Donor-Based Single Electron Pumps with Tunable Donor Binding

Jan 23, 2012 - Modeling the pumping of electrons through a single dopant atom in a Si MOSFET. Joost van der Heijden , Giuseppe C. Tettamanzi , Sven Ro...
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Letter pubs.acs.org/NanoLett

Donor-Based Single Electron Pumps with Tunable Donor Binding Energy G. P. Lansbergen,* Y. Ono, and A. Fujiwara NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa, 243-0198, Japan S Supporting Information *

ABSTRACT: We report on single electron pumping via a tunable number of individual donors. We use a device that essentially consists of a silicon nanowire with local arsenic implantation between a set of fine gates. A temperaturedependent characterization of the pumped current allows us to extract the ionization energy of a single arsenic donor. We observe the ionization energy to be tunable by the gate electric field over a large range of energies. KEYWORDS: Single dopant, single electron pump, binding energy, nanowire, arsenic

A

currents in a fashion analogue of parallel quantum dot-based transfer devices.27 Apart from their direct applicability, our donor-based electron pumps also allow us to study the ionization energy of a single donor atom as a function of the surrounding potential landscape. As we will show, the amount of current pumped via any individual donor atom in the active device area depends on its particular (electric field dependent) ionization energy, which is tunable over a large range of values by means of nearby gate electrodes. The ability to electrically control the (Coulomb) confinement of a single dopant atom is key feature in a wide range of donor-based computation schemes.3−5 Recent experimental work has shown the ionization energy of an individual donor can be tuned by positioning another Coulomb potential nearby in an STM-based setup. 28 Furthermore, an electronic gate-induced confinement transition of donor bound electrons has been observed for (multiple) fixed gate potentials.29 Continuous electronic control over a single dopants confinement potential however has not been shown yet. Our devices consist of Si-wire MOSFETs in series fabricated on a silicon-on-insulator (SOI) wafer, see Figure 1a,b. A stacked gate layer structure is employed; the lower layer consist of three fine gates (LG, MG, and RG) defined by electron beam lithography and the top layer consist of a large single upper gate (UG). The fine gates are used to induce and control local electron barriers in the silicon nanowire. In some samples, donor atoms (arsenic) are introduced by ion implantation in the region between MG and RG before fine gate fabrication. The donors were implanted through a 60 nm wide aperture (with its width along the nanowire direction) in a predesigned

s semiconductor devices are scaled to ever decreasing spacial dimensions, their characteristics are more and more determined by the position, and exact number, of the limited amount of dopants in the active device area.1,2 These developments have spurred a radically new approach to semiconductor devices: structures whose very functionality is based on individual dopants.3 Several proposals for computation based on single dopants have been put forward, being either charge- or spin-based schemes.4−7 Electrical control over the charge and spin of of a single dopant in silicon has recently been demonstrated by several groups applying a variety of devices.2,8−11 Furthermore, fabrication techniques to create devices where the position of each dopant atom in the active device area is controlled are currently being developed taking both top-down12,13 and bottom-up approaches.14,15 Here, we investigate a novel device concept based on single dopant functionality, that is, we demonstrate multiple-donorbased single electron (SE) pumps. Charge pumping using random potential wells in the highly doped channel of a MOSFET has already been shown experimentally.16,17 In our experiment, we will show we can pump a quantized number of electrons in a silicon nanowire from a source electrode via a tunable number of individual donors to a drain electrode. The ability of SE pumps18,19 to generate single electrons on demand is useful in a variety of device concepts,20,21 including acting as a current standard in the metrological triangle.22 Similar to their quantum-dot based counterparts,19,23−25 donorbased charge transfer devices should be capable of gigahertz operation; transferring electron to and from a (shallow) donor atom is a subnanosecond process at high enough electric fields.26 However, donor-based charge transfer devices also have several advantages. Donor atoms form a very reproducible potential in the silicon lattice that do not require tuning by external gates.8 Furthermore, by utilizing multiple isolated donors these device would be capable of generating high © 2012 American Chemical Society

Received: October 21, 2011 Revised: January 5, 2012 Published: January 23, 2012 763

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The concept of operation of our donor-based electron pump devices is depicted in Figure 1c, which depicts the conduction band diagram in the silicon nanowire around the middle- and right-fine gates. For charge transfer operation, we apply an ac signal to the middle of the three fine gates (MG). The rightmost of the fine gates (RG) is tuned such that it induces a small barrier in the Si nanowire beneath it. The leftmost fine gate (LG) does not play a role in the experiment. When the barrier formed by VMG is in its low state (I), electrons from the source region are captured on the donor sites (and for large VUG also in the electrically induced inversion layer at the SiO2 interface). When the barrier is subsequently ramped up (II) to its high state (III) by VMG, it generates an electric field large enough to ionize the donors and evacuate their bound electrons to the drain region. Figure 2a shows the source/drain current ISD (in units of electron charge per pump cycle) as a function of VUG for the

Figure 1. (a) Schematic view of the device. The Si nanowire (yellow) has a thickness (t) of 25 nm and a width (W) of 80 nm, the fine gates (light brown) have a length (L) of 100 nm and are spaced 60 nm apart. Arsenic donors (black spheres) are implanted between MG and RG through a predesigned aperture in an e-beam mask. (The region between LG, MG, and RG has been made transparent.) (b) Scanning electron micrograph of the device (before upper gate formation). (c) Schematic diagrams of the conduction band energy in around the fine gates MG and RG during a single pumping cycle (I−III). (LG is not used.) Electron flow from the source into the island region when the barrier formed by VMG is low (I), are captured by multiple donors (II), and emitted when the potential barrier is high (III).

e-beam mask. The upper gate layer is used to control the electron density in the silicon; application of a positive voltage leads to electron inversion in the undoped SOI layer beneath. The wide UG layer furthermore serves as a mask during an ion implantation step which forms the n+-type contact areas. The SOI substrate is used as a back gate electrode (BG). The number of donors implanted per surface area was low enough such that the donor atoms still formed discrete potentials in the island region. The donor concentration in the island region was estimated from a characterization of micrometer-sized MOSFETS located on the same wafer. These large-scale MOSFETs have received exactly the same dose as our donor-based electron pump devices. In this study we investigate undoped devices and devices with two different implantation doses: 2 × 1012 and 5 × 1012 cm2. The (activated) donor concentrations follow from the threshold shift of the large-scale MOSFETs and were found to be 3 × 1017 and 7 × 1017 cm3 respectively. Since our charge transfer devices are implanted through a small aperture in an e-beam mask, the concentrations of arsenic they contain is most probably even lower than their corresponding value in the large MOSFETs. Although arsenic donors are expected to form an impurity band at these concentrations, band tail formation will only take place at order of magnitude higher concentrations.30 The presence of localized states, and the absence of band tail formation, is confirmed by observation of the hopping current in the doped samples, in line with previous investigations of the hopping current in phosphorus doped MOSFETs.31 (See section I of the Supporting Information.)

Figure 2. (a) Source drain current (ISD) in units of ef as a function of upper gate voltage (VUG) for several donor implantation doses. Here, VBG = 0 V. (b) Band diagram in the island region between UG and BG for VUG = VUG,th (upper panel) and VUG ≫ VUG,th (lower panel).

three different doping concentrations. Here, we set VRG to −0.5 V, VLG to +1 V, and cycle VMG between +1 V (low state) and −3 V (high state). The current onset marked by VUG,th is the threshold voltage of the parasitic undoped region below the upper gate, indicated in yellow in Figure 1a. (This threshold is also present when all fine gates are open; VLG = VMG = VRG = +1 V) A hallmark characteristic of charge pumping is that the generated current is equal to the pumping frequency multiplied by the amount of charge captured in the active device area. We indeed observe that the normalized current ISD is virtually the same for 2.5 and 5 MHz, showing ISD originates from charge pumped by the AC signal on MG. Next, we turn our attention to the undoped sample. For this sample, charge capture in the island starts when the conduction band in the island region (between MG and RG) is pushed below the Fermi energy (EF) and electrons can start to accumulate. The upper gate voltage required for inversion in the island region (VUG,is) is actually higher than for the parasitic region VUG,th due to screening of the upper gate field by MG and LG. After inversion in the island region (VUG ≥ VUG,is), the current scales with ISD ∼ CUGVUG, with CUG being the island capacitance to the upper gate. Charge transfer thus takes place via a quantum dot formed by the inversion layer in the island region and the electron barriers invoked by VMG and VRG. The devices studied in this work do not show any quantization in 764

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voltages can thus be employed to tune the number of donors participating in the transport. Due to the different capacitive coupling between the donors in the depletion layer and the Si/ SiO2 interface where inversion takes place, the average slope of ISD−VUG for VUG < VUG,is is different from the slope at VUG > VUG,is. Now that we can observe distinguishable plateaus associated with individual donor atoms, we investigate the donor ionization energy by means of the temperature dependence. Figure 4a shows ISD as a function of VUG at VRG = −1.3 V (red curve in Figure 3a) for four different temperatures. We observe that for increased temperature the current ISD reduces at the onset of plateaus. This reduction is caused by an increased probability of electron escape back to the source due to thermal emission when VMG is still being ramped up (stage I to stage II in Figure 1b). This situation is schematically depicted in Figure 4b. Only when the confining barrier is large enough at the moment the donor potential is raised above EF, will the electron be captured and transferred to the drain electrode with high probability. This process is not surprising in itself, as a similar process is known to govern the electron capture in undoped silicon charge pump devices (similar to our undoped device),25 where the electrons are transferred via a quantum dot formed in the island region by VMG, VRG, and VUG. In the case of our doped devices, it is the donor potential itself which acts as the confining potential over which thermal emission takes place. The magnitude of thermal emission is governed by the ionization energy of the dopant Eion. An important implication of the electron escape being thermally activated (or ISD being thermally deactivated) is that Eion must be tunable by VUG, otherwise we would not observe ISD to be tunable by VUG. The ionization energy that governs the thermal activation can be determined from its proper Arrhenius relation. However, before we extract Eion we need to derive an expression for this Arrhenius relation, that is, how ISD scales with Eion and the temperature T. The current ISD associated with a single plateau is equal to the donor occupancy P at the moment of emission to the drain (stage III in Figure 1c) multiplied by a factor ef. Before ramping up VMG (stage I), P = 1 since the donor potential is lower than EF (to allow electrons to enter the island region from the source). Within the finite time it takes to ramp up VMG (stage II), the electron has a certain probability to escape back to the source (Figure 4b). The donor occupancy P can be described by the rate equation

the charge transfer via this electrically formed quantum dot; its dimensions (a width (W) of 80 nm and a length of 60 nm) are too large and the charging energy is subsequently too small. (Undoped devices where W is scaled down to 30 nm however, do show quantized charge transfer.25) Implantation of donors in the island region of our devices introduces positive charge and has two observable effects on the characteristics displayed in Figure 2a. First the positive charge shifts down VUG,is close to the level of VUG,th. Second the donors are able to bind electrons and thus increases the charge transfer per cycle. Since VUG,is will still be slightly higher than VUG,th (on the order of the donor ionization energy), at VUG = VUG,th there is no inversion layer yet. As a result, all the charge transfer takes place via donor sites (see upper panel of Figure 2b). The current ISD at VUG = VUG,th agrees with the expected number of activated donors in the island region (ND) within the margins set by the expected fluctuations on ND due to alignment issues. Only when VUG is increased beyond VUG,is inversion will take place (lower panel of Figure 2b), and we observe a current which scales with ISD ∼ qND + CUGVUG. As a result, at VUG ∼ VUG,th we observe a small flat region. Further confirmation that the plateau originates from transfer (exclusively) via donors comes from the dependence of the characteristics on the applied VBG, see Section II of the Supporting Information. Next, we show the amount of donors participating in the charge transfer can be tuned by means of the fine gate voltages. Figure 3a shows the charge transfer characteristics ISD versus

Figure 3. (a) Device characteristics ISD−VUG as a function of VRG for a device with 2 × 1012 cm−2 implantation dose, showing integer charge transfer up to ISD = 6 ef. The black dots (roughly) indicate VUG,is. (b) Schematic diagram of operation of charge transfer as a function of VRG; for increasingly negative VRG, a depletion layer in the channel is formed, reducing the number of donors participating in the charge transfer.

dP P =− dt τout

VUG for increasingly negative right fine gate voltage (VRG). We observe a decrease in ISD for more negative VRG combined with clear integer steps developing as a function of VUG. When a negative potential is applied to VRG (at fixed VUG) it induces a depletion region extending well into the island region, making less donors available for charge transfer (see Figure 3b). When we subsequently increase VUG to higher positive values, in some cases donor are neutralized again, shifting the potential where inversion occurs to higher positive values. The threshold voltage of the island region VUG,is is (roughly) indicated by the black dots. In Section III of the Supporting Information, we discuss the ISD−VUG versus VRG characteristics in more details and show that the formation of plateaus indeed only occurs at VUG < VUG,is, as expected from discrete donor states below the conduction band. As Figure 3a shows, the right fine gate

(1)

where τout is the emission time from the donor. In our case, the emission rate is thermally activated. In silicon, thermal emission from a quantum state scales with temperature as;26,32

⎛ E ion(t ) ⎞ 1 2 τ− ⎟ out = AT exp⎜ − kBT ⎠ ⎝

(2)

where A is a constant and kB is the Boltzmann constant. We expressed the ionization energy as Eion(t) to stress that in our electron pump device Eion is a function of time, due to its dependence on VMG. Without any a priori knowledge of Eion(t), we cannot derive a general solution of the differential eq 1. However, one can show that upon the condition 765

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Figure 4. (a) Current ISD as a function of VUG for four different temperatures. The data is acquired from the same samples as Figure 3a at VRG = −1.3 V. We observe that higher temperatures lead to a reduced current. The dashed box indicates the fourth charge plateau, which will be analyzed in detail. (b) Schematic diagram of the conduction band in the Si nanowire channel between VMG and VRG as VMG is ramped up during a charge transfer cycle (stage I to stage II in Figure 1c). As VMG is ramped up, a finite chance of thermally exciting a donor-bound electron (τout) exists, resulting in its escape back to the source and a decrease in ISD. (c) Ionization energy of the as donor responsible for the fourth charge plateau as a function of VUG, obtained from fitting to an Arrhenius Law (eq 5). The error bars indicate the standard error in Eion of each separate fit. The dash-dotted line indicates the bulk ionization energy of Arsenic donors (54 meV). Inset: Arrhenius law (eq 5) plot of the transport characteristics log[−log(ISD − Ioff)/T3)] versus 1/T for six values of VUG and the respective linear fits. (d) The inverse of the prefactor CA in eq 5 versus the extracted ionization energy Eion. The inverse of CA scales with ΔE = EB − Eion, which is in accordance with a simple model of the charge transfer (see eq 10). For clarity, the derived values of ΔE and EB are indicated in the graph (black arrow and black-dashed line, respectively).

d E ion(t ) >> dt kBT

d2 E ion(t ) dt 2 kBT

CA = (3)

the solution of eq 1 can be written as

⎛ ⎛ Eion(t = 0) ⎞ ⎞ ⎜− ⎟⎟ ⎜ kBT ⎝ ⎠⎟ 3 ⎜ P = exp − AkBT exp dE ion(t ) ⎟ ⎜ ⎜ ⎟ dt ⎝ t=0 ⎠

(6)

The inset of Figure 4c shows the data plotted according to the Arrhenius law defined by eq 5, that is, we plot log[−log(ISD − Ioff)/T3] versus 1/T, where each curve represents a single fixed VUG. Here, we have subtracted an offset Ioff equal to 3.09 ef from ISD, 3 ef since we intend to focus on the fourth plateau exclusively, and 0.09 ef of systematic offset. For clarity, we only plot the result for six voltages. Finally, a fit to the linear Arrhenius curves yields the desired Eion at t = 0, which is plotted in Figure 4c with its corresponding error bars. We observe that the value Eion is close to its bulk value of 54 meV33 for VUG ∼ 1.2 V. For VUG < 1.2 V, Eion decreases significantly for decreasing values of VUG. This correlation is attributed to an electric field induced barrier lowering of Eion due to the decreased value of VUG, as schematically depicted in Figure 4b. For VUG > 1.2 V the electric field is reversed as compared to VUG < 1.2 V, actually pushing electrons toward the drain side of the device. As a result, for VUG > 1.2 V we observe ISD = 4 ef in Figure 4a for all temperatures. The results of Figure 4 thus

(4)

Here t = 0 refers to the point in time where the donor potential crosses EF and emission starts. The condition of eq 3 essentially states that within an energy range of kBT, one should be able to describe Eion(t) by a linear function of t. Given that we raise VMG with a constant speed, we assume condition eq 3 to be met. Equation 4 can be written in an Arrhenius law form as

⎛ log P ⎞ E (t = 0) ⎟ = log(CA ) − ion log⎜ − 3 ⎝ kBT T ⎠

AkB dE ion(t ) dt t=0

(5)

where CA is the pre-exponential term (independent of T), which is given by 766

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expected values. The zero-field donor binding energy EB also might have deviated partly from its bulk value due to Coulomb interactions with nearby donors, due to the impurity band that one expects to have been formed at the donor concentrations present in the current device.30 Furthermore, it is noteworthy that the local electric field in the device (F) required to induce the observed ΔE is on the order of MV/m, a very realistic value for such devices (ΔE = 30 meV corresponds to 1.8 MV/m, see eq 8). In conclusion, we have studied single electron charge transfer by multiple donors, implanted in the island region of a charge transfer devices. The voltage condition of the devices can be tuned such that electrons are exclusively transferred via individual donor atoms. The ionization energy of an individual donor atom was extracted based on the appropriate Arrhenius law of the thermally deactivated current. The ionization energy was shown to depend on the upper gate voltage and as such was shown to be electrically tunable over a large range of energies, that is, from ∼25 to about 54 meV.

show Eion to be tunable by VUG, as already suggested by the thermally deactivated nature of ISD. The fit to eq 5 also yields a value for the pre-exponential term CA. As we will show, this term contains information on the rise time of the barrier trise and the unperturbed (zero field) ionization energy EB. To extract an estimate for trise and EB from the value of CA, we first derive an estimate expression for the term Eion(t). We model Eion simply by the 1D Poole−Frenkel effect. We thus take

E ion = EB − ΔE where ΔE is the barrier lowering given by

ΔE = q

qF πεsi

(7)

(8)

where εsi is the dielectric constant of silicon and F is the local electric field induced by VMG. For simplicity we furthermore assume the local electric field F to be a linear function of time. Furthermore, we assume a constant time trise is required to lower the field from its maximum value F0 at t = 0 to F = 0 at t = trise, where the barrier induced by VMG is higher than the barrier induced by VRG and emitted electrons will end up in the drain electrode. The electric field F is thus expressed as

⎛1 − t ⎞ F = F0⎜ ⎟ ⎝ t rise ⎠

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ASSOCIATED CONTENT

* Supporting Information S

Measurements and discussion of the electron localization, and the right gate- and back gate-voltage dependence of the charge transfer characteristics. This material is available free of charge via the Internet at http://pubs.acs.org.

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(9)

It should be noted that substituting eq 7 to eq 9 in eq 3 yields eq 4 holds as long as ΔE ≫ kBT. From eq 6 to eq 9 it follows that

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

ACKNOWLEDGMENTS This work was partly supported by KAKENHI 20241036, 22310062, and the Funding Program for Next Generation World-Leading Researchers of JSPS (GR103). Fruitful discussions with G. Yamahata are acknowledged.

1 1 ΔE(t = 0) = CA 2AkB t rise (10) Figure 4d plots the inverse of the pre-exponential terms (1/ CA) versus the fitted value of the ionization energy Eion including error bars. We observe 1/CA indeed scales with ΔE, as prescribed by eq 10; ΔE is close to zero around Eion = EB and increases for decreasing values of Eion. The red line shows a linear fit of 1/CA versus Eion in accordance with eq 10. Here, we applied an orthogonal distance regression method34 to take the fluctuating variance of the data points into account. Furthermore, only data points in the region of ΔE > 2kBT ∼ 6 meV were fitted, which is in accordance with the condition set by eq 3. Here, we used A = 3.3 × 108 s−1 K−2 which should hold for a shallow donor in silicon, in correspondence with Rosencher et al.26 As a result, we find trise = 16 ± 1 ns. The value we obtained for the rise time should be compared with the amount of time it takes to raise VMG from the threshold of the MOSFET (∼0 V) to VMG = VRG = 1.3 V. Since we raise VMG with the equivalent of 25 ns V−1, trise is estimated to be 32 ns. The correspondence between the fitted and the expected value of trise shows the time-scale of the electron emission τ (and thus the capture cross-section represented by A) corresponds with electron emission from a shallow donor state. For the zero-field donor binding energy we find EB = 45 ± 1 meV, which roughly corresponds with the bulk value of 54 meV we would expect. The relatively small uncertainties quoted for the fitted trise and EB are fitting errors only; the much larger deviation between fitted values and model values are attributed to systematic errors originating from the simplistic modeling. In light of this simplistic modeling, the values we obtain for trise and EB from fitting to eq 10 thus corresponds quite well to their

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