The Effect of Electrostatic Screening on a Nanometer Scale Electrometer
aa r X i v : . [ c ond - m a t . m e s - h a ll ] J un The Effect of Electrostatic Screening on a Nanometer Scale Electrometer
K. MacLean, ∗ T. S. Mentzel, and M. A. Kastner Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
We investigate the effect of electrostatic screening on a nanoscale silicon MOSFET electrometer.We find that screening by the lightly doped p -type substrate, on which the MOSFET is fabricated,significantly affects the sensitivity of the device. We are able to tune the rate and magnitude ofthe screening effect by varying the temperature and the voltages applied to the device, respectively.We show that despite this screening effect, the electrometer is still very sensitive to its electrostaticenvironment, even at room temperature. PACS numbers: 73.63.-b, 85.35.-p, 85.30.-z
Nanoscale electrometers have emerged as powerfultools for studying a wide variety of solid state systems.These sensors can be integrated on a semiconductor chipadjacent to a solid state structure of interest [1], ormounted on a scanning probe tip [2]. Utilized in theseconfigurations, nanoscale electrometers have had a greatimpact on the study of single electron devices [3–7], disor-dered materials [8, 9], and high mobility two dimensionalelectron gases [10, 11]. The small size of these electrom-eters can lead to high charge sensitivities [12], which arecentral to many of these applications. It is widely recog-nized that, of the many factors that may limit the sensi-tivity of a nanoscale electrometer, electrostatic screeningis likely to be one of the most important. However, be-cause in most cases the effect of the screening is more orless fixed, and cannot be easily tuned, there have beenfew if any experimental investigations of this effect.In this Letter, we characterize the effect of electrostaticscreening on the sensitivity of a nanoscale MOSFET(metal-oxide-silicon field-effect-transistor) electrometer.For our device, we find that screening by the lightlydoped p -type silicon substrate, on which the MOSFET isfabricated, significantly affects the charge sensitivity ofthe device. However, because this screening is caused bya lightly doped semiconductor as opposed to a metal, weare able to tune both the rate and the magnitude of thescreening effect in situ by varying the temperature anddepth of the depletion region in the substrate, respec-tively. This tunability allows us to quantify the effect ofscreening for our system. We demonstrate that, despitethe effects of electrostatic screening, our nanoscale elec-trometer can still detect very small charge fluctuations,even at room temperature.The device used in these experiments has been dis-cussed previously [9], and consists of a nanometer scalesilicon MOSFET that is electrostatically coupled to astrip of hydrogenated amorphous silicon (a-Si:H). Anelectron micrograph of the device is shown in Fig. 1(a).The n -channel MOSFET is fabricated using standardCMOS techniques on a silicon substrate. The substrate islightly doped p -type with boron ( N B ≈ × cm − ).Adjacent to the gate of the MOSFET, we nanopattern G M ( µ S ) V a S i ( V )
210 time (s)3.53.02.5 G M ( µ S ) ∆ Au ∆ aSi L D (a) AuGatea-Si:H (c)(b) gate oxidea-Si:H Au inversion depletionp-Si (d)
500 nm
FIG. 1: (a) Electron micrograph of MOSFET gate , a-Si:Hstrip, and gold contacts. (b) Sketch of the cross-section ofthe device along the dashed red line in (a). When a positivevoltage is applied to the gate, an inversion layer forms atthe Si-SiO interface. A depletion region forms in the p -typesilicon substrate beneath the Si-SiO interface, as discussedin the main text. The depth of the depletion region below theSi-SiO interface is denoted L D . (c) Voltage sequence appliedto one of the gold contacts (top trace) and the conductanceof the MOSFET in response to changes in charge on the gold(∆ Au ) and a-Si:H (∆ aSi ) (bottom trace), at T = 125 K, asdiscussed in the main text. (d) Result of stepping the voltageapplied to the gold contacts at T = 79 K for a device in whichthe strip of a-Si:H is connected to only one of the two goldcontacts, as discussed in the main text. For the blue (green)data the gold contact connected (not connected) to the a-Si:Hstrip is changed. For these data V sub = 0 V. a strip of phosphorous doped a-Si:H. We make electri-cal contact to the a-Si:H using two gold contacts, whichare visible as the bright regions in the two lower cornersof the electron micrograph in Fig. 1(a). For all of thework discussed here, a positive voltage is applied to thegate of the MOSFET, so that an inversion layer forms atthe Si-SiO interface beneath the gate, as shown in Fig.1(b). The conductance of the MOSFET inversion layer, G M , is limited by its narrowest portion, which is locatedunderneath the ≈
60 nm wide constriction in the gate.Electrical contact is made to the inversion layer throughtwo degenerately doped n -type silicon regions located oneither side of the constriction (not shown in the micro-graph). We measure G M by applying a small voltage ∼ p -type substrate through the back of the chip. Forthe data reported below, we negatively bias the p -typesubstrate by V sub = -3 V relative to the n -type contactsunless otherwise indicated.The conductance of the MOSFET is extremely sensi-tive to its electrostatic environment. In particular, G M is sensitive to changes in charge in either the a-Si:H orthe gold contacts. As we show below, this sensitivity issignificantly affected by screening by the p -type siliconsubstrate: If charge Q is added to the a-Si:H or goldcontacts, an oppositely charged region will form in thesubstrate underneath, thereby reducing the effect of Q on G M . This screening charge is located at the Si-SiO interface, or, if the silicon beneath the Si-SiO interfaceis depleted of holes (Fig. 1(b)), the screening charge willbe located a distance L D beneath the Si-SiO interface.Our measurement consists of stepping the voltage V aSi applied to one of the a-Si:H gold contacts while simulta-neously monitoring G M . An example is shown in Fig.1(c). Here we set the voltage applied to one gold contactto 0 V, and apply the voltage sequence shown in the toptrace of Fig. 1(c) to the other contact [13]. The bottomtrace of Fig. 1(c) shows the variation in G M in responseto the voltage sequence. When V aSi is first stepped from-1.8 V to -2.7 V, G M drops by an amount ∆ Au in a timetoo short to measure, and then decreases slowly by anamount ∆ aSi .As we have demonstrated in MacLean et al. [9], theslow change ∆ aSi in G M is caused by the slow addition ofnegative charge to the a-Si:H. The MOSFET electrom-eter senses this change in charge electrostatically, and G M decreases as negative charge is added to the a-Si:H.The time scale of this charging is a direct measurementof the resistance of the a-Si:H strip [9]. The much morerapid drop ∆ Au in G M is caused by the negative chargeadded to the gold contacts, which charge up very quicklybecause of their low electrical resistance. When V aSi isreturned to -1.8 V, the same responses ∆ Au and ∆ aSi areobserved but with the opposite sign, as negative chargeis now removed from the gold and the a-Si:H. A similarresponse is observed when the voltage sequence is appliedto the other gold contact, or to both contacts at the sametime.To confirm that our interpretation of the data is cor-rect, we study a separate device where, like the deviceshown in Fig. 1(a), a strip of a-Si:H is patterned adja-cent to a nanoscale MOSFET. However, for this device,the strip of a-Si:H is connected to only one of the twogold contacts. The data is shown in Fig. 1(d). At t = 0 -1.0-0.50.0 V a S i ( V ) G M ( µ S ) r S ( H z ) -1 )10 ∆ r S ( H z ) -1 ) (a) (b)(c) FIG. 2: (a) Observation of the screening effect at T = 9.8 K,as discussed in the main text. The top trace shows the voltagestep applied to the a-Si:H gold contact. For the lower trace,the solid black curve is a fit to an exponential, as discussed inthe main text. (b) Screening rate r S as a function of inversetemperature. (c) Change in screening rate ∆ r S as a functionof inverse temperature, as described in the main text. Thesolid line is a theoretical fit described in the main text. Forall of these data, V sub = 0. we step one contact from 0 to -9.9 V, while the othercontact is held constant at 0 V. A rapid drop ∆ Au is ob-served when the pulse is applied to either one of the goldcontacts, but the slower response ∆ aSi is only observedwhen the pulse is applied to the gold which is connectedto the strip of a-Si:H, confirming our interpretation ofthe data.The sensitivity of G M to its electrostatic environmentdepends on screening by the underlying p -type siliconsubstrate. To demonstrate this, we examine the responseof the MOSFET to changes in charge in the gold contactsat a temperature T ≈
10 K, lower than the temperatureat which the data shown in Fig. 1 are acquired. Atthis temperature, the a-Si:H is so resistive that it doesnot charge up on the time scale of the experiment [9], sothat we can add charge to the a-Si:H gold contacts butnot to the a-Si:H itself. The results are shown in Fig.2(a). When we change the voltage applied to the a-Si:Hgold contacts from 0 to -1 V (top trace), we see a largedecrease in the MOSFET conductance, which graduallydies away as time progresses (bottom trace).The gradual dying away of the decrease in G M can beunderstood in terms of screening. When we add chargeto the gold contact, an opposing charge in the p -typesubstrate is induced, reducing the overall effect on G M .At low temperatures, the resistance of the substrate ishigh, and this charge is induced at a slow rate. To quan-tify this rate, we fit the G M trace to an exponential G M ( t ) = G ∞ + G scr e − r S t , where G ∞ and G scr are con-stants that depend on the voltages applied to the MOS-FET gate, p -type substrate, and gold electrodes, and r S is the screening rate.To show that this screening effect is caused by the p -type silicon substrate, we measure r S as a function oftemperature. The results are shown in Fig. 2(b). As thetemperature is reduced, r S drops, saturating at a mini-mum value r min ≈ r S = r S - r min as a function of inverse temperature, and fit to anactivated temperature dependence ∆ r S ∝ e − E A /kT . Weobtain E A = 45 ± N D will move the Fermi level into the acceptor band [15].In our case, the number of defects required is only N D ∼ cm − . Because the required density is so small, weexpect the Fermi level to lie in the acceptor band, andthe activation energy required for the generation of holesin the valence band to be the boron acceptor binding en-ergy. The correspondence between the activation energyfor the screening and the boron acceptor binding energydemonstrates that the conductivity of the boron dopedsubstrate limits r S . Presumably r S saturates at a min-imum value r min because some conduction mechanismother than activation of holes in the p -type substratedominates at low temperature. It is possible that thislow temperature conduction occurs via tunneling of elec-trons between acceptor states [15] in the p -type substrate.In any case, from this data it is clear that screening byholes in the boron doped substrate significantly reducesthe sensitivity of the MOSFET.At higher temperatures T >
25 K, r S becomes toofast for us to measure. In this regime, we investigate thedependence of ∆ aSi and ∆ Au on V aSi . The results areshown in Fig. 3. Here we step the voltage applied to bothgold contacts from V aSi to V aSi − ∆ V , where ∆ V = 0.5V. We extract ∆ aSi and ∆ Au from the resulting G M ( t )trace as depicted in Fig. 1(c). We measure both ∆ aSi and ∆ Au as a function of V aSi and find that both of thesequantities decrease as V aSi is made more negative. Thedecreases in ∆ aSi and ∆ Au are clearly visible when the G M ( t ) traces taken at different V aSi values are compared,as is shown in the inset to Fig. 3.These results can be understood in terms of screeningby the p -type substrate in the following way: At V aSi = 0V, the p -type substrate beneath the Si-SiO is depleted,as depicted in Fig. 1(a). As V aSi is made more negative, L D is reduced beneath the gold and the a-Si:H. This hasthe effect of making the screening more effective, becauseit brings the holes in the substrate closer to the charge ∆ ( µ S ) -20 -10 0V aSi (V) G M ( µ S ) FIG. 3: ∆ aSi (blue circles) and ∆ Au (gold circles) measuredas a function of V aSi at T = 139 K, as discussed in the maintext. For these data, we make the MOSFET gate voltagemore positive as V aSi is made more negative so that G M ≈ µ S at the start of each G M ( t ) trace. (Inset) Examples of datafrom which ∆ aSi and ∆ Au are extracted for two different V aSi values. For both G M ( t ) traces, V aSi is stepped by -0.5 V at t = 0. The data are offset vertically by a small amount forclarity. The blue and red data sets are taken at the positionsof the blue and red arrows, respectively. The decrease inboth ∆ aSi and ∆ Au with increasingly negative V aSi is clearlyvisible. they are screening. As a result, both ∆ Au and ∆ aSi decrease as V aSi is made more negative [16].The response of G M to the gold ∆ Au decreases as V aSi is made more negative until V aSi ≈ -8 V, at which pointit saturates. This saturation is expected, because oncethe depletion layer below the gold shrinks to zero, so thatthe Si-SiO interface underneath the gold is in accumu-lation, the distance between the charge on the gold andthe screening charge is fixed at the SiO thickness (100nm). ∆ aSi does not appear to saturate as V aSi is mademore negative. This is not surprising, because the a-Si:His very close to the MOSFET gate. Because there mustalways be a depletion layer between the inversion layerof the MOSFET and the p -type substrate, the Si-SiO interface underneath the a-Si:H cannot be brought intoaccumulation, and the signal does not saturate. It is how-ever surprising that for V aSi < -10 V, ∆ Au is larger than∆ aSi . Although the gold contacts are physically muchlarger than the a-Si:H strip, which enhances their effecton G M relative to the a-Si:H, the a-Si:H strip is muchcloser to the MOSFET, so one would not expect ∆ Au ever to be significantly larger than ∆ aSi . Thus, although I a S i ( n A ) G M ( µ S ) -0.50.0 c ( τ ) -100 0 100 τ (s) (a)(b) FIG. 4: Noise correlations measured at room temperature.(a) Current through a-Si:H strip I aSi (top trace) and tran-sistor conductance G M (bottom trace) as a function of time.Here we apply a constant voltage bias of 2 V across the a-Si:Hstrip. (c) Correlation between I aSi and G M , as discussed inthe main text. the dependencies of ∆ aSi and ∆ Au on V aSi can be un-derstood in terms of screening, the relative magnitudes ofthese quantities are not currently understood. We havealso measured the dependence of ∆ Au and ∆ aSi on V aSi at T = 98 K and T = 179 K. The results are qualita-tively similar, but the relative magnitudes of ∆ aSi and∆ Au change somewhat depending on the temperature, aresult that is also currently not understood.We have thus seen that screening by holes in the p -type substrate decreases the sensitivity of our MOSFETelectrometer. We expect that there are other sourcesof screening in our system, for instance by the metallicgate of the MOSFET. Despite the effect of screening, ourelectrometer is still sensitive to very small charge fluc-tuations in the a-Si:H, even at room temperature. Anintriguing demonstration of this is the sensitivity of theMOSFET to telegraph noise switches in the a-Si:H. 1 /f noise and discrete telegraph switches have been observedpreviously in the resistance of macroscopic a-Si:H sam-ples [17]. The discrete switching that is sometimes ob-served occurs for samples where the conductance is domi-nated by filaments small enough to be affected by a singleswitch. While the microscopic origin of 1 /f noise in a-Si:H is unclear, its phenomenology is quite rich, and itis closely connected with Staebler-Wronski effect [18], asdemonstrated in Parman et al. [19].At room temperature, where the resistance of the a-Si:H is not too large, we apply a voltage between the two gold a-Si:H contacts and measure the current I aSi that flows through the a-Si:H strip. The top trace of Fig.4(a) shows I aSi measured as a function of time, exhibit-ing clear telegraph noise. This switching appeared anddisappeared apparently randomly, lasting ∼ p -type substrate. For example, we find that we mustchange the MOSFET gate voltage by ∼
30 V in orderto produce a change in I aSi as large as the ∼ I aSi (t), we simultaneously measure G M (t), and the results are plotted in the bottom trace ofFig. 4(a). We see that I aSi and G M are anti-correlated.When I aSi jumps up, G M jumps down, and vice versa.This anti-correlation is demonstrated quantitatively inFig. 4(b). Here we measure I aSi and G M simultane-ously for a much longer time than shown in Fig. 4(a),and compute the cross-correlation function between thetwo signals c ( τ ) [20]. Here we have normalized c ( τ ) bysubtracting the product of the means of I aSi and G M ,and then dividing by the product of their standard devi-ations [21]. We see that for our data c ( τ ) has a negativepeak at τ = 0 with a value ≈ − .
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