*Article* **Photoluminescent Microbit Inscripion Inside Dielectric Crystals by Ultrashort Laser Pulses for Archival Applications**

**Sergey Kudryashov \* , Pavel Danilov , Nikita Smirnov, Evgeny Kuzmin , Alexey Rupasov, Roman Khmelnitsky, George Krasin , Irina Mushkarina and Alexey Gorevoy**

> Lebedev Physical Institute, 119991 Moscow, Russia; danilovpa@lebedev.ru (P.D.); smirnovna@lebedev.ru (N.S.); kuzmine@lebedev.ru (E.K.); rupasovan@lebedev.ru (A.R.); khmelnitskyra@lebedev.ru (R.K.); krasingk@lebedev.ru (G.K.); i.mushkarina@lebedev.ru (I.M.); a.gorevoy@lebedev.ru (A.G.)

**\*** Correspondence: kudryashovsi@lebedev.ru

**Abstract:** Inscription of embedded photoluminescent microbits inside micromechanically positioned bulk natural diamond, LiF and CaF<sup>2</sup> crystals was performed in sub-filamentation (geometrical focusing) regime by 525 nm 0.2 ps laser pulses focused by 0.65 NA micro-objective as a function of pulse energy, exposure and inter-layer separation. The resulting microbits were visualized by 3D-scanning confocal Raman/photoluminescence microscopy as conglomerates of photo-induced quasi-molecular color centers and tested regarding their spatial resolution and thermal stability via high-temperature annealing. Minimal lateral and longitudinal microbit separations, enabling their robust optical read-out through micromechanical positioning, were measured in the most promising crystalline material, LiF, as 1.5 and 13 microns, respectively, to be improved regarding information storage capacity by more elaborate focusing systems. These findings pave a way to novel optomechanical memory storage platforms, utilizing ultrashort-pulse laser inscription of photoluminescent microbits as carriers of archival memory.

**Keywords:** fluorides; diamond; ultrashort-pulse laser; direct laser inscription; photoluminescent microbits; vacancy clusters

### **1. Introduction**

Photoluminescence (PL) is one of the most important optical processes, underlying relaxation of two-level quasi-molecular systems upon their complementary optical excitation [1]. Even single PL photons could be acquired and spatially resolved much easier than differential absorption of single photons. As a result, PL characterization in 2D- or 3Dscanning confocal micro- or nano-spectroscopy mode became an enabling tool for probing local molecular or crystalline structures [2,3], or electromagnetic near-fields [4,5].

Ultrashort-pulse lasers proved to work as a versatile tool for time-resolved and/or nonlinear spectroscopy [6,7], precise surface nano- and micro-machining of any—absorbing or transparent—materials [8,9], micro-modification and inscription inside bulk transparent media [10–12]. In the latter case, (sub)microscale laser modification of molecular or crystalline structures and related PL spectra underlies facile and robust encoding of bulk diamonds for their tracing applications in identifying synthetic diamonds from natural ones in large commercial diamond collections [13], protecting trademarks of high-quality natural (potentially, synthetic too) diamond manufacturers [14], limiting commercial trading and marketing of illegal diamonds. This PL-based encoding appears unique to diamonds, where other popular encoding technologies—ablation fabrication of optically-contrasted (sub)microscale voids [15] or ablative birefringent nanogratings [16,17]—do not work in the ultra-hard diamond lattice, tending to be better for graphitization [18], while PL read-out is simpler and more sensitive. Similarly, many other crystalline scintillators and luminophores undergo ultrashort-pulse laser modification of their crystalline structures and related PL

**Citation:** Kudryashov, S.; Danilov, P.; Smirnov, N.; Kuzmin, E.; Rupasov, A.; Khmelnitsky, R.; Krasin, G.; Mushkarina, I.; Gorevoy, A. Photoluminescent Microbit Inscripion Inside Dielectric Crystals by Ultrashort Laser Pulses for Archival Applications. *Micromachines* **2023**, *14*, 1300. https://doi.org/ 10.3390/mi14071300

Academic Editors: Zeheng Wang and Jingkai Huang

Received: 25 May 2023 Revised: 16 June 2023 Accepted: 21 June 2023 Published: 24 June 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

spectra [19–21], which is potentially promising for 3D optical encoding (writing/read-out) applications in storage devices (5D optical storage for specific advanced technologies [16]). Such 3D optical memory storage in bulk transparent media is an evergreen dream since the 1990s or even earlier [22], being highly promising and competitive compared to the previous 2D surface laser patterning compact disk (CD) and digital versatile (video) disk (DVD) technologies (common diameter—120 mm, thickness—1 mm, capacity—up to 17 GB for double-side, double-layer disks) utilizing 650 nm writing lasers, and the present 405 nm laser Blu-ray disk technology, supporting storage capacity up to 128 GB per four-layer disk. Other modern storage technologies enable even higher capacities—up to several TB, while possessing other technical advantages and drawbacks. Hence, rewritable, ultrahighcapacity, low-power or autonomous high-speed memory, remaining robust to radiation, humidity and thermal shocks is still needed for quick-access and archival applications.

In this work we report a brief experimental evaluation study of natural diamond, LiF and CaF<sup>2</sup> crystals as optical platforms for microscale photoluminescent encoding by ultrashort-pulse lasers for micromechanically-accessed archival optical storage, of their mechanisms of laser-induced color-center inscription, tests of potential 3D memory capacity and thermal stability.

#### **2. Materials and Methods**

In these studies, a 2 mm thick colorless brick of IaA-type natural diamond (total concentration of nitrogen atoms ≈ 130 ppm), and 5 mm thick slabs of undoped LiF and CaF<sup>2</sup> crystals grown by Bridgman–Stockbarger method were utilized, being optically transparent at the writing laser wavelength of 525 nm (Figure 1a). The samples were characterized in the spectral range of 350–750 nm by room-temperature (RT) optical transmission microspectroscopy (Figure 1b), using an ultraviolet (UV)−near-IR microscope-spectrometer MFUK (LOMO, Saint-Petersburg, Russia). Inscription inside these bulk crystals at the depths of 100 µm (fluorides) and of 120 µm (diamond) in their transparency spectral regions (Figure 1b), accounting for their 525 nm refractive indexes of 2.4 (diamond), 1.4 (LiF) and 1.4 (CaF2) [23], was performed by second-harmonic (525 nm) pulses of the TEMA Yb-crystal laser (Avesta Project, Moscow, Russia) with the pulsewidth (full width at a half maximum) of 0.2 ps, repetition rate of 80 MHz split in pulse bunches of 0.05 ÷ 10 s duration by a mechanical shutter, and 50 nJ (average power—4 W) maximum output pulse energy E in the TEM<sup>00</sup> mode. The 525 nm laser pulses with variable energies E up to 50 nJ were focused in a sub-filamentary regime (the 515 nm, 0.3 ps laser filamentation threshold energy ≈300 nJ (diamond) and 260 nJ (CaF2) [24]) by a 0.65 NA micro-objective into ≈1 µm wide spots (1/e-intensity diameter) inside the crystals, providing the peak laser fluence <6 J/cm<sup>2</sup> and peak laser intensity <30 TW/cm<sup>2</sup> . The samples were mounted on a computer-driven three-dimensional motorized micropositioning stage and exposed in separate positions with variable transverse spacings in the range of 1–5 microns and longitudinal spacings in the range of 1–28 microns.

Since different alkali or alkali-earth fluorides are rather similar during high-temperature annealing due to high vacancy mobility (activation energy for diffusion ~0.1 eV [25]) and low-temperature aggregation [26], annealing of fluoride samples was performed only for the LiF sample at different temperatures in the range of 25–300 ◦C (20 min temperature ramp, 30 min stationary heating), using a temperature-controlled mount for Raman microspectroscopy, while the diamond sample was annealed in an evacuated oven for 1 h at different temperatures in the range of 25–1200 ◦C.

In our characterization studies, top-view and side-view (cross-sectional) photoluminescence imaging at the 532 nm continuous-wave pump laser wavelength and 100× magnification (NA = 1.45, spatial resolution ~1 µm) was performed by means of a Confotec MR520 3D-scanning confocal photoluminescence/Raman microscope (SOL Instruments, Minsk, Belarus) to measure relative intensity, spatial dimensions and optical PL-acquired separation of PL microbits (Figure 2).

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 3 of 11

**Figure 1.** (**a**) Laser inscription setup, sketching the bulk PL-microbit inscription procedure; (**b**) transmittance spectra of natural diamond, LiF and CaF<sup>2</sup> crystals, with the laser writing wavelength of 525 nm shown in their transparency spectral region by the green triangle. MR520 3D-scanning confocal photoluminescence/Raman microscope (SOL Instruments, Minsk, Belarus) to measure relative intensity, spatial dimensions and optical PL-acquired separation of PL microbits (Figure 2).

driven three-dimensional motorized micropositioning stage and exposed in separate positions with variable transverse spacings in the range of 1–5 microns and longitudinal

**Figure 1.** (**a**) Laser inscription setup, sketching the bulk PL-microbit inscription procedure; (**b**) trans-

spectra [19–21], which is potentially promising for 3D optical encoding (writing/read-out) applications in storage devices (5D optical storage for specific advanced technologies [16]).Such 3D optical memory storage in bulk transparent media is an evergreen dream since the 1990s or even earlier [22], being highly promising and competitive compared to the previous 2D surface laser patterning compact disk (CD) and digital versatile (video) disk (DVD) technologies (common diameter—120 mm, thickness—1 mm, capacity—up to 17 GB for double-side, double-layer disks) utilizing 650 nm writing lasers, and the present 405 nm laser Blu-ray disk technology, supporting storage capacity up to 128 GB per four-layer disk. Other modern storage technologies enable even higher capacities—up to several TB, while possessing other technical advantages and drawbacks. Hence, rewritable, ultrahigh-capacity, low-power or autonomous high-speed memory, remaining robust to radiation, humidity and thermal shocks is still needed for

In this work we report a brief experimental evaluation study of natural diamond, LiF and CaF<sup>2</sup> crystals as optical platforms for microscale photoluminescent encoding by ultrashort-pulse lasers for micromechanically-accessed archival optical storage, of their mechanisms of laser-induced color-center inscription, tests of potential 3D memory capacity

In these studies, a 2 mm thick colorless brick of IaA-type natural diamond (total concentration of nitrogen atoms 130 ppm), and 5 mm thick slabs of undoped LiF and CaF<sup>2</sup> crystals grown by Bridgman–Stockbarger method were utilized, being optically transparent at the writing laser wavelength of 525 nm (Figure 1a). The samples were characterized in the spectral range of 350–750 nm by room-temperature (RT) optical transmission microspectroscopy (Figure 1b), using an ultraviolet (UV)−near-IR microscope-spectrometer MFUK (LOMO, Saint-Petersburg, Russia). Inscription inside these bulk crystals at the depths of 100 m (fluorides) and of 120 m (diamond) in their transparency spectral regions (Figure 1b), accounting for their 525 nm refractive indexes of 2.4 (diamond), 1.4 (LiF) and 1.4 (CaF2) [23], was performed by second-harmonic (525 nm) pulses of the TEMA Ybcrystal laser (Avesta Project, Moscow, Russia) with the pulsewidth (full width at a half maximum) of 0.2 ps, repetition rate of 80 MHz split in pulse bunches of 0.05 10 s duration by a mechanical shutter, and 50 nJ (average power—4 W) maximum output pulse energy E in the TEM<sup>00</sup> mode. The 525 nm laser pulses with variable energies E up to 50 nJ were focused in a sub-filamentary regime (the 515 nm, 0.3 ps laser filamentation threshold energy 300 nJ (diamond) and 260 nJ (CaF2) [24]) by a 0.65 NA micro-objective into 1 μm wide spots (1/e-intensity diameter) inside the crystals, providing the peak laser fluence <6

. The samples were mounted on a computer-

quick-access and archival applications.

J/cm<sup>2</sup> and peak laser intensity <30 TW/cm<sup>2</sup>

spacings in the range of 1–28 microns.

and thermal stability.

**2. Materials and Methods**

**Figure 2.** (**left**) Top-view PL images of linear slices of square PL microbit arrays inscribed at different laser conditions and acquired at 755 nm in CaF<sup>2</sup> (**a**), at 650 nm in LiF (**b**), at 650 nm in natural diamond (**c**). (**right**) Their corresponding front-view images of neighboring PL microbits inscribed in these dielectrics at different lateral separations, varying in the range of 1–6 m. **Figure 2.** (**left**) Top-view PL images of linear slices of square PL microbit arrays inscribed at different laser conditions and acquired at 755 nm in CaF<sup>2</sup> (**a**), at 650 nm in LiF (**b**), at 650 nm in natural diamond (**c**). (**right**) Their corresponding front-view images of neighboring PL microbits inscribed in these dielectrics at different lateral separations, varying in the range of 1–6 µm.

#### **3. Experimental Results and Discussion 3. Experimental Results and Discussion**

#### *3.1. Inscription of Photo-Luminescent Microbits 3.1. Inscription of Photo-Luminescent Microbits*

PL microbits were inscribed in the bulk crystalline CaF<sup>2</sup> and LiF slabs, as well as in the diamond plate, at different pulse energies (Figure 2a–c, left side). Specifically, the PL microbits inside the CaF<sup>2</sup> slab exhibit the corresponding energy-dependent microbit dimensions above the inscription threshold value of 3 nJ at the exposure of 107-–10<sup>9</sup> pulses/microbit. Similarly, the PL microbits were inscribed inside the LiF slab in the same energy range, while the threshold energy appears considerably higher (5 nJ, Figure 2b, left side) at the exposure of 107-–10<sup>9</sup> pulses/microbit, reflecting the higher bandgap energy of 13.0–14.2 eV in LiF [27,28], comparing to CaF<sup>2</sup> with 11.5–11.8 eV [29,30]. Finally, in the diamond plate, the PL microbits were inscribed as a function of laser pulse energy, demonstrating their increasing dimensions at the exposure of 107-–10<sup>9</sup> pulses/microbit (Figure 2c, left side). Surprisingly, contrary to our expectations, the inscribed microbits appear inhomogeneous at higher magnifications (Figure 2a–c, right side) because of the non-linear photoexcitation/damage character and well-known high degree of clustering up to nanoscale—for fluorine atoms to form dislocation loops [26] or around dislocations PL microbits were inscribed in the bulk crystalline CaF<sup>2</sup> and LiF slabs, as well as in the diamond plate, at different pulse energies (Figure 2a–c, left side). Specifically, the PL microbits inside the CaF<sup>2</sup> slab exhibit the corresponding energy-dependent microbit dimensions above the inscription threshold value of <sup>≈</sup>3 nJ at the exposure of 107−–10<sup>9</sup> pulses/microbit. Similarly, the PL microbits were inscribed inside the LiF slab in the same energy range, while the threshold energy appears considerably higher (≈5 nJ, Figure 2b, left side) at the exposure of 107−–10<sup>9</sup> pulses/microbit, reflecting the higher bandgap energy of 13.0–14.2 eV in LiF [27,28], comparing to CaF<sup>2</sup> with 11.5–11.8 eV [29,30]. Finally, in the diamond plate, the PL microbits were inscribed as a function of laser pulse energy, demonstrating their increasing dimensions at the exposure of 107−–10<sup>9</sup> pulses/microbit (Figure 2c, left side). Surprisingly, contrary to our expectations, the inscribed microbits appear inhomogeneous at higher magnifications (Figure 2a–c, right side) because of the non-linear photoexcitation/damage character and well-known high degree of clustering—up to nanoscale—for fluorine atoms to form dislocation loops [26] or around dislocations in the fluoride crystals [25]. In diamonds, such segregation of vacancies and interstitials also occurs in the

form of multi-vacancies (voids) [31] or interstitial aggregates in B2-centers [31]. In the same line, these microbits look diffuse owing to the low diffusion energies of ~0.1 eV of interstitials and vacancies [26], facilitating room-temperature internal segregation and external collateral spreading of point-defect concentrations in the PL microbits. also occurs in the form of multi-vacancies (voids) [31] or interstitial aggregates in B2-centers [31]. In the same line, these microbits look diffuse owing to the low diffusion energies of 0.1 eV of interstitials and vacancies [26], facilitating room-temperature internal segregation and external collateral spreading of point-defect concentrations in the PL microbits. In terms of spatial resolution of the PL microbits during the laser inscription process,

in the fluoride crystals [25]. In diamonds, such segregation of vacancies and interstitials

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 4 of 11

In terms of spatial resolution of the PL microbits during the laser inscription process, even at low above-threshold pulse energies these features could be more or less resolved only at their 2 µm separation (Figure 2a–c, right side). The main reason for such moderate lateral (transverse) resolution is apparently the initial focal 1/e-diameter of 1 µm at the focusing NA = 0.65 (see Section 2—Materials and Methods), additionally increased by ≈1 µm lateral diffusion length of fs-laser generated electron-hole plasma during its electron-lattice thermalization over 1–2 picoseconds [32]. The corresponding point beam stability upon the focusing could result in negligible lateral displacements of ~10 nm. As a result, distinct resolution of the neighboring PL microbits becomes possible for their lateral separations, exceeding 2 µm distance. Meanwhile, it could be considerably improved till ~1–1.5 µm, utilizing specially designed high-NA (0.75–0.9) air focusing micro-objectives. Below, in Section 3.4, the longitudinal (interlayer) spatial resolution will be tested in the case of a brightly luminescent LiF crystal to evaluate the potential optical storage capacity of PL microbit arrays. even at low above-threshold pulse energies these features could be more or less resolved only at their 2 m separation (Figure 2a–c, right side). The main reason for such moderate lateral (transverse) resolution is apparently the initial focal 1/e-diameter of 1 m at the focusing NA = 0.65 (see Section 2—Materials and Methods), additionally increased by 1 m lateral diffusion length of fs-laser generated electron-hole plasma during its electronlattice thermalization over 1–2 picoseconds [32]. The corresponding point beam stability upon the focusing could result in negligible lateral displacements of 10 nm. As a result, distinct resolution of the neighboring PL microbits becomes possible for their lateral separations, exceeding 2 m distance. Meanwhile, it could be considerably improved till 1– 1.5 m, utilizing specially designed high-NA (0.75–0.9) air focusing micro-objectives. Below, in Section 3.4, the longitudinal (interlayer) spatial resolution will be tested in the case of a brightly luminescent LiF crystal to evaluate the potential optical storage capacity of PL microbit arrays.

#### *3.2. Photo-Luminescence Spectra of Microbits: Atomistic Inscription and Annealing Mechanisms 3.2. Photo-Luminescence Spectra of Microbits: Atomistic Inscription and Annealing Mechanisms*

Typical PL spectra acquired in the laser-inscribed microbits by 3D-scanning confocal PL micro-spectroscopy are presented in Figure 3 in comparison to the corresponding spectra of the background non-modified materials. Specifically, the CaF<sup>2</sup> slab exhibits the strongly enhanced PL yield in the region of 650–850 nm, peaked at 740 nm (Figure 3a). Though PL spectra of electronic excitations in fluorides are rather flexible due to high mobility of Frenkel defects and the multitude of their complexes [25,33,34], the observed peak could be assigned to some of these vacancy aggregates (F<sup>x</sup> 0,+, where F is the fluorine vacancy with the trapped electron, x > 2 and upper indexes "0,+" denote the charged states) [25,26]. Similarly, in the LiF slab, the increased PL band in the range of 550–750 nm could be assigned to F<sup>2</sup> (peak at 670 nm [33]) and F<sup>3</sup> (peak at 650 nm [33]) centers, while the emerging PL band with its peak at 800–850 nm could also related to some as yet unknown Fx 0,+ centers [25,33,34]. Typical PL spectra acquired in the laser-inscribed microbits by 3D-scanning confocal PL micro-spectroscopy are presented in Figure 3 in comparison to the corresponding spectra of the background non-modified materials. Specifically, the CaF<sup>2</sup> slab exhibits the strongly enhanced PL yield in the region of 650–850 nm, peaked at 740 nm (Figure 3a). Though PL spectra of electronic excitations in fluorides are rather flexible due to high mobility of Frenkel defects and the multitude of their complexes [25,33,34], the observed peak could be assigned to some of these vacancy aggregates (F<sup>x</sup> 0,+, where F is the fluorine vacancy with the trapped electron, x > 2 and upper indexes "0,+" denote the charged states)[25,26]. Similarly, in the LiF slab, the increased PL band in the range of 550–750 nm could be assigned to F<sup>2</sup> (peak at 670 nm [33]) and F<sup>3</sup> (peak at 650 nm [33]) centers, while the emerging PL band with its peak at 800–850 nm could also related to some as yet unknown Fx 0,+ centers [25,33,34].

**Figure 3.** PL spectra of separate PL microbits (red curves) inscribed in CaF<sup>2</sup> (**a**), LiF (**b**) and natural diamond (**c**) regarding their background spectra of the unmodified materials (dark curves). **Figure 3.** PL spectra of separate PL microbits (red curves) inscribed in CaF<sup>2</sup> (**a**), LiF (**b**) and natural diamond (**c**) regarding their background spectra of the unmodified materials (dark curves).

Finally, the observed, strongly—by one order of magnitude—enhanced PL band in the micromark inscribed inside the diamond slab exhibits the main spectral features, representing the neutral (NV<sup>0</sup> , zero-phonon line, ZPL, at 575 nm [31]) and negatively charged nitrogen-vacancy (NV−, zero-phonon line at 637 nm [31]) centers of substitutional nitrogen atoms with a photo-generated vacancy, as well as their red-shifted phonon replica.

Atomistic processes underlying the observed laser-induced transformations of PL spectra in LiF and CaF<sup>2</sup> are supposed to be associated with aggregation of mobile neutral (I-center [25,26]) and negatively charged (F-center [25,26]) vacancies, along with fluorine neutral (H-center [25,26]) and negatively charged (α-centers [25,26]) interstitials (Equation (1)), approaching to hundreds of aggregated defects usually concentrated in dislocation loops [25,26]. Likewise, in the diamond plate, the mobile photo-generated vacancies could be trapped by substitutional nitrogen atoms (C-centers [31]), resulting in well-known neutral or charged NV complexes [18,31] (Equation (1)): Atomistic processes underlying the observed laser-induced transformations of PL spectra in LiF and CaF<sup>2</sup> are supposed to be associated with aggregation of mobile neutral (I-center [25,26]) and negatively charged (F-center [25,26]) vacancies, along with fluorine neutral (H-center [25,26]) and negatively charged (-centers [25,26]) interstitials (Equation (1)), approaching to hundreds of aggregated defects usually concentrated in dislocation loops [25,26]. Likewise, in the diamond plate, the mobile photo-generated vacancies could be trapped by substitutional nitrogen atoms (C-centers [31]), resulting in well-known neutral or charged NV complexes [18,31] (Equation (1)):

atoms with a photo-generated vacancy, as well as their red-shifted phonon replica.

Finally, the observed, strongly—by one order of magnitude—enhanced PL band in the micromark inscribed inside the diamond slab exhibits the main spectral features, rep-

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 5 of 11

resenting the neutral (NV<sup>0</sup>

nitrogen-vacancy (NV<sup>−</sup>

$$
\delta I \\
\text{forides}: H + H \to H\_{2\nu} \\
H + V\_{\mathcal{K}} \to F\_{3\nu}^{-}$$
 
$$
\delta \Lambda \\
\text{land} \\
\text{and} \\
: N\_{\mathcal{S}} + V^{0} \to N V. \tag{1}$$

−

, zero-phonon line, ZPL, at 575 nm [31]) and negatively charged

, zero-phonon line at 637 nm [31]) centers of substitutional nitrogen

Equation (1)—Atomistic processes, resulting in photo-induced vacancy complexes in fluorides and diamond. Equation (1)—Atomistic processes, resulting in photo-induced vacancy complexes in fluorides and diamond.

In the same line, one can see strong stationary annealing of mobile vacancy-related color centers in LiF already at temperatures elevated by 200–300 ◦C (Figure 4a), almost deleting the microbit signal. In contrast, in denser and more rigid diamond lattice the Frenkel vacancies anchored by C-centers, remain rather stable even at high temperatures, approaching 1200 ◦C (Figure 4b). In the same line, one can see strong stationary annealing of mobile vacancy-related color centers in LiF already at temperatures elevated by 200–300 °C (Figure 4a), almost deleting the microbit signal. In contrast, in denser and more rigid diamond lattice the Frenkel vacancies anchored by C-centers, remain rather stable even at high temperatures, approaching 1200 °C (Figure 4b).

**Figure 4.** PL spectra of LiF (**a**) and natural diamond (**b**) upon annealing in the corresponding different temperature ranges, regarding the unannealed non-modified materials. **Figure 4.** PL spectra of LiF (**a**) and natural diamond (**b**) upon annealing in the corresponding different temperature ranges, regarding the unannealed non-modified materials.

#### *3.3. Photogeneration of Frenkel Pairs of Point Defects in LiF during Atomistic Inscription 3.3. Photogeneration of Frenkel Pairs of Point Defects in LiF during Atomistic Inscription*

PL yield at 670 nm—in the peak related to F2-centers—was used to track fs-laser photogeneration of Frenkel pairs in LiF, underlying the formation of these centers. As can be seen in Figure 5a,c, the PL yield in LiF exhibits the non-linear (power slope in the range of 3.3–3.8) monotonic dependence on pulse energy E = 2.5–13 nJ (peak fluence 0.3–1.7 J/cm<sup>2</sup> , peak intensity 1.5–9 TW/cm<sup>2</sup> ) (previously—in diamond [35]) and exposure of (4– 800) × 10<sup>6</sup> pulses/spot (at room temperature, Figure 5b,d). Moreover, the abovementioned annealing effect at the temperatures of 200 °C and 300 °C results not only in the decreased PL intensity at 670 nm (Figure 5c), but also in the different exposure trends (Figure 5d) apparently related to cumulative heating of the material at the ultra-high 80 MHz exposure of the static sample, which is well-known to be favorable for self-trapped exciton PL yield at 670 nm—in the peak related to F2-centers—was used to track fs-laser photogeneration of Frenkel pairs in LiF, underlying the formation of these centers. As can be seen in Figure 5a,c, the PL yield in LiF exhibits the non-linear (power slope in the range of ≈3.3–3.8) monotonic dependence on pulse energy E = 2.5–13 nJ (peak fluence <sup>≈</sup> 0.3–1.7 J/cm<sup>2</sup> , peak intensity <sup>≈</sup> 1.5–9 TW/cm<sup>2</sup> ) (previously—in diamond [35]) and exposure of (4–800) <sup>×</sup> <sup>10</sup><sup>6</sup> pulses/spot (at room temperature, Figure 5b,d). Moreover, the abovementioned annealing effect at the temperatures of 200 ◦C and 300 ◦C results not only in the decreased PL intensity at 670 nm (Figure 5c), but also in the different exposure trends (Figure 5d) apparently related to cumulative heating of the material at the ultra-high 80 MHz exposure of the static sample, which is well-known to be favorable for self-trapped exciton stabilization via Frenkel pair formation [25]. The cumulative heating effect is more pronounced at room temperature (Figure 5d), while the elevated temperatures make it less distinct.

distinct.

= e <sup>2</sup>E<sup>2</sup>

/(4mopt<sup>2</sup>

stabilization via Frenkel pair formation [25]. The cumulative heating effect is more pronounced at room temperature (Figure 5d), while the elevated temperatures make it less

We have analyzed the observed PL yield at 670 nm vs. pulse energy E in LiF (Figure 5c), representing the concentration of F2-centers in the probed confocal volume, alike to our previous similar studies of NV-center yield upon fs-laser exposure in diamond [35]. According to high bandgap energy of Edir(Г-point) ≈ 13.0–14.2 eV in LiF [27,28], formation of F2-centers requires either N = Edir/ħω ≈ 6 photons at the 525 nm wavelength (photon energy ħω 2.4 eV), or "hot" non-equilibrium electron of this energy (effectively, considerably higher to fulfill both the quasi-momentum and energy conservation laws). The evaluated laser-induced prompt ponderomotive enhancement of the bandgap [36,37], U<sup>p</sup>

), is minor (<1 eV) in the utilized intensity range of 9–30 TW/cm<sup>2</sup>

field strength E = 15–30 MV/cm) for the arbitrary optical mass of electron-hole pair mopt =

memh/(me+mh) = m0/2, assuming me,m<sup>h</sup> = m<sup>0</sup> (free-electron mass).

(electric

**Figure 5.** (**a**) PL spectra of microbits in LiF inscribed at variable pulse energy (see the frame inset) and the fixed exposure of 10 s (×80 MHz), spectral assignment after [33]; (**b**) PL spectra of microbits in LiF inscribed at the variable exposures (see the frame inset) and the fixed pulse energy of 13 nJ (spectral assignment after [33]); (**c**) PL intensity of 670 nm (F2-center [33]) peak in the spectra as a function of pulse energy (peak fluence—0.2–2.4 J/cm<sup>2</sup> , peak intensity—1–12 TW/cm<sup>2</sup> ) at the maximal exposure of 10 s without annealing (25 °C, black circles) and after annealing at 200 °C (red squares) and 300 °C (blue triangles) as well as their linear fitting curves of the same colors with the corresponding slopes; (**d**) PL intensity of 670 nm (F2-center [33]) peak in the spectra as a function of exposure at the pulse energy of 13 nJ without annealing (25 °C, black circles) and after annealing at 200 °C (red squares) and 300 °C (blue triangles). **Figure 5.** (**a**) PL spectra of microbits in LiF inscribed at variable pulse energy (see the frame inset) and the fixed exposure of 10 s (×80 MHz), spectral assignment after [33]; (**b**) PL spectra of microbits in LiF inscribed at the variable exposures (see the frame inset) and the fixed pulse energy of 13 nJ (spectral assignment after [33]); (**c**) PL intensity of 670 nm (F<sup>2</sup> -center [33]) peak in the spectra as a function of pulse energy (peak fluence—0.2–2.4 J/cm<sup>2</sup> , peak intensity—1–12 TW/cm<sup>2</sup> ) at the maximal exposure of 10 s without annealing (25 ◦C, black circles) and after annealing at 200 ◦C (red squares) and 300 ◦C (blue triangles) as well as their linear fitting curves of the same colors with the corresponding slopes; (**d**) PL intensity of 670 nm (F<sup>2</sup> -center [33]) peak in the spectra as a function of exposure at the pulse energy of 13 nJ without annealing (25 ◦C, black circles) and after annealing at 200 ◦C (red squares) and 300 ◦C (blue triangles).

We have analyzed the observed PL yield at 670 nm vs. pulse energy E in LiF (Figure 5c), representing the concentration of F2-centers in the probed confocal volume, alike to our previous similar studies of NV-center yield upon fs-laser exposure in diamond [35]. According to high bandgap energy of Edir(Γ-point) ≈ 13.0–14.2 eV in LiF [27,28], formation of F2-centers requires either N = Edir/*h*¯ ω ≈ 6 photons at the 525 nm wavelength (photon energy *h*¯ ω ≈ 2.4 eV), or "hot" non-equilibrium electron of this energy (effectively, considerably higher to fulfill both the quasi-momentum and energy conservation laws). The evaluated laser-induced prompt ponderomotive enhancement of the bandgap [36,37], U<sup>p</sup> = e2E <sup>2</sup>/(4moptω<sup>2</sup> ), is minor (<1 eV) in the utilized intensity range of 9–30 TW/cm<sup>2</sup> (electric field strength E = 15–30 MV/cm) for the arbitrary optical mass of electron-hole pair mopt = memh/(me+mh) = m0/2, assuming me,m<sup>h</sup> = m<sup>0</sup> (free-electron mass).

Recently, for such analysis of electron-hole plasma and PL dynamics, a kinetic rate model for electron-hole plasma density ρeh was enlighteningly used in the common form [38], including (1) ultrafast, pulsewidth-limited multiphoton (cross-section σN), (2) impact ionization (coefficient α), (3,4) fast picosecond three-body Auger (coefficient γ) and slow binary radiative (coefficient β) recombination, as well as (5) fast self-trapping of electron-hole pairs (excitons, characteristic time τstr) to produce one color center per selftrapped excitons [25] as the consecutive terms, respectively, and describing the corresponding continuous-wave-laser pumped PL yield ΦPL as follows (Equation (2)) [32]: ionization (coefficient ), (3,4) fast picosecond three-body Auger (coefficient ) and slow binary radiative (coefficient ) recombination, as well as (5) fast self-trapping of electronhole pairs (excitons, characteristic time str) to produce one color center per self-trapped excitons [25] as the consecutive terms, respectively, and describing the corresponding continuous-wave-laser pumped PL yield PL as follows (Equation (2)) [32]: ℎ ℎ 2

Recently, for such analysis of electron-hole plasma and PL dynamics, a kinetic rate model for electron-hole plasma density eh was enlighteningly used in the common form [38], including (1) ultrafast, pulsewidth-limited multiphoton (cross-section N), (2) impact

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 7 of 11

$$\frac{d\rho\_{\rm eh}}{dt} = \sigma\_N I^N + aI\rho\_{\rm eh} - \gamma \rho\_{\rm eh}^3 - \beta \rho\_{\rm eh}^2 - \frac{\rho\_{\rm eh}^2}{\tau\_{\rm str}}, \Phi \propto \int \rho\_{\rm eh}^2 dt\tag{2}$$

2

4

$$\frac{d\rho\_{\rm eh}}{dt} = \sigma\_{\rm 6} \mathbf{I}^{6} - \gamma \rho\_{\rm eh}^{3} - \frac{\rho\_{\rm eh}^{2}}{\tau\_{\rm str}}, \sigma\_{\rm 6} \mathbf{I}^{6} \approx \gamma \rho\_{\rm eh}^{3}, \rho\_{\rm eh} \approx \mathbf{I}\_{0}^{2}, \boldsymbol{\Phi} \propto \int \rho\_{\rm eh}^{2} \mathbf{dt} \approx \mathbf{I}\_{0}^{4}.\tag{3}$$

Equations (2) and (3)—Kinetic rate equations for electron-hole plasma and related PL yield ΦPL of the F2-centers produced via exciton self-trapping [25]: (2) general form, (3) case-specific form for our experiments in LiF. PL of the F2-centers produced via exciton self-trapping [25]: (2) general form, (3) casespecific form for our experiments in LiF. In the case of LiF, Equation (2) could be presented in the case-specific form (Equation

In the case of LiF, Equation (2) could be presented in the case-specific form (Equation (3)), where only six-photon ionization and Auger recombination balance each other, while excitonic self-trapping accompanies the electron-hole plasma relaxation. As a result, PL yield could follow the non-linear dependence on the peak fs-laser intensity I<sup>0</sup> with the power slope ≈4, being consistent with the measured values of 3.3–3.8 (Figure 5c). For the used nJ-level pulse laser energies, strong electron-hole plasma absorption is not achieved [32,39], thus enabling rather delicate inscription of PL nano- and microbits. (3)), where only six-photon ionization and Auger recombination balance each other, while excitonic self-trapping accompanies the electron-hole plasma relaxation. As a result, PL yield could follow the non-linear dependence on the peak fs-laser intensity I<sup>0</sup> with the power slope 4, being consistent with the measured values of 3.3–3.8 (Figure 5c). For the used nJ-level pulse laser energies, strong electron-hole plasma absorption is not achieved [32,39], thus enabling rather delicate inscription of PL nano- and microbits. For comparison, in diamond, both the energy and exposure dependences of the NV*<sup>0</sup>*

For comparison, in diamond, both the energy and exposure dependences of the NV<sup>0</sup> and NV− color center yield exhibit non-linear (Figure 6a,c) and linear (Figure 6b,d) trends, respectively. Only linear dependence of the PL intensity on exposure time indicated the proceeding, unsaturated accumulation of the color centers. However, in terms of the pulse energy, PL intensity of NV<sup>−</sup> centers exhibit highly-nonlinear yield (power slope—5.5 ± 0.2), while the corresponding weaker NV<sup>0</sup> peak (Figure 6a,b) rises similarly above the noise level at higher pulse energies (Figure 6c). and NV<sup>−</sup> color center yield exhibit non-linear (Figure 6a,c) and linear (Figure 6b,d) trends, respectively. Only linear dependence of the PL intensity on exposure time indicated the proceeding, unsaturated accumulation of the color centers. However, in terms of the pulse energy, PL intensity of NV<sup>−</sup> centers exhibit highly-nonlinear yield (power slope—5.5 0.2), while the corresponding weaker NV<sup>0</sup> peak (Figure 6a,b) rises similarly above the noise level at higher pulse energies (Figure 6c).

**Figure 6.** *Cont*.

**Figure 6.** (**a**) PL spectra of microbits in diamond inscribed at variable pulse energy (see the frame inset) and fixed exposure of 20 s (×80 MHz), spectral assignment after [31]; (**b**) PL spectra of microbits in diamond inscribed at variable exposure (see the frame inset) and fixed pulse energy of 30 nJ (spectral assignment after [31]); (**c**) PL intensity of NV<sup>0</sup> (575 nm [31], black circles) and NV<sup>−</sup> (637 nm [31], red squares) peaks in the spectra as a function of pulse energy at exposure of 20 s and linear fitting curve for NV<sup>−</sup> with its slope indicated; (**d**) PL intensity of NV<sup>0</sup> (black circles) and NV<sup>−</sup> (red squares) peaks in the spectra as a function of exposure at energy of 30 nJ. **Figure 6.** (**a**) PL spectra of microbits in diamond inscribed at variable pulse energy (see the frame inset) and fixed exposure of 20 s (×80 MHz), spectral assignment after [31]; (**b**) PL spectra of microbits in diamond inscribed at variable exposure (see the frame inset) and fixed pulse energy of 30 nJ (spectral assignment after [31]); (**c**) PL intensity of NV<sup>0</sup> (575 nm [31], black circles) and NV− (637 nm [31], red squares) peaks in the spectra as a function of pulse energy at exposure of 20 s and linear fitting curve for NV<sup>−</sup> with its slope indicated; (**d**) PL intensity of NV<sup>0</sup> (black circles) and NV− (red squares) peaks in the spectra as a function of exposure at energy of 30 nJ.

Similarly to Equations (2,3), in the case of diamond, its weak non-linear photoexcitation process across the minimal direct -point bandgap of 7.3 eV, which is distinct in Figure 6c, could be represented in the following familiar form [32] ℎ Similarly to Equations (2) and (3), in the case of diamond, its weak non-linear photoexcitation process across the minimal direct Γ-point bandgap of 7.3 eV, which is distinct in Figure 6c, could be represented in the following familiar form [32]

$$\frac{d\rho\_{e\hbar}}{dt} = \sigma\_3 I^3, \ \rho\_{e\hbar} \propto I\_0^3, \ \Phi \propto \int \rho\_{e\hbar}^2 dt \propto I\_0^6. \tag{4}$$

plasma and related PL yield PL produced via exciton self-trapping in diamond [31]. Here, marginal photogenerated electron-hole pairs become intermixed in the EHP, Equation (4)—Kinetic rate equations for three-photon excitation of electron-hole plasma and related PL yield ΦPL produced via exciton self-trapping in diamond [31].

losing their initial correlation during the photogeneration and appear independently with the overall 2N-fold slope in the excitonic recombination [32], preceding NV-center formation. The observed difference in the fs-laser driven formation of Frenkel I–V pairs in LiF and diamond is apparently related to their drastically differing ionicity, favorable for excitonic self-trapping in fluorides [25,26], as compared to the predominating electron(hole)-lattice interactions in diamond [32]. Here, marginal photogenerated electron-hole pairs become intermixed in the EHP, losing their initial correlation during the photogeneration and appear independently with the overall 2N-fold slope in the excitonic recombination [32], preceding NV-center formation. The observed difference in the fs-laser driven formation of Frenkel I–V pairs in LiF and diamond is apparently related to their drastically differing ionicity, favorable for excitonic self-trapping in fluorides [25,26], as compared to the predominating electron(hole)-lattice interactions in diamond [32].

#### *3.4. Evaluation of Storage Capacity Utilizing Photo-Luminescent Microbit Arrays* Finally, we have performed experimental evaluation of PL microbit density, which *3.4. Evaluation of Storage Capacity Utilizing Photo-Luminescent Microbit Arrays*

is the key characteristic of archival optical storage. Above, we inscribed PL bits in the natural diamond, LIF and CaF<sup>2</sup> samples with ≥2 m lateral separation, exceeding the micropositioning accuracy, which could be easily resolved in the PL images (Figure 2). Furthermore, we undertook inscription and confocal PL visualization of separate linear arrays of PL microbits with variable vertical (depth) separation changed in the range of 1–28 m (Figure 7), in order to evaluate the minimal resolvable vertical separation. PL visualization was performed by means of Olympus (40×) and Nikon (100×) microscope objectives with vertical resolution z = 1 or 2 m, respectively (Figure 7a,b). The corresponding side-view PL imaging results for the same microstructure of paired linear arrays are presented in Figure 7c,d. Finally, we have performed experimental evaluation of PL microbit density, which is the key characteristic of archival optical storage. Above, we inscribed PL bits in the natural diamond, LIF and CaF<sup>2</sup> samples with ≥2 µm lateral separation, exceeding the micropositioning accuracy, which could be easily resolved in the PL images (Figure 2). Furthermore, we undertook inscription and confocal PL visualization of separate linear arrays of PL microbits with variable vertical (depth) separation changed in the range of 1–28 µm (Figure 7), in order to evaluate the minimal resolvable vertical separation. PL visualization was performed by means of Olympus (40×) and Nikon (100×) microscope objectives with vertical resolution ∆z = 1 or 2 µm, respectively (Figure 7a,b). The corresponding side-view PL imaging results for the same microstructure of paired linear arrays are presented in Figure 7c,d.

**Figure 7.** PL imaging of stair-like set of pairs of linear microbit arrays in LiF with variable intra-pair vertical separation in the range of 1–28 m using Olympus (**a**,**c**) and Nikon (**b**,**d**) microscope objectives with the vertical resolution z = 1 or 2 m, respectively: (**a**,**b**) 3D view; (**c**,**d**) side-view images of neighboring PL microbit arrays, showing their resolvable separation, starting from 11 m (**c**) or 16 m (**d**). **Figure 7.** PL imaging of stair-like set of pairs of linear microbit arrays in LiF with variable intrapair vertical separation in the range of 1–28 µm using Olympus (**a**,**c**) and Nikon (**b**,**d**) microscope objectives with the vertical resolution ∆z = 1 or 2 µm, respectively: (**a**,**b**) 3D view; (**c**,**d**) side-view images of neighboring PL microbit arrays, showing their resolvable separation, starting from 11 µm (**c**) or 16 µm (**d**).

Here, one can find that the pairs of microbit lines become visibly separable, starting from 11 m for the 1 m resolution visualization (Figure 7c), while only at 16 or 21 m for the 2 m resolution visualization (Figure 7d). Hence, accounting for the appropriately resolvable 2 m intra-layer separation of microbits and their 11 m inter-layer separation, one can evaluate the bulk microbit density of 25 Gbits per cubic centimeter for the simple cubic lattice of microbits, i.e., about 3 Tbits per disk for the 120 mm diameter of the standard CD or DVD disks and the 10 mm thickness. This optical storage capacity is comparable to previous optical memory writing technologies (visible microvoids [15], birefringent nanotrenches [16,17], photoluminescent microbits [40]), but they have clear benefits in the confocal non-linear memory read-out due to non-destructive laser inscription technology. Moreover, considerable, few-fold additional increase in the storage capacity could be achieved by higher-NA (NA > 0.65) inscription and other advanced optical means. Here, one can find that the pairs of microbit lines become visibly separable, starting from 11 µm for the 1 µm resolution visualization (Figure 7c), while only at 16 or 21 µm—for the 2 µm resolution visualization (Figure 7d). Hence, accounting for the appropriately resolvable 2 µm intra-layer separation of microbits and their 11 µm inter-layer separation, one can evaluate the bulk microbit density of 25 Gbits per cubic centimeter for the simple cubic lattice of microbits, i.e., about 3 Tbits per disk for the 120 mm diameter of the standard CD or DVD disks and the 10 mm thickness. This optical storage capacity is comparable to previous optical memory writing technologies (visible microvoids [15], birefringent nanotrenches [16,17], photoluminescent microbits [40]), but they have clear benefits in the confocal non-linear memory read-out due to non-destructive laser inscription technology. Moreover, considerable, few-fold additional increase in the storage capacity could be achieved by higher-NA (NA > 0.65) inscription and other advanced optical means.

#### **4. Conclusions 4. Conclusions**

In this study, bulk high-NA inscription (writing) of photo-luminescent microbits in LiF, CaF<sup>2</sup> and diamond crystals, as a delicate laser micromachining process, was performed by means of ultrashort-pulse laser and tested (read-out) by 3D-scanning confocal photoluminescence micro-spectroscopy. Preliminarily, optical storage density for the simple cubic lattice of microbits was evaluated as high as 25 Gbits/cm<sup>3</sup> , provided by the precise micromechanical positioning, but could be few-fold increased by using more sophisticated optical focusing tools during the encoding procedure. The underlying photo-luminescent color centers were identified in the fluorides (fluorine vacancy-based F2-centers and similar vacancy-based specifies) and diamond (carbon vacancy-based NV-centers) by PL micro-spectroscopy, while their laser inscription mechanism was revealed in fluorides for the first time, comparing to the more or less known mechanisms for synthetic and natural diamonds. Moreover, the color centers could be easily annealed in the fluorides at In this study, bulk high-NA inscription (writing) of photo-luminescent microbits in LiF, CaF<sup>2</sup> and diamond crystals, as a delicate laser micromachining process, was performed by means of ultrashort-pulse laser and tested (read-out) by 3D-scanning confocal photoluminescence micro-spectroscopy. Preliminarily, optical storage density for the simple cubic lattice of microbits was evaluated as high as 25 Gbits/cm<sup>3</sup> , provided by the precise micromechanical positioning, but could be few-fold increased by using more sophisticated optical focusing tools during the encoding procedure. The underlying photo-luminescent color centers were identified in the fluorides (fluorine vacancy-based F2-centers and similar vacancy-based specifies) and diamond (carbon vacancy-based NV-centers) by PL microspectroscopy, while their laser inscription mechanism was revealed in fluorides for the first time, comparing to the more or less known mechanisms for synthetic and natural diamonds. Moreover, the color centers could be easily annealed in the fluorides at moderate

temperatures of 300 ◦C due to the high lability of the centers and room-temperature mobility of their atomistic constituents, comparing to the relatively robust color (NV) centers in diamond, persisting even at rather elevated temperatures of ≈1200 ◦C. Our first-step research highlights the way for potential implications of laser-inscribed photo-luminescent microbits in archival optical storage with micromechanical access for its read-out.

**Author Contributions:** Conceptualization, S.K., P.D. and A.G.; methodology, I.M.; validation, E.K.; investigation, A.R., P.D., N.S., R.K. and E.K.; resources, A.R., G.K. and R.K.; writing—original draft preparation, S.K.; writing—review and editing, A.G. and S.K.; visualization, P.D., E.K. and N.S.; supervision, A.G.; project administration, S.K.; and funding acquisition, S.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Russian Science Foundation (project No. 21-79-30063); https://rscf.ru/en/project/21-79-30063/ (accessed on 4 April 2023).

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


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## *Article* **A FIN-LDMOS with Bulk Electron Accumulation Effect**

**Weizhong Chen 1,2, Zubing Duan 2,\*, Hongsheng Zhang <sup>1</sup> , Zhengsheng Han <sup>2</sup> and Zeheng Wang 3,\***


**Abstract:** A thin Silicon-On-Insulator (SOI) LDMOS with ultralow Specific On-Resistance (*R*on,sp) is proposed, and the physical mechanism is investigated by Sentaurus. It features a FIN gate and an extended superjunction trench gate to obtain a Bulk Electron Accumulation (BEA) effect. The BEA consists of two p-regions and two integrated back-to-back diodes, then the gate potential *V*GS is extended through the whole p-region. Additionally, the gate oxide *W*oxide is inserted between the extended superjunction trench gate and N-drift. In the on-state, the 3D electron channel is produced at the P-well by the FIN gate, and the high-density electron accumulation layer formed in the drift region surface provides an extremely low-resistance current path, which dramatically decreases the *R*on,sp and eases the dependence of *R*on,sp on the drift doping concentration (*N*drift). In the off-state, the two p-regions and N-drift deplete from each other through the gate oxide *W*oxide like the conventional SJ. Meanwhile, the Extended Drain (ED) increases the interface charge and reduces the *<sup>R</sup>*on,sp. The 3D simulation results show that the *BV* and *<sup>R</sup>*on,sp are 314 V and 1.84 mΩ·cm−<sup>2</sup> , respectively. Consequently, the *FOM* is high, reaching up to 53.49 MW/cm<sup>2</sup> , which breaks through the silicon limit of the RESURF.

**Keywords:** bulk electron accumulation (BEA); extended superjunction trench gate; extended drain (ED); *BV* and *R*on,sp

### **1. Introduction**

The Lateral Double-diffused Metal–Oxide Semiconductor (LDMOS) is a very important device in power-integrated circuits and electronic power systems [1–3], which are used in many places in our daily life. The Breakdown Voltage (*BV*) and the Specific On-Resistance (*R*on,sp) are significant parameters to evaluate the quality of devices [4–7]. For the conventional LDMOS, there is an unavoidable trade-off relationship between the *BV* and *R*on,sp, which can be written as *R*on ∝ *BV*2.5, while what we need are high *BV* and low *R*on,sp. Baliga's Figure Of Merit (*FOM*) is calculated by *BV*2/*R*on,sp to evaluate the device, where a higher value is better [8–10]. Many advanced theories and structures have been investigated to increase the *FOM* of the power devices [11–14]. For example, for the BFG LDMOS proposed in [11], the author made half of the device into a grid, and for the HKGF LDMOS proposed in [14], the authors distinguished the device drift into three parts, each surrounded by a three-dimensional High-K dielectric, both of which greatly enhanced the control ability of the device and greatly reduced the *R*on,sp of the device. The Enhanced Dielectric layer Field (ENDIF) theory can introduce a higher electric field between the top layer of silicon and the buried oxygen layer, which can obviously enhance *BV* [15–17]. However, it is possible to increase *R*on,sp with the application of ENDIF theory. For example, the T-SJ LDMOS proposed in [17] enhances the *BV* of the device by making the top layer of silicon near the drain extremely thin, but greatly reduces the volume of the device drift region, thus reducing the *R*on,sp of the device. The SuperJunction (SJ) structure can effectively increase the drift doping concentration by using N-type semiconductors

**Citation:** Chen, W.; Duan, Z.; Zhang, H.; Han, Z.; Wang, Z. A FIN-LDMOS with Bulk Electron Accumulation Effect. *Micromachines* **2023**, *14*, 1225. https://doi.org/10.3390/ mi14061225

Academic Editor: Ha Duong Ngo

Received: 2 May 2023 Revised: 24 May 2023 Accepted: 8 June 2023 Published: 10 June 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

and P-type semiconductors to assist each other; thus, the *R*on,sp is reduced and the BV is guaranteed simultaneously, and thus the *FOM* can be effectively improved [18–21]. However, the superjunction structure is often placed on the P-type substrate in lateral devices, and the surface superjunction region is affected by the Substrate-Assisted Depletion (SAD) effect, which results in reduced pressure tolerance. Moreover, the power FINFET with a 3D electron channel and the LDMOS with an Accumulation Extended Gate (AEG LDMOS) are also used to improve the device [22].

In this paper, the FIN-LDMOS with Bulk Electron Accumulation (BEA-LDMOS) is first proposed. The device adopts an SOI structure, which can effectively suppress the SAD effect. The bulk electron accumulation effect produced by the extended superjunction trench gate in the N-drift and the ENDIF effect produced by the Extended Drain are produced. Moreover, the assisted depletion effect is performed by the extended superjunction trench gate, which dramatically reduces the *R*on,sp while *BV* is guaranteed. The devices are performed by Synopsys Sentaurus, and the main physics models are as follows: Effectice Intrinsic Density, Mobility (High Field Saturation Enormal PhuMob DopingDependence), and Recombination (SRH Auger Avalanche) [23].

### **2. Device Structure and Mechanism**

### *2.1. Device Structure of the BEA*

The FIN-LDMOS, AEG-LDMOS, and the proposed BEA-LDMOS are compared together in Figure 1. The FIN-LDMOS greatly increases the channel area of the device by turning the one-dimensional gate into a three-dimensional one, to reduce the *R*on,sp. The AEG-LDMOS structure is characterized by extending the gate, which is only near the source region in the conventional LDMOS, to the drain, separated by SiO2. In order to extend the drain potential better, two back-to-back PN junctions are used in the extension gate to generate a charge accumulation effect at the top of the N-drift area, forming a low-resistance channel and greatly reducing the *R*on,sp of the device. However, the *BV* will be affected by the PN junction in the extension grid, which reduces the *BV* of the device. The 3-D structure of the BEA-LDMOS is shown in Figure 1. The extended superjunction trench gate is formed as follows: the two back-to-back diodes are introduced at the collector, and the P-region and N-drift are separated by the SiO2. Moreover, the two ends of the P-region are, respectively, shortly connected to the gate electrode and the drain electrode, as shown in Figure 1a. When the device is in the on-state, the positive *V*GS is extended through most of the P-region to the positively biased D1, and positive *V*DS is extended through the P-region to the positively biased D2. Thus, the P-region is covered by the *V*GS and *V*DS; then, a Bulk Electron Accumulation (BEA) is generated in the drift region, as shown in Figure 1b, and the metal–insulator–semiconductor structure is composed of P-region/oxide/N-drift. It is equivalent to a low-resistance 3-D channel in the drift region. Therefore, the *R*on,sp of the device is greatly reduced. Figure 1c indicates the breakdown mechanism of the BEA-LDMOS in the off-state, and it is similar to the conventional superjunction. The P-region and the N-drift region are separated by SiO2, and there is still a built-in electric field from the N-drift region toward the P-region, resulting in the formation of a depletion region near SiO2. Therefore, the electric field of the N-drift is modulated, thus helping to increase *BV*. At the same time, the Extended Drain structure is also introduced in the drift area, which can not only introduce the high electric field near the drain region into the more voltage-resistant silicon dioxide buried layer to increase the *BV* of the device, but also play the role of low-resistance channel, reducing the *R*on,sp of the device. The key parameters of the devices are listed in Table 1, with a drift length L<sup>D</sup> of 21.0 µm, depth *T*<sup>D</sup> of 5.0 µm, Extended Drain length *L* of 9 µm, and thickness of 0.4 µm. The optimized drift doping *<sup>N</sup>*drift of 2.2 <sup>×</sup> <sup>10</sup><sup>15</sup> cm−<sup>3</sup> is designed for the BEA-LDMOS.

**Figure 1.** The three-dimensional (3D) schematic and mechanism of the three proposed devices. (**a**) FIN-LDMOS, (**b**) AEG-LDMOS, (**c**) BEA-LDMOS, (**d**) the Bulk Electron Accumulation (BEA) effect induced at the N-drift, (**e**) the assisted depletion between the P-region and N-drift in the Off-state. Diode D1 is formed by the (P−/N+) and D2 is formed by the (P/N+) junction. **Figure 1.** The three-dimensional (3D) schematic and mechanism of the three proposed devices. (**a**) FIN-LDMOS, (**b**) AEG-LDMOS, (**c**) BEA-LDMOS, (**d**) the Bulk Electron Accumulation (BEA) effect induced at the N-drift, (**e**) the assisted depletion between the P-region and N-drift in the Off-state. Diode D1 is formed by the (P−/N+) and D2 is formed by the (P/N+) junction.


**SUB**

Thermal oxidation, (**d**) Electrode deposition.

**SUB**


**N-drift P-well PG+ P- N+ p Dn ED BOX P+ (a) (b) N-drift P-well P+ N+ PG+ P− N+ p Dn Gate ED BOX P+ Source Drain** The simplified production process of the BEA-LDMOS is given as follows: The emphasis is the extended superjunction trench gate and Extended Drain. The SOI wafer in Figure 2a is injected with oxygen ions and annealed to form a silicon dioxide isolation layer. The P-well and Extended Drain are obtained by implantation, as shown in Figure 2b. The following undergo thermal oxidation to grow the isolation layer and undergo secondary ion implantation doping, as shown in Figure 2c. The subsequent processes such as metallization and passivation are compatible with conventional LDMOSs in Figure 2d.

**Figure 2.** Simplified key process of the proposed BEA-LDMOS. (**a**) SOI substate, (**b**) Ion doping, (**c**)

**SUB**

**SUB**

**(c) (d)**

**Figure 2.** Simplified key process of the proposed BEA-LDMOS. (**a**) SOI substate, (**b**) Ion doping, (**c**) Thermal oxidation, (**d**) Electrode deposition. **Figure 2.** Simplified key process of the proposed BEA-LDMOS. (**a**) SOI substate, (**b**) Ion doping, (**c**) Thermal oxidation, (**d**) Electrode deposition.

#### *2.2. Mainly Applied Physical Models*

**N-drift**

*L***<sup>D</sup>**

**Gate**

**PG+**

*T***<sup>D</sup>**

*W***gate**

*T***<sup>D</sup>**

**Source Drain**

**BOX SUB**

**N-drift**

**Source Drain**

**BOX**

*L***<sup>D</sup>**

*H*

Diode D1 is formed by the (P−/N+) and D2 is formed by the (P/N+) junction.

**SUB**

(**c**)

**Dn**

**P− N+ p**

*W***EG**

**ED**

**D1**

*L*

**P-well**

**P+ N+**

**Y X**

**Z**

(**a**) (**b**)

**Dn**

**Figure 1.** The three-dimensional (3D) schematic and mechanism of the three proposed devices. (**a**) FIN-LDMOS, (**b**) AEG-LDMOS, (**c**) BEA-LDMOS, (**d**) the Bulk Electron Accumulation (BEA) effect induced at the N-drift, (**e**) the assisted depletion between the P-region and N-drift in the Off-state.

The simplified production process of the BEA-LDMOS is given as follows: The emphasis is the extended superjunction trench gate and Extended Drain. The SOI wafer in Figure 2a is injected with oxygen ions and annealed to form a silicon dioxide isolation layer. The P-well and Extended Drain are obtained by implantation, as shown in Figure 2b. The following undergo thermal oxidation to grow the isolation layer and undergo secondary ion implantation doping, as shown in Figure 2c. The subsequent processes such as metallization and passivation are compatible with conventional LDMOSs in Figure 2d.

**P+**

**D2**

**Gate**

*W***gate**

*T***<sup>D</sup>** *L***<sup>D</sup>**

P+

**N-drift**

**Source Drain**

**BOX SUB**

**N-drift P**

**N-drift**

**Dn**

P+ <sup>P</sup> *<sup>W</sup>* <sup>P</sup><sup>−</sup> N+ **EG**

**SUB BOX**

**On-state:VGS>VTH,VGD>VDS,VDS>0** (**d**)

**P**

**SUB BOX**

**Off-state:VGS=0,VDS>0**

(**e**)

**P-well**

**P-well**

**P+ N+**

**Y X**

**P+ N+**

**Y X**

**Z**

**Z**

**Gate**

*W***gate**

The main physical models used in this simulation include the carrier mobility model, carrier recombination model, and avalanche breakdown generation model [24–26]. Carrier mobility is expressed as follows:

$$\frac{1}{\mu} = \frac{\exp\left(-\frac{\chi}{l\_{\rm crit}}\right)}{\mu\_{\rm ac}} + \frac{\exp\left(-\frac{\chi}{l\_{\rm crit}}\right)}{\mu\_{\rm sr}} + \frac{1}{\mu\_b} + \frac{1}{\mu\_F} \tag{1}$$

where *µ*ac represents the surface phonon scattering model, *µ*sr represents the surface roughness scattering model, *x* represents the distance between the insulator and the semiconductor interface, *µ<sup>b</sup>* represents the low-field-mobility model, and *µ<sup>F</sup>* represents the high-field-mobility model.

In the simulation, we use the SRH carrier recombination model, which can accurately simulate the recombination mechanism of carrier under quantum effects. The carrier recombination model is expressed as follows:

$$R\_{net}^{\rm SRH} = \frac{np - \gamma\_n \gamma\_p n\_{i,eff}}{T\_p \left(n + \gamma\_n n\_{i,eff}\right) + T\_n \left(p + \gamma\_p n\_{i,eff}\right)}\tag{2a}$$

$$\gamma\_{\rm n} = \frac{n}{N\_{\rm C}} \exp(-\frac{E\_{\rm Fn} - E\_{\rm C}}{kT\_{\rm n}}) \tag{2b}$$

$$\gamma\_p = \frac{p}{N\_V} \exp(-\frac{E\_V - E\_{Fp}}{kTp}) \tag{2c}$$

In the formula, *T<sup>n</sup>* represents the lifetime of non-equilibrium minority electron, *T<sup>p</sup>* represents the lifetime of non-equilibrium minority hole, *N<sup>C</sup>* represents the effective state density of the conduction band, *N<sup>V</sup>* represents the effective state density of the valence band, *EFn* represents the quasi-Fermi level of the conduction band, *EFp* represents the quasi-Fermi level of the valence band.

In order to accurately simulate the breakdown voltage of the device, the avalanche breakdown generation model is introduced in the simulation process. When the device is working in the blocking voltage, as the drain voltage continues to increase, the internal electric field of the device becomes stronger. When the maximum electric field inside the device is greater than or equal to the critical breakdown electric field of silicon, the charge multiplication effect will occur, and the leakage of the device will increase sharply, resulting in electrical breakdown of the device. The avalanche breakdown generation model is expressed as follows:

*G Avalanche* = *αnnv<sup>n</sup>* + *α<sup>p</sup> pv<sup>p</sup>* (3a)

$$
\alpha = \gamma a e^{-\frac{\gamma b}{F}} \tag{3b}
$$

$$\gamma = \frac{\tanh(\frac{\hbar \omega\_{op}}{2kT\_0})}{\tanh(\frac{\hbar \omega\_{op}}{2kT})} \tag{3c}$$

In the formula, *α* is the ionization factor, it's the inverse of the mean free path, *F* represents the Vector mechanics, *hωop* represents the optical phonon energy, *y* represents the Dependence coefficient of phonon.

#### **3. Results and Discussion**

### *3.1. Control Mechanism and Bulk Electron Accumulation Effect of the BEA*

Figure 3 shows the transfer, transconductance (*g*m), and gate potential characteristics for the devices. Figure 3a shows that when *V*GS is increased from 6 V to 16 V, and the *V*DS of the drain is grounded, *V*GS is extended through the whole P-region, and it is shunted by the negatively biased D2. Figure 3b compares the transfer and *g*<sup>m</sup> characteristics for the CON-LDMOS, AEG-LDMOS, FIN-LDMOS, and BEA-LDMOS. The peak *g*<sup>m</sup> for the devices is 2.26, 3.16, 4.21, and 18.33 mS/mm, respectively. Because the higher peak *g*<sup>m</sup> can be achieved by the 3-D bulk electron channel, the BEA shows the best control capability of *I*DS.

Figure 4 shows the electron current densities of devices in the on-state. It can be seen that the electron current density of the AEG-LDMOS and BEA-LDMOS are much higher than those of the other two devices due to the existence of a charge accumulation effect. Moreover, because of the 3-D charge accumulation effect of the BEA-LDMOS, while the charge accumulation effect of the AEG is one-dimensional, the area of the low-resistance channel formed by the BEA-LDMOS is much higher than that of AEG-LDMOS, so the electron current density of the BEA-LDMOS is the largest of all four devices.

Figure 5 shows the output *I*DS-*V*DS characteristics of the four devices at the forward conduction. For the proposed BEA-LDMOS, the P-region is covered by *V*GS and *V*DS to obtain a 3-D low-resistance channel, so the linear current and saturation current in the drift region are much higher than those of the CON-LDMOS, AEG-LDMOS, and FIN-LDMOS under the same *V*DS. Thus, stronger conductivity and ultra-low *R*on,sp are achieved.

### *3.2. Specifics of Resistance Ron,sp and Breakdown Voltage BV*

Figure 6 shows the influence of the thickness of the top layer of silicon on *R*on, sp and *BV* of the device. It can be seen from the figure that *R*on,sp gradually decreases with the increase in *T*<sup>D</sup> under different gate voltages. This can be explained by the formula for volume resistance:

$$R = R\_s \frac{L}{W} \tag{4a}$$

$$R\_s = \frac{\rho}{T\_\text{D}}\tag{4b}$$

where *L* and *W* are the length and width of the device channel, respectively; *R<sup>s</sup>* is the resistance of the block; *ρ* is the resistivity; and *T*<sup>D</sup> is the thickness of the silicon film. However, the *BV* first increases and then decreases with the increase in *T*D, and the

optimum *BV* is 314 V when *T*<sup>D</sup> is 5.0 µm. This is because when *T*<sup>D</sup> is small, the longitudinal breakdown voltage of the device is very low, and the *BV* of the device mainly depends on the longitudinal breakdown voltage. When *T*<sup>D</sup> is too large, the relationship between *N*drift and *T*<sup>D</sup> does not conform to the RESURF theory [27], the device will breakdown in advance, as shown in Figure 6b, and the electric field will be 0 at half of the drift area of the device. CON-LDMOS, AEG-LDMOS, FIN-LDMOS, and BEA-LDMOS. The peak *g*m for the devices is 2.26, 3.16, 4.21, and 18.33 mS/mm, respectively. Because the higher peak *g*m can be achieved by the 3-D bulk electron channel, the BEA shows the best control capability of *I*DS.

*3.1. Control Mechanism and Bulk Electron Accumulation Effect of the BEA* 

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 5 of 14

the Dependence coefficient of phonon.

**3. Results and Discussion** 

௩ = + (3a)

ி (3b)

(3c)

= ିఊ

ℎ( ℎ

ℎ( ℎ

In the formula, *α* is the ionization factor, it's the inverse of the mean free path, *F* rep-

Figure 3 shows the transfer, transconductance (*g*m), and gate potential characteristics

for the devices. Figure 3a shows that when *V*GS is increased from 6 V to 16 V, and the *V*DS of the drain is grounded, *V*GS is extended through the whole P-region, and it is shunted by the negatively biased D2. Figure 3b compares the transfer and *g*m characteristics for the

resents the Vector mechanics, ℎ represents the optical phonon energy, *y* represents

2 )

2 )

=

**Figure 3.** The gate potential *V*GS in the on-state, transfer, and *g*<sup>m</sup> characteristics for the devices. (**a**) Potential distribution along the p–n–p for the BEA-LDMOS. (**b**) Transfer and *g<sup>m</sup>* of the CON-LDMOS, FIN-LDMOS, AEG-LDMOS, and BEA-LDMOS.

LDMOS, FIN-LDMOS, AEG-LDMOS, and BEA-LDMOS.

**Figure 4.** The electgron Current density distribution for the four devices at the On-state. **Figure 4.** The electgron Current density distribution for the four devices at the On-state. under the same *V*DS. Thus, stronger conductivity and ultra-low *R*on,sp are achieved.

**Figure 3.** The gate potential *V*GS in the on-state, transfer, and *g*m characteristics for the devices. (**a**) Potential distribution along the p–n–p for the BEA-LDMOS. (**b**) Transfer and *gm* of the CON-

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 6 of 14

LDMOS, FIN-LDMOS, AEG-LDMOS, and BEA-LDMOS.

that the electron current density of the AEG-LDMOS and BEA-LDMOS are much higher than those of the other two devices due to the existence of a charge accumulation effect. Moreover, because of the 3-D charge accumulation effect of the BEA-LDMOS, while the charge accumulation effect of the AEG is one-dimensional, the area of the low-resistance

electron current density of the BEA-LDMOS is the largest of all four devices.

Figure 4 shows the electron current densities of devices in the on-state. It can be seen

electron current density of the BEA-LDMOS is the largest of all four devices.

**Figure 3.** The gate potential *V*GS in the on-state, transfer, and *g*m characteristics for the devices. (**a**) Potential distribution along the p–n–p for the BEA-LDMOS. (**b**) Transfer and *gm* of the CON-

that the electron current density of the AEG-LDMOS and BEA-LDMOS are much higher than those of the other two devices due to the existence of a charge accumulation effect. Moreover, because of the 3-D charge accumulation effect of the BEA-LDMOS, while the charge accumulation effect of the AEG is one-dimensional, the area of the low-resistance channel formed by the BEA-LDMOS is much higher than that of AEG-LDMOS, so the

Figure 4 shows the electron current densities of devices in the on-state. It can be seen

**Figure 5.** Output characteristics of the devices, and *V*GS of 15 and 20 V are applied. **Figure 5.** Output characteristics of the devices, and *V*GS of 15 and 20 V are applied.

**Figure 5.** Output characteristics of the devices, and *V*GS of 15 and 20 V are applied. *3.2. Specifics of Resistance Ron,sp and Breakdown Voltage BV*  Figure 6 shows the influence of the thickness of the top layer of silicon on *R*on, sp and *BV* of the device. It can be seen from the figure that *R*on,sp gradually decreases with the *3.2. Specifics of Resistance Ron,sp and Breakdown Voltage BV*  Figure 6 shows the influence of the thickness of the top layer of silicon on *R*on, sp and *BV* of the device. It can be seen from the figure that *R*on,sp gradually decreases with the Figure 7 shows the influences of the doping *N*drift on the *R*on,sp and *BV* for the devices. For the CON-LDMOS, the optimized *BV* and *<sup>R</sup>*on,sp are 329 V and 14.54 mΩ·cm<sup>2</sup> when the *<sup>N</sup>*drift is 2.5 <sup>×</sup> <sup>10</sup><sup>15</sup> cm−<sup>3</sup> , respectively. For the FIN-LDMOS, the optimized *BV* and *<sup>R</sup>*on,sp are 323 V and 11.78 mΩ·cm<sup>2</sup> when the *<sup>N</sup>*drift is 2.5 <sup>×</sup> <sup>10</sup><sup>15</sup> cm−<sup>3</sup> , respectively. For the BEA-LDMOS, the optimized *BV* and *<sup>R</sup>*on,sp are 314 V and 1.84 mΩ·cm<sup>2</sup> when the *<sup>N</sup>*drift is 2.2 <sup>×</sup> <sup>10</sup><sup>15</sup> cm−<sup>3</sup> , respectively. It can be seen that the *BV* of the four devices increases first and then decreases with the increase in *N*drift. This is because when the doping concentration is very low, the maximum electric field of the device is near the drain region, and the breakdown voltage of the device mainly depends on the heterojunction formation of the drain region and N-drift region. When the doping concentration in the N-drift region gradually increases, the PN junction formed in the drift region and the P-well also begins to participate in the voltage resistance. When the N-drift region doping concentration continues to increase, the maximum electric field of the device will appear near the source

region, and the doping concentration difference between the drain and the drift region is very small. The breakdown voltage of the device mainly depends on the PN junction formed by the drift region and P-well. The breakdown voltage reaches its maximum when the two electric field spikes are almost high. The *R*on,sp of CON-LDMOS and FIN-LDMOS decreases obviously with the increase in *N*drift, but the *R*on,sp of AEG-LDMOS and BEA-LDMOS almost does not change with the change in *N*drift. This is because these two devices have low-resistance channels formed by the electron accumulation effect, so *R*on,sp does not depend on *N*drift. Consequently, Baliga's Figures OF Merit (FOMs) of the CON-LDMOS, FIN-LDMOS, AEG-LDMOS, and BEA-LDMOS are calculated as 7.42 MW/cm<sup>2</sup> , 8.86 MW/cm<sup>2</sup> , 20.02 MW/cm<sup>2</sup> , and 53.43 MW/cm<sup>2</sup> , respectively. drift region and P-well. The breakdown voltage reaches its maximum when the two electric field spikes are almost high. The *R*on,sp of CON-LDMOS and FIN-LDMOS decreases obviously with the increase in *N*drift, but the *R*on,sp of AEG-LDMOS and BEA-LDMOS almost does not change with the change in *N*drift. This is because these two devices have lowresistance channels formed by the electron accumulation effect, so *R*on,sp does not depend on *N*drift. Consequently, Baliga's Figures OF Merit (FOMs) of the CON-LDMOS, FIN-LDMOS, AEG-LDMOS, and BEA-LDMOS are calculated as 7.42 MW/cm2, 8.86 MW/cm2, 20.02 MW/cm2, and 53.43 MW/cm2, respectively.

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 7 of 14

ume resistance:

increase in *T*D under different gate voltages. This can be explained by the formula for vol-

=௦

௦ <sup>=</sup>

where *L* and *W* are the length and width of the device channel, respectively; *R*s is the resistance of the block; is the resistivity; and *T*D is the thickness of the silicon film. However, the *BV* first increases and then decreases with the increase in *T*D, and the optimum *BV* is 314 V when *T*D is 5.0 µm. This is because when *T*D is small, the longitudinal breakdown voltage of the device is very low, and the *BV* of the device mainly depends on the longitudinal breakdown voltage. When *T*D is too large, the relationship between *N*drift and *T*D does not conform to the RESURF theory [27], the device will breakdown in advance, as shown in Figure 6b, and the electric field will be 0 at half of the drift area of the device.

ୈ

Figure 7 shows the influences of the doping *N*drift on the *R*on,sp and *BV* for the devices.

For the CON-LDMOS, the optimized *BV* and *R*on,sp are 329 V and 14.54 mΩ·cm2 when the *N*drift is 2.5 × 1015 cm<sup>−</sup>3, respectively. For the FIN-LDMOS, the optimized *BV* and *R*on,sp are 323 V and 11.78 mΩ·cm2 when the *N*drift is 2.5 × 1015 cm<sup>−</sup>3, respectively. For the BEA-LDMOS, the optimized *BV* and *R*on,sp are 314 V and 1.84 mΩ·cm2 when the *N*drift is 2.2 × 1015 cm<sup>−</sup>3, respectively. It can be seen that the *BV* of the four devices increases first and then decreases with the increase in *N*drift. This is because when the doping concentration is very low, the maximum electric field of the device is near the drain region, and the breakdown voltage of the device mainly depends on the heterojunction formation of the drain region and N-drift region. When the doping concentration in the N-drift region gradually increases, the PN junction formed in the drift region and the P-well also begins to participate in the voltage resistance. When the N-drift region doping concentration continues to increase, the maximum electric field of the device will appear near the source region, and the doping concentration difference between the drain and the drift region is very small. The breakdown voltage of the device mainly depends on the PN junction formed by the

(4a)

(4b)

**Figure 6.** Influence of key parameter *T*D on the *R*on,sp, *BV,* and electric field for the BEA-LDMOS (*T*<sup>D</sup> is the thickness of the N-drift). (**a**) Influence on the *R*on,sp and *BV*, (**b**) influence on the electric field of top layer. **Figure 6.** Influence of key parameter *T*<sup>D</sup> on the *R*on,sp, *BV*, and electric field for the BEA-LDMOS (*T*<sup>D</sup> is the thickness of the N-drift). (**a**) Influence on the *R*on,sp and *BV*, (**b**) influence on the electric field of top layer.

**Figure 7.** Effect of doping concentration of N-drift region on *BV* and *R*on,sp forthe four devices.

Figure 8 shows the corresponding equipotential distribution at the avalanche breakdown for the four devices. The yellow area in the figure is the N-drift area, the brown area is the buried oxygen layer, the green area is the P-type substrate, the top left is the drain, the right is the source and the gate. It is noted that the BVs of the CON-LDMOS, FIN-LDMOS, AEG-LDMOS, and BEA-LDMOS are 315, 306, 297, and 314 V, respectively. The CON-LDMOS, FIN-LDMOS, and AEG-LDMOS have a similar distribution of potential lines, but there is no distribution of potential lines in the area near the drain of the BEA-LDMOS. This is because the Extended Drain introduces the higher electric field into the silicon dioxide layer, so the silicon dioxide layer below the Extended Drain has a denser distribution of the potential line. Because SiO2 has a smaller interfacial defect density and a larger dielectric constant than silicon, SiO2 can withstand a higher voltage and can im-

prove the *BV* of the device.

top layer.

(**b**)

**Figure 6.** Influence of key parameter *T*D on the *R*on,sp, *BV,* and electric field for the BEA-LDMOS (*T*<sup>D</sup> is the thickness of the N-drift). (**a**) Influence on the *R*on,sp and *BV*, (**b**) influence on the electric field of

**Figure 7.** Effect of doping concentration of N-drift region on *BV* and *R*on,sp forthe four devices. **Figure 7.** Effect of doping concentration of N-drift region on *BV* and *R*on,sp for the four devices.

Figure 8 shows the corresponding equipotential distribution at the avalanche breakdown for the four devices. The yellow area in the figure is the N-drift area, the brown area is the buried oxygen layer, the green area is the P-type substrate, the top left is the drain, the right is the source and the gate. It is noted that the BVs of the CON-LDMOS, FIN-LDMOS, AEG-LDMOS, and BEA-LDMOS are 315, 306, 297, and 314 V, respectively. The CON-LDMOS, FIN-LDMOS, and AEG-LDMOS have a similar distribution of potential lines, but there is no distribution of potential lines in the area near the drain of the BEA-LDMOS. This is because the Extended Drain introduces the higher electric field into the Figure 8 shows the corresponding equipotential distribution at the avalanche breakdown for the four devices. The yellow area in the figure is the N-drift area, the brown area is the buried oxygen layer, the green area is the P-type substrate, the top left is the drain, the right is the source and the gate. It is noted that the BVs of the CON-LDMOS, FIN-LDMOS, AEG-LDMOS, and BEA-LDMOS are 315, 306, 297, and 314 V, respectively. The CON-LDMOS, FIN-LDMOS, and AEG-LDMOS have a similar distribution of potential lines, but there is no distribution of potential lines in the area near the drain of the BEA-LDMOS. This is because the Extended Drain introduces the higher electric field into the silicon dioxide layer, so the silicon dioxide layer below the Extended Drain has a denser distribution of the potential line. Because SiO<sup>2</sup> has a smaller interfacial defect density and a larger dielectric constant than silicon, SiO<sup>2</sup> can withstand a higher voltage and can improve the *BV* of the device. *Micromachines* **2023**, *14*, x FOR PEER REVIEW 9 of 14

Figure 9 demonstrates the electric field Efield distribution along the cut line of X = 1.9 µm, Z = 6 µm and X = 1.9 µm, Z = 4.9 µm. It is noted that the Efield in the N-drift of the BEA-LDMOS reaches a maximum at the end of the Extended Drain and then drops rap-

tions, electrons and holes are unevenly distributed on both sides due to different material doping concentrations. Since the concentration of electrons in the highly doped region is higher than that in the low-doped region, electrons will diffuse from the high-doped region to the low-doped region, while holes will diffuse from the low-doped region to the high-doped region. Electrons and holes will meet at the center of the junction, resulting in a large number of recombination. This recombination results in a region of space charges near the junction, and the uneven distribution of charges in this region leads to the formation of a sharp electric field. Meanwhile, the Efield in the buried silicon dioxide layer of the BEA-LDMOS is much higher than those of the other three devices, as shown in Figure 9b. This is because the Extended Drain draws the high electric field in the N-drift

region into the buried silicon dioxide layer, which can withstand higher voltages.

**Figure 8.** The 3-D equipotential contours at the avalanche breakdown at the same *N*drift. **Figure 8.** The 3-D equipotential contours at the avalanche breakdown at the same *N*drift.

(**a**)

Figure 9 demonstrates the electric field Efield distribution along the cut line of X = 1.9 µm, Z = 6 µm and X = 1.9 µm, Z = 4.9 µm. It is noted that the Efield in the Ndrift of the BEA-LDMOS reaches a maximum at the end of the Extended Drain and then drops rapidly, as shown in Figure 9a. This is because the Extended Drain of high doping forms a heterojunction with the drift region of low doping concentration. In heterogeneous junctions, electrons and holes are unevenly distributed on both sides due to different material doping concentrations. Since the concentration of electrons in the highly doped region is higher than that in the low-doped region, electrons will diffuse from the high-doped region to the low-doped region, while holes will diffuse from the low-doped region to the high-doped region. Electrons and holes will meet at the center of the junction, resulting in a large number of recombination. This recombination results in a region of space charges near the junction, and the uneven distribution of charges in this region leads to the formation of a sharp electric field. Meanwhile, the Efield in the buried silicon dioxide layer of the BEA-LDMOS is much higher than those of the other three devices, as shown in Figure 9b. This is because the Extended Drain draws the high electric field in the N-drift region into the buried silicon dioxide layer, which can withstand higher voltages. µm, Z = 6 µm and X = 1.9 µm, Z = 4.9 µm. It is noted that the Efield in the N-drift of the BEA-LDMOS reaches a maximum at the end of the Extended Drain and then drops rapidly, as shown in Figure 9a. This is because the Extended Drain of high doping forms a heterojunction with the drift region of low doping concentration. In heterogeneous junctions, electrons and holes are unevenly distributed on both sides due to different material doping concentrations. Since the concentration of electrons in the highly doped region is higher than that in the low-doped region, electrons will diffuse from the high-doped region to the low-doped region, while holes will diffuse from the low-doped region to the high-doped region. Electrons and holes will meet at the center of the junction, resulting in a large number of recombination. This recombination results in a region of space charges near the junction, and the uneven distribution of charges in this region leads to the formation of a sharp electric field. Meanwhile, the Efield in the buried silicon dioxide layer of the BEA-LDMOS is much higher than those of the other three devices, as shown in Figure 9b. This is because the Extended Drain draws the high electric field in the N-drift region into the buried silicon dioxide layer, which can withstand higher voltages.

**Figure 8.** The 3-D equipotential contours at the avalanche breakdown at the same *N*drift.

Figure 9 demonstrates the electric field Efield distribution along the cut line of X = 1.9

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**Figure 9.** The electric field distribution at the avalanche breakdown at (**a**) X = 1.9 µm, Z = 6 µm; (**b**) X = 1.9 µm, Z = 4.9 µm. **Figure 9.** The electric field distribution at the avalanche breakdown at (**a**) X = 1.9 µm, Z = 6 µm; (**b**) X = 1.9 µm, Z = 4.9 µm.

thickness of 0.4 µm and length of 9 µm are selected as the best parameters.

(**a**)

*3.3. Influence of Unique Key Parameters on the Ron,sp, Peak gm, and BV of the BEA LDMOS* 

Drain on the *R*on,sp and *BV* for the BEA-LDMOS. In Figure 10a, the Extended Drain is equivalent to a low-resistance channel, so increasing the thickness of the Extended Drain is equivalent to increasing the volume of the low-resistance channel. Consequently, the specific conduction resistance decreases with increase in thickness of the Extended Drain. In Figure 10b, the specific conduction resistance decreases with increase in the length of the Extended Drain. The *BV* of the device generally increases first and then decreases with the increase in the thickness and length of the Extended Drain. This is because at the beginning, with the increase in the volume of the Extended Drain, the high electric field can be better introduced into the silicon dioxide layer. However, when the increase exceeds a certain range, it is equivalent to increasing the drift concentration, which will reduce the breakdown voltage. Considering the trade-off property between the *R*on,sp and *BV*, the

#### *3.3. Influence of Unique Key Parameters on the Ron,sp, Peak gm, and BV of the BEA LDMOS* Drain on the *R*on,sp and *BV* for the BEA-LDMOS. In Figure 10a, the Extended Drain is equiv-

**Figure 9.** The electric field distribution at the avalanche breakdown at (**a**) X = 1.9 µm, Z = 6 µm; (**b**)

Figure 10 shows the influence of the length (*L*) and thickness (*H*) of the Extended

*3.3. Influence of Unique Key Parameters on the Ron,sp, Peak gm, and BV of the BEA LDMOS* 

(**b**)

X = 1.9 µm, Z = 4.9 µm.

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 10 of 14

Figure 10 shows the influence of the length (*L*) and thickness (*H*) of the Extended Drain on the *R*on,sp and *BV* for the BEA-LDMOS. In Figure 10a, the Extended Drain is equivalent to a low-resistance channel, so increasing the thickness of the Extended Drain is equivalent to increasing the volume of the low-resistance channel. Consequently, the specific conduction resistance decreases with increase in thickness of the Extended Drain. In Figure 10b, the specific conduction resistance decreases with increase in the length of the Extended Drain. The *BV* of the device generally increases first and then decreases with the increase in the thickness and length of the Extended Drain. This is because at the beginning, with the increase in the volume of the Extended Drain, the high electric field can be better introduced into the silicon dioxide layer. However, when the increase exceeds a certain range, it is equivalent to increasing the drift concentration, which will reduce the breakdown voltage. Considering the trade-off property between the *R*on,sp and *BV*, the thickness of 0.4 µm and length of 9 µm are selected as the best parameters. alent to a low-resistance channel, so increasing the thickness of the Extended Drain is equivalent to increasing the volume of the low-resistance channel. Consequently, the specific conduction resistance decreases with increase in thickness of the Extended Drain. In Figure 10b, the specific conduction resistance decreases with increase in the length of the Extended Drain. The *BV* of the device generally increases first and then decreases with the increase in the thickness and length of the Extended Drain. This is because at the beginning, with the increase in the volume of the Extended Drain, the high electric field can be better introduced into the silicon dioxide layer. However, when the increase exceeds a certain range, it is equivalent to increasing the drift concentration, which will reduce the breakdown voltage. Considering the trade-off property between the *R*on,sp and *BV*, the thickness of 0.4 µm and length of 9 µm are selected as the best parameters.

**Figure 10.** Key parameters: (**a**) thickness (*H*) of the Extended Drain, (**b**) length (*L*) influence on the *R*on,sp, peak *g*m, and *BV* for the BEA-LDMOS. **Figure 10.** Key parameters: (**a**) thickness (*H*) of the Extended Drain, (**b**) length (*L*) influence on the *R*on,sp, peak *g*m, and *BV* for the BEA-LDMOS.

mance of the device can be improved by reducing the width of the gate.

The switching characteristics under inductive load are shown in Figure 11a, and a

slower turn-on speed *T*ON and turn-off speed *T*OFF of the BEA-LDMOS are observed com-

LDMOS not only has a FIN structure, but also has an extended superjunction trench gate, so the gate area is much larger than those of the other three devices. Figure 11b shows the effect of different widths of the gate on the switching speed of the device. It can be seen that the wider the gate, the lower the switching speed of the device. The switching perfor-

(**a**)

*3.4. Dynamic Characteristics* 

#### *3.4. Dynamic Characteristics* slower turn-on speed *T*ON and turn-off speed *T*OFF of the BEA-LDMOS are observed com-

*3.4. Dynamic Characteristics* 

*R*on,sp, peak *g*m, and *BV* for the BEA-LDMOS.

The switching characteristics under inductive load are shown in Figure 11a, and a slower turn-on speed *T*ON and turn-off speed *T*OFF of the BEA-LDMOS are observed compared to the CON-LDMOS, AEG-LDMOS, and FIN-LDMOS. Because the gate capacity is proportional to the gate area, the larger the area, the larger the gate capacity. The BEA-LDMOS not only has a FIN structure, but also has an extended superjunction trench gate, so the gate area is much larger than those of the other three devices. Figure 11b shows the effect of different widths of the gate on the switching speed of the device. It can be seen that the wider the gate, the lower the switching speed of the device. The switching performance of the device can be improved by reducing the width of the gate. pared to the CON-LDMOS, AEG-LDMOS, and FIN-LDMOS. Because the gate capacity is proportional to the gate area, the larger the area, the larger the gate capacity. The BEA-LDMOS not only has a FIN structure, but also has an extended superjunction trench gate, so the gate area is much larger than those of the other three devices. Figure 11b shows the effect of different widths of the gate on the switching speed of the device. It can be seen that the wider the gate, the lower the switching speed of the device. The switching performance of the device can be improved by reducing the width of the gate.

(**b**)

**Figure 10.** Key parameters: (**a**) thickness (*H*) of the Extended Drain, (**b**) length (*L*) influence on the

The switching characteristics under inductive load are shown in Figure 11a, and a

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 11 of 14

**Figure 11.** (a)Capacitance switching characteristics of the four devices. Turn-on and turn-off curves under inductive load.(b) Switching characteristic curves at different gate widths. **Figure 11.** (**a**) Capacitance switching characteristics of the four devices. Turn-on and turn-off curves under inductive load.(**b**) Switching characteristic curves at different gate widths.

Figure 12 demonstrates the trade-off characteristic and FOM for the BEA LDMOS,

single RESURF, double RESURF, and triple RESURF in Ref. [9], which are the classic three structures. It can be seen from the figure that the *R*on,sp of the device is still very low at a

largest and achieves the best trade-off property. The main performance indexes of the four

**Figure 12.** The trade-off relationship between *R*on,sp and *BV* for the BEA-LDMOSs and the RESURF.

**Symbol FIN-LDMOS CON-LDMOS AEG-LDMOS BEA-LDMOS** 

*BV* (V) 323 329 297 314 *Ron,sp* (mΩ∙cm−2) 11.78 14.54 4.41 1.84

*FOM* 8.86 7.42 20.01 53.43 *Ndrift* (cm−3) 2.5 × 1015 2.5 × 1015 2.5 × 1015 2.5 × 1015

The mechanism and electric characteristics of the BEA-LDMOS are proposed and researched. The *V*GS of the BEA is extended through the P-region, and the full buck

The *FOM* is calculated by the *FOM* = *BV*2/*R*on,sp.

**4. Conclusions** 

**Table 2.** Trade-off Property between the *R*on,sp and *BV*.

devices compared in this paper are shown in Table 2.

*3.5. The Trade-Off Property between the Ron,sp and BV* 

#### *3.5. The Trade-Off Property between the Ron,sp and BV* single RESURF, double RESURF, and triple RESURF in Ref. [9], which are the classic three

Figure 12 demonstrates the trade-off characteristic and FOM for the BEA LDMOS, single RESURF, double RESURF, and triple RESURF in Ref. [9], which are the classic three structures. It can be seen from the figure that the *R*on,sp of the device is still very low at a larger *BV*. According to *FOM* = *BV*2/*R*on,sp, it can be concluded that the *FOM* of BEA is largest and achieves the best trade-off property. The main performance indexes of the four devices compared in this paper are shown in Table 2. structures. It can be seen from the figure that the *R*on,sp of the device is still very low at a larger *BV*. According to *FOM* = *BV*2/*R*on,sp, it can be concluded that the *FOM* of BEA is largest and achieves the best trade-off property. The main performance indexes of the four devices compared in this paper are shown in Table 2.

under inductive load.(b) Switching characteristic curves at different gate widths.

**Figure 11.** (a)Capacitance switching characteristics of the four devices. Turn-on and turn-off curves

Figure 12 demonstrates the trade-off characteristic and FOM for the BEA LDMOS,

(**b**)

*3.5. The Trade-Off Property between the Ron,sp and BV* 

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 12 of 14

**Figure 12.** The trade-off relationship between *R*on,sp and *BV* for the BEA-LDMOSs and the RESURF. The *FOM* is calculated by the *FOM* = *BV*2/*R*on,sp. **Figure 12.** The trade-off relationship between *R*on,sp and *BV* for the BEA-LDMOSs and the RESURF. The *FOM* is calculated by the *FOM* = *BV*2/*R*on,sp.

**Table 2.** Trade-off Property between the *R*on,sp and *BV*.


#### *FOM* 8.86 7.42 20.01 53.43 **4. Conclusions**

*Ndrift* (cm−3) 2.5 × 1015 2.5 × 1015 2.5 × 1015 2.5 × 1015 **4. Conclusions**  The mechanism and electric characteristics of the BEA-LDMOS are proposed and researched. The *V*GS of the BEA is extended through the P-region, and the full buck The mechanism and electric characteristics of the BEA-LDMOS are proposed and researched. The *V*GS of the BEA is extended through the P-region, and the full buck accumulation effect is formed at the inside of the N-drift, where a 3-D low-resistance channel at the N-drift is achieved. In addition, the Extended Drain is also equivalent to a low-resistance channel. Thus, the *R*on,sp is significantly decreased. Simultaneously, the superior *BV* is guaranteed by the charge compensation and assisted depletion effect between the P-type doping and N-drift. Consequently, a *FOM* of 53.49 MW/cm<sup>2</sup> is achieved, which breaks through the silicon limit of the RESURF.

**Author Contributions:** Conceptualization, Z.D. and W.C.; methodology, W.C.; software, Z.D.; validation, Z.D., W.C. and H.Z.; formal analysis, Z.D.; investigation, Z.D. and Z.W.; resources, Z.D. and W.C.; data curation, Z.D.; writing—original draft preparation, Z.D.; writing—review and editing, W.C. and Z.W.; visualization, Z.D.; supervision, H.Z.; project administration, Z.H.; funding acquisition, Z.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Data is unavailable due to privacy or ethical restrictions.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


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