The Effect of Doping on the Digital Etching of Silicon-Selective Silicon–Germanium Using Nitric Acids

Gate-all-around (GAA) field-effect transistors have been proposed as one of the most important developments for CMOS logic devices at the 3 nm technology node and beyond. Isotropic etching of silicon–germanium (SiGe) for the definition of nano-scale channels in vertical GAA CMOS and tunneling FETs has attracted more and more attention. In this work, the effect of doping on the digital etching of Si-selective SiGe with alternative nitric acids (HNO3) and buffered oxide etching (BOE) was investigated in detail. It was found that the HNO3 digital etching of SiGe was selective to n+-Si, p+-Si, and intrinsic Si. Extensive studies were performed. It turned out that the selectivity of SiGe/Si was dependent on the doped types of silicon and the HNO3 concentration. As a result, at 31.5% HNO3 concentration, the relative etched amount per cycle (REPC) and the etching selectivity of Si0.72Ge0.28 for n+-Si was identical to that for p+-Si. This is particularly important for applications of vertical GAA CMOS and tunneling FETs, which have to expose both the n+ and p+ sources/drains at the same time. In addition, the values of the REPC and selectivity were obtained. A controllable etching rate and atomically smooth surface could be achieved, which enhanced carrier mobility.


Introduction
Gate-all-around (GAA) nanowire transistors are ideal candidates for various CMOS applications due to their outstanding gate control, excellent performance, immunity to short-channel effects, and scalability [1][2][3]. Tunneling field-effect transistors (TFETs) have arisen as promising devices with emerging device concepts by breaking through the subthreshold swing limit of 60 mV/dec for low-power applications [4][5][6]. GAA nanowire TFETs have become candidates for substitutes for conventional MOS technology, especially in terms of their energy efficiency and scaling due to the better electrostatic control of the tunneling carriers provided by their nanowire structure [7][8][9][10]. SiGe channel materials have been introduced due to their excellent bandgap, high mobility, high density of states, and high compatibility with existing CMOS technology [11,12]. In order to precisely define the nanowire diameter and effective gate length, SiGe materials need to be selectively etched with accurate etching depth control and high selectivity for both n + -Si and p + -Si for

Materials and Methods
The substrates were 8 inch p-type Si (100) wafers with a resistivity of 8-12 ohm·cm. The p + -Si/SiGe/n + -Si stack layers were grown in an ASM E2000 plus RPCVD reactor (ASM, Munich, Germany). First, after a standard pre-epitaxial cleaning, the wafers were baked at 900 • C in ambient H 2 with a pressure of 20 Torr for 5 min, achieving a pure and smooth silicon surface [32]. Then, the p + -Si/SiGe/n + -Si stack layers and p + -Si/SiGe/i-Si stack layers were grown at 650 • C using an adjusted gas source with H 2 as a carrier gas. Dichlorosilane (SiH 2 Cl 2 ), germane (GeH 4 ), diborane (B 2 H 6 ), and phosphine (PH 3 ) were utilized as gas precursors of Si, Ge, B, and P, respectively. The Ge incorporation, P concentration, and B concentration in silicon were achieved by tuning the gas flow and gas pressure. Finally, the epitaxial stack layers were fabricated. Then, a hard mask was deposited on the epitaxial stacked layers, and the pattern was formatted with an optical lithography with an I-line. The Si/SiGe stack layers were etched using hydrogen bromide (HBr)-based dry anisotropic etching. The details of the sample preparation can be found in [32]. Afterwards, the prepared samples were cut into same-sized slices of about 3 × 3 cm 2 to facilitate the etching experiments.
There were five kinds of Si/SiGe stack layer structures, as shown in Figure 1a-c. Sample I was a laminated structure in which~300 nm p-type doped Si with a boron dopant concentration of 1.0 × 10 20 cm −3 , 55 nm intrinsic Si 0.72 Ge 0. 28 , and 120 nm n-type doped Si with a phosphorus dopant concentration of 1.7 × 10 19 cm −3 were epitaxially grown in sequence. Bottom p-type doped Si was etched to~120 nm. The structural diagram is shown in Figure 1a. Sample II was a laminated structure in which~300 nm p-type doped Si with a boron dopant concentration of 9 × 10 19 cm −3 , 55 nm intrinsic Si 0.72 Ge 0.28 , and 120 nm intrinsic Si were grown in situ and in sequence. The structural diagram is shown in Figure 1b. In Sample III, arsenic (As) ion implantation with the energy of 30 keV and dose of 4 × 10 15 cm −2 was performed on the top intrinsic Si, and then 900 • C spike annealing was carried out to activate arsenic in the top Si. The structural diagram is shown in Figure 1c. This sample was employed to demonstrate the digital etching characteristics of n-type doped Si with the implantation of As. Sample IV was a laminated structure with nine Si 0.72 Ge 0.28 layers, as shown in Figure 1d. The n + -SiGe layers with in situ phosphorus included SiGe layer 1, SiGe layer 2, and SiGe layer 3. The concentrations were 2 × 10 19 , 1.3 × 10 19 , and 2 × 10 19 cm −3 , respectively. The intrinsic SiGe layers consisted of SiGe layer 4, SiGe layer 5, and SiGe layer 6. The p + -SiGe layers with in situ boron included SiGe layer 7 and SiGe layer 8 with a concentration of 4 × 10 19 cm −3 . SiGe layer 9 was doped with boron with a concentration of 4 × 10 19 cm −3 and arsenic with a concentration of 4 × 10 19 cm −3 . The thickness of the SiGe was~35 nm. The thickness of the Si was~50 nm. The sample was used for the investigation of the digital etching characteristics of doped SiGe. Sample V was a laminated structure with~30 nm n + -Si layers and~35 nm n + -SiGe layers with a varying Ge fraction; these layers were alternated, and the sample was used to examine the influence of the Ge mole fraction.
quence. Bottom p-type doped Si was etched to ~120 nm. The structural diagram is shown in Figure 1a. Sample II was a laminated structure in which ~300 nm p-type doped Si with a boron dopant concentration of 9 × 10 19 cm −3 , 55 nm intrinsic Si0.72Ge0.28, and 120 nm intrinsic Si were grown in situ and in sequence. The structural diagram is shown in Figure  1b. In Sample III, arsenic (As) ion implantation with the energy of 30 keV and dose of 4 × 10 15 cm −2 was performed on the top intrinsic Si, and then 900 °C spike annealing was carried out to activate arsenic in the top Si. The structural diagram is shown in Figure 1c. This sample was employed to demonstrate the digital etching characteristics of n-type doped Si with the implantation of As. Sample IV was a laminated structure with nine Si0.72Ge0.28 layers, as shown in Figure 1d. The n + -SiGe layers with in situ phosphorus included SiGe layer 1, SiGe layer 2, and SiGe layer 3. The concentrations were 2 × 10 19 , 1.3 × 10 19 , and 2 × 10 19 cm −3 , respectively. The intrinsic SiGe layers consisted of SiGe layer 4, SiGe layer 5, and SiGe layer 6. The p + -SiGe layers with in situ boron included SiGe layer 7 and SiGe layer 8 with a concentration of 4 × 10 19 cm −3 . SiGe layer 9 was doped with boron with a concentration of 4 × 10 19 cm −3 and arsenic with a concentration of 4 × 10 19 cm −3 . The thickness of the SiGe was ~35 nm. The thickness of the Si was ~50 nm. The sample was used for the investigation of the digital etching characteristics of doped SiGe. Sample V was a laminated structure with ~30 nm n + -Si layers and ~35 nm n + -SiGe layers with a varying Ge fraction; these layers were alternated, and the sample was used to examine the influence of the Ge mole fraction. The q-ALE process of digital wet etching, including oxidation, deionized (DI) water rinsing, oxide removal, and DI water rinsing, and the investigations on the self-limiting The q-ALE process of digital wet etching, including oxidation, deionized (DI) water rinsing, oxide removal, and DI water rinsing, and the investigations on the self-limiting behavior of SiGe etching were described previously [31,32]. The flow is shown in Figure 2. The diluted BOE solutions were utilized for sample pretreatment. The steps within dotted Nanomaterials 2021, 11, 1209 4 of 14 border, including HNO 3 oxidation, DI water rinsing, oxide removal, and DI water rinsing, were repeated for many cycles until the desired etching amount was reached. The HNO 3 solutions in the experiments were prepared by adjusting the volume of analytical-grade nitric acid (70% (wt/wt)) and the volume of deionized water under the condition that the total volume of the solution was kept constant (2 L). The concentrations of the HNO 3 solutions were monitored with a high-precision density meter. The values of concentrations mentioned in this paper represent mass fractions. The nitric acid solutions were employed for oxidation, and were then cooled to room temperature before use. The oxidation time was set to 60 s. It was long enough to reach saturation with an oxidation time of 27.6 s [31]. The BOE solutions used in the experiments were prepared by diluting the original BOEs (NH 4 F 34.8%, HF 6.23%) 50 times with deionized water, and the total volumes of the BOE solutions were kept at 2 L. The BOE solutions were used for oxide removal. HF/BOE concentrations that were too high would damage the Si or SiGe layers. The oxide removal time and DI water rinsing time were fixed at 60 s, which ensured the complete removal of oxides and the non-existent cross-contamination of solutions. The temperature of the control recipe was kept at room temperature (20.5 ± 0.5 • C). Unless otherwise specified, the oxidation-etching procedure in every experiment was performed for 50 cycles repeatedly. Additionally, the H 2 O 2 (30% (wt/wt)) solutions were prepared for the H 2 O 2 q-ALE experiments as a comparison with the HNO 3 q-ALE experiments.
behavior of SiGe etching were described previously [31,32]. The flow is shown 2. The diluted BOE solutions were utilized for sample pretreatment. The steps w ted border, including HNO3 oxidation, DI water rinsing, oxide removal, and rinsing, were repeated for many cycles until the desired etching amount was reac HNO3 solutions in the experiments were prepared by adjusting the volume of a grade nitric acid (70% (wt/wt)) and the volume of deionized water under the c that the total volume of the solution was kept constant (2 L). The concentratio HNO3 solutions were monitored with a high-precision density meter. The value centrations mentioned in this paper represent mass fractions. The nitric acid were employed for oxidation, and were then cooled to room temperature before oxidation time was set to 60 s. It was long enough to reach saturation with an o time of 27.6 s [31]. The BOE solutions used in the experiments were prepared by the original BOEs (NH4F 34.8%, HF 6.23%) 50 times with deionized water, and volumes of the BOE solutions were kept at 2 L. The BOE solutions were used removal. HF/BOE concentrations that were too high would damage the Si or SiG The oxide removal time and DI water rinsing time were fixed at 60 s, which ens complete removal of oxides and the non-existent cross-contamination of solut temperature of the control recipe was kept at room temperature (20.5 ± 0.5 °C otherwise specified, the oxidation-etching procedure in every experiment was p for 50 cycles repeatedly. Additionally, the H2O2 (30% (wt/wt)) solutions were pre the H2O2 q-ALE experiments as a comparison with the HNO3 q-ALE experiment The etched morphology of the samples and the etched depth were exami scanning electron microscopy (SEM) (Hitachi, Tokyo, Japan). Secondary ion m troscopy (SIMS) was used to analyze the doping and mole fraction. Atomic forc copy (AFM) (Dimension Icon AFM, Bruker, Billerica, MA, USA) was used to me surface roughness. High-resolution X-ray diffraction (HRXRD) (Delta-X, Bruker, MA, USA) was used to determine the crystallinity and strain relaxation of the S structures.

n-Type Doped Si Selectivity with H2O2 or HNO3 q-ALE
The digital etching of SiGe and selectivity of SiGe for p + -Si were previously i with H2O2-dBOE q-ALE and HNO3-dBOE q-ALE [31,32]. We chose the above tw processes to investigate the selectivity of n-type silicon. Figure 3a,b show the SE section images of Sample I with n + -Si and in situ phosphorus after etching for The etched morphology of the samples and the etched depth were examined with scanning electron microscopy (SEM) (Hitachi, Tokyo, Japan). Secondary ion mass spectroscopy (SIMS) was used to analyze the doping and mole fraction. Atomic force microscopy (AFM) (Dimension Icon AFM, Bruker, Billerica, MA, USA) was used to measure the surface roughness. High-resolution X-ray diffraction (HRXRD) (Delta-X, Bruker, Billerica, MA, USA) was used to determine the crystallinity and strain relaxation of the Si/SiGe/Si structures.

n-Type Doped Si Selectivity with H 2 O 2 or HNO 3 q-ALE
The digital etching of SiGe and selectivity of SiGe for p + -Si were previously identified with H 2 O 2 -dBOE q-ALE and HNO 3 -dBOE q-ALE [31,32]. We chose the above two q-ALE processes to investigate the selectivity of n-type silicon. Figure 3a,b show the SEM crosssection images of Sample I with n + -Si and in situ phosphorus after etching for 40 cycles with 30% H 2 O 2 q-ALE and 40 cycles with 31.5% HNO 3 q-ALE. The relative etching amounts (REAs) of SiGe/p + -Si with H 2 O 2 and with HNO 3 were 18.4 nm (see Figure 3a) and 24.8 nm (see Figure 3b), respectively. The REPC was calculated by dividing the REA by the number of etching cycles. The REPC with H 2 O 2 was 0.46 nm, which was almost identical to the previous results [32]. The REPC with HNO 3 was 0.62 nm, 20% higher than the previous value [31]. This may have been caused by the increase in nitric acid concentration.
the Ge/Si fraction. The results showed that the dopant concentration was above cm −3 within a depth of about 100 nm. Such high arsenic doping might lead to lo crystalline or even amorphous characteristics, which enhance the etching reactio dition, a phenomenon that was not easy to observe was that the etching rate of S the n-type Si was slightly faster than that near the p-type Si. In the arsenic dopin shown in Figure 4c, the arsenic was distributed in the SiGe. This might have been by arsenic implantations. However, the boron distribution in SiGe was negligibl considered that the digital etching of SiGe is dependent on the doping of SiGe. perform an in-depth study in the third part.  It is shown in Figure 3a that the REA of SiGe/n + -Si with H 2 O 2 was just 3.9 nm, which is smaller than that of SiGe/p + -Si, indicating poor selectivity for n + -Si and the high reactivity of n-Si. Therefore, H 2 O 2 -dBOE q-ALE was not suitable for p + -Si/SiGe/n + -Si structure etching. The differences between n + -Si and p + -Si in terms of selectivity and etching rate might be related to the types of carriers or the dopant types. Sample III with the arsenic ion implantation was assessed using 50 cycles with the H 2 O 2 -dBOE and HNO 3 -dBOE q-ALE process. The SEM cross-section images of Sample III are shown in Figure 4a,b. The results are almost consistent. As shown in Figure 4a, with H 2 O 2 q-ALE, Sample III exhibited weak selectivity for n + -Si formed by As implantation. It was demonstrated that the carrier type-instead of dopant type-enhanced the etching rate of n + -Si in the H 2 O 2 q-ALE process. The high concentration of electrons in n + -Si might accelerate oxide growth in H 2 O 2 solutions, which could be explained by the improved relativity of Si-Si back bonds [33].
As shown in Figure 3a,b, the REA of SiGe/n + -Si with HNO 3 was obviously larger than with H 2 O 2 , and was close to that of p + -Si. Similar results are shown in Figure 4a,b. This indicates the excellent selectivity for n + -Si with the HNO 3 q-ALE process compared with the H 2 O 2 q-ALE process, regardless of if in situ doped Si or implanted Si is used. In addition, the etched notch on top of Sample III shown in Figure 4b is assumed to be the result of high dose implantation. Figure 4c shows the SIMS data of boron/arsenic doping and the Ge/Si fraction. The results showed that the dopant concentration was above 1 × 10 20 cm −3 within a depth of about 100 nm. Such high arsenic doping might lead to local polycrystalline or even amorphous characteristics, which enhance the etching reaction. In addition, a phenomenon that was not easy to observe was that the etching rate of SiGe near the n-type Si was slightly faster than that near the p-type Si. In the arsenic doping profile shown in Figure 4c, the arsenic was distributed in the SiGe. This might have been caused by arsenic implantations. However, the boron distribution in SiGe was negligible. It was considered that the digital etching of SiGe is dependent on the doping of SiGe. We will perform an in-depth study in the third part.

Effect of Doped Si and HNO3 Concentration Dependence
In order to explore the effect of doping in silicon on the selectivity of SiGe etching, 31.5% HNO3 q-ALE experiments were carried out with Sample I and Sample II. The structures of SiGe/n + -Si, SiGe/p + -Si, and SiGe/i-Si were included and could be investigated. All of the samples were processed together. Groups of samples including Sample I and Sample II were taken out every 50 cycles. For samples with different doping conditions between the top silicon and bottom silicon, the etching morphologies of the top and bottom silicon might be different. For example, the SEM images of Sample II shown in Figure S1 exhibited different REA values for SiGe/i-Si from those of SiGe/p + -Si and different i-Si losses with p + -Si loss.
The structural diagram of the etching morphology is shown in Figure 5. The dashed line in Figure 5 represents the initial envelope lines of the fresh sample. The solid boxes are the envelope lines as they were etched. The angle between the etching slope at the surface of the etched Si and the horizontal direction is θ. Silicon was etched in the vertical and lateral directions. The etching amounts are described as the vertical Si loss (Si loss_v) and lateral Si loss (Si loss_l). As discussed in a previous work [31], the influence of crystal planes on the etching rate was ignored, that is, Si loss_v was almost equal to Si loss_l. The etching amount in the vertical direction could be directly measured. Therefore, the etching amount in the vertical direction is usually regarded as the Si etching amount (Si loss) in the following section. Silicon-germanium was only etched laterally. The etching amount

Effect of Doped Si and HNO 3 Concentration Dependence
In order to explore the effect of doping in silicon on the selectivity of SiGe etching, 31.5% HNO 3 q-ALE experiments were carried out with Sample I and Sample II. The structures of SiGe/n + -Si, SiGe/p + -Si, and SiGe/i-Si were included and could be investigated. All of the samples were processed together. Groups of samples including Sample I and Sample II were taken out every 50 cycles. For samples with different doping conditions between the top silicon and bottom silicon, the etching morphologies of the top and bottom silicon might be different. For example, the SEM images of Sample II shown in Figure S1 exhibited different REA values for SiGe/i-Si from those of SiGe/p + -Si and different i-Si losses with p + -Si loss.
The structural diagram of the etching morphology is shown in Figure 5. The dashed line in Figure 5 represents the initial envelope lines of the fresh sample. The solid boxes are the envelope lines as they were etched. The angle between the etching slope at the surface of the etched Si and the horizontal direction is θ. Silicon was etched in the vertical and lateral directions. The etching amounts are described as the vertical Si loss (Si loss_v) and lateral Si loss (Si loss_l). As discussed in a previous work [31], the influence of crystal planes on the etching rate was ignored, that is, Si loss_v was almost equal to Si loss_l. The etching amount in the vertical direction could be directly measured. Therefore, the etching amount in the vertical direction is usually regarded as the Si etching amount (Si loss) in the following section. Silicon-germanium was only etched laterally. The etching amount can Nanomaterials 2021, 11, 1209 7 of 14 be described as the sum of the REA and Si loss_l. The selectivity can be expressed as the ratio of SiGe loss to Si loss, as described in Equation (1). selectivity = (REA + Si loss) Si loss = 1 + cotθ (1) can be described as the sum of the REA and Si loss_l. The selectivity can be expressed as the ratio of SiGe loss to Si loss, as described in Equation (1) In addition, in Sample I and Sample II, the diffusion of impurities from silicon to silicon-germanium was negligible, and SiGe could be regarded as intrinsic. The germanium component was fixed in the whole SiGe layer. Therefore, the q-ALE etching of SiGe/Si1 and the q-ALE etching of SiGe/Si2 were independent of each other. The selectivity could be separately calculated by using the Equation (1). According to the angle calculation method and the length calculation method, the values of the selection ratios were very close. This was proved by our experimental data.  Figure 6 shows the dependence of the REA and Si loss on the number of etching cycles for SiGe/n + -Si, SiGe/p + -Si, and SiGe/i-Si. The scatters in Figure 6 are the data points obtained through the experiments, and the lines are the curves fitted linearly according to the experimental data. It is shown that the REA of SiGe/n + -Si, REA of SiGe/p + -Si, and REA of SiGe/i-Si were highly linear dependent on the number of etching cycles, which was confirmed by the R_square up to 0.975. The Si losses of n + -Si, p + -Si, and i-Si were also linearly related to the number of cycles. In the table embedded in Figure 6, the fitting slopes of the REA curves and the Si loss curves represent the REPC and silicon etching amount of each cycle (EPC). It was shown that the REPC of SiGe/p + -Si was 0.6079 nm, which was close to the REPC value of SiGe/n + -Si (0.6389 nm). The EPC of p + -Si was 0.2262 nm, which was also close to the EPC value of n + -Si (0.2255 nm). The results indicate that the 31.5% HNO3 concentration had the same etching rate for p + -Si and n + -Si. The concentration is expected to be used for the digital etching of p + -Si/SiGe/n + -Si stack structures, such as GAA CMOS and TFET applications. Moreover, the slopes in the fitting curves of SiGe/i-Si REA are lower than that of doped Si, suggesting its poor selectivity for i-Si. The EPC of i-Si was 0.3732 nm. It was demonstrated that the etching rate was larger than that of doped Si. It was considered that the doping of silicon contributed to the better selectivity for silicon with the nitric acid etching of SiGe. In addition, in Sample I and Sample II, the diffusion of impurities from silicon to silicon-germanium was negligible, and SiGe could be regarded as intrinsic. The germanium component was fixed in the whole SiGe layer. Therefore, the q-ALE etching of SiGe/Si1 and the q-ALE etching of SiGe/Si2 were independent of each other. The selectivity could be separately calculated by using the Equation (1). According to the angle calculation method and the length calculation method, the values of the selection ratios were very close. This was proved by our experimental data. Figure 6 shows the dependence of the REA and Si loss on the number of etching cycles for SiGe/n + -Si, SiGe/p + -Si, and SiGe/i-Si. The scatters in Figure 6 are the data points obtained through the experiments, and the lines are the curves fitted linearly according to the experimental data. It is shown that the REA of SiGe/n + -Si, REA of SiGe/p + -Si, and REA of SiGe/i-Si were highly linear dependent on the number of etching cycles, which was confirmed by the R_square up to 0.975. The Si losses of n + -Si, p + -Si, and i-Si were also linearly related to the number of cycles. In the table embedded in Figure 6, the fitting slopes of the REA curves and the Si loss curves represent the REPC and silicon etching amount of each cycle (EPC). It was shown that the REPC of SiGe/p + -Si was 0.6079 nm, which was close to the REPC value of SiGe/n + -Si (0.6389 nm). The EPC of p + -Si was 0.2262 nm, which was also close to the EPC value of n + -Si (0.2255 nm). The results indicate that the 31.5% HNO 3 concentration had the same etching rate for p + -Si and n + -Si. The concentration is expected to be used for the digital etching of p + -Si/SiGe/n + -Si stack structures, such as GAA CMOS and TFET applications. Moreover, the slopes in the fitting curves of SiGe/i-Si REA are lower than that of doped Si, suggesting its poor selectivity for i-Si. The EPC of i-Si was 0.3732 nm. It was demonstrated that the etching rate was larger than that of doped Si. It was considered that the doping of silicon contributed to the better selectivity for silicon with the nitric acid etching of SiGe. Figure 7 shows the selectivity of SiGe/n + -Si, SiGe/p + -Si, and SiGe/i-Si. The selectivity was calculated with Equation (1). The experimental data were obtained by measuring the SEM images of Sample I and Sample II with the 31.5% HNO 3 q-ALE process. We carried out the experiments six times on Sample I and Sample II, and six sets of data were obtained. The mean values of the SiGe/n + -Si, SiGe/p + -Si, and SiGe/i-Si selectivity were 3.59, 3.68, and 2.56, respectively. The values of the standard deviations were 0.0759, 0.1228, and 0.2512, respectively. The results show the significant improvements in selectivity for doped Si compared with intrinsic Si. The selectivity of SiGe/n + -Si and SiGe/p + -Si was similar-40% larger than that of intrinsic silicon. It was demonstrated that doped Si was more difficult to etch in the process of digital etching, which might be due to the oxidation difficulty in the HNO 3 solutions. Moreover, it was observed that the variation in SiGe/n + -Si was larger than that in SiGe/p + -Si. This indicates that it is more susceptible to process factors, such as concentration monitoring and solution preparation. The selectivity might be sensitive to the actual HNO 3 concentration.  Figure 7 shows the selectivity of SiGe/n + -Si, SiGe/p + -Si, and SiGe/i-Si. The selectivity was calculated with Equation (1). The experimental data were obtained by measuring the SEM images of Sample I and Sample II with the 31.5% HNO3 q-ALE process. We carried out the experiments six times on Sample I and Sample II, and six sets of data were obtained. The mean values of the SiGe/n + -Si, SiGe/p + -Si, and SiGe/i-Si selectivity were 3.59, 3.68, and 2.56, respectively. The values of the standard deviations were 0.0759, 0.1228, and 0.2512, respectively. The results show the significant improvements in selectivity for doped Si compared with intrinsic Si. The selectivity of SiGe/n + -Si and SiGe/p + -Si was similar-40% larger than that of intrinsic silicon. It was demonstrated that doped Si was more difficult to etch in the process of digital etching, which might be due to the oxidation difficulty in the HNO3 solutions. Moreover, it was observed that the variation in SiGe/n + -Si was larger than that in SiGe/p + -Si. This indicates that it is more susceptible to process factors, such as concentration monitoring and solution preparation. The selectivity might be sensitive to the actual HNO3 concentration. In order to explore the effect of nitric acid concentration, we carried out digital etching experiments on Sample I and Sample II with different HNO3 concentrations. Figure 8 shows the REPC of SiGe/n + -Si, SiGe/p + -Si, and SiGe/i-Si as a function of HNO3 concentration. As described in Figure 8, with the increase in HNO3 concentration, the REPC of SiGe/p + -Si increased and became saturated at 0.61 nm/cycle with the 29.5% HNO3 concen- In order to explore the effect of nitric acid concentration, we carried out digital etching experiments on Sample I and Sample II with different HNO 3 concentrations. Figure 8 shows the REPC of SiGe/n + -Si, SiGe/p + -Si, and SiGe/i-Si as a function of HNO 3 concentration. As described in Figure 8, with the increase in HNO 3 concentration, the REPC of SiGe/p + -Si increased and became saturated at 0.61 nm/cycle with the 29.5% HNO 3 concentration. The appearance of saturation is helpful for the stability of the process. However, to achieve accurate etching control for small-sized devices, a controllable etching rate is expected. Moreover, when the concentration was lower than 26.5%, the etched surface of SiGe was very rough, as shown in (Supporting Information, Figure S2a). In the case of high concentrations, damage occurred on the etched surface, as shown in (Supporting Information, Figure S2c). The critical concentration might be between 47.5% and 52%, and the 52% concentration exceeded this limit, resulting in etching damage as shown in (Supporting Information, Figure S2c,d). Therefore, there is a tradeoff between the controllable etching rate, high etching control, small process variations, and excellent etched surfaces when choosing a HNO 3 concentration for the digital etching of SiGe that is selective of p + -Si. was equal to that of SiGe/n + -Si at the 30% HNO3 concentration. However, there was a large process variation, which is a burden in the control of the etching process. Through many repeated experiments with fine concentration intervals, the HNO3 concentration relationship can be further verified.

Effect of Doped SiGe and Ge Fraction Dependence
In the first part, it was observed that the diffusion of arsenic into SiGe might enhance the etching rate of SiGe. Sample IV with in situ doping in SiGe was treated with the 31.5% HNO3 q-ALE process. To make the effect of doping more obvious and easier to observe, 300 cycles of etching were performed. Figure 9 shows the SEM cross-section images of Sample IV after digital etching at 40, 100, 200, and 300 cycles with 31.5% HNO3-dBOE q-ALE. It was shown that SiGe layer 1 disappeared at 100 cycles, which might have been due to the etching from the top. The SiGe layer 2 was penetrated horizontally at 200 cycles. It was observed that the remaining SiGe layer 3 at 300 cycles was the lowest. The etching amounts of the intrinsic SiGe layers, including SiGe layer 4, SiGe layer 5, and SiGe layer 6, were almost equal-slightly more than in the p-type SiGe, such as in SiGe layer 7 and SiGe layer 8. The results demonstrate that the relationship of the etching rate with the doping type is: p-type < intrinsic < n-type. The etching rate increased with the increase in n-type dopant concentration. As shown in Figure 9, the remaining amount of SiGe layer 9 doped by almost equal concentrations of arsenic and boron was similar to that of the intrinsic SiGe layers. This indicates the dependence on the carrier type instead of the dopant type. Additionally, it is demonstrated that the etching selectivity between the same doped SiGe and Si always exists regardless of the doping type. As discussed above, the concentration range from 26.5% to 47.5% led to an etching morphology with a smooth surface that was free of damage, showing that the study on HNO 3 concentration was meaningful. In this concentration range, it was observed that the REPC of SiGe/n + -Si had a trend of first increasing and then decreasing. At the concentration of 36.5%, the REPC reached the maximum. The etching rate might be the least influenced by concentration fluctuations. The HNO 3 concentration might be used for the fabrication of GAA transistors due to the small process variations. At the concentrations of 31.5% and 40%, the fitting curves of SiGe/n + -Si and SiGe/p + -Si intersected. Despite its identical relative etching rate, the 40% HNO 3 concentration requires a greater nitric acid concentration, thus increasing the cost. It was considered that 31.5% is the most suitable concentration for the digital etching of p + -Si/SiGe/n + -Si stack structures, such as for GAA CMOS and TFET applications, which must expose both the n + and p + sources/drains at the same time.
For the digital etching of SiGe/i-Si, the REPC first increased and then decreased with the increase in HNO 3 concentration. The REPC of SiGe/i-Si reached the maximum, which was equal to that of SiGe/n + -Si at the 30% HNO 3 concentration. However, there was a large process variation, which is a burden in the control of the etching process. Through many repeated experiments with fine concentration intervals, the HNO 3 concentration relationship can be further verified.

Effect of Doped SiGe and Ge Fraction Dependence
In the first part, it was observed that the diffusion of arsenic into SiGe might enhance the etching rate of SiGe. Sample IV with in situ doping in SiGe was treated with the 31.5% HNO 3 q-ALE process. To make the effect of doping more obvious and easier to observe, 300 cycles of etching were performed. Figure 9 shows the SEM cross-section images of Sample IV after digital etching at 40, 100, 200, and 300 cycles with 31.5% HNO 3 -dBOE q-ALE. It was shown that SiGe layer 1 disappeared at 100 cycles, which might have been due to the etching from the top. The SiGe layer 2 was penetrated horizontally at 200 cycles. It was observed that the remaining SiGe layer 3 at 300 cycles was the lowest. The etching amounts of the intrinsic SiGe layers, including SiGe layer 4, SiGe layer 5, and SiGe layer 6, were almost equal-slightly more than in the p-type SiGe, such as in SiGe layer 7 and SiGe layer 8. The results demonstrate that the relationship of the etching rate with the doping type is: p-type < intrinsic < n-type. The etching rate increased with the increase in n-type dopant concentration. As shown in Figure 9, the remaining amount of SiGe layer 9 doped by almost equal concentrations of arsenic and boron was similar to that of the intrinsic SiGe layers. This indicates the dependence on the carrier type instead of the dopant type. Additionally, it is demonstrated that the etching selectivity between the same doped SiGe and Si always exists regardless of the doping type. To investigate the influence of the Ge fraction on the selectivity and etching rate of n + -SiGe/n + -Si, Sample V was etched with 31.5% HNO3-dBOE q-ALE for 100 cycles. Figure  10 shows the SEM cross-section images of Sample V after digital etching with 31.5% HNO3-dBOE q-ALE for 100 cycles. As shown in Figure 10, there is a selectivity for n + -Si in the n + -SiGe digital etching. The top SiGe might have been etched from the top opening. The REA of the n + -SiGe increased with the increase in the Ge fraction. This might have been due to the easier hole injection and larger valence band offset [18]. It was demonstrated that increasing the Ge fraction could increase the etching rate of n + -SiGe and the selectivity of n + -SiGe/n + -Si. To investigate the influence of the Ge fraction on the selectivity and etching rate of n + -SiGe/n + -Si, Sample V was etched with 31.5% HNO 3 -dBOE q-ALE for 100 cycles. Figure 10 shows the SEM cross-section images of Sample V after digital etching with 31.5% HNO 3 -dBOE q-ALE for 100 cycles. As shown in Figure 10, there is a selectivity for n + -Si in the n + -SiGe digital etching. The top SiGe might have been etched from the top opening. The REA of the n + -SiGe increased with the increase in the Ge fraction. This might have been due to the easier hole injection and larger valence band offset [18]. It was demonstrated that increasing the Ge fraction could increase the etching rate of n + -SiGe and the selectivity of n + -SiGe/n + -Si.
HNO3-dBOE q-ALE for 100 cycles. As shown in Figure 10, there is a selectivity for n + -Si in the n + -SiGe digital etching. The top SiGe might have been etched from the top opening. The REA of the n + -SiGe increased with the increase in the Ge fraction. This might have been due to the easier hole injection and larger valence band offset [18]. It was demonstrated that increasing the Ge fraction could increase the etching rate of n + -SiGe and the selectivity of n + -SiGe/n + -Si.

Strain and Material Quality Analyses
In order to further determine the strain and material quality of the samples after the etching process, the HRXRD analysis scanning around the (004) diffraction order has been performed on p + -Si/SiGe/n + -Si stack layers as grown, after vertical stack etch, and after SiGe q-ALE with 31.5% HNO 3 . The HRXRD rocking curves are shown in Figure 11. For the epitaxial growth sample, the SiGe signal was intense, and many fringes were observed around the SiGe peak due to X-ray interference at the SiGe/Si interface, which indicated a high-quality SiGe/Si interface. Therefore, the subsequent etching experiments could be implemented based on the high-quality epitaxial film.

Strain and Material Quality Analyses
In order to further determine the strain and material quality of the samples after the etching process, the HRXRD analysis scanning around the (004) diffraction order has been performed on p + -Si/SiGe/n + -Si stack layers as grown, after vertical stack etch, and after SiGe q-ALE with 31.5% HNO3. The HRXRD rocking curves are shown in Figure 11. For the epitaxial growth sample, the SiGe signal was intense, and many fringes were observed around the SiGe peak due to X-ray interference at the SiGe/Si interface, which indicated a high-quality SiGe/Si interface. Therefore, the subsequent etching experiments could be implemented based on the high-quality epitaxial film.
A high full-width at half-maximum (FWHM) is a characteristic of a material's quality [34]. Compared with the epitaxial growth sample, the intensity of the SiGe peak after the etching process was weaker, which might be due to the reduction of SiGe material into chips after etching. There was also a slight shift of the SiGe peak towards the Si peak, which is an indicator of strain in the SiGe layer. As shown, the SiGe peak of the stacketched sample was shifted toward the Si substrate peak compared to the SiGe peak of the as-grown sample. This was a result of a strain relaxation induced by the stack-etching process. No continued shift of SiGe peak was detected after SiGe q-ALE etching, indicating that there was no further strain relaxation. This is important point out in the SiGe channel because the energy band and carrier mobility are dependent on the strain. Figure 11. HRXRD rocking curves around the (004) reflection of the as-grown p + -Si/SiGe/n + -Si stack layers after vertical stack etching and after 31.5% HNO3 q-ALE with 50 cycles.
In vertical GAA CMOS and TFET applications, SiGe is often used as a channel material, and the etched surface can be used as a channel interface. It is necessary to check the surface roughness after it is etched. Figure 12 shows the AFM morphology of the SiGe surface on as-grown epi-SiGe after etched with HNO3:HF:H2O mixtures and after etched with q-ALE. It was found that the root mean square (RMS) roughness of the q-ALE process still maintained a comparatively low value after many cycles. The RMS was 0.418 nm at 50 cycles and 0.474 nm at 30 cycles. AFM measurements were performed at many sites. The RMS was always in the range of 0.40 to 0.50 nm. It turned out that the RMS variation OMEGA-2THETA(arcsec) as grown stack etch HNO 3 q-ALE SiGe peak Figure 11. HRXRD rocking curves around the (004) reflection of the as-grown p + -Si/SiGe/n + -Si stack layers after vertical stack etching and after 31.5% HNO 3 q-ALE with 50 cycles.
A high full-width at half-maximum (FWHM) is a characteristic of a material's quality [34]. Compared with the epitaxial growth sample, the intensity of the SiGe peak after the etching process was weaker, which might be due to the reduction of SiGe material into chips after etching. There was also a slight shift of the SiGe peak towards the Si peak, which is an indicator of strain in the SiGe layer. As shown, the SiGe peak of the stack-etched sample was shifted toward the Si substrate peak compared to the SiGe peak of the as-grown sample. This was a result of a strain relaxation induced by the stack-etching process. No continued shift of SiGe peak was detected after SiGe q-ALE etching, indicating that there was no further strain relaxation. This is important point out in the SiGe channel because the energy band and carrier mobility are dependent on the strain.
In vertical GAA CMOS and TFET applications, SiGe is often used as a channel material, and the etched surface can be used as a channel interface. It is necessary to check the surface roughness after it is etched. Figure 12 shows the AFM morphology of the SiGe surface on as-grown epi-SiGe after etched with HNO 3 :HF:H 2 O mixtures and after etched with q-ALE. It was found that the root mean square (RMS) roughness of the q-ALE process still maintained a comparatively low value after many cycles. The RMS was 0.418 nm at 50 cycles and 0.474 nm at 30 cycles. AFM measurements were performed at many sites. The RMS was always in the range of 0.40 to 0.50 nm. It turned out that the RMS variation was due to differences in the test sites, and there was no dependence on the number of cycles. It was demonstrated that the surface roughness after the HNO 3 -dBOE q-ALE process stayed in the range of 0.40 to 0.50 nm and was better than dry [35] and wet chemical continuous etching.

Conclusions
The HNO3-dBOE q-ALE process consists of alternative HNO3 oxidation and dBOE oxide removal. Compared with the H2O2-dBOE q-ALE process, excellent selectivity for ntype doped Si could be found with HNO3-dBOE q-ALE. Doping plays an important role