A Comparative Analysis between Standard and mm-Wave Optimized BEOL in a Nanoscale CMOS Technology

: This paper presents an extensive comparison of two 28-nm CMOS technologies, i


Introduction
In recent years, CMOS technologies have reached active device performance comparable to that provided by bipolar processes up to the W-band. Moreover, thanks to higher transistor density for analog/digital sections and lower costs for mass-market production, they are an advantageous alternative for the design of a mm-wave system-on-a-chip (SoC) for automotive radar and 5G communications [1]. On the other hand, the improvements in the transition frequency, f T , and maximum oscillation frequency, f MAX , for both MOS and bipolar transistors have been so remarkable that high-frequency IC performance is now mainly limited by the passive component losses (i.e., losses in inductors, transformers, metal interconnections, etc.) [2,3]. In this scenario, a key role is played by the back-end-of-line (BEOL) of the integration process. Traditionally, bipolar and BiCMOS technologies benefit from optimized BEOL for RF/mm-wave application [4][5][6][7] with at least two thick copper top metals, along with thick intermetal oxide layers to reduce distributed ohmic losses and parasitic capacitance, respectively. An optimized BEOL is not usually available in standard CMOS technologies, leading to lower quality passive devices. mm-wave-optimized BiCMOS process and a 28-nm CMOS technology with standard BEOL [4,9]. The dilemma is still about the impact of the BEOL on the performance of mm-wave ICs and whether the technological investments can be justified by an effective performance improvement in actual applications. Although several works have faced this issue by comparing stand-alone passive components fabricated in different BEOLs, no analysis on complete mm-wave macroblocks has been published to the authors' knowledge.  [4] and (b) 28 nm CMOS technology with standard BEOL [9].
The aim of this paper is to make an extensive comparison between two 28-nm CMOS technologies, i.e., one with a standard BEOL [9] and one with an improved BEOL (i.e., thick metals and oxides), and the ones available in BiCMOS technologies [4][5][6]. The proposed comparison uses as a demonstrative vehicle a 77-GHz down-converter for radar applications [10], by emphasizing the impact of passive component losses on its overall performance. The choice of this mm-wave macroblock for the proposed comparison is motivated by the stringent and contrasting specifications imposed by radar sensor applications [11,12], in the performance parameters such as noise figure (NF), conversion gain, linearity and power consumption. Indeed, they will be used as a multi-criteria benchmark to highlight the pros and cons of standard and mm-wave oriented CMOS BEOL.
The paper is organized as follows. The adopted testbench for the BEOL comparison is discussed in Section 2. Section 3 deals with the performance comparison of both stand-alone passive components and the overall down-converter, whereas main conclusions are drawn in Section 4.

Testbench for the BEOL Comparison: Integrated Transformers and 77 GHz Down-Converter
The proposed BEOL comparison was carried out at two different levels, i.e., at both component and circuit level. Initially, the performance of stand-alone integrated transformers designed with different BEOLs is compared, then the analysis is completed by using a 77-GHz down-converter for radar applications, as a macro-circuit testbench. This approach is motivated by the considerations Figure 1. Back-end-of-line (BEOL) comparison between (a) mm-wave-optimized BiCMOS technology [4] and (b) 28 nm CMOS technology with standard BEOL [9].
The aim of this paper is to make an extensive comparison between two 28-nm CMOS technologies, i.e., one with a standard BEOL [9] and one with an improved BEOL (i.e., thick metals and oxides), and the ones available in BiCMOS technologies [4][5][6]. The proposed comparison uses as a demonstrative vehicle a 77-GHz down-converter for radar applications [10], by emphasizing the impact of passive component losses on its overall performance. The choice of this mm-wave macroblock for the proposed comparison is motivated by the stringent and contrasting specifications imposed by radar sensor applications [11,12], in the performance parameters such as noise figure (NF), conversion gain, linearity and power consumption. Indeed, they will be used as a multi-criteria benchmark to highlight the pros and cons of standard and mm-wave oriented CMOS BEOL.
The paper is organized as follows. The adopted testbench for the BEOL comparison is discussed in Section 2. Section 3 deals with the performance comparison of both stand-alone passive components and the overall down-converter, whereas main conclusions are drawn in Section 4.

Testbench for the BEOL Comparison: Integrated Transformers and 77 GHz Down-Converter
The proposed BEOL comparison was carried out at two different levels, i.e., at both component and circuit level. Initially, the performance of stand-alone integrated transformers designed with different BEOLs is compared, then the analysis is completed by using a 77-GHz down-converter for radar applications, as a macro-circuit testbench. This approach is motivated by the considerations Electronics 2020, 9, 2124 3 of 15 discussed below. Integrated transformers are very important passive components, especially at mm-wave frequencies, since they are extensively adopted to implement several crucial functions, such as single-ended-to-differential and differential-to-single-ended conversions along with electrostatic discharge (ESD) protection at input/output antenna interfaces [13][14][15][16][17], resonant load in RF/mm-wave amplification stages [18,19], LC tank in oscillators [20][21][22], power combining [23,24], etc. Moreover, differently from simple spiral inductors that can highly benefit from top thick metal along with multi-layer structures and maximum oxide thickness to outdistance from the substrate, integrated transformer configurations provide more complete information on the BEOL, since they also include the effects of lower metals and intermetal oxide thickness. Typical performance parameters for the comparison of integrated transformers are the Q-factors of the primary and secondary windings, Q P and Q S , and the magnetic coupling coefficient, k. Q-factors are directly related to the energy losses occurring in the metal layers that form the transformer coils, as well as in the conductive layers below. They are usually referred to as series and parallel losses, respectively [25,26]. The magnetic coupling coefficient measures how much the primary and secondary windings are magnetically coupled to each other and it is mainly dependent on the transformer topology, i.e., interleaved, stacked or mixed topologies with increasing values of k [25][26][27], as depicted in Figure 2.
Electronics 2020, 9, x FOR PEER REVIEW  3 of 16 along with multi-layer structures and maximum oxide thickness to outdistance from the substrate, integrated transformer configurations provide more complete information on the BEOL, since they also include the effects of lower metals and intermetal oxide thickness. Typical performance parameters for the comparison of integrated transformers are the Q-factors of the primary and secondary windings, QP and QS, and the magnetic coupling coefficient, k. Q-factors are directly related to the energy losses occurring in the metal layers that form the transformer coils, as well as in the conductive layers below. They are usually referred to as series and parallel losses, respectively [25,26]. The magnetic coupling coefficient measures how much the primary and secondary windings are magnetically coupled to each other and it is mainly dependent on the transformer topology, i.e., interleaved, stacked or mixed topologies with increasing values of k [25][26][27], as depicted in Figure 2. However, when the transformer is exploited in signal conversion/power combining and resonant load, the insertion loss, IL, and the transformer characteristic resistance, TCR, [28] are the more suitable parameters, respectively. Specifically, the IL provides a significant performance characterization when the transformer is operated under a 50-Ω termination at both the primary and secondary windings. Typically, this happens when the transformer is used at the input interface between the antenna and the RF receiver (RX) front-end (i.e., the RF down-converter). In this situation, the IL directly affects both the gain and NF of the RX front-end. On the other hand, the TCR is the generalization of the well-known ωQL product for transformer-loaded circuits. It represents the equivalent impedance offered by the transformer in the resonance condition and is the reference performance parameter when the gain of a transformer-loaded stage has to be maximized. For the sake of completeness, the expressions for IL and TCR are reported below. However, when the transformer is exploited in signal conversion/power combining and resonant load, the insertion loss, IL, and the transformer characteristic resistance, TCR, [28] are the more suitable parameters, respectively. Specifically, the IL provides a significant performance characterization when the transformer is operated under a 50-Ω termination at both the primary and secondary windings. Typically, this happens when the transformer is used at the input interface between the antenna and the RF receiver (RX) front-end (i.e., the RF down-converter). In this situation, the IL directly affects both the gain and NF of the RX front-end. On the other hand, the TCR is the generalization of the well-known ωQL product for transformer-loaded circuits. It represents the equivalent impedance offered by the transformer in the resonance condition and is the reference performance parameter when the gain of a transformer-loaded stage has to be maximized. For the sake of completeness, the expressions for IL and TCR are reported below.
Electronics 2020, 9, 2124 4 of 15 where L P , Q P , Q S and k are the primary winding inductance, the primary winding Q-factor, the secondary winding Q-factor and the magnetic coupling coefficient, respectively. As far as the 77-GHz down-converter is concerned, the adopted testbench allows a fair comparison between BEOLs since both stacked and interleaved transformer configurations are used, thus providing an overall combined effect at the macroblock level.

BEOLs and Integrated Transformers
The reference CMOS technology is a 28-nm fully-depleted silicon-on-insulator (FD-SOI) CMOS process by STMicroelectronics [9,29,30]. It provides a standard BEOL with eight metal layers with two thin Cu metals (i.e., <1 µm) plus an Al layer at the top of the stack, as shown in Figure 1b. The other technology under comparison differs only for the BEOL, which is oriented to mm-wave applications, as is the one available in SiGe HBT BiCMOS technologies [4]. Specifically, the last two metals are much thicker (around 2.5 µm). Moreover, such a BEOL benefits from a significantly larger distance of the top metal from the silicon substrate compared with the standard one (i.e., about 10 µm against 4 µm for the top Al metal layer). For both technologies, the last three metal layers from the top are referred to as LB, IB, and IA.
The last two copper metals, in addition to the aluminum one, were used to design integrated transformers for the W-band down-converter with the aim of minimizing the parasitic capacitances towards the substrate and winding resistive losses. In both technologies, transformers adopt octagonal single-turn stacked and interleaved configurations. The primary and secondary windings of the stacked transformers are built in LB/IB and IA respectively, whereas in the interleaved configuration both primary and secondary coils are built in LB/IB, as shown in Figure 3. Due to fabrication issues, the top Al layer, LB, exhibits a hole in transformer coils, as is visible in Figure 3. It is worth mentioning that the adoption of highly involved inter-stacked configurations to maximize the magnetic coupling is mandatory only in presence of very thick intermetal oxides [18,31]. No patterned ground shield (PGS) was included since it would have a detrimental effect on the Q-factor at W-band frequencies. Indeed, the ohmic losses induced in the shield itself are so high to frustrate the reduction in substrate losses, as described in [32]. Furthermore, avoiding the PGS prevents detrimental resonating phenomena of the shielding structure, mainly due to the undesired inductive path towards the ground in circuit applications. Finally, to avoid additional losses, conductive dummy fillers are not present below the transformer, but only at a safe distance, within a transition region around the spirals, which is sufficiently high to guarantee homogeneity and planarity between metal levels. According to experimental data from the technology provider, such arrangement does not degrade the transformer performance.

BEOLs and Integrated Transformers
The reference CMOS technology is a 28-nm fully-depleted silicon-on-insulator (FD-SOI) CMOS process by STMicroelectronics [9,29,30]. It provides a standard BEOL with eight metal layers with two thin Cu metals (i.e., <1 μm) plus an Al layer at the top of the stack, as shown in Figure 1b. The other technology under comparison differs only for the BEOL, which is oriented to mm-wave applications, as is the one available in SiGe HBT BiCMOS technologies [4]. Specifically, the last two metals are much thicker (around 2.5 μm). Moreover, such a BEOL benefits from a significantly larger distance of the top metal from the silicon substrate compared with the standard one (i.e., about 10 µ m against 4 µ m for the top Al metal layer). For both technologies, the last three metal layers from the top are referred to as LB, IB, and IA.
The last two copper metals, in addition to the aluminum one, were used to design integrated transformers for the W-band down-converter with the aim of minimizing the parasitic capacitances towards the substrate and winding resistive losses. In both technologies, transformers adopt octagonal single-turn stacked and interleaved configurations. The primary and secondary windings of the stacked transformers are built in LB/IB and IA respectively, whereas in the interleaved configuration both primary and secondary coils are built in LB/IB, as shown in Figure 3. Due to fabrication issues, the top Al layer, LB, exhibits a hole in transformer coils, as is visible in Figure 3. It is worth mentioning that the adoption of highly involved inter-stacked configurations to maximize the magnetic coupling is mandatory only in presence of very thick intermetal oxides [18,31]. No patterned ground shield (PGS) was included since it would have a detrimental effect on the Q-factor at W-band frequencies. Indeed, the ohmic losses induced in the shield itself are so high to frustrate the reduction in substrate losses, as described in [32]. Furthermore, avoiding the PGS prevents detrimental resonating phenomena of the shielding structure, mainly due to the undesired inductive path towards the ground in circuit applications. Finally, to avoid additional losses, conductive dummy fillers are not present below the transformer, but only at a safe distance, within a transition region around the spirals, which is sufficiently high to guarantee homogeneity and planarity between metal levels. According to experimental data from the technology provider, such arrangement does not degrade the transformer performance. As far as geometrical sizing is concerned, transformer windings were designed to achieve a self-resonance frequency (SRF) of about twice the operating frequency (i.e., 77 GHz). This condition is necessary to guarantee enough room for correct transformer operation in actual applications despite intrinsic and extrinsic parasitic capacitances of active components and interconnections, respectively.

77 GHz Down-Converter
The adopted circuit testbench for the BEOL comparison is a 77-GHz direct-conversion down-converter for frequency modulated continuous wave (FMCW) long-range/medium-range (LR/MR) radar applications [33]. This is one of the most critical blocks of a mm-wave radar sensor As far as geometrical sizing is concerned, transformer windings were designed to achieve a self-resonance frequency (SRF) of about twice the operating frequency (i.e., 77 GHz). This condition is necessary to guarantee enough room for correct transformer operation in actual applications despite intrinsic and extrinsic parasitic capacitances of active components and interconnections, respectively.

77 GHz Down-Converter
The adopted circuit testbench for the BEOL comparison is a 77-GHz direct-conversion down-converter for frequency modulated continuous wave (FMCW) long-range/medium-range (LR/MR) radar applications [33]. This is one of the most critical blocks of a mm-wave radar sensor since it determines the receiver noise/linearity performance, while significantly contributing to its gain. Specifically, in a LR/MR scenario the distance between the sensor and the target, R, spans from about 250 m to 2 m and thus the power range of the corresponding echo signal is very wide (i.e., −110 to −30 dBm with typical values of transmitted power, RX/TX antenna gains and radar cross section). Consequently, the radar receiver and hence the mm-wave down-converter, have to achieve a very low NF along with a wide dynamic range (i.e., high-linearity performance). The implementation of a W-band down-converter in a nanoscale CMOS technology also has to comply with a supply voltage as low as 1 V, which further exacerbates the linearity issue. Finally, overall performance must be guaranteed at low current consumption since a radar sensor typically adopts a multi receiver architecture [11,12].
A simplified block-diagram of the 77-GHz down-converter used for the BEOL comparison is shown in Figure 4. It exploits a fully differential mixer-first approach consisting of an input transformer, T 1 , a voltage-to-current (V-I) converter, a passive mixer quad and a transresistance feedback amplifier [10]. Transformer T 1 performs a single-ended-to-differential conversion, ESD protection and 50-Ω input matching. The V-I converter uses transformer T 2 as its load and achieves a transconductance gain. It drives the mixer, whose output signal current is delivered to the transresistance amplifier. The down-converter design requires careful optimization of both T 1 and T 2 , whose performances are highly dependent on the available BEOL. Specifically, transformer T 1 mainly affects the down-converter NF and therefore its IL must be reduced as much as possible. On the other hand, transformer T 2 can impact the conversion gain if the resonant load impedance of the V-I converter at the operating frequency is not high enough with respect to the mixer input impedance. Indeed, the higher its TCR, the more efficiently the RF current is delivered to the passive mixer, thus preserving the conversion gain.
Electronics 2020, 9, x FOR PEER REVIEW 5 of 16 since it determines the receiver noise/linearity performance, while significantly contributing to its gain. Specifically, in a LR/MR scenario the distance between the sensor and the target, R, spans from about 250 m to 2 m and thus the power range of the corresponding echo signal is very wide (i.e., −110 to −30 dBm with typical values of transmitted power, RX/TX antenna gains and radar cross section). Consequently, the radar receiver and hence the mm-wave down-converter, have to achieve a very low NF along with a wide dynamic range (i.e., high-linearity performance). The implementation of a W-band down-converter in a nanoscale CMOS technology also has to comply with a supply voltage as low as 1 V, which further exacerbates the linearity issue. Finally, overall performance must be guaranteed at low current consumption since a radar sensor typically adopts a multi receiver architecture [11,12]. A simplified block-diagram of the 77-GHz down-converter used for the BEOL comparison is shown in Figure 4. It exploits a fully differential mixer-first approach consisting of an input transformer, T1, a voltage-to-current (V-I) converter, a passive mixer quad and a transresistance feedback amplifier [10]. Transformer T1 performs a single-ended-to-differential conversion, ESD protection and 50-Ω input matching. The V-I converter uses transformer T2 as its load and achieves a transconductance gain. It drives the mixer, whose output signal current is delivered to the transresistance amplifier. The down-converter design requires careful optimization of both T1 and T2, whose performances are highly dependent on the available BEOL. Specifically, transformer T1 mainly affects the down-converter NF and therefore its IL must be reduced as much as possible. On the other hand, transformer T2 can impact the conversion gain if the resonant load impedance of the V-I converter at the operating frequency is not high enough with respect to the mixer input impedance. Indeed, the higher its TCR, the more efficiently the RF current is delivered to the passive mixer, thus preserving the conversion gain.
Transformers T1 and T2 exploit proper configurations (i.e., stacked and interleaved) as shown in Figure 3, to minimize the IL and maximize the TCR, respectively.

Experimental Validation for the BEOL Analysis
Down-converter transformers, T1 and T2, were designed in both standard-and mm-waveoriented BEOL, as previously discussed. To this end, extensive 2D electromagnetic (EM) simulations in Advanced Design System (ADS) Momentum by Keysight Technologies were used [34,35], which represent a consolidated design flow for RF and mm-wave ICs, as demonstrated by several published papers in the K-and W-bands [14][15][16][17][18]21]. To obtain highly reliable results at mm-wave frequencies, the EM simulations required an accurate set-up. The latter was defined and experimentally validated by taking advantage of on-wafer S-parameter measurements for a reference stacked transformer, TR, fabricated in the 28-nm FD-SOI CMOS reference technology [9,30]. Figure 5 displays the micrograph of the ground-signal-ground (GSG) structure adopted for on-wafer measurement of TR. It consists of two identical series-connected transformers TR, which are put in resonance at 77 GHz by means of an integrated capacitance, CR, of about 70 fF. This arrangement was exploited to properly draw a meaningful IL measurement of TR, since in actual applications it is operated in a resonance condition. As demonstrated in Appendix A, the IL of the single transformer TR can easily be from the IL of the test structure after de-embedding of the GSG pad loss. The comparison between the estimated and Transformers T 1 and T 2 exploit proper configurations (i.e., stacked and interleaved) as shown in Figure 3, to minimize the IL and maximize the TCR, respectively.

Experimental Validation for the BEOL Analysis
Down-converter transformers, T 1 and T 2 , were designed in both standard-and mm-wave-oriented BEOL, as previously discussed. To this end, extensive 2D electromagnetic (EM) simulations in Advanced Design System (ADS) Momentum by Keysight Technologies were used [34,35], which represent a consolidated design flow for RF and mm-wave ICs, as demonstrated by several published papers in the Kand W-bands [14][15][16][17][18]21]. To obtain highly reliable results at mm-wave frequencies, the EM simulations required an accurate set-up. The latter was defined and experimentally validated by taking advantage of on-wafer S-parameter measurements for a reference stacked transformer, T R , fabricated in the 28-nm FD-SOI CMOS reference technology [9,30]. Figure 5 displays the micrograph of the ground-signal-ground (GSG) structure adopted for on-wafer measurement of T R . It consists of two identical series-connected transformers T R , which are put in resonance at 77 GHz by means of an integrated capacitance, C R, of about 70 fF. This arrangement was exploited to properly draw a meaningful IL measurement of T R , since in actual applications it is operated in a resonance condition. As demonstrated in Appendix A, the IL of the single transformer T R can easily be from the IL of the test structure after de-embedding of the GSG pad loss. The comparison between the estimated and measured IL of transformer T R is reported in Figure 6. An excellent agreement can be observed with an error of only 0.3 dB at 77 GHz, which is a very accurate result for such a small component. For the sake of completeness, the measured RL at 77 GHz is about 24 dB, thus confirming the soundness of the adopted extraction method for the IL (see Appendix A). The experimental results for transformer T R were properly used for the EM simulation set-up before designing down-converter transformers T 1 and T 2 for the BEOL comparison.
Electronics 2020, 9, x FOR PEER REVIEW 6 of 16 measured IL of transformer TR is reported in Figure 6. An excellent agreement can be observed with an error of only 0.3 dB at 77 GHz, which is a very accurate result for such a small component. For the sake of completeness, the measured RL at 77 GHz is about 24 dB, thus confirming the soundness of the adopted extraction method for the IL (see Appendix A). The experimental results for transformer TR were properly used for the EM simulation set-up before designing down-converter transformers T1 and T2 for the BEOL comparison.

BEOL Comparison
The first step of the BEOL comparison was the geometrical sizing of the down-converter transformers, T1 and T2, with the aim of optimizing device performance parameters, while  Electronics 2020, 9, x FOR PEER REVIEW 6 of 16 measured IL of transformer TR is reported in Figure 6. An excellent agreement can be observed with an error of only 0.3 dB at 77 GHz, which is a very accurate result for such a small component. For the sake of completeness, the measured RL at 77 GHz is about 24 dB, thus confirming the soundness of the adopted extraction method for the IL (see Appendix A). The experimental results for transformer TR were properly used for the EM simulation set-up before designing down-converter transformers T1 and T2 for the BEOL comparison.

BEOL Comparison
The first step of the BEOL comparison was the geometrical sizing of the down-converter transformers, T1 and T2, with the aim of optimizing device performance parameters, while

BEOL Comparison
The first step of the BEOL comparison was the geometrical sizing of the down-converter transformers, T 1 and T 2 , with the aim of optimizing device performance parameters, while guaranteeing the same SRF (i.e., at least two times the operating frequency). Indeed, the simple use of the same transformer geometry in two BEOLs could be not suitable for a fair comparative performance evaluation since the two transformers would have different SRF and hence different levels of optimization. After the stand-alone transformer evaluation in both BEOLs, the comparison was carried out at macroblock level by considering the improvements in terms of NF and conversion gain. Table 1 reports the geometrical parameters of stacked transformer T 1 , in standard and mm-wave-optimized CMOS BEOL. Main performance parameters, such as winding inductances, Q-factors, magnetic coupling coefficient, k, insertion loss, IL, and transformer characteristic resistance, TCR, are compared at the operating frequency of the down-converter (i.e., 77 GHz). For the sake of completeness, the BEOL comparison in terms of Q-factors, k and TCR was also carried out throughout the useful frequency range in Figures 7 and 8. Several considerations arise from these results.  Table 1 reports the geometrical parameters of stacked transformer T1, in standard and mm-waveoptimized CMOS BEOL. Main performance parameters, such as winding inductances, Q-factors, magnetic coupling coefficient, k, insertion loss, IL, and transformer characteristic resistance, TCR, are compared at the operating frequency of the down-converter (i.e., 77 GHz). For the sake of completeness, the BEOL comparison in terms of Q-factors, k and TCR was also carried out throughout the useful frequency range in Figures 7 and 8. Several considerations arise from these results.    As already stated, the transformer comparison was carried out at the same SRF, which was set equal to 170 GHz. In the mm-wave-optimized BEOL, the stacked geometry benefits from a larger inner diameter and hence higher values of primary and secondary coil inductances (of about 42 and 38% at 77 GHz, respectively) thanks to thicker oxide layers and consequent lower parasitic capacitances. Moreover, thanks to thicker top Cu metal layers (2.5 µm instead of 1 µm) the Q-factor of both primary and secondary coils is improved at the cost of a small reduction of k due to the thicker intermetal oxide between windings. In particular, the secondary coil highly benefits from the thick IA Cu layer (see Figure 3a) since its Q-factor is improved in a wide operative frequency and achieves an increment of about 23% at 77 GHz, as shown in Figure 7b. The improvements of the IL and the TCR at 77 GHz are of 0.2 dB and 56%, respectively, as a direct consequence of higher inductance and Q-factor values and an almost constant magnetic coupling, as shown in Figure 8a. The TCR for the optimized BEOL at 77 GHz in Table 1 is comparable with the ones achieved by interleaved configurations in both BEOLs (see next subsection). Table 2 reports geometrical and performance parameters of interleaved transformer T 2 designed in standard and mm-wave-optimized CMOS BEOL, whereas Figures 9 and 10 show the BEOL comparison in terms of Q-factors, k and TCR as a function of frequency. Looking at Table 2, it can be noted that, despite the mm-optimized BEOL having thicker oxide layers between the transformer windings (i.e., AL + IB) and the substrate, identical geometrical dimensions (i.e., w and d IN ) lead to the same SRF (i.e., 175 GHz). On the other hand, the winding inductance values are slightly lower, i.e., about 8 and 9% for primary and secondary coils, respectively, due to a higher value of the metal ratio thickness to width (t/w) according to the well-known effect analyzed in [36]. Moreover, there is a negligible increment in both primary and secondary winding Q-factors of about 2%, as is also visible in Figure 9. Consequently, the TCR as defined in Equation (2) results are about the same, as shown in Figure 10b, while the magnetic coupling coefficient, k, is slightly improved in the mm-wave-optimized BEOL transformer. These results seem highly counterintuitive since significant improvements in terms of Q-factor and TCR would be expected in the best BEOL thanks to thicker metals and oxides. However, the issue should be seen under the correct perspective by starting from the above mentioned SRF invariancy in the interleaved configuration.   Let us we consider the well-known equation for a parallel plate capacitor, commonly adopted to evaluate the parasitic capacitances in integrated components:  Table 2: (a) primary coil Q-factor, Q P ; (b) secondary coil Q-factor, Q S .  Let us we consider the well-known equation for a parallel plate capacitor, commonly adopted to evaluate the parasitic capacitances in integrated components: Let us we consider the well-known equation for a parallel plate capacitor, commonly adopted to evaluate the parasitic capacitances in integrated components:

Interleaved Transformer
where ε, W, L and D are the dielectric permittivity, the width, the length and the distance from the silicon substrate, respectively. The equation can be usefully expressed as a function of the capacitor aspect ratio, b = D/W. According to Equation (5), an increased distance of IB from the substrate (from about 3 to 8 µm) would produce a reduction in the transformer capacitance of about 2.5 times with a consequent SRF increase of about 60%. On the contrary, an SRF invariancy was detected by EM analysis, as shown in Table 2. This can be mainly ascribed to the very small size of the mm-wave transformers and therefore to the non-negligible effect of the fringing electric field. Indeed, the capacitance of a parallel plate capacitor in Equation (5) was formulated assuming that the separation between the electrode plates is very narrow and then the electric charge density on the plates is uniform, which allows the fringing effects to be neglected. Actually, a crucial role is played by the aspect ratio, b. Equation (5) works quite well only for b < 0.03 with an underestimation of about 10%, whereas for b ≈ 0.5 it gives errors of about 100%, as depicted in Figure 11 [37,38]. Introducing proper corrections to Equation (5), transformer parasitic capacitances can be better evaluated for the interleaved structure previously analyzed, finding out that the thicker oxide in the mm-wave-optimized BEOL produces a reduction of the capacitance toward the substrate and a contemporary increment of the fringing capacitance of about 75%, which explains the observed SRF invariancy. Therefore, the above analyzed phenomenon tends to frustrate the benefits provided by the optimized BEOL for interleaved transformers. Moreover, this simple analysis can better explain the results in Table 1 and Figures 7 and 8 related to stacked transformers, which highly benefit from the improved BEOL thanks to the lack of significant fringing capacitive effects (i.e., single-turn configuration is used). about 3 to 8 μm) would produce a reduction in the transformer capacitance of about 2.5 times with a consequent SRF increase of about 60%. On the contrary, an SRF invariancy was detected by EM analysis, as shown in Table 2. This can be mainly ascribed to the very small size of the mm-wave transformers and therefore to the non-negligible effect of the fringing electric field. Indeed, the capacitance of a parallel plate capacitor in Equation (5) was formulated assuming that the separation between the electrode plates is very narrow and then the electric charge density on the plates is uniform, which allows the fringing effects to be neglected. Actually, a crucial role is played by the aspect ratio, b. Equation (5) works quite well only for b < 0.03 with an underestimation of about 10%, whereas for b ≈ 0.5 it gives errors of about 100%, as depicted in Figure 11 [37,38]. Introducing proper corrections to Equation (5), transformer parasitic capacitances can be better evaluated for the interleaved structure previously analyzed, finding out that the thicker oxide in the mm-waveoptimized BEOL produces a reduction of the capacitance toward the substrate and a contemporary increment of the fringing capacitance of about 75%, which explains the observed SRF invariancy. Therefore, the above analyzed phenomenon tends to frustrate the benefits provided by the optimized BEOL for interleaved transformers. Moreover, this simple analysis can better explain the results in Table 1 and Figures 7 and 8 related to stacked transformers, which highly benefit from the improved BEOL thanks to the lack of significant fringing capacitive effects (i.e., single-turn configuration is used). It is worth mentioning that all the above considerations are limited to the analyzed transformer geometries, which are typically adopted at mm-wave frequencies. On the other hand, an improved BEOL could have a very important impact for inductive components operated at lower frequencies where higher inductances and hence larger coils are used, since the percentage effect of the fringing capacitances is greatly reduced.  Figure 11. Underestimation of Equation (5) as a function of the aspect ratio, b, based on data in [37].
It is worth mentioning that all the above considerations are limited to the analyzed transformer geometries, which are typically adopted at mm-wave frequencies. On the other hand, an improved BEOL could have a very important impact for inductive components operated at lower frequencies where higher inductances and hence larger coils are used, since the percentage effect of the fringing capacitances is greatly reduced.

77 GHz Down-Converter
Based on transformer performance comparison, a macro-circuit analysis was carried out by exploiting the 77 GHz down-converter architecture for radar applications in Figure 4 [10,30]. Specifically, the BEOL benefits were evaluated in terms of the main performance parameters, i.e., the NF and the conversion gain. As mentioned before, transformers T 1 and T 2 exploit stacked and interleaved configurations, respectively, with the aim of minimizing the IL and maximizing the TCR, which directly affect the NF and conversion gain, respectively. As far as the IL is concerned, the stacked transformer represents the best solution for the implementation of the input balun in both technologies with values of about 0.6 dB at 77 GHz. Concerning the TCR the standard and mm-wave-optimized BEOL provide the highest values with interleaved and stacked configurations, respectively. Nevertheless, to make a meaningful comparison in terms of down-converter performance, the interleaved structure was chosen for the implementation of the inter-stage transformer. This choice is also supported by the very close TCR values (about 3 kΩ) achieved by both standard BEOL interleaved and mm-wave-optimized BEOL stacked transformers (see Tables 1 and 2).
The short-circuit transconductance conversion gain and the NF of the 77 GHz down-converter are shown in Figure 12 for both technologies. As expected, the two BEOLs provide similar NF values (around 9 dB at 1 MHz), whereas the mm-optimized process allows achievement of a slightly greater conversion gain at 77 GHz (40.9 mS vs. 40.3 mS). Table 3 compares the main performance of the down-converter in the two BEOLs. From these results, it appears that the advantages offered by adopting an optimized BEOL in terms of down-converter performance are almost irrelevant at mm-wave frequencies, as already anticipated by the stand-alone transformer comparison.
exploiting the 77 GHz down-converter architecture for radar applications in Figure 4 [10,30]. Specifically, the BEOL benefits were evaluated in terms of the main performance parameters, i.e., the NF and the conversion gain. As mentioned before, transformers T1 and T2 exploit stacked and interleaved configurations, respectively, with the aim of minimizing the IL and maximizing the TCR, which directly affect the NF and conversion gain, respectively. As far as the IL is concerned, the stacked transformer represents the best solution for the implementation of the input balun in both technologies with values of about 0.6 dB at 77 GHz. Concerning the TCR the standard and mm-waveoptimized BEOL provide the highest values with interleaved and stacked configurations, respectively. Nevertheless, to make a meaningful comparison in terms of down-converter performance, the interleaved structure was chosen for the implementation of the inter-stage transformer. This choice is also supported by the very close TCR values (about 3 kΩ) achieved by both standard BEOL interleaved and mm-wave-optimized BEOL stacked transformers (see Tables 1  and 2).
The short-circuit transconductance conversion gain and the NF of the 77 GHz down-converter are shown in Figure 12 for both technologies. As expected, the two BEOLs provide similar NF values (around 9 dB at 1 MHz), whereas the mm-optimized process allows achievement of a slightly greater conversion gain at 77 GHz (40.9 mS vs. 40.3 mS). Table 3 compares the main performance of the down-converter in the two BEOLs. From these results, it appears that the advantages offered by adopting an optimized BEOL in terms of down-converter performance are almost irrelevant at mm-wave frequencies, as already anticipated by the stand-alone transformer comparison.

Conclusions
Integrated transformers have been designed for a W-band down-converter in two 28-nm CMOS technologies, i.e., with a standard and with a mm-wave-optimized BEOL. Despite thicker metals and intermetal oxides providing some advantages, especially for the stacked configuration, mm-wave

Conclusions
Integrated transformers have been designed for a W-band down-converter in two 28-nm CMOS technologies, i.e., with a standard and with a mm-wave-optimized BEOL. Despite thicker metals and intermetal oxides providing some advantages, especially for the stacked configuration, mm-wave transformer performance improvements are highly reduced by the EM fringing effects. Indeed, these are not negligible when the transformer size is comparable with the chip vertical dimensions, as happens at mm-wave frequencies. The evaluation of the adopted circuit testcase (i.e., 77 GHz down-converter) further confirms that very limited enhancements can be obtained thanks to an optimized BEOL technology. The reported results question the pros and cons of more expensive and complex BEOLs for nanometer CMOS platforms, providing a different perspective on technology developments for mm-wave applications.
Author Contributions: Conceptualization, E.R. and G.P. (Giuseppe Papotto); validation, C.N. and A.C.; formal analysis, E.R. and S.S.; investigation, A.C. and C.N.; methodology, E.R. and G.P. (Giuseppe Papotto); project administration, G.P. (Giuseppe Palmisano); supervision, E.R. and G.P. (Giuseppe Papotto); writing-original draft, E.R. and S.S.; writing-review and editing, E.R. All authors have read and agreed to the published version of the manuscript.  It is worth noting that assuming Equation (A9) means that the 11 * is null or equivalently the return loss, RL * , is infinite according to Equation (A7). Therefore, the approximation in Equation (A8) can be done in a narrow frequency band in which the test structure is 50 Ω matched, as shown in Figure 5.