Measuring Charge Transport in an Amorphous Semiconductor Using Charge Sensing
aa r X i v : . [ c ond - m a t . m e s - h a ll ] S e p Measuring Charge Transport in an Amorphous Semiconductor Using Charge Sensing
K. MacLean, ∗ T. S. Mentzel, and M. A. Kastner Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
We measure charge transport in hydrogenated amorphous silicon (a-Si:H) using a nanometerscale silicon MOSFET as a charge sensor. This charge detection technique makes possible themeasurement of extremely large resistances. At high temperatures, where the a-Si:H resistance isnot too large, the charge detection measurement agrees with a direct measurement of current. Thedevice geometry allows us to probe both the field effect and dispersive transport in the a-Si:H usingcharge sensing and to extract the density of states near the Fermi energy.
PACS numbers: 72.80.Ng, 79.60.Jv, 71.23.Cq
A variety of technologically promising materials anddevices, from arrays of semiconducting nanocrystals, thatare candidates for solar energy harvesting [1], to lateralquantum dots that hold potential for quantum informa-tion processing [2], are highly resistive [3, 4]. For the lat-ter, charge measurement using a sensor integrated withthe device [5] has recently been widely utilized to probequantum mechanical phenomena that would be impossi-ble to observe by measuring current [6]. For the study ofhighly resistive materials scanning probe techniques havebeen used to determine the charge distribution [7, 8].However, a study of the charge transport properties of aresistive material using an integrated charge sensor hasyet to be realized.In this Letter, we illustrate the power of this chargesensing technique by investigating transport in hydro-genated amorphous silicon (a-Si:H). By patterning a stripof a-Si:H thin film adjacent to a nanometer scale siliconMOSFET, we are able to detect charging of the a-Si:Hand measure extremely high resistances ( ∼ Ω) us-ing moderate voltages ( ∼ n -channel MOSFETthat is electrostatically coupled to a strip of a-Si:H. Anelectron micrograph of the structure is shown in Fig. 1(a).The MOSFET is fabricated using standard techniques[14] on a p -type Silicon substrate. The n + polysilicongate of the MOSFET is patterned using electron beamlithography and reactive ion etching and tapers down to (a) (b) a-Si:HGate
200 nm
Gate a-Si:HOxidep-SiInversion
FIG. 1: (a) Electron micrograph of MOSFET gate and a-Si:Hstrip. A positive voltage is applied to the MOSFET gate,forming an inversion layer underneath. (b) Vertical sketchof the device geometry along the dashed line in (a). Theconductance through the inversion layer formed under thegate is sensitive to the charge on the a-Si:H strip. a width of ≈
60 nm. The characteristics of this narrowchannel MOSFET are similar to those reported previ-ously [15]. Because of its narrow width, the MOSFET isextremely sensitive to its electrostatic environment [16].Furthermore, it has a relatively thick gate oxide (thick-ness d ox = 100 nm), which ensures that the metallicpolysilicon gate does not effectively screen the inversionlayer from nearby electrostatic fluctuations. Adjacent tothe MOSFET, we pattern a strip of phosphorous dopeda-Si:H. The narrowest portion of the strip is located ≈
70 nm from the narrowest portion of the MOSFET.The a-Si:H is deposited by plasma enhanced chemicalvapor deposition [17], with a gas phase doping ratio andhydrogen dilution of [PH ] / [SiH ] = 2 × − and [H ]/ [SiH + H ] = 0.5, respectively. Because we use a rela-tively large doping level, we expect a large defect density N D ∼ cm − [17]. The deposition substrate temper-ature is T s = 200 C, and the deposition rate is ≈ ≈ µ m),and the MOSFET inversion layer is contacted throughtwo degenerately doped n + regions, none of which areshown in Fig. 1(a). After sample preparation, the deviceis loaded into a cryostat, and kept in Helium exchangegas throughout the course of the measurements discussed Γ ( H z ) -1 )10 -17 -15 -13 -11 G a S i ( S ) T (K) 120180 G M ( µ S ) (a)(b) FIG. 2: (a) G M as a function of time at T = 125 K (closed cir-cles) and 140 K (open squares), the latter is offset for clarity.At t = 0 the voltage applied to one of the a-Si:H contacts ischanged from -1.8 V to -2.7 V. For these traces multiple chargetransients have been averaged to improve signal-to-noise. Thesolid lines are theoretical fits described in the main text. (b)Conductance G aSi obtained from charge transients (closed tri-angles) and direct conductance measurements (open circles),measured with V ds ≈ -2.3 V. For the charge transient mea-surement, Γ is given on the right hand axis. The dashed lineis a theoretical fit described in the main text. here.The parameters used to deposit our a-Si:H are simi-lar to those studied previously, and thicker a-Si:H filmsthan those used for our charge sensing measurements, de-posited under the same conditions, have conductivitiesand activation energies similar to those reported else-where [17]. However, the sample studied in this workis nanopatterned ( ≈
100 nm wide at its narrowest point)and also is only ≈
50 nm thick. Thus, although the char-acteristics reported below are similar to what one wouldexpect for thick heavily doped films, we expect that forour sample surface effects may be significant [19], andthere may also be differences in morphology and hydro-gen content as compared with thicker films.Our measurement consists of monitoring the MOSFETconductance G M as a function of time after changing thevoltage applied to one of the a-Si:H contacts (Fig. 2(a)).We set the voltage of one of the a-Si:H contacts to 0 V(relative to the p -type substrate), and, at t = 0, rapidlychange the voltage applied to the other a-Si:H contactfrom -1.8 V to -2.7 V. This causes additional electrons to move onto the a-Si:H strip from the gold contacts. TheMOSFET senses this change in charge electrostatically,and G M decreases. This effect is shown in Fig. 2(a).Following the voltage step, G M decreases with time ata rate that increases when the temperature is increased.A similar decrease in G M is observed when the step isapplied to the other a-Si:H contact or to both contactssimultaneously. This decrease in G M is caused by thecharging of the a-Si:H strip capacitor, and we henceforthrefer to it as a charge transient [20]. When the a-Si:Hcontact voltage is changed back to its original value, thesame transient is observed but with the opposite sign.For a resistive film with a distributed capacitance, thecharge stored as a function of position and time σ ( x, t )obeys the diffusion equation, with a diffusion constantgiven by D − = CR sq [8, 21]. Here C is the capacitanceper unit area between the a-Si:H and the underlying sub-strate, and R sq is the resistance per square of the a-Si:Hfilm. Because C is reduced by any depletion in the p -type silicon underneath the a-Si:H, C will vary with thevoltages applied to the MOSFET gate, a-Si:H contacts,and p -type substrate. However, we estimate that for therange of voltages used to collect the data reported below, C remains within a factor of 5 of the oxide capacitance( C ox = κ ox ǫ /d ox ), and, in view of the large variationsin D reported below, can be treated as a constant [22].For a strip of material of length L , for which the po-tential at one end is changed from V to V + ∆ V at t = 0, the charge at any point along the strip varies ex-ponentially with time as σ ( t ) ≈ σ ∞ − σ ∆ e − Γ t for suffi-ciently large t . Here Γ = π D/L , and σ ∞ and σ ∆ areconstants that depend on V , ∆ V , and C. For a suffi-ciently small voltage step G M varies linearly with σ , so G M ( t ) ≈ G ∞ + G ∆ e − Γ t , where the sign of G ∆ is oppositeto the sign of ∆ V . The solid curves shown in Fig. 2(a)are fits to this equation, from which we extract Γ [23].From our measurement of Γ and the values of L and C for our a-Si:H strip, we extract R sq , and from thiscompute the conductance G aSi = w/ ( R sq L ), where w iswidth of the a-Si:H strip. In Fig. 2(b) we plot G aSi and Γand as functions of temperature. G M is weakly temper-ature dependent, and for this data we therefore adjustthe MOSFET gate voltage as we vary the temperatureto keep G M approximately constant. At higher temper-atures we are able to directly measure G aSi = dI/dV ds ,where V ds is the voltage between the a-Si:H contacts, andthese results are also shown in Fig. 2(b). At T ≈
180 K,we can measure G aSi using both techniques, and the re-sults are in good agreement. The measurements are com-plementary, in that the charge transient technique is eas-ier to implement for smaller conductances G aSi becausethe charging is slower, while a measurement of current isonly possible for larger values G aSi . The dashed line inFig. 2(b) is a fit to G aSi ( T ) = G e − E a /kT . The data arethus consistent with an activated transport mechanism,with an activation energy E a ≈
200 meV, as is typically -1 Γ ( H z ) g (V) α ( V - ) -1 ) FIG. 3: Γ as a function of V g at T = 98 K (circles), 139 K(triangles), and 179 K (squares). The solid lines are theoret-ical fits described in the main text. (Inset) α as a functionof inverse temperature. The dashed line is a theoretical fitdescribed in the main text. observed for a-Si:H films heavily doped with phospho-rous [17]. We note that at the lowest temperatures, wemeasure resistances as high as ∼ Ω.We can also measure Γ as a function of gate voltage(Fig. 3). For this measurement, we apply the same volt-age V aSi to both a-Si:H contacts relative to the p -typesubstrate. The effective gate voltage is then V g = − V aSi .We then add a small voltage step ∆ V ≈ . V to V aSi to produce a charge transient, from which Γ is extractedas in Fig. 2(a). For all of the measurements shown herethe substrate voltage is held constant at -3 V, and volt-ages are quoted relative to this value. Unlike previous re-ports [12], our geometry allows us to maintain an approx-imately constant value for the MOSFET conductance,and thus to maintain a high charge sensitivity, as wemake large changes in V aSi by applying smaller compen-sating voltage shifts to the MOSFET gate voltage. Thisallows us to perform this field effect measurement for alarge range of sample conductances.In Fig. 3 we plot Γ as a function of V g at three differenttemperatures. We see that Γ rises with V g , indicating n -type conduction through the a-Si:H, as expected fora phosphorous doped sample. The exponential increasein Γ with V g is consistent with the activated conductionfound in Fig. 2(b), provided we assume an approximatelyconstant density of localized states. We have:Γ = ω e − E A /kT (1) Here ω is a prefactor that depends only weakly on tem-perature, and the activation energy E A is reduced as thegate voltage moves the Fermi level closer to the mobil-ity edge. The logarithmic slope α = ∂ln (Γ) /∂V g is thengiven by α = kT ∂E A /∂V g = C/ ( ekT ρ ( E F ) s tf ), where ρ ( E F ) and s tf are the density of states at the Fermi en-ergy and Thomas-Fermi Screening length, respectively[4, 24]. Thus we expect an exponential increase in Γwith V g as long as the product ρ ( E F ) s tf is constant.At each temperature, we fit the data to obtain α (solidlines in Fig. 3), and, in the inset to Fig. 3, we plot α asa function of inverse temperature. The dashed line is alinear fit (constrained to pass through zero) and is con-sistent with the data. From the slope of this fit we obtain s tf ρ ( E F ) ≈ × eV − cm − , and, expressing s tf interms of ρ ( E F ) and the a-Si:H dielectric constant [4], wesolve for ρ ( E F ) ∼ eV − cm − . The density of statesat the Fermi level for phosphorous doped amorphous hy-drogenated silicon obtained from more commonly usedtransport techniques is typically ∼ eV − cm − [9].The fact that our ρ ( E F ) is somewhat high is not surpris-ing, given the large gas phase doping level used in oura-Si:H film deposition. For the range of voltages usedhere E F moves by an amount comparable to values ofthe band tail width commonly found for a-Si:H films [17],so we expect that ρ ( E F ) should increase somewhat as V g is made more positive and the Fermi level is moved inthe band tail. This may cause the observed decrease inlogarithmic slope α for V g >
15 V in Fig. 3.At lower temperatures, where the time scale for charg-ing is longer, we observe dispersive transport [10, 11](Fig. 4(a)). When we step V aSi from 0 V to -24 V, G M quickly drops. However, when V aSi is stepped back to 0V, G M rises at slower rate, and does not regain its orig-inal value. This behavior can be understood as follows:After the negative V aSi step the a-Si:H quickly charges,as electrons can enter the a-Si:H at energies close to theconduction band. However, as time progresses, theseelectrons get trapped in localized states deeper in theband gap. When the voltage is returned to its originalvalue, the a-Si:H therefore takes a much longer time todischarge: From Eq. (1), the time necessary to releaseelectrons from states at an energy E A below the trans-port energy is t ∼ Γ − = ω − e − E A /kT . As electronsdeeper and deeper in the gap are released, t grows, andthus the transport process becomes dispersive [10, 11].This can be made quantitative: At a time t after thenegative voltage step, only electrons in localized stateswith energies E A < E max = kT ln ( ω t ) [10, 11] are ableto escape from the a-Si:H. The charge on the a-Si:H isthen given by σ ( t ) = e R E max s tf ρ ( E A ) dE A (up to anadditive constant). Assuming a constant density of statesand differentiating with respect to time we obtain: ∂σ/∂t = es tf ρ ( E F ) kT /t (2) -3 -2 -1 d G M / d t ( µ S / s ) time (s)35302520 G M ( µ S ) V a S i ( V ) (a) (b) FIG. 4: (a) Voltage applied (top panel) and transistor con-ductance (lower panel) used to measure dispersive transportat T = 89 K, as discussed in the main text (b) ∂G M ( t ) /∂t extracted from the data shown in (a). The solid line is atheoretical fit described in the main text. In Fig. 4(b) we plot the derivative of G M with respectto time on a log-log plot: A fit to a power law depen-dence (solid line) yields a power of -1 ± es tf ρ ( E F ) r ,where r is the conversion between σ and G M that can beestimated from the decrease in G M after pulsing V aSi to-24 volts. We obtain ρ ( E F ) ∼ eV − cm − , consistentwith the value extracted from the data in Fig. 3.There are some aspects of our charge transient tech-nique that are not fully understood. While the measure-ments of Γ shown in Fig. 2 and Fig. 3 do not dependstrongly on the voltage applied between the a-Si:H con-tacts V ds for V ds <
1, we observe a large nonlinearity in G aSi at room temperature when we measure current asa function of voltage at V ds ≈