Charge Transport in Uniform Metal-Assisted Chemical Etching for 3D High-Aspect-Ratio Micro- and Nanofabrication on Silicon

Recently,metal-assistedchemicaletching(MaCE)hasbeenproposedasapromisingmethodformicro-andnanostructuresfabricationonsilicon(Si)withhighaspectratio,highgeometricuniformityandlowcost.InMaCE,electronholes(h + ) are injected into Si through catalytic reduction of H 2 O 2 on metal catalyst thin ﬁlm patterns. Si beneath the metal is etched through a redox reaction where h + are involved. This work investigated a fundamental electrochemical process during MaCE: the transport of h + , and revealed its unique correlation with the 3D proﬁle of the etching results. It is discovered that under the uniform etching condition, etching occurs both in the Si beneath the catalysts as well as on the sidewall of the etched space. On N-type Si, the sidewall etching is intrinsically depressed, and highly vertical HAR structures are formed; on P-type Si and undoped Si, the sidewall tapering becomes signiﬁcant as the pattern number and density increase. The variation of the 3D proﬁle can be explained by the CT during etching using a Schottky junction model, which show dependence on the intrinsic properties of the Si. CT involved in the two etching process can further be correlated by diffusion or drift of h + , which explains the inﬂuence of catalysts geometry.

Fabrication of micro-and nanostructures on silicon (Si) is a key step in manufacturing of modern electronic and optoelectronic devices. Especially, the high-aspect-ratio (HAR) structures, of which the vertical dimension is much larger than the lateral dimension, enable orders-of-magnitude higher integration density and superior system performance compared to that of traditional planar structures by utilizing the space inside Si. HAR structures, such as deep trenches and deep holes, have been widely used in advanced Si-based devices. For example, deep trenches are the core structures in the microelectromechanical systems; 1 deep holes serve as the interconnect routes in the emerging 3D integration technology in microelectronic packaging. 2 Most of these HAR structures are fabricated by selective removal of certain volume of Si from the bulk Si substrate, which is generally referred to as the etching of Si. Until now, the major applicable Si etching method for HAR structures fabrication is the deep reactive ion etching (DRIE). 3,4 In DRIE, Si is put in a gas chamber and etched by plasma. Although DRIE is able to fabricate a wide range of HAR structures, it is suffered from high cost. On the other hand, metal-assisted chemical etching (MaCE), a novel low-cost wet chemical etching method, has attracted attention from both academia and industry. [5][6][7][8] In MaCE, a thin layer of noble metal is deposited on top of Si. When the metalloaded Si substrate is immersed in a hydrofluoric acid (HF)-hydrogen peroxide (H 2 O 2 ) mixture solution, H 2 O 2 is catalytically reduced on the metal surface and electron holes (h + ) are generated. With the presence of h + , Si underneath the metal catalysts is etched by HF. MaCE for fabrication of HAR nanostructures on Si, such as nanowires, [9][10][11][12][13][14][15][16] nanogratings 17 and nanopores, 18 have been extensively studied. Recently, capability of MaCE in fabricating uniform micrometer-scale HAR structures was demonstrated. [19][20][21][22] The geometry of HAR structures in the 3D space plays the key role in the performance of the devices where they are involved. Thus, controllability over the 3D geometry of the etching profile (referred to as "3D profile" in the following discussion) is essential for any HAR Si etching method. In DRIE, the 3D profile can be controlled by the chemistry of plasma. 4,23 In MaCE for nanostructures fabrication (referred to as nano-MaCE), it has been reported that the 3D profile could be influenced by the etchant composition, 24 the doping type and doping level of Si substrates. 25 The chemistry in micro-MaCE is fundamentally different from nano-MaCE. Here 13 However, if micro-MaCE was conducted in such high-ρ etchant, deformation and disintegration of the catalysts were observed. 20 In order to obtain decent etching uniformity, ρ has to be lowered to ensure the stable movement of catalyst in micro-MaCE. The use of low-ρ etchant can be regarded as a uniform MaCE (UMaCE) condition. In the low-ρ etchant solution, the sidewall of the 3D profile can be either vertical or tapered. 20,21 In the context of MaCE for microstructures fabrication (referred to as micro-MaCE), controllability of the 3D profile has not been well studied.
In this work, we propose that under the UMaCE condition, the 3D profile in micro-MaCE can be correlated to the charge transport process during etching. Considering the fact that MaCE is essentially a redox reaction where electron holes (h + ) are involved, the transport of h + may critically influence the 3D profiles of MaCE. In this paper, we refer to the transport of h + as the charge transport process (CT). To investigate the correlation between the CT and the 3D profile, the effects of two sets of "intrinsic" parameters are investigated in this work: the intrinsic property of the Si substrates and the geometry of the catalyst. A series of experiments under the UMaCE condition are conducted on Si substrates with different dopant type and doping level; straightline shapes Au catalysts with different number of patterns, width and spacing distance are used in each experiment. Interestingly, the 3D profiles in these experiments show sharp contrast as presented below.

Experimental
All the Si substrates in this work were single crystalline with (100)orientation from University Wafer, MA. The received Si was washed in Piranha solution (H 2 SO 4 (96%wt): H 2 O 2 (32%wt), volumetric ratio 1:1) at 120 • C for 10 min and rinsed by deionized (DI) water. After dried in N 2 gas, a layer of photoresist (Shipley S1813) was spin-cast onto the Si and exposed under 405 nm light in a Karl Suss Mask Aligner for photolithography. After developing in MF-319 developer (Shipley), the Si was cleaned by argon/oxygen plasma (Advanced Vacuum Vision RIE system). A layer of Au was then deposited by a Denton Explorer E-Beam Evaporator at a rate of 0.5 Å/sec in a vacuum chamber of 3 × 10 −6 Torr. The nominal thickness of all the Au film used in the work is 10 nm. Atomic force microscope (AFM) image of the Au film was collected from a Veeco Dimension Edge AFM system with a Si tip (Bruker MPP 11100-10). The Au-loaded Si substrates were cut into pieces (1 × 2 cm 2 in lateral size) and directly immersed in HF-H 2 O 2 etchant solution for MaCE of 10 min. Each piece contains one block of line-shaped patterns with same geometry. HF and H 2 O 2 were provided by VWR International and directly used  7 The h + distribution was calculated by a Matlab software (version R2014b).

Results and Discussion
As listed in Table I, n-type and p-type doped Si with resistivity are labeled as N-Si and P-Si for the convenience of discussion. Undoped Si is named as U-Si, while the heavily dope n-type and p-type Si are named as (N+)-Si and (P+)-Si. To study the effect of Si type and catalyst geometry, all the other experimental conditions were strictly fixed as described in the Experimental section, including the catalyst thickness and morphology, etchant solution composition and volume, etching time, temperature and etc. The overall processing flow is il- lustrated in Scheme 1. At the initial step, blocks of line patterns are transferred onto Si by photolithography. Each block contains a certain number (n) of parallel line patterns ("lines" for short) with the same line width w 0 and line spacing distance s. Each block is named by its n, w 0 and s value in the format of w 0 × n@s. Within the lines, bare Si surface is exposed; while the Si surface outside the lines is covered by photoresist. The photoresist has been proven to block the etching of Si in MaCE of 2 hr. 7 After deposition of Au, only the Au in the line pattern (referred to as "Au lines") is in direct contact with Si surface and able to induce MaCE. Thus the pattern number, width and spacing distance of the Au catalyst that are actually involved in MaCE equal to w 0 , n and s, respectively. SEM images of some selected blocks of lines after Au deposition are shown in  0.2 μm. The real thickness of Au catalyst on all Si is measured to be 13.3 ± 0.5 nm by AFM. Nanoporous morphology of the Au catalyst can be observed under high-magnification SEM ( Figure 1d). These nanopores allow the access of HF to remove the oxidized Si beneath the Au catalyst, which also ensures the uniformity of MaCE. 20 After MaCE, Au was found moving vertically into the Si and deep trenches were formed. Cross-sectional SEM images of the trenches on U-Si, P-Si and N-Si are shown in Figure 2 to Figure 4, respectively. The depth (d) and the top width variation ( w t ) of trenches are measured from the SEM images. As illustrated in Figure 1, d is defined as the vertical distance between the top edge and the bottom of a trench, while w t is defined as the difference between the top width of the trench after MaCE and the original width of the line pattern before MaCE: w t = w t -w 0 . The value of d and w t are averaged from five independent measurements at different locations of a block and plotted against w 0 , n and s in Figure 5. Under the same condition, MaCE experiments were also conducted on N(+)-Si and P(+)-Si. However, unlike the uniform trenches shown in Figure 2 to Figure  4, trenches on these heavily-doped Si are non-uniform. Also, porous region can be observed between the trenches (  Figure 5e and Figure 5f), if the w 0 increases to 5 μm and 10 μm while keeping n = 50, the absolute value of w t also increases accordingly on P-Si and U-Si, with keeping the same decreasing trend against s. However, with the same s, w t (P-Si)> w t (U-Si). For N-Si, w t remains much lower than U-Si and P-Si through Figures 5c to 5d, and showing little dependence on n, s and w 0 .
To understand these trends, it is necessary to review the chemistry of MaCE. In MaCE, the chemical reactions can be written as: From Eq. 2, HF and h + can be identified as the chemical species that directly induce the etching. Thus, the 3D profile is related to the distribution of HF and h + in the 3D space. In this regard, an orthogonal Cartesian coordination system is established where the origin is set at the geometric center of a line, and the y and z axis are set along the line and perpendicular to the Si surface, respectively (Figure 8a). The etching rate at position (x, y, z) and time t can be expressed as a vector r : Where c HF (x, y, z, t) and c h + (x, y, z, t)are the concentration of HF and h + at position (x, y, z) and time t, respectively; while C, a and  b are constants to be determined. The vector r h+ is the unit vector that points to the direction of the h + movement. We further set the start time of MaCE as t = 0. At t = 0, r |(x, y, z, 0)| = 0. Since w t is larger than 0 in all the etching results, the trenches width after etching is always larger than w 0 . The increase in w during MaCE indicates that the Si both beneath the Au catalysts and on the sidewall are etched. We refer to these two etching processes as the vertical etching and sidewall etching. Conceivably, d and w t can be related to the reaction rate of vertical etching and sidewall etching, i.e. the components of r along the z-and x-axis: It has been demonstrated that under current UMaCE condition, | r z | is constant within 10 min. 20 Then we can assume that the vertical etching is under a steady state: c HF (x, y, z, t) and c h + (x, y, z, t) in Eq. 5 are constant over time. For HF, since the initial concentration of HF equals to that in bulk solution, then: c HF (x, y, z, t) = c HF (x, y, z, 0) = 1.5 mol/L [ 6 ] Eq. 6 means that during the MaCE within 10 min, although the Au catalyst keeps moving into Si substrate, the etchant solution can quickly flow into the etched space above Au and a steady state is established within every infinitesimal time period, so that the local concentration of HF at the Au -Si interface maintains the constant value. It is conceivable that the c HF (x, y, z, t) in Eq. 5 also equals to c HF (x, y, z, 0), since the sidewall and Au-Si are subjected to the same etchant solution. These facts indicate that within 10 min, MaCE is reaction-controlled, while the process becomes diffusion-controlled as the etching proceeds. One of the probable factors that cause the transition is that as the etching proceeds, the aspect ratio of the etched trench is increasing and the difficulty of HF and H 2 O 2 molecules diffusion to the etching front, i.e. the Au-Si, is also increasing. By agitation of the solution, the diffusion of HF and H 2 O 2 can be promoted and a higher etching rate over long-time etching can be achieved. The reaction-controlled mechanism validates the assumption that HF concentration inside the etching profile keeps constant within 10 min (Eq. 6).
If we assume that the etching is homogeneous along the y-axis, we can focus our study of etching rate on a 2D plane that is perpendicular to the y-axis (i.e. the x-z plane). Then Eqs. 4 and 5 can be simplified to: Where C 1 is a constant. Eqs. 7 and 8 show that under the UMaCE condition where the vertical etching is in steady state, the 3D profile is only related to the c h+ (x, z, t), which is determined by CT during MaCE.
It should be noted that in the HF-H 2 O 2 etching solution, HF will undergo the following reaction: where K 1 and K 2 are the equilibrium constant of Eqs. 9 and 10, respectively.

[H + ], [F − ], [HF] and [HF 2
− ] refer to the activity of the corresponding species. Thus the fluoride species that are actually involved in the dissolution of oxidized Si (Eq. 2) may contain HF, F − and HF 2− . To qualitatively evaluate the effect of fluoride species concentration distribution, we did the MaCE on N-Si in etchant solution with H 2 SO 4 , NH 3 •H 2 O and NH 4 F as additives, respectively. We adopted the value of 1.3 × 10 −3 and 0.104 for K 1 and K 2 , respectively, at the ionic strength of 1 M. 26 Here we neglect the change of these value over the ionic strength in the solution, and substitute all the activity terms with concentration in the expression of K 1 and K 2 . Then the two values can be used to estimate the concentration of each fluoride species. It has been reported that in HF solution with concentration over 1 M, some polymer of HF ((HF) n F − , n = 2-6) can be formed. Here the formation of HF is not taken into account to simplify the calculation of fluoride species concentration. Due to the low acidity of H 2 O 2 , the contribution of H + from H 2 O 2 is also neglected. The calculated concentration of etching solution is listed in Table II. In the etchant solution used in the aforementioned MaCE experiments without any additives, the majority fluoride species is HF. With addition of H 2 SO 4 , the c(HF) slightly increase, while c(HF 2 − ) and c(F − ) sharply decrease. The etching depth slight decreases with the addition of H 2 SO 4 . However, the etching depth has a significant increase with the addition of NH 3 •H 2 O or NH 4 F, where c(H + ) decreases but c(HF 2 − ) and c(F − ) increase. The results may be explained by the fact that HF 2 − dissolves the oxidized Si much faster than HF. 27 Considering the fact that H + is also involved in the reduction of H 2 O 2 (Eq. 1), the relation between c(H + ) and etching depth indicates that the dissolution of oxidized Si (Eq. 2) may be the rate limiting step in MaCE. In order to simplify the following discussion, however, the term HF is used to represent all the fluoride species. This generalization of terminology will not impair the validity of the conclusion derived from the data in Figure 5, because all the etching experiments are conducted in the etchant solution with the same composition. CT in vertical etching and sidewall etching are illustrated in Figure 8a and labeled as CT1 and CT2, respectively. To study the c h+ (x, z, t) in CT1 and CT2, the source of h + needs to be clarified first. Although it has been reported that the bare Si surface without the coverage of metal could also be etched in HF-H 2 O 2 , its etching rate is on the order of 0.1-1.0 nm/min, 28 which is negligibly small compared to that of MaCE. Thus, h + in CT1 is primarily originated from the catalytic reduction of H 2 O 2 on Au surface (Eq. 1), It follows that in CT1 h + is transported from Au to Si, rather than from etchant solution to Si. It has long been known that CT through a metal-semiconductor interface can be described by the Schottky junction model. 29 In the context of vertical etching, metal and semiconductor correspond to Au and Si, respectively. Since h + are transported from Au to Si, Si can be regarded as negatively biased against Au (Figure 8a). The negative bias raises up the energy level of both the valence band and conduction band of the Si, regardless of its doping type. For N-Si, the negative bias favors the transport of h + from Au to Si (referred to as a "forward bias" for N-Si); for P-Si, however, the negative bias increases the difficulty in the h + transport (referred to as a "reverse bias" for P-Si). 6,29 Then c h+ in Eq. 7 follows the order of: c h+ (P-Si) < c h+ (U-Si) < c h+ (N-Si). Accordingly, we have d(P-Si) < d(U-Si) < d (N-Si), which is consistent with the results in Figure 5a.
Regarding CT2, etching on the sidewall have been attributed to the dissolution and redeposition process of metal catalyst in literature about nano-MaCE where silver (Ag) was used as the catalyst. 25,30 It was assumed that Ag at the bottom of the etching profile could be partially dissolved by HF-H 2 O 2 and redeposited on the sidewall. Once deposited by Ag, h + is transported from Ag to Si by a process similar to that in CT1. In the present work, if the sidewall etching is induced by the dissolution and redeposition of Au, CT2 should resemble CT1 and the variation of w t should be the same as that of d. However, as can be clearly observed in Figure 5b, w t follows the order of w t (P-Si) < w t (N-Si) < w t (U-Si); in Figures 5c-5f, w t follows the order of w t (N-Si) < w t (U-Si) < w t (P-Si). Both trends are in sharp contrast to that of d. Then the charge transport from Au to Si can be excluded in CT2. As mentioned before, under the UMaCE condition, low-ρ etchant is used and the h + generated from H 2 O 2 on Au surface cannot be completed consumed by the vertical etching process. The excessive h + from Au have a chance to be transported to the sidewall and induce the sidewall etching. In this sense, contrary to the vertical etching, the sidewall etching is a pure electrochemical process as described in Eq. 2, where h + are transported from Si to the etchant solution. Under this condition, Si is positively biased against the etchant solution. The process resembles the well-known electrochemical etching of Si. The electrochemical etching could also be described by a Schottky junction model. [31][32][33] Here a positive bias is a forward bias for P-Si but a reverse bias for N-Si. Thus, in the sidewall etching the transport of h + is favored on P-Si but suppressed on N-Si. To further confirm this point, electrochemical etching experiments were conducted to mimic the sidewall etching process. Bare Si were connected to a potentiostat as the working electrode and immersed in a 1.5 mol/L HF solution. A linear-increasing voltage was applied to the bare Si and the corresponding current density value was recorded. As shown in Figure 8b, for P-Si, when the voltage is scanned from −1.0 V (vs. Pt counter electrode) toward +4.0 V, current density increases sharply after the voltage passes −0.2 V. In contrast, for N-Si, no significant current density can be observed within the scan range. Given the fact that the doping level of N-Si and P-Si are similar, the result supports the point that once a positive bias is applied, h + can be favorably transported from P-Si to HF solution, while h + transport from N-Si to HF solution is intrinsically suppressed. It is observed that the current density of U-Si is also low, which may be attributed to the low doping level of U-Si (Table I). For P(+) and N(+)-Si, however, due to a high doping level, h + can easily tunnel through the Si-HF solution interface regardless of the dopant type, thus their current density increases faster than P-Si. 29 During MaCE of the heavily doped Si, the tunneling process not only induces sidewall etching, but also makes the Si between trenches highly porous on both substrates (Figure 6), which is consistent with results from previous results of electrochemical etching 34 and nano-MaCE 35-37 on heavily-doped Si. Now that CT1 and CT2 have been discussed, we can further investigate the correlation between CT1 and CT2. As discussed above, h + in both CT1 and CT2 are originated from the reduction of H 2 O 2 on Au surface. Under the steady state, c h+ in CT1 is constant over time, which means Au can be regarded as a source that constantly emits h + into Si while moving along the z-axis at constant velocity (v): [11] where c h+ETCH (x, z, t) is the amount of h + that are consumed in the vertical etching, while c h+EX (x, z, t) is the amount of excessive h + . Since the vertical etching rate is constant, then c h+ETCH (x, z, t) is constant, which makes c h+EX (x, z, t) also constant: These excessive h + can be transported to the sidewall through diffusion or drift. Here the term "diffusion" refers to the movement of h+ driven by the gradient of c h+ , while "drift" refers to that driven by electric field. If we assume that the excessive h + is the only source of h + in CT2 and transported to the sidewall only through diffusion, then we can establish a diffusion model to calculate c h+ in Eq. 8 by Fick's Second Law: ∂c h+ (x, z, t) ∂t = D∇ 2 c h+ (x, z, t) [13] where D is the diffusion constant of h + in Si. Here D is set as constant over space and time. If we introduce a new variable r = √ x 2 + z 2 , the boundary condition and initial condition can be written as: Assuming the total c h+ is the sum of the contribution of each Au lines in a w 0 × n@s block, we have: 38 It has been reported that in the electrochemical etching process, Si is completely removed when c h+ exceeds a certain critical value c h+crit , while porous Si is formed when c h+ is below c h+crit . 31 Then using the diffusion model, w t can be calculated by Eq. 17 if we assume that w t is only related to the c h+ on the Si top surface at z = 0 (referred to as c h+ (x, 0, 10 min)). The c h+ (x, 0, 10 min) equals to c h+crit at the position of ( w t , 0). Figure 9a shows the calculated c h+ (x, 0, 10 min) in MaCE of 2 μm × 1, 5 μm × 5, 10 μm × 1 blocks on U-Si along x-axis where the origin is set at the geometric center of Au lines. The c h+ is calculated by fitting Eq. 17 with w t in Figure 5b and expressed in arbitrary unit (a.u.). The fitting gives nominal value of c h+crit = 0.164 and D = 0.008 μm 2 /s. The boundaries between the edge of Au and Si are indicated as the vertical dot lines at x = ±w 0 /2. For example, the boundaries of 2 μm × 1 block locate at x = ±1 μm. As the w 0 increases, c h+ within the boundary increases and the curve extends farther out of the boundary, which is consistent with results in Figure 5b. To calculate w t , the c h+ curve outside the boundaries is detailed in Figure 9b, where the x-axis is set to start at the boundary of Au in each curve of Figure 9a and extend out of the boundary. Then the curves in Figure 9b represent the c h+ in the sidewall, which is involved in CT2. Given c h+crit = 0.164, w t of each curve in Figure 5 can be identified by locating the intersection point of the curves with the c h+ = 0.164 line (horizontal black dash line). We name these w t value as the modeled value. The modeled w t for P-Si and U-Si are plotted in Figure 5b as solid lines and labeled as P(M) and U(M), which shows good consistence with the experimentally measured value. The same c h+crit and D value are used to obtain the modeled w t in MaCE of other blocks, which are plotted in Figure 5c to 5e. For U-Si, the modeled w t are close to the measured value. For P-Si, c h+crit and D are fit to be 0.340 and 0.003 μm 2 /s from Figure 5b. However, although the modeled w t well match the measured value Figure 5b, they are far below the measured value in Figures 5c to 5e. The comparison between the modeled and measured w t in Figure 5b to 5e indicates that for U-Si, h + transported from Au to the sidewall is likely to be a diffusion process mainly from the excessive h + around Au. For P-Si, in single line etching, h + is also transported from Au through diffusion; in multiple line etching, however, the actual h + concentration in the sidewall region is much higher than the amount that transported through diffusion. The sharp increase of w t with n on P-Si has not been reported before. Considering the fact that a large amount of h + is transported from Au to Si, a strong electric field may be established around every Au lines. Based on the depth of etching as ∼6 μm on P-Si, the amount of Si etched per unit area r z in the etching of 10 min is: Where ρ, V, M Si are the density, etched volume and molecular weight of Si. 39 Assuming etching of each Si atom consumes 4 h + , then the current density of h + is estimated to be:  [19] According to Figure 8b, the current correspond to a bias over 3 V. In MaCE of multiple Au lines, the increase of n may significantly increase the synergistic electric field from all Au lines, which resulted in an increased amount of intrinsic h + that are involved in CT2 and an accelerated movement of h + toward sidewall. Besides, in P-Si, a considerable amount of h + exist at the dopant atoms in Si as intrinsic h + . These h + also have a chance to be transported to the sidewall under the electric field. Therefore, although in the single Au line etching, w t (U-Si) is larger than w t (P-Si) due to a higher amount of excessive h + in CT1 (Figure 5b), w t (P-Si) quickly exceeds w t (U-Si) as n increases (Figures 5c-5e). However, further study is needed to figure out the spatial distribution of the electric field and its interaction with h + inside Si.
In order to investigate the MaCE results on Si with other crystalline orientation, we conducted MaCE on the P-Si with (111)-orientation under the same condition as that on P-Si with (100)-orientation. As shown in Figure 10, after MaCE vertical trenches were formed on the (111)-Si substrates, in consistence with previous results. 21 Similar to the results from (100)-Si, here the w t also shows an increase when n increases. The increase of w t support the aforementioned mechanism that the charge transport during MaCE can be described by the Schottky models, where the doping of the Si plays the major role. The etching depth is much lower than that on (100)-Si. The slower etching rate on (111)-Si may be explained by the fact that the back bonds density is higher along the 111 orientation than that along 100 orientation.

Conclusions
In conclusion, 3D profiles of MaCE using Au lines with different line width (w 0 ), number (n) and spacing distance (s) on P-Si, N-Si, USi, P(+)-Si and N(+)-Si have been presented. Uniform trenches were formed on P-Si, N-Si and U-Si, while the 3D profiles on P(+)-Si and N(+)-Si are non-uniform. The depth d and lateral width variation w t of the 3D profiles on P-Si, N-Si and U-Si are measured and correlated to the CT1 and CT2, respectively. The depth follows the order of d(P-Si) < d(U-Si) < d (N-Si),while the w t of N-Si is lower than that of U-Si and P-Si. The variation of d and w t over the dopant type of Si can be explained by Schottky junction model, which indicates that CT1 is favored on N-Si and CT2 is favored on P-Si. The variation of w t over w 0 , n and s can be further explained by the correlation between CT1 and CT2: in U-Si, h + in CT2 are mainly originated from excessive h + in CT1 through diffusion; in P-Si, the actual h + concentration in CT2 is much higher than that calculated from the diffusion model, which may be attributed to the drift of h + . The fundamental aspects revealed by the present work will serve as a reference for future MaCE research. It is expected that by deeper study about the effect of electric bias, etchant composition and other parameters, a complete controllability of 3D profiles in MaCE can be achieved. The novel insight is also meaningful in general electrochemistry where charge transport process in micro-and nanoscale are concerned, such as microfluidics and MEMS. Practically, the results pave the way to the fabrication of high-density micro-and nanostructures by MaCE: vertical HAR structures can be readily formed on N-Si; the sidewall of the etched structures will be tapered on P-Si and U-Si as the pattern number and density increase, where the effect of lateral geometry of the structures should also be considered.