Modulation Doping of Silicon using Aluminium-induced Acceptor States in Silicon Dioxide

All electronic, optoelectronic or photovoltaic applications of silicon depend on controlling majority charge carriers via doping with impurity atoms. Nanoscale silicon is omnipresent in fundamental research (quantum dots, nanowires) but also approached in future technology nodes of the microelectronics industry. In general, silicon nanovolumes, irrespective of their intended purpose, suffer from effects that impede conventional doping due to fundamental physical principles such as out-diffusion, statistics of small numbers, quantum- or dielectric confinement. In analogy to the concept of modulation doping, originally invented for III-V semiconductors, we demonstrate a heterostructure modulation doping method for silicon. Our approach utilizes a specific acceptor state of aluminium atoms in silicon dioxide to generate holes as majority carriers in adjacent silicon. By relocating the dopants from silicon to silicon dioxide, Si nanoscale doping problems are circumvented. In addition, the concept of aluminium-induced acceptor states for passivating hole selective tunnelling contacts as required for high-efficiency photovoltaics is presented and corroborated by first carrier lifetime and tunnelling current measurements.

Conventional silicon doping is increasingly impeded due to the spatial dimensions approached by nanotechnology. Several fundamental physical principles counteract the substitutional incorporation of dopant impurities (e.g. B, P, or As) on Si lattice sites and their ionization to become electronically active donors of majority charge carriers. The formation energy for the substitutional dopant integration 1,2 as well as the ionization energy [3][4][5][6] increase strongly with decreasing Si dimensions. Moreover, conventional doping of Si nanoscale devices faces severe technological challenges: diffusion-related, steep radial gradients in the doping profile of Si nanowires [7][8][9] ; the inadvertent but inevitable diffusion of source/drain dopants into field-effect transistor (FET)-channels 10 ; surface segregation and inactivation of dopants 11 ; and statistical fluctuations by random numbers/positions of dopants in Si nanovolumes [12][13][14] . These problems render conventional Si doping unsuitable for future nanoelectronics.
As an alternative to classical impurity doping, modulation doping of III-V semiconductors was introduced in the late 1970s 15 . Homostructure modulation doping was proposed for Si and Ge nanowires using conventional dopants in a Si shell around nanowires, allowing for separation of majority charge carriers from their parent donor impurities 16,17 . However, this approach does not solve issues of dopant inter-diffusion, deficient dopant ionization or statistical distributions of dopant number and position. An impressive work-around, referring back to junctionless FETs (Lilienfeld, 1925), was demonstrated by Colinge et al. 18 . This approach solves the problem of highly abrupt p-n junctions, though ultimately scaled devices again suffer from nanoscale-Si doping obstacles. Hypervalent doping of free-standing Si quantum dots was demonstrated using chemical surface engineering 19 . However, so far this approach is not at all CMOS compatible. Molecular monolayer doping 20,21 was developed to achieve ultra-shallow p-n junctions via RTA-diffusion. Since this concept is based on classical impurity dopants, its applicability in low-dimensional systems is subject to the same constraints outlined above.
Here, we demonstrate a novel approach: modulation doping of Si by aluminium (Al)-induced acceptor states in silicon dioxide (SiO 2 ). Using computer-aided materials design, we predict that Al atoms in SiO 2 generate acceptor states 0.8 eV below the Si valence band edge. These states capture electrons from Si over a distance of several nanometres, providing holes to Si as majority charge carriers. We confirm this concept experimentally via capacitance-voltage (CV) and deep level transient spectroscopy (DLTS) on SiO 2 :Al/Si-based MOS capacitors. This doping technique is robust against out-diffusion, quantum confinement, dielectric confinement, and self-purification since it relocates doping from confined Si nanovolumes to adjacent bulk-like SiO 2 .

Results
Density functional theory simulations. Acceptor modulation doping of SiO 2 was modelled via realspace density functional theory (DFT). We embedded a Si 10 nanocrystal 22 in three monolayers (MLs) of SiO 2 , presenting the ultimate theoretical test of the doping concept because Si nanocrystal, SiO 2 and modulation acceptor (Al) form one approximant. Figure 1a and b show the highest occupied (HO) molecular orbital (MO) and the lowest unoccupied (LU) MO associated with Al. High probability densities occur within the Si 10 nanocrystal and at the Al acceptor, although both are separated by 3 ML of perfect SiO 2 . This finding shows that the Si 10 nanocrystal can still be positively ionized despite significant quantum confinement-induced bandgap widening. Figure 1c shows the electronic density of states (DOS) of the Si 10 nanocrystals in pure SiO 2 vs. SiO 2 :Al, along with the HOMO and LUMO of a 1.9 nm Si nanocrystal, fully terminated with hydroxyl (OH) groups, featuring SiO 2 embedding 23 . The Al acceptor state (β -LUMO) exists 0.26 eV below the HOMO of the 1.9 nm Si nanocrystal, clearly showing that Si nanocrystals of d ≥ 1.9 nm can obtain positive majority charge carriers (holes) from Al acceptors in SiO 2 . Transferring the situation to bulk Si, the Al acceptor state is located ~0.8 eV below the valence band edge. The principle of direct acceptor modulation doping is shown in the electronic band structures in Fig. 1d for Si nanocrystals and in Fig. 1e for bulk Si.  structures were annealed for 30 sec at 1000 °C in Ar ambient; subsequently, thermally evaporated aluminium contacts were structured. As evident from Fig. 1e, successful modulation doping of Si will manifest itself as a negative fixed charge Q fix in the SiO 2 :Al film. Using 1 MHz high-frequency capacitance-voltage (CV), we measured a change in the fixed charge of Δ Q fix = − 2.3 × 10 12 cm −2 for 1 ALD Al-O ML in SiO 2 (Al1) compared with pure SiO 2 reference samples (Al0) (Fig. 2b). The flatband voltage V FB was + 0.9 V and + 1.9 V for samples Al1 and Al2, respectively, whereas for the reference sample Al0, the flatband condition was achieved for − 0.2 V. By using n-type Si with a donor density of 3.5 × 10 15 cm −3 and Al as the gate metal, we keep the work function difference between the gate and n-Si negligible (− 0.004 eV). High-frequency CV does not allow for a contribution of Si/ SiO 2 interface states to the CV signal 24 , which can therefore be ruled out as having an effect on the CV curve. High energy resolution deep level transient spectroscopy (HERA-DLTS) was carried out to further characterize the Al-induced acceptor state. Figure 2d plots the transient capacitance over the reverse bias V R at 102 K. Clearly, sample Al1 shows a dominant signal at V R = − 3.5 V, whereas no transient capacitance is detected for the reference sample. The peak originates from electrons escaping from the Al-state into the Si wafer via direct tunnelling (scattering, trap-assisted tunnelling and hopping are suppressed at low temperatures). The transient time constant T W = 31 ms was kept comparatively short at the cost of signal intensity to further eliminate any trap-assisted tunnelling that is less dynamic. Using the Poisson equation, the energetic position of the Al-acceptor state in the SiO 2 bandgap was calculated to be 0.5 eV below the Si valence band edge. This energy value underlines the accuracy of DFT calculations, yielding 0.8 eV. The full with half maximum (FWHM) of V R was Δ V R = 0.66 V, cf. Fig. 2c. The FWHM translates into a vertical-spatial distribution of Al atoms of ca. 0.27 nm, accounting for RTO interface roughness and binding of Al to the RTO, as well as binding to the CVD capping oxide.

Electrical characterisation of modulation doped silicon.
This finding confirms our h-DFT results, where Al in SiO 2 provides an acceptor state even for small Si NCs and corroborates that Al undergoes virtually no diffusion during the activation anneal, in accordance with its diminutive diffusion coefficient 25 . In Fig. 2e, we demonstrate the reverse pulse scheme to sample electron capture into Al acceptors and plot transient capacitance over the pulse time t P at 502 K. The modulation doped sample Al1 showed one broad peak at t P = 2.0 s, with a maximum transient signal of 146 nF/cm 2 or 9.11 × 10 11 cm −2 transferred charge, accounting for ca. 40% of all negative Al acceptors. No electron capture signal was detected for the reference sample. Time constants T W and t p were chosen to be large compared to low-temperature electron escape in order to account for the maximum density of charged Al acceptors. The substantially higher two-peak signal of sample Al2 shows that we control the density of active modulation acceptors in SiO 2 , which was confirmed by HF-CV results.

Field effect passivation and improved hole tunnelling by Al-induced acceptor states.
First results on carrier lifetime measurements carried out by quasi-steady-state photoconductance (QSSPC) 26 are shown in Fig. 3a using mechanical grade double side polished 525 μ m thick Cz-Si wafers with an ultrathin rapid-thermal oxide. Samples were not passivated in hydrogen (H 2 ) or forming gas (FG). The spectra show a minority (hole) carrier lifetime τ hole = 1 ms at an excess majority carrier density corresponding to 1 sun illumination (Δ p = 10 15 cm −3 ), presenting an increase over the reference sample with undoped annealed CVD-SiO 2 by a factor of 100. The corresponding emitter saturation current density 27 is j 0 = 1.05 × 10 −13 A/cm 2 . This low value obtained on preliminary samples shows the potential of SiO 2 modulation doping for high efficiency silicon solar cells. With a high negative Q fix we can approximate the surface recombination velocity by 28 S eff = d wafer /2τ hole , yielding 26 cm/s. In Fig. 3b current-voltage measurements on 3 nm thick RTO/SiO 2 stacks on p-type Si wafers are shown. Current densities of ca. 40 mA/cm 2 which correspond to maximum power point (MPP) operation of high efficiency solar cells incur a potential drop of ca. 0.23 V for the reference sample while the SiO 2 doped with 1 ML Al reduces this potential drop by 74% to 0.06 V. While a high negative Q fix accelerates holes to the tunnelling barrier, the Al-induced acceptor states do not have to be charged for increasing the transition probability through the tunnelling barrier. Such states contribute to improved hole tunnelling already in their neutral form due to diminishing the tunnelling barrier from the valence band offset from Si to SiO 2 of ca. 4.5 eV 29 to merely 0.5 eV by introducing a lateral defect band. The improved lifetimes and tunnelling currents obtained for preliminary, non-optimized Cz-wafers indicate the promising potential of SiO 2 :Al for passivating hole selective tunnelling contacts in high efficiency silicon solar cells.

Discussion
Heterostructure modulation doping of Si using intentionally designed impurities in SiO 2 presents a true paradigm shift by "outsourcing" dopants to the surrounding matrix. This approach can acceptor-dope Si MOS-FETs by incorporating Al atoms in the insulating SiO 2 trench or into the base and coating for fin-FETs, which circumvents all mentioned nanoscale doping problems. As shown exemplarily in Fig. 4a,c, the source and drain areas of an intrinsic Si fin-FET become p-type conductive by incorporating Al-atoms in the buried oxide (BOX). The absence of dopants within the active Si volume eliminates dopant impurity scattering, resulting in lower heat generation, higher carrier mobilities and consequently lower operating voltages. These features are very beneficial for advancing ultra-large scale integration (ULSI) and ultra-low power applications. Moreover, modulation doping avoids the so-called dopant fingerprint of nanoscale MOS-devices, i.e. statistical performance fluctuations due to variations in the exact number and distribution of dopants 4,12,14 . Coulomb repulsion between the charged Al-induced acceptor states self-regulates the amount of holes generated and prevents that all such states capture an electron. In fact, approximately only one in a hundred acceptor states (1 Al-O monolayer) can be charged and hole-doping is easily controlled via the areal coverage of the Si nanovolume with SiO 2 :Al.
Apart from microelectronics, Si-modulation doping can enhance passivating tunnelling contacts in heterojunction with intrinsic thin layer (HIT) solar cells 30 , cf. Fig. 4b,d. Very recently, the conventional HIT-cell concept was complemented by the DASH cell concept (dopant-free asymmetric heterocontacts) 31 . Bullock et al. propose alkali metal fluorides such as LiF x on intrinsic a-Si:H as electron selective heterocontacts 31 and MoO x /a-Si:H(i) as hole selective heterocontacts 32 and achieve impressive conversion efficiencies. In a different approach, electron-selective contacts were realized by ALD-TiO 2 on ultrathin tunnel-SiO 2 33 . We propose that the Si modulation doping approach represents a competitive technology to improve efficiencies even further: Modulation acceptors in ultrathin SiO 2 significantly improve hole tunnelling transport via a strongly decreased tunnelling barrier (0.5 eV vs. 4.5 eV in undoped SiO 2 ), cf. Fig. 3b. Additionally, the acceptor states provide a negative drift field for repelling electrons as the minority carrier type, complemented by the unparalleled chemical Si surface passivation quality of SiO 2 . A massive increase in minority carrier lifetime and ensuing ultra-low emitter saturation current density as compared to unpassivated samples is evident from Fig. 3. Currently used amorphous Si surface layers are far from featuring such properties. Interestingly, a recent theoretical screening study investigated several elements concerning their defect state energies in SiO 2 with respect to Si, in order to improve field-effect passivation and transport for majorities 34 . However, the energetic position derived for Al in that study differs vastly from our theoretical DFT and experimental DLTS values.
Finally, we note that one or two Al-O monolayers in SiO 2 do not constitute an Al 2 O 3 phase. Field effect passivation by negative Q fix were also demonstrated with Al 2 O 3 films prepared by pyrolysis 35 , sputtering 36 , PECVD 37 , and ALD [38][39][40][41] . These stacks often require annealings in the range of 400 to 800 °C to build up the negative Q fix , depending on the deposition technique. Remarkably, it was shown that 1 to 2 nm silicon oxide inevitably grow during deposition and annealing and that the negative charges are majorly located at the SiO 2 /Al 2 O 3 interface 38,39 . We hypothesize that Al 2 O 3 undergoes an interface reaction with underlying Si most likely during the anneal to form an ultrathin layer of SiO 2 , thereby creating O-deficient Al 2 O 3 (Al 2 O x , x < 3) which contains O vacancies. This situation is in striking analogy to F-deficient aluminium fluoride (AlF x , x < 3) as mentioned below 42,43 . In one work 39 the origin of the negative Q fix is ascribed to excess oxygen (O) within AlO x (i.e. x > 3). Since O is very reactive and either a radical (monatomic form) or a gas (O 2 ) and the respective samples require an activation anneal for 15 min at 425 °C 39 , it is inconceivable how excess O could exist in such AlO x layers. As a result, we have reasonable doubt to consider excess O as the origin of the negative Q fix . On the other hand, average values of Q fix = − 4 × 10 12 cm −2 and midgap Si/SiO 2 interface trap densities of 3 × 10 10 cm −2 measured by mercury-probe CV (Hg-CV) wafer maps have been routinely obtained for F-deficient AlF 3 (AlF x ) on Si wafers with ultrathin SiO 2 42 . Light soaking increases the average value of this negative Q fix to − 4.85 × 10 12 cm −2 43 . DFT calculations show that F vacancies are acceptor type defects which can localize electrons originating from Si and tunnelling though SiO 2 42-45 , yielding a negative Q fix . We note here that O was not present in AlF x nor did the ultrathin SiO 2 layer on the Si wafer contain excess O 43 . These findings clearly support the picture that O vacancies provide the acceptor type defect states in AlO x manifesting the negative Q fix . In contrast, modulation acceptor states in SiO 2 :Al owe their existence to one O dangling bond next to a single Al atom which substitutes Si in SiO 2 , see Fig. 1a-c. Although Al 2 O 3 thin films provide field effect passivation in analogy to Al-doped SiO 2 on Si, the insulating nature of Al 2 O 3 in compound with the 2 nm SiO 2 layer formed during the anneal prevents improved hole tunnelling as demonstrated here for 1 Al-O monolayer in SiO 2 , cf. Fig. 3b. Doping SiO 2 with Al also eliminates oxidizing interface reactions whereby sample processing becomes more controllable which can be a technological advantage. The performance of Al 2 O 3 was also investigated in the limit of 1 and 4 plasma ALD-cycles and corresponding thicknesses of 1 and 5 Å 40,41 . The thickness of 1 Å corresponds to one thermal ALD cycle as used by us to dope SiO 2 with 1 ML Al-O. It turns out that these ultrathin films deposited directly on Si create significantly less negative Q fix , though a superposition with the high positive fixed charge density in the SiN x capping cannot be ruled out.
In summary, we developed in theory and experiment a heterostructure Si-modulation doping method based on aluminium-induced acceptor states in SiO 2 . Providing holes as majority charge carriers with such a fundamental principle represents a paradigm shift in silicon science and technology. It allows for a different strategy to define and control majority charge carriers in nanoelectronic devices and allows for passivating hole-selective contacts in high-efficiency solar cells. More generally, our modulation doping concept is transferable to other group-IV semiconductors, such as diamond or germanium, if energetically suitable combinations of impurity elements and dielectric matrices are found.

Methods
Density functional theory simulations and Poisson solver. Approximants were structurally optimized for the maximum integral over all bond energies defining the most stable configuration, using the Hartree-Fock (HF) method with 3-21G molecular orbital basis set (MO-BS) 22,46 for structural optimizations and the B3LYP hybrid DF 47,48 with 6-31G(d) MO-BS 22,49 for electronic structure calculations with the Gaussian09 software suite 50 . RMS and peak force convergence limits were 8 meV/Å and 12 meV/Å, respectively. Ultrafine integration grids and tight convergence criteria were applied to the self-consistent field routine. During all calculations, no symmetry constraints were applied to the MOs. Further accuracy evaluations can be found elsewhere 22,23 . A one-dimensional (1-D) Poisson solver for MIS structures was coded in MatLab following Nicollian and Bruce 24 .
Fabrication and characterization of SiO 2 :Al samples. PECVD SiO 2 tunnel oxides (1.5 nm) were deposited 51 onto wet-chemically cleaned 100 mm Czochralski P-doped Si wafers (1.6 Ωcm) in a modified Oxford Instruments PlasmaLab-FlexAL cluster. Subsequently, the wafers were transferred under vacuum into the thermal ALD chamber for deposition of Al-O monolayers via TMA (trimethylaluminium) and H 2 O at 200 °C (sample Al1: 1 ALD cycle, Al2: 2 ALD cycles, Al0: H 2 O pulse only). Finally, the capping SiO 2 layer (10 nm) was deposited in the PECVD chamber. The lifetime wafers were rapid-thermally oxidized (RTO, 2.5 nm) and then transferred into the ALD-PECVD cluster for Al-O monolayer and capping oxide deposition. All wafers were RTP-annealed (1000 °C, 30 s, Ar atmosphere). Electrical top-and substrate contacts (Al) were thermally evaporated and lithographically structured to fabricate MOS capacitors. The hole tunnelling samples were fabricated similarly on B-doped Cz-Si wafers (2.4 Ωcm) with 1.5 nm RTO and capping oxide to enable direct tunnelling and thermally evaporated Pd contacts. All silicon oxide thicknesses were measured by ellipsometry. DLTS and HF-CV were measured with a PhysTech FT1030 High energy resolution analysis (HERA) setup using a JANIS VPF 800 Cryostat. I-V was measured with an Agilent B1500A. Minority (hole) carrier lifetime was measured as average value over the entire wafer with QSSPC using a lifetime tester from Sinton Consulting.