized in the late 1980s by the invention of electrospray ionization ( esi ) 1 and matrix - assisted laser desorption / ionization ( maldi ) 2 , 3 , which jointly provided means of generating ions from previously inaccessible large molecules such as proteins and peptides . mass analyzer designs , such as the time - of - flight ( tof ) methods , have since evolved to accommodate the large ions that are produced , providing dramatic improvements in performance . mass spectrometry has become one of the most attractive methods for rapid identification and the classification of complex proteins . these tremendous improvements over the past decades helped to complete the genome sequencing . in the most common method of mass spectrometry maldi - tof , molecules are first vaporized and typically singly or doubly ionized , before being accelerated in an electric field , and directed into a field - free drift tube where they separate by mass - to - charge ratio ( m / z ). finally , the ions interact with a detector . since the ions acquire the same kinetic energy when they are accelerated , their velocity and time of flight differs according to their m / z - ratio . the use of tof mass analyzers provides an unlimited m / z - range and hence is particularly important for the mass analysis of large ions with low charge states produced with maldi . despite the essentially unlimited m / z - range of tof , the m / z - range of mass spectrometers is limited by the detectors . in these conventional detectors ions are identified by secondary electron generation , such as in electron multipliers ( em ) or micro - channel plates ( mcp ) 4 . the efficiency of these detectors is proportional to the velocity of the incident ion . in tof mass spectrometry , ions with higher mass inherently have lower velocity , this leads to a decrease in ion detection efficiency for large ions 5 - 10 . obviously , this creates a big demand for a detector with detection efficiency independent of ion velocity . the ideal tof detector fulfills the following criteria 11 : ( 1 ) it should have a large area , as the ion packets can have considerable spatial extent by the time they reach the end of the drift tube ; ( 2 ) it should be fast in responding to the incoming ions and in order to provide the necessary timing resolution between ions as well as successive ion packets ; ( 3 ) it should be sensitive , so that as few ions as possible can be detected ; and ( 4 ) it should be compatible with existing mass spectrometer technology . in this example we demonstrate the feasibility of an unconventional operating principle of nanomechanical systems for mass spectrometry , namely to measure the impact of impinging biomolecules onto a nanomechanical system . mechanical systems typically interact with their environment either by ( i ) statically deforming their shape or ( ii ) in a dynamical fashion with an alteration of their resonance frequency or ( iii ) by the onset of oscillations , also labeled the quasi - dynamic mode . the fundamental idea of the static mode ( i ) is the transduction of the surface stress induced by intermolecular force into a displacement of the mechanical system , e . g . cantilever . as molecules are adsorbed on the cantilever surface , charge will be removed from or added to the bonds between the cantilever surface atoms depending on the electronegativity of the adsorbate molecules , i . e . electron donor or acceptor , with respect to the cantilever surface . the change of the charge density between the cantilever surface bonds decreases or increases the tensile surface stress , resulting in mechanically bending the cantilever 12 . this bending can be determined straight forwardly with a laser interferometer 13 - 15 . fritz et al . 16 have first demonstrated the detection of dna - strands using functionalized surface of cantilevers . functionalization of a cantilever &# 39 ; s surface can be achieved by immobilizing a monolayer of receptor molecules on one side of it . in a liquid environment , the cantilevers are then susceptible to spurious deflection caused by temperature changes and fluidic disturbances . differential measurement , which is a simultaneous measurement of an in situ reference cantilever aligned with the sensor cantilever , can eliminate these environmental factors 15 . this mode of operation has demonstrated its unique ability for label - free detection of various bio - molecules and their interactions , but fails to meet the first two and the last criteria for mass spectrometer detectors . in the dynamic mode ( ii ), the resonance frequency of the nanomechanical resonator , usually a cantilever or doubly clamped beam , is perturbed , e . g . by surface adsorption of molecules . this mode enables the measurement of masses with high sensitivity . the resonance frequency of nanomechanical resonators is connected to the effective mass of the resonator . as molecules are adsorbed on the resonator , the effective mass of the resonator increases , resulting in a resonance frequency shift . the relation between this shift and the mass change , assuming that the adsorbed mass is distributed evenly along the resonator , can be expressed by δ ⁢ ⁢ f = - f 0 2 ⁢ m 0 ⁢ δ ⁢ ⁢ m ( 1 ) where the δf is the shift in resonance frequency , f 0 is the resonance frequency , m 0 is the initial mass of the nanomechanical resonator , and δm is the change in mass . a detailed analysis of the responsivity function r ( x ), which is the ratio of the shift in resonance frequency δf to the change in mass δm , as a function of position x , of the adsorbed mass along the beam can be performed 17 . this mode of operation has been demonstrated exceptional mass sensitivity in air or vacuum 17 - 25 . however , in liquid environment , viscosity severely degrades mass resolution and sensitivity . burg et al 26 - 28 eliminate viscosity damping by placing the solution inside a hollow resonator and have demonstrated weighing of single nanoparticles , single bacterial cells and biomolecules with sub - femtogram resolution . biosensors in this mode of operation exhibit extraordinary sensitivity , but suffer from long response times . the quasi - dynamic mode ( ii ) finally is based on the transduction of the kinetic energy of the bio - molecules bombarding the surface the nanomembrane into the mechanical oscillations 29 . as high - energy ion packets hit the nanomembrane , the kinetic energy is transformed into thermal energy . this raises the temperature in the vicinity of the impact site causing a non - uniform temperature gradient over the nanomembrane . this results in a force , which in turn leads to a thermal deformation and mechanical vibration of the nanomembrane . unless a successive ion packet arrives , the vibration ceases , and eventually the nanomembrane falls back to its equilibrium position . the vibration of the nanomembrane can be detected by a position sensor 29 , which is in our case by means of field emission 11 . the induced vibrations of the nanomembrane caused by the thermal gradient can be expressed by 30 ρ ⁢ ⁢ h ⁢ ⁢ ζ ¨ + d ⁢ ⁢ δ 2 ⁢ ζ - f ⁢ ⁢ δ ⁢ ⁢ ζ = - e ⁢ ⁢ α 3 ⁢ ( 1 - 2 ⁢ σ ) ⁢ ∇ t ( 2 ) where ζ is the vertical displacement , ρ is the density , h is thickness of the nanomembrane , d = eh 3 / 12 ( 1 − σ 2 ) is the flexure rigidity , e is young &# 39 ; s modulus , σ is the poisson ratio , f is the stretching force per unit length of the edge of the nanomembrane , α is the thermal expansion coefficient , and t is the temperature increase above a uniform ambient level . the characteristic frequencies for the vibration of the nanomembrane , f i , j can be expressed by 30 f i , j = 1 2 ⁢ l ⁢ f ⁡ ( i 2 + j 2 ) ρ ⁢ ⁢ h ( 3 ) where i and j are integer values , l is the side length of the nanomembrane , ρ is the density , h is thickness , and f is the stretching force per unit length of the edge of the nanomembrane . in an early experiment it was shown that the vibrations of beryllium foil windows can be driven by plasma particle bombardment 29 . recently , we successfully demonstrated ion detection using this mode of operation with a maldi - tof analysis of proteins 11 . the mass range investigated was in between 5 , 729 ( insulin ) up to 150 , 000 ( immunoglobulin g ) dalton 11 . this mode of operation provides a convenient and practicable approach of sensing molecules by a nanomechanical sensor . as mentioned above our approach to mass spectrometry is based upon the quasi - dynamic mode of operation of large cross - section nanomembranes . in fig1 a the detector composition is shown consisting of four parts : a nanomembrane , an extraction gate , an mcp , and an anode . in the present work this detector is placed at the end of the flight tube in a commercial maldi - tof mass spectrometer ( perseptive biosystems voyager - de str ). the square nanomembrane with a cross sectional area of 5 × 5 - mm 2 is composed by a suspended tri - layer of al / si 3 n 4 / al . the metal layers on top and below the si 3 n 4 act as a cathode for electron emission and absorber of incident ions , respectively . the fabrication of the suspended tri - layer nanomembrane is as follows : a thin layer of silicon nitride ( si 3 n 4 , 42 ˜ 46 nm ) is deposited on both sides of a silicon wafer ( 100 ) using low - pressure chemical vapor deposition ( lpcvd ). the membrane area is defined by optical lithography and reactive ion etching of si 3 n 4 on the backside of the silicon wafer . finally , a square ( 5 × 5 mm 2 ) triple layer of al / si 3 n 4 / al is formed by anisotropic etching of the silicon wafer by potassium hydroxide ( koh ) solution followed by metal sputtering (˜ 13 nm ) on both sides of the si 3 n 4 membrane . the principle of operation of the detector is illustrated in fig1 b : with the voltage applied between the nanomembrane and the extraction gate , mechanical vibrations of the nanomembrane excited by ion bombardment translate into corresponding oscillation in the field emission current . the modulated field emission current is then amplified by the mcp and collected by the anode before being recorded on the oscilloscope . in addition to the force , which is induced by the ion bombardment , the dc voltage applied between the nanomembrane and the extraction gate will induce the electrostatic force . the vibrations and the deformation due to the thermal force and dc voltage can be expressed by ρ ⁢ ⁢ h ⁢ ⁢ ζ ¨ + d ⁢ ⁢ δ 2 ⁢ ζ - f ⁢ ⁢ δ ⁢ ⁢ ζ = - e ⁢ ⁢ α 3 ⁢ ( 1 - 2 ⁢ σ ) ⁢ ∇ t - 1 2 ⁢ v 2 ⁢ ⅆ c ⅆ ζ ( 4 ) where v and c are the voltage and capacitance between the nanomembrane and the extraction gate , respectively . fig1 c shows a maldi mass spectrum obtained using the nanomembrane detector for angiotensin ( 1 , 296 dalton ( da )) in an α - cyano - 4 - hydroxycinnamic acid matrix . the molar concentration of the angiotensin is 10 μm . in addition to the singly charged angiotensin peak , the tetramer matrix and the tetramer matrix adduct angiotensin peaks are observed at a time - of - flight of 26 . 5 μs and 43 . 5 μs , respectively . the voltage and distance between the nanomembrane and the extraction gate are set to 1 . 6 kv and 127 μm , respectively , while the acceleration voltage is set to 20 kv . in order to compare a conventional mcp to the nanomembrane detector , we measured the same spectra and swapped the two detectors in the same maldi - tof unit . the result is shown in fig1 : the upper panel gives the nanomembrane detector &# 39 ; s response , while the lower panel shows the same bsa spectrum traced with a chevron mcp detector . the molar concentration of the bsa is 10 μm . both spectra are calibrated to have a standard mass of bsa when the time of flight is converted to the corresponding m / z . the nanomembrane detector ‘ sees ’ more peaks than the mcp under the same conditions such as laser power and mcp bias . the additional resonances are only detected by the nanomembrane detector and can be attributed to either fragment ions generated in the maldi process or during the tof transition . if the proteins fragment within the tof - unit , it is possible that the nanomembrane can ‘ see ’ uncharged molecules , typically labeled as neutrals . the resonance frequency of the most dominant mode was found to be ˜ 18 . 8 mhz ( with voltage between the nanomembrane and the extraction gate set to 1 . 7 kv and acceleration voltage set to 25 kv ). the height of the resonances over the entire mass range of interest for angiotensin and bsa remains constant with only small variations as shown in fig1 c and 12 . in order to test the nanomembrane detector with a more complex protein mixture we use an equimolar protein mixture ( 3 . 3 μm each ) of insulin ( 5 , 729 da ), bsa , and immunoglobulin g ( igg , ˜ 150 , 000 da ) in a sinapinic acid matrix . fig1 a shows the resulting maldi mass spectrum obtained using our nanomembrane detector with the voltage between the nanomembrane and the extraction gate set to 1 . 25 kv and an acceleration voltage of 20 kv . in addition to the three singly charged insulin , bsa , and igg peaks , additional peaks are revealed . we speculate that these are fragment ions or neutrals generated in the maldi - tof unit . fig1 b shows the expanded regions for insulin , bsa , and igg peaks in the sub - microsecond range . on this time scale the mechanical vibrations of the nanomembrane can be clearly resolved . with the appearance of the first peak ( labeled as ∇) enough energy is transferred to cause the onset of mechanical oscillations . fig1 c shows the height of the first peak ( labeled as ∇ in fig1 b ) for each protein ( dots ) and their linear regression ( line ). the height of the first peak of insulin , bsa and igg is normalized to the height of first peak of insulin . as seen , the normalized peak height is reduced only slightly at higher masses ( less than 20 % up to 150 kda ). the inset shows the extrapolation of a linear regression to zero intensity in log - scale and indicates that the upper mass limit of the detector is found to be 1 . 5 mda . an interesting aspect of this detector is the fact that the height of the peak is not highly dependent upon the m / z value . these features of the nanomembrane detector offer potential for improved performance in the analysis of large molecules . in order to examine the resolving power ( δm ), we use the full - width - at - half - maximum ( fwhm ) of the envelope of the oscillations as a definition for δm , as indicated by the two arrows in the inset of fig1 a . it shows the expanded region of the bsa peak along with the envelope ( red line ) and fwhm ( blue arrows ) of the oscillations . fig1 a shows this resolving power of the nanomembrane detector ( black circles ) and their linear regression ( red line ) over the mass range from 5 kda to 150 kda . in order to test the validity of our definition of the resolving power , we now focus on an expanded region of the detector &# 39 ; s response . fig1 b shows the expanded region of the peak , which is enclosed in the blue box in fig1 a . it demonstrates the separation of two ion packets with m / z of 39 , 533 and 39 , 773 da arriving at the detector with a temporal difference corresponding to ˜ 240 da . this resolving power of 240 da is labeled by a * in fig1 a . it directly matches the linear regression of resolving power obtained from the data . it should be noted that the fwhm of the oscillations is highly dependent on the relaxation time , which in turn is determined by the mechanical properties of the nanomembrane . therefore , the resolving power can be strongly improved by exciting higher order modes of oscillations , which dissipates its energy quickly . fig1 shows the comparison of the nanomembrane detector ( top panel ) and a commercial detector ( bottom panel ) for the maldi analysis of the protein mixture originally used in fig1 . the commercial detector consists of a chevron mcp , a phosphor screen , and a photomultiplier tube . the mass spectrum obtained using the commercial detector shows the limitation of the conventional detector for the analysis of large m / z mixture ions , where detector saturation effects come in to play . the mcp detector barely shows the bsa peak and cannot reveal the igg , while the nanomembrane detector provides a rich spectrum . in conclusion , this example demonstrates an unprecedented mass range delivered by nanomembrane detectors operating in the quasi - dynamic mode . this extremely broad mass range lends itself for the analysis of large ions with a mass to above 1 mda . the detector can be readily applied to commercial mass spectrometry , as we have shown . 1 . fenn , j . b ., mann , m ., meng , c . k . & amp ; wong , s . f . electrospray ionization for mass spectrometry of large biomolecules . science 246 , 64 - 71 ( 1989 ). 2 . tanaka , k ., waki , h ., ido , y ., akita , s ., yoshida , y ., yoshida , t . & amp ; matsuo , t . protein and polymer analyses up to m / z 100 , 000 by laser ionization time - of - flight mass spectrometry . rapid commun . mass spectrom . 2 , 151 - 153 ( 1988 ). 3 . karas , m . & amp ; hillenkamp , f . laser desorption ionization of protein with molecular masses exceeding 10 , 000 daltons . anal . chem . 60 , 2299 - 2301 ( 1988 ). 4 . geno , p . w . ion detection in ms . in : mass spectrometry in the biological sciences : a tutorial . kluwer academic publ ., netherlands , ( 1992 ). 5 . chen , x ., westphall , m . s . & amp ; smith , l . m . mass spectrometry analysis of dna mixtures : instrumental effects responsible for decreased sensitivity with increasing mass . anal . chem . 75 , 5944 - 5952 ( 2003 ). 6 . geno , p . w . & amp ; macfarlane , r . d . secondary electron emission induced by impact of low velocity molecular ions on a microchannel plate . int . j . mass spectrom . ion processes 92 , 195 - 210 ( 1989 ). 7 . westmacott , g ., frank , m ., labov , s . e . & amp ; benner , w . h . using a superconducting tunnel junction detector to measure the secondary electron emission efficiency for a microchannel plate detector bombarded by large molecular ions . rapid commun . mass spectrom . 14 , 1854 - 1861 ( 2000 ). 8 . westmacott , g ., ens , w . & amp ; standing , k . g . secondary ion and electron yield measyrements for surfaces bombarded with large molecular ions . nucl . instrum methods phys . res . b 108 , 282 - 289 ( 1996 ). 9 . beuhler , r . j . & amp ; friedman , l . threshold studies of secondary emission induced by macro - ion impact on solid surfaces . nucl . instrum . methods 170 , 309 - 315 ( 1980 ). 10 . meier , r . & amp ; eberhardt , 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knudsen , s . m ., shen , w ., carlson , g ., foster , j . s ., babcock , k . & amp ; manalis , s . r . weighing of biomolecules , single cells and single nanoparticles in fluid . nature 446 , 1066 - 1069 ( 2007 ). 29 . sato , t ., ochiai , i ., kato , y . & amp ; murayama , s . vibration of beryllium foil window caused by plasma particle bombardment in plasma focus x - ray source . jpn . j . appl . phys . 30 , 385 - 391 ( 1991 ). 30 . landau , l . d . & amp ; lifshitz , e . m . theory of elasticity . 3 - rd edition . pergamon press , new york ( 1986 ). all references throughout this application , for example patent documents including issued or granted patents or equivalents ; patent application publications ; and non - patent literature documents or other source material ; are hereby incorporated by reference herein in their entireties , as though individually incorporated by reference , to the extent each reference is at least partially not inconsistent with the disclosure in this application ( for example , a reference that is partially inconsistent is incorporated by reference except for the partially inconsistent portion of the reference ). u . s . patent publication nos . us - 2007 - 0023621 and 2010 - 0320372 relate to detectors for mass spectrometry having a nano - or microstructured membrane geometry and are hereby incorporated by reference . the terms and expressions which have been employed herein are used as terms of description and not of limitation , and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof , but it is recognized that various modifications are possible within the scope of the invention claimed . thus , it should be understood that although the present invention has been specifically disclosed by preferred embodiments , exemplary embodiments and optional features , modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art , and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims . the specific embodiments provided herein are examples of useful embodiments of the present invention and it will be apparent to one skilled in the art that the present invention may be carried out using a large number of variations of the devices , device components , methods steps set forth in the present description . as will be obvious to one of skill in the art , methods and devices useful for the present methods can include a large number of optional composition and processing elements and steps . when a group of substituents is disclosed herein , it is understood that all individual members of that group and all subgroups , including any isomers , enantiomers , and diastereomers of the group members , are disclosed separately . when a markush group or other grouping is used herein , all individual members of the group and all combinations and subcombinations possible of the group are intended to be individually included in the disclosure . when a compound is described herein such that a particular isomer , enantiomer or diastereomer of the compound is not specified , for example , in a formula or in a chemical name , that description is intended to include each isomers and enantiomer of the compound described individual or in any combination . additionally , unless otherwise specified , all isotopic variants of compounds disclosed herein are intended to be encompassed by the disclosure . for example , it will be understood that any one or more hydrogens in a molecule disclosed can be replaced with deuterium or tritium . isotopic variants of a molecule are generally useful as standards in assays for the molecule and in chemical and biological research related to the molecule or its use . methods for making such isotopic variants are known in the art . specific names of compounds are intended to be exemplary , as it is known that one of ordinary skill in the art can name the same compounds differently . many of the molecules disclosed herein contain one or more ionizable groups [ groups from which a proton can be removed ( e . g ., — cooh ) or added ( e . g ., amines ) or which can be quaternized ( e . g ., amines )]. all possible ionic forms of such molecules and salts thereof are intended to be included individually in the disclosure herein . with regard to salts of the compounds herein , one of ordinary skill in the art can select from among a wide variety of available counterions those that are appropriate for preparation of salts of this invention for a given application . in specific applications , the selection of a given anion or cation for preparation of a salt may result in increased or decreased solubility of that salt . every formulation or combination of components described or exemplified herein can be used to practice the invention , unless otherwise stated . whenever a range is given in the specification , for example , a temperature range , a time range , or a composition or concentration range , all intermediate ranges and subranges , as well as all individual values included in the ranges given are intended to be included in the disclosure . it will be understood that any subranges or individual values in a range or subrange that are included in the description herein can be excluded from the claims herein . all patents and publications mentioned in the specification are indicative of the levels of skill of those skilled in the art to which the invention pertains . references cited herein are incorporated by reference herein in their entirety to indicate the state of the art as of their publication or filing date and it is intended that this information can be employed herein , if needed , to exclude specific embodiments that are in the prior art . for example , when composition of matter are claimed , it should be understood that compounds known and available in the art prior to applicant &# 39 ; s invention , including compounds for which an enabling disclosure is provided in the references cited herein , are not intended to be included in the composition of matter claims herein . unless defined otherwise , all technical and scientific terms used herein have the same meanings as commonly understood by one of ordinary skill in the art to which this invention belongs . although any methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present invention , the preferred methods and materials are now described . nothing herein is to be construed as an admission that the invention is not entitled to antedate such disclosure by virtue of prior invention . as used herein , “ comprising ” is synonymous with “ including ,” “ containing ,” or “ characterized by ,” and is inclusive or open - ended and does not exclude additional , unrecited elements or method steps . as used herein , “ consisting of ” excludes any element , step , or ingredient not specified in the claim element . as used herein , “ consisting essentially of ” does not exclude materials or steps that do not materially affect the basic and novel characteristics of the claim . in each instance herein any of the terms “ comprising ”, “ consisting essentially of ” and “ consisting of ” may be replaced with either of the other two terms . the invention illustratively described herein suitably may be practiced in the absence of any element or elements , limitation or limitations which is not specifically disclosed herein . it must be noted that as used herein and in the appended claims , the singular forms “ a ”, “ an ”, and “ the ” include plural reference unless the context clearly dictates otherwise . thus , for example , reference to “ a cell ” includes a plurality of such cells and equivalents thereof known to those skilled in the art , and so forth . as well , the terms “ a ” ( or “ an ”), “ one or more ” and “ at least one ” can be used interchangeably herein . it is also to be noted that the terms “ comprising ”, “ including ”, and “ having ” can be used interchangeably . the expression “ of any of claims xx - yy ” ( wherein xx and yy refer to claim numbers ) is intended to provide a multiple dependent claim in the alternative form , and in some embodiments is interchangeable with the expression “ as in any one of claims xx - yy .” one of ordinary skill in the art will appreciate that starting materials , biological materials , reagents , synthetic methods , purification methods , analytical methods , assay methods , and biological methods other than those specifically exemplified can be employed in the practice of the invention without resort to undue experimentation . all art - known functional equivalents , of any such materials and methods are intended to be included in this invention . the terms and expressions which have been employed are used as terms of description and not of limitation , and there is no intention that in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof , but it is recognized that various modifications are possible within the scope of the invention claimed . thus , it should be understood that although the present invention has been specifically disclosed by preferred embodiments and optional features , modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art , and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims .