Received 20 December 2024; revised 5 March 2025; accepted 12 April 2025.
Date of current version 8 May 2025.

Digital Object Identifier 10.1109/JMW.2025.3564466

Universal Electromagnetic Reference Skin
Model for APD Evaluation at 6–100 GHz

ARTEM BORISKIN <sup>1,2</sup> (Senior Member, IEEE), MASSINISSA ZIANE <sup>1</sup>, MARIEM MAFAMANE<sup>1</sup>, SHOAIB MUHAMMAD ANWAR <sup>3</sup>, LARS JACOB FOGED <sup>4</sup> (Senior Member, IEEE), AND MAXIM ZHADOBOV <sup>1</sup> (Senior Member, IEEE)

(Regular Paper)

CORRESPONDING AUTHOR: M. Zhadobov (e-mail: maxim.zhadobov@univ-rennes.fr).

This work was supported in part by the French National Research Program for Environmental and Occupational Health of ANSES through EXPO-5G Project under Grant ANSES-23-RF-03; in part by Labex CominLabs through EM-ART Project under Grant ANR-10-LABX-07-01; in part by eSkin-ART Innovation Action, in part by ANR through NF-JEN PEPR Project under Grant ANR-22-PEFT-0008; and in part European Union through European Regional Development Fund (ERDF), Ministry of Higher Education and Research, CNRS, Brittany Region, Conseils Departementaux d'Ile-et-Vilaine and Cotes d'Armor, Rennes Metropole, and Lannion Tregor Communaute, through the CPER Project CyMoCod.

**ABSTRACT** The increasing use of the upper part of the microwave spectrum for wireless communications requires appropriate methods and instrumentation for user exposure assessment. In this context, the IEC TC106 is developing a new international standard for user exposure compliance testing of the next generation 5G/6G wireless devices operating above 6 GHz. As a part of this initiative, the development of a universal reference skin model (RSM) is fundamental for definition of reference data to be included in specifications for body phantom design. In this study, we systematically analyze the impact of the human body near-surface tissue structure on the electromagnetic field (EMF) reflection from the skin surface in the 6–100 GHz range. A conventional multi-layer model is used to calculate skin reflectance as a function of the tissue thickness for the range of thicknesses corresponding to that of typical human skin and near-surface body tissues at four body sites concerned by the 5G/6G wireless use-case scenarios, namely: head, torso, forearm, and palm. The dominant contribution from the epidermis/dermis (ED) layer to the skin reflectance is demonstrated for all body sites in the considered frequency range. A high variation in the reflectance of the palm skin at frequencies above 20 GHz is demonstrated and explained by the matching layer effect associated with a thick stratum corneum (SC). The dry skin model, represented by a semi-infinite homogeneous medium with complex permittivity equivalent to that of the ED tissue, is shown to be an appropriate RSM both for the experimental and numerical evaluation of the absorbed power density (APD) in the 6–100 GHz range. The reference data for the antenna loading and APD at the skin surface are provided for standard reference feeds at 10 GHz, 30 GHz, 60 GHz, and 90 GHz.

**INDEX TERMS** Absorbed power density (APD), compliance testing, dosimetry, electromagnetic field (EMF), human exposure, millimeter waves (mmWaves), phantom, skin model, wireless, 5G, 6G.

# I. INTRODUCTION

In the frequency range 6–100 GHz, the health safety guidelines (e.g., ICNIRP [1]) and standards (e.g., IEEE C95.1 [2]) define the limits for user exposure to electromagnetic fields (EMF) emitted by wireless devices operating in proximity to human body. Compliance of such devices with exposure

limits is tested using protocols and procedures defined by local regulations, which are often based on the international IEC/IEEE standards. Equivalent body models, referred to as electromagnetic (EM) phantoms, represent an essential building block of EM dosimetry systems used for user exposure compliance testing (e.g., [3]). Such phantoms reproduce the

<footnote n="1">¹Univ Rennes, CNRS, IETR (Institut d'Electronique et des Technologies du numéRique), 35042 Rennes, France</footnote>

<footnote n="2">²Wavelis, 35510 Cesson-Sévigné, France</footnote>

<footnote n="3">³MVG industries, 29280 Villejust, France</footnote>

<footnote n="4">⁴Microwave Vision Italy SRL, 00071 Pomezia, Italy</footnote>
antenna/body interaction in near-field exposure scenarios in-
cluding: (i) antenna loading, which can cause a decrease of
the radiated power and absorbed power density (APD) due
to antenna detuning, and/or (ii) multiple reflections between
the wireless device and human body, which can lead to an
increase in APD [4], [5].

Dosimetry measurements are routinely performed in the FR1 frequency range (0.41–7.125 GHz) to evaluate the specific absorption rate (SAR). For this purpose, mainly tissue-equivalent liquid or gel phantoms are used, whose specifications are defined in terms of geometry and permittivity of the tissue-equivalent medium [6]. The shift of the operating frequencies to the higher bands (i.e., FR2: 24.25–71.0 GHz and FR3: 7.125–24.25 GHz) has triggered a revision of the international guidelines, standards, and regulations to account for a shallow penetration depth and enhanced localized absorption of EMF in the near-surface tissues at mmWave frequencies. The new dosimetry metric introduced by ICNIRP for this purpose is APD at the skin surface [1], referred to as the epithelial power density in the IEEE C95.1 standard [2]. This metric is also used in the IEC/IEEE technical report [7] and in the future IEC/IEEE standard related to APD evaluation in the 6 to 300 GHz range.

The definition of the phantom requirements represents an
important element of the future IEC/IEEE standard [7]. Al-
though there have been several phantoms reported recently
for APD measurements, e.g., [8], [9], [10], [11], [12], [13],
[14], their EM properties diverge because these phantoms
were designed using different body models as a target refer-
ence. Because of this, the use of these phantoms can lead to
different APD for the same device under test (DUT). From
this perspective, a universal Reference Skin Model (RSM) is
needed above 6 GHz to harmonize APD evaluation methods.

The main purpose of this study is to derive a grounded
proposal for the RSM in the 6–100 GHz range. To this end,
we performed a systematic study of skin reflectance variation
as a function of the near-surface tissue thickness, analyzed
the physical phenomena that influence the EMF reflection
from human skin at different body sites, and demonstrated the
potential of the homogeneous dry skin model to serve as an
RSM for APD evaluation.

The paper is organized as follows. Section II discusses phantom requirements. Section III introduces near-surface tissue models. Section IV presents an analytical model used for describing the complex permittivity of each tissue. Section V reports analysis of skin reflectance versus tissues thickness. Section VI provides reference data on APD and antenna loading, with conclusions derived in Section VII.

II. PHANTOM REQUIREMENTS

For wireless devices operating at frequencies above 6 GHz
(including handheld and wearable devices such as smart-
phones, tablets, etc.), the main contribution to the bidirec-
tional interaction between the device and the human body
comes from the EMF scattered from the skin surface. This

phenomenon can be reproduced, for instance, using EM phan-
toms with a reflection coefficient similar to that of human
skin, hereafter referred to as reflectivity-based phantoms [11],
[12], [14]. According to the energy conservation principle,
if a phantom has the same reflection properties as those of
the skin, it automatically reproduces the APD at the air/skin
interface. The near-field phenomena can also be accounted
for by such reflectivity-based phantoms with a certain toler-
ance, which depends on the near-field modal spectrum of a
specific DUT and the phantom efficiency in reproducing the
skin reflectance in the corresponding angular range, including
complex incident angles associated with evanescent fields.
Although direct measurements of the evanescent fields are
challenging, the analysis of antenna loading in the presence
of an RSM and a phantom can be used as a quantitative metric
for assessing the equivalence between the two.

Based on the above considerations, the IEC requirements for a phantom suitable for APD evaluation include: (i) the skin reflection coefficient for a certain range of incident angles and (ii) the DUT antenna input reflection coefficient, referred hereafter as antenna loading, S<sub>11</sub> [7]. This definition is different from that in [6] because it only requires equivalence in terms of the reflection coefficient, without specifying phantom structure and bulk material dielectric properties, thus representing a technology-agnostic definition which does not restrict phantom design and implementation principles.

However, to be applicable in practice, these phantom re-
quirements shall be defined quantitatively with respect to the
target reflection coefficient of an RSM, representative of hu-
man skin. Such an RSM shall provide a unique definition
for the reflection coefficient from the human skin surface
at each frequency, reproducible numerically and measurable
experimentally. The minimum phantom requirement can thus
be formulated in terms of the power reflection coefficient at
the normal incidence that can be directly measured for any
physical phantom, for instance using a quasi-optical method
[14]. If the normal incidence reflectance is well matched to the
skin reference, this also ensures a reasonably good match for a
certain cone of incident angles (at least up to ~45°). For most
FR2 antennas, this angular range has a dominant contribution
to the standing wave phenomenon both due to the propagation
direction of reflected fields and due to the typical half-power
beamwidth of the antenna radiation pattern. Thus, a discrep-
ancy at larger angles can be neglected in most practical cases.

The RSM can also be used to define the reference data for
a DUT loading, as well as the reference APD values (peak
and spatial average) at any frequency (e.g., at 10, 30, 60,
and 90 GHz), which correspond to standard IEC reference
feeds defined in the IEC/IEEE 63195 standard for incident
power density assessment [15] and later suggested in [7] for
APD evaluation. The antenna loading (S<sub>11</sub>) of the reference
feeds in proximity of the phantom can be measured using a
VNA for any separation distance between the phantom and
the feeds and compared with the target reference simulated in
presence of an RSM. Such a procedure enables quantitative
<figure><img src="image_1.png" /><figcaption>FIGURE 1. Anatomic models of near-surface human tissues at different body sites concerned by 5G/6G use cases.</figcaption></figure>

<figure><img src="image_2.png" /><figcaption>FIGURE 2. Real and imaginary parts of the complex permittivity of each tissue derived using the Cole-Cole model.</figcaption></figure>

assessment of the phantom equivalence with respect to the RSM in both far-field (based on the reflection coefficient) and near-field (based on $S_{11}$) exposure scenarios. Note that $S_{11}$ of an antenna under test (AUT), when placed close to a phantom, accounts for the effect of both propagating and evanescent modes, associated respectively with real and complex incident angles in the plane wave spectrum [16].

In such a way, benchmarking of the phantom EM characteristics versus an RSM model can be used to assess the phantom design and fabrication tolerance, as well as its compliance with the IEC/IEEE standard [7], prior its use for APD measurement, regardless of the phantom type and operating principle (e.g., conventional liquid-based or solid reflectivity-based). A discrepancy between the phantom and RSM characteristics shall be included in the system uncertainty budget.

### III. NEAR-SURFACE TISSUE MODEL

Above 6 GHz, EMF absorption is limited to the near-surface tissues (skin, fat, and muscle). Skin is the main target organ at these frequencies. The generic anatomic model of the near-surface tissues [17] is schematically shown in Fig. 1 with indication of the body sites considered in the present study. According to earlier studies (e.g., [18], [19], [20], [21]), the

<figure><img src="image_3.png" /><figcaption>FIGURE 3. The EMF penetration depth in each tissue.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>FIGURE 4. Multi-layer models: (a) Four-layer SC|ED|FA|MU model with infinite MU layer, (b) three-layer SC|ED|FA model with infinite FA layer, (c) three-layer ED|FA|MU model with infinite MU layer, (d) one-layer ED homogeneous model, (e) two-layer SC|ED model with infinite ED layer.</figcaption></figure>

<table><caption>TABLE 1. Thickness of Near-Surface Tissues (Thin Skin): Typical [20] and Selected Body Sites (Head, Torso, and Forearm)</caption><thead><tr><th>Tissue</th><th>T range, mm</th><th>T<sub>typ</sub><sup>thin</sup>, mm</th><th>T<sub>hea</sub>, mm</th><th>T<sub>tor</sub>, mm</th><th>T<sub>arm</sub>, mm</th></tr></thead><tbody><tr><td>SC</td><td>0.01 – 0.02</td><td>0.015</td><td>0.015</td><td>0.015</td><td>0.015</td></tr><tr><td>ED</td><td>0.40 – 2.60</td><td>1.45</td><td>1.5</td><td>2.0</td><td>1.08</td></tr><tr><td>FA</td><td>1.1 – 7.0 (∞)</td><td>3.0</td><td>1.5</td><td>7.0</td><td>3.0</td></tr><tr><td>MU</td><td>2.5 – 50.0 (∞)</td><td>∞</td><td>2.5</td><td>∞</td><td>∞</td></tr></tbody></table>

<table><caption>TABLE 2. Thickness of Near-Surface Tissues (Thick Skin): Typical [20] and Palm</caption><thead><tr><th>Tissue</th><th>T range, mm</th><th>T<sub>typ</sub><sup>thick</sup>, mm</th><th>T<sub>pal</sub>, mm</th></tr></thead><tbody><tr><td>SC</td><td>0.02 – 1.50</td><td>1.2</td><td>0.4 – 1.0</td></tr><tr><td>ED</td><td>0.40 – 2.60</td><td>1.45</td><td>1.8</td></tr><tr><td>FA</td><td>1.1 – 7.0 (∞)</td><td>3.0</td><td>1.5</td></tr><tr><td>MU</td><td>2.5 – 50.0 (∞)</td><td>∞</td><td>2.5</td></tr></tbody></table>

EM response of the human body can be analyzed using a four-layer model comprising a stratum corneum (SC) representing the outer layer mostly composed of dead cells, an epidermis/dermis (ED) layer including the network of blood vessels, a fat (FA) layer, and a muscle (MU) layer. The typical range of thickness variation for each tissue at different body sites is provided in Tables 1 and 2, defined based on the data reported in [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28]. The former regroups the data related to the body
<figure><img src="image_5.png" /><figcaption>FIGURE 5. Thin skin reflectance vs. ED and FA thickness for the three-layer model in Fig. 4(c) at different frequencies with ED and FA thickness variation range typical for thin skin: (a) 6 GHz, (b) 10 GHz, (c) 20 GHz, (d) 30 GHz, (e) 60 GHz, (f) 90 GHz.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>FIGURE 6. The wavelength in the near-surface body tissues.</figcaption></figure>

<caption>FIGURE 7. Thin skin reflectance at the selected body sites.</caption>

sites with a thin SC ($T_{sc} \le 0.02$ mm), namely head, torso, and forearm. The latter provides the data for palm, characterized by a thick SC ($0.02 \le T_{sc} \le 1.5$ mm). A large variation in the palm SC thickness is explained by the natural diversity in the human population. It also varies depending on age [24] as well as environmental and physiological conditions. The values indicated as 'typical' are those reported in [20].

In this study, we limit the scope of discussion to four body sites representative of mmWave 5G/6G use cases where handheld and wearable wireless devices are subject for user exposure compliance testing, namely the head, torso, forearm,

and palm (Fig. 1). However, the proposed methodology can be applied to other body sites by substituting the appropriate data for the tissue thickness. For instance, the data reported in [18] allow us to predict that the EM response of the quadriceps and abdomen body sites will be similar to that of torso.

## IV. EM PROPERTIES OF NEAR-SURFACE TISSUES

The complex dielectric permittivity of the tissues considered in this study is defined using the analytical Cole-Cole model
<figure><img src="image_7.png" /><figcaption>FIGURE 8. Thick skin reflectance vs. SC and ED thickness for the three-layer model in Fig. 4(b) at different frequencies with SC and ED thickness variation range typical for thick skin: (a) 6 GHz, (b) 10 GHz, (c) 20 GHz, (d) 30 GHz, (e) 60 GHz, (f) 90 GHz.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>FIGURE 9. Reflectance at different frequencies for thick skin for different SC thickness.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>FIGURE 10. Reflectance of homogeneous dry skin ($R_{dsk}$) and the two-layer SC/ED model for different SC thickness ($T^{SC}$).</figcaption></figure>

<table><caption>TABLE 3. Weight Coefficients of the Cole-Cole Model</caption><thead><tr><th></th><th>SC</th><th>ED</th><th>FA</th><th>MU</th></tr></thead><tbody><tr><td>ε<sub>r</sub></td><td>2.96</td><td>4.0</td><td>2.5</td><td>4.0</td></tr><tr><td>Δε</td><td>1.5</td><td>32.4</td><td>3.0</td><td>50.0</td></tr><tr><td>σ<sub>i</sub>, S/m</td><td>0</td><td>1.4</td><td>0.01</td><td>0.1</td></tr><tr><td>τ × 10<sup>12</sup>, s</td><td>6.9</td><td>6.9</td><td>7.96</td><td>7.23</td></tr><tr><td>α</td><td>0</td><td>0</td><td>0.2</td><td>0.1</td></tr></tbody></table>

with the weighting coefficients provided in Table 3 [20]:

$$ \epsilon = \epsilon_0 (\epsilon'_r - j\epsilon''_r) = \epsilon_\infty + \frac{\sigma_i}{j\omega\epsilon_0} + \frac{\Delta\epsilon}{1 + (j\omega\tau)^{1-\alpha}}, \quad (1) $$

where $\epsilon_\infty$ is the permittivity in the optical range, $\Delta\epsilon$ is the difference between the static permittivity and $\epsilon_\infty$, $\omega$ is the angular frequency ($\omega = 2\pi f$), $\tau$ (s) is the relaxation time, $\sigma_i$ (S/m) is the ionic conductivity, and $\alpha$ ($0 \le \alpha \le 1$) is a parameter indicating the breadth of the relaxation time distribution.

The frequency-dependent variations of the real and imaginary parts of the complex permittivity for each layer are shown in Fig. 2. The difference in permittivity for the SC and FA layers (characterized by low real and imaginary parts) and the ED and MU layers (characterized by high real and imaginary parts) suggests that reflection from the skin surface and absorption inside the body is mostly associated with ED and MU. The partial contributions of ED and MU depend on the EMF penetration depth ($d_i$) and thus varies as a function
<figure><img src="image_10.png" /><figcaption>FIGURE 11. Simulated APD at dry skin surface for 10 GHz reference sources: (a) Slotted horn, (b) dipole array.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>FIGURE 12. Simulated APD at the skin surface for 30 GHz reference sources: (a) Slotted horn, (b) dipole array.</figcaption></figure>

of frequency:

$$d_i = 1/\alpha_i \approx (\pi f \varepsilon''_{ri}(\varepsilon_0 \mu_0 / \varepsilon'_{ri})^{1/2})^{-1} \quad (2)$$

where $\alpha_i$ is the attenuation constant in the corresponding medium characterized by complex permittivity $\varepsilon_i$.

In Fig. 3, the EMF penetration depth $d_i$ ($i = 1, 2, 3, 4$) in homogeneous media with the complex permittivity equivalent to that of the considered tissues is plotted versus frequency. For the lossy ED and MU, it varies between about 10 mm at 6 GHz ($\lambda_0 \approx 50$ mm at 6 GHz) to a fraction of mm above 20 GHz ($\lambda_0 \approx 15$ mm at 20 GHz). Comparison with the typical thickness of the ED tissue (Table 1) demonstrates that above 20 GHz the main contribution to the skin reflection and absorption comes from the ED layer.

## V. ANALYSIS OF SKIN REFLECTANCE

In this section, the impact of the layers thickness on the reflectance from skin is analyzed using a layered planar tissue model at 6 GHz, 10 GHz, 30 GHz, 60 GHz, and 90 GHz, which correspond to the operating frequency of the IEC reference sources [15]. An additional point at 20 GHz is included in the analysis as a representative case when the EMF penetration depth becomes comparable with the typical thickness of the ED layer. The age and temperature-related variations are not considered in this study because, based on [19], [20], [22], [24], [25], their influence on skin reflectance for a selected individual is estimated as relatively small (within ±5% from the estimate obtained for normal ambient conditions and mid-age of 35 years). The impact of gender and skin pigmentation is also considered negligible compared to the reflectance variation caused by tissue thickness [25].
<figure><img src="image_12.png" /><figcaption>FIGURE 13. Simulated APD at dry skin surface for 60 GHz reference sources: (a) Slotted horn, (b) dipole array.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>FIGURE 14. Simulated APD at dry skin surface for 90 GHz reference slotted horn antenna.</figcaption></figure>

Five models are considered (Fig. 4), including a four-layer model, as well as simplified three-, two-, and one-layer models. The latter is referred hereafter as “dry skin model” and is represented by a semi-infinite homogeneous dielectric medium with the complex permittivity of ED tissue [20].

A. THIN SKIN

We first consider the three-layer model (Fig. 4(c)), which differs from the four-layer model in the absence of the SC skin layer. This simplification is justified for a thin SC ($T_{sc} \le 0.02$ mm), typical for head, torso, and forearm, as demonstrated in Section V-C. This simplification allows for a convenient graphical representation of the power reflection coefficient (i.e., reflectance R) from the skin surface as a function of ED and FA layer thickness, which have the dominant contribution to the reflectance in case of a thin SC.

The reflectance from the surface of a multi-layer dielectric structure can be determined in a number of ways, including the propagation matrix approach or the recursive simulation of the reflection response at each interface using the Fresnel formulas available elsewhere.

Fig. 5 presents the skin reflectance R at the normal incidence for the three-layer tissue model shown in Fig. 4(c). The color scale represents R versus thickness of the ED layer

<table><caption>TABLE 4. Thin Skin Reflectance of the Three-Layer ED|FA|MU Model (Min, Max, BW, Typical, and Standard Deviation) at Different Body Sites, and the Typical Reflectance for Thin Skin According to [20]</caption><thead><tr><th>Freq.</th><th>R<sub>min</sub></th><th>R<sub>max</sub></th><th>BW</th><th>R<sup>thin</sup><sub>typ</sub></th><th>R<sub>dsk</sub></th><th>R<sub>hea</sub></th><th>R<sub>arm</sub></th><th>R<sub>tor</sub></th><th>σ</th></tr></thead><tbody><tr><td>6 GHz</td><td>0.07</td><td>0.78</td><td>167%</td><td>0.63</td><td>0.52</td><td>0.50</td><td>0.50</td><td>0.78</td><td>13.1%</td></tr><tr><td>10 GHz</td><td>0.19</td><td>0.73</td><td>117%</td><td>0.72</td><td>0.51</td><td>0.67</td><td>0.71</td><td>0.52</td><td>8.01%</td></tr><tr><td>20 GHz</td><td>0.43</td><td>0.65</td><td>40.7%</td><td>0.44</td><td>0.50</td><td>0.43</td><td>0.49</td><td>0.50</td><td>2.75%</td></tr><tr><td>30 GHz</td><td>0.42</td><td>0.60</td><td>35.3%</td><td>0.45</td><td>0.46</td><td>0.46</td><td>0.44</td><td>0.46</td><td>0.79%</td></tr><tr><td>60 GHz</td><td>0.36</td><td>0.46</td><td>24.4%</td><td>0.38</td><td>0.39</td><td>0.38</td><td>0.38</td><td>0.38</td><td>0.12%</td></tr><tr><td>90 GHz</td><td>0.30</td><td>0.35</td><td>15.4%</td><td>0.32</td><td>0.32</td><td>0.32</td><td>0.32</td><td>0.32</td><td>0.00%</td></tr></tbody></table>

$(T_1)$, horizontal axis) and FA layer $(T_2)$, vertical axis) whose variation range is taken from Table 1. The presence of the thin SC layer is neglected (validity of this assumption is explained in Section V-C). The MU layer is considered infinitely thick. The white circular marks indicate three combinations of ED and FA thickness typical for the selected body sites, and the red circular mark corresponds to the typical thickness of the corresponding layers according to [20].

The quantitative data from Fig. 5 are summarized in Table 4, including the R variation range described by $R_{min}$ and
<figure><img src="image_14.png" /><figcaption>FIGURE 15. Loading (S11) of the 10 GHz reference feeds in free space and in presence of dry skin RSM: (a) Slotted horn, (b) dipole array.</figcaption></figure>

$R_{max}$ values corresponding to the minimum and maximum R values at the selected frequency, bandwidth (BW) defined in % as

$$BW = \frac{2(R_{max} - R_{min})}{R_{max} + R_{min}} \cdot 100, \quad (3)$$

as well as the reflectance data for the typical thin skin, dry skin, and selected body sites, namely head ($R_{hea}$), torso ($R_{tor}$), and forearm ($R_{for}$), and the standard deviation $\sigma$ defined for the three body sites as follows:

$$\sigma = \left[ \frac{1}{N} \sum_{i=1}^{N} (R_i - R_{av})^2 \right]^{0.5}, \quad R_{av} = \frac{1}{N} \sum_{i=1}^{N} R_i. \quad (4)$$

The first observation from Fig. 5 is the large BW of the reflectance variation vs. ED/FA thickness below 10 GHz (>117%). At frequencies above 20 GHz, the BW is limited to 40.7% and continuously decreases to 15.4% at 90 GHz.

The second observation from Fig. 5 is about the relative position of the red mark inside the triangle formed by the white marks, which demonstrates consistency between the data reported by different research groups. The standard deviation $\sigma(R)$ between the three sites of interest varies from 13%

<figure><img src="image_15.png" /><figcaption>FIGURE 16. Loading (S11) of the 30 GHz reference feeds in free space and in presence of dry skin RSM: (a) Slotted horn, (b) dipole array.</figcaption></figure>

at 6 GHz to 2.75% at 20 GHz, and then continuously tends to zero (Table 4).

The higher variation at lower frequencies is explained by the interference between the forward and backward waves reflected at the interfaces between ED/FA and FA/MU tissue layers. The dashed black line visible in Fig. 5(b), (c), (d) indicates the EMF penetration depth in ED and FA layers. Each point of this curve represents a combination of two values ($T_1, T_2$) defined by analyzing the E-field attenuation along the propagation path:

$$T_2 = d_2 (1 - T_1/d_1) \quad (5)$$

where $d_1$ and $d_2$ represent the penetration depth in ED and FA tissues, respectively, and are defined by (2).

For a given ED thickness ($T_1$), the value of $T_2$ indicates a penetration depth inside FA layer at which the E-field amplitude decreases by a factor of e compared to its initial value at the skin surface. Above this line, the impact on R from the EMF reflected at the FA/MU interface is negligible because of significant attenuation in ED and FA layers. This explains a small reflectance variation observed for all three selected body sites at 20 GHz and above. Below the line, the EMF reflected at both ED/FA and FA/MU interfaces can reach the
<figure><img src="image_16.png" /><figcaption>FIGURE 17. Loading (S11) of the 60 GHz reference feeds in free space and in presence of dry skin RSM: (a) Slotted horn, (b) dipole array.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>FIGURE 18. Loading (S11) of the 90 GHz slotted horn in free space and in presence of dry skin RSM.</figcaption></figure>

skin surface and influence reflectance. However, the impact of these reflected fields decreases fast with the increase of the ED thickness. Both constructive and destructive interference are possible depending on the ED and FA layer thickness.

At 6 GHz (Fig. 5(a)), a zone of high reflectance is observed for thick ED and FA tissues intrinsic to torso body area. While the forearm and head body areas, characterized by thinner ED and FA tissues, demonstrate a lower reflectance.

At 10 GHz (Fig. 5(b)), the opposite behavior is observed with a higher reflectance occurring for the forearm and head and lower for torso. The shift of the high reflectance zone towards the thinner ED and FA tissues is explained by a shorter wavelength. The maximum reflectance is observed when both $T_1$ and $T_2$ are close to the half wavelength in the corresponding media (Fig. 6).

At 20 GHz (Fig. 5(c)), the standing wave phenomenon is less pronounced because it is mitigated by a stronger EMF attenuation in the ED layer caused by higher losses and larger relative thickness.

At 30 GHz and above, the skin reflectance is fully determined by the EM properties of the ED layer because its thickness becomes larger than the EMF penetration depth in the ED medium (Fig. 3).

Fig. 7 provides a visual representation of the data extracted from Fig. 5, which is then summarized in Table 4. The vertical black lines show the range of R variation between $R_{min}$ and $R_{max}$ at each frequency, the dashed color lines connect R values for the selected body sites, and the red dotted line denotes reflectance of the typical thin skin. Finally, a thick line in magenta color represents reflectance of the homogeneous dry skin model (Fig. 4(d)). Above 30 GHz, all three body sites are characterized by R values close to that of the dry skin model (Fig. 7). At 20 GHz, the response is still close to the dry skin model (within 10%), whereas at 10 GHz and 6 GHz the deeper penetration leads to significant R variation versus ED and FA thickness as well as between different body sites (Table 4). These observations highlight the difficulties in using a layered model as RSM.

Unlike the layered model, reflectance of the homogeneous dry skin model ($R_{dsk}$) remains in the middle of the R variation range, aligned with the lower R values for all three body sites both at 6 GHz and 10 GHz and can be thus considered as a more balanced and conservative representation of the human skin from the APD evaluation viewpoint. Note that the higher the skin reflectance, the lower the APD value. Consequently, using a high-reflectance RSM may cause underestimation of APD. At the same time, using a low-reflectance phantom (with R close to $R_{min}$) may also lead to underestimation of the APD because this choice neglects the DUT and human body interaction both in terms of the antenna load and the standing wave phenomenon that may cause a multifold enhancement of APD due to the EMF energy trapped and bouncing between the DUT and skin surface [4].

Based on the considerations above, the homogeneous dry skin model is identified as a promising candidate for the universal electromagnetic RSM for head, torso, and forearm body sites in the entire 6–100 GHz range.

## B. THICK SKIN

We demonstrate hereafter that a larger thickness of the SC layer, intrinsic to palm, can significantly change the skin reflectance at mmWaves.

The reflectance for the thick skin is analyzed using the model in Fig. 4(b) versus thickness of the SC and ED layers,
<table><caption>TABLE 5. Reflectance Data Extracted From Fig. 9</caption><thead><tr><th rowspan="2">Freq.</th><th rowspan="2">R<sub>min</sub></th><th rowspan="2">R<sub>max</sub></th><th rowspan="2">BW</th><th colspan="4">R<sub>pal</sub> for different T<sup>sc</sup><sub>pal</sub> (mm)</th><th rowspan="2">σ</th></tr><tr><th>T<sup>sc</sup><sub>pal</sub>=0.015</th><th>=0.4</th><th>=0.7</th><th>=1.2</th></tr></thead><tbody><tr><td>6 GHz</td><td>0.314</td><td>0.69</td><td>75.3%</td><td>0.59</td><td>0.95</td><td>0.60</td><td>0.59</td><td>15.7%</td></tr><tr><td>10 GHz</td><td>0.282</td><td>0.66</td><td>80.6%</td><td>0.65</td><td>0.65</td><td>0.64</td><td>0.59</td><td>2.3%</td></tr><tr><td>20 GHz</td><td>0.035</td><td>0.60</td><td>178%</td><td>0.52</td><td>0.46</td><td>0.37</td><td>0.15</td><td>13.9%</td></tr><tr><td>30 GHz</td><td>0.0</td><td>0.55</td><td>200%</td><td>0.43</td><td>0.34</td><td>0.19</td><td>0.00</td><td>16.3%</td></tr><tr><td>60 GHz</td><td>0.0</td><td>0.43</td><td>200%</td><td>0.38</td><td>0.12</td><td>0.01</td><td>0.24</td><td>13.7%</td></tr><tr><td>90 GHz</td><td>0.0</td><td>0.33</td><td>200%</td><td>0.31</td><td>0.00</td><td>0.18</td><td>0.07</td><td>11.7%</td></tr></tbody></table>

for the set of thicknesses listed in Table 2 under the assumption of infinitely thick FA layer (Fig. 8). The data extracted from Fig. 8 are summarized in Table 5 and illustrated in Fig. 9.

The data reported in Fig. 8 are derived and illustrated in the same way as in Fig. 5 with the white and red markers indicating respectively the combinations of the SC and ED thickness values representative of the selected body site and the typical thick skin values suggested in [20]. These results demonstrate a strong impact of the SC thickness on the reflectance, especially above 20 GHz, which is explained by the matching layer effect associated with thick SC layer, which is in line with earlier studies [8], [20]. This phenomenon is best visible at 90 GHz (Fig. 8(f)) in the form of two vertical zones of low reflectance (in blue color) observed around to T₁ equal to 1/4 and 3/4 wavelength in SC medium. The first low-reflectance zone is also visible in Fig. 8(c)–(e) with the low R zone width and position shifted with respect to the wavelength. The data in Table 5 and Fig. 9 quantify the R variation bandwidth and standard deviation in R for different SC thickness.

Although the EM response of the palm skin with a given SC thickness can be reproduced using a double-layer phantom comprising a low permittivity layer (representing SC) attached to a higher-permittivity layer (representing ED) as suggested in [8], the question about a conservative palm skin model, representative of different individuals, remains open and requires further investigation to account for the human population diversity and the physical effects that may affect APD under the low skin reflectance condition (e.g., antenna loading by human body) and under the high skin reflectance condition (e.g., standing wave phenomenon).

### C. HOMOGENEOUS DRY SKIN MODEL

In this section, we analyze the reflectance of the dry skin model, composed of a homogeneous semi-infinite ED layer (Fig. 4(d)) and compare it with the two-layer skin model (Fig. 4(e)), comprising a top SC layer overlaid on a semi-infinite ED layer.

As shown in Fig. 10, the presence of a thin SC layer typical to head, torso and forearm body sites ($T_{sc} = 0.015$ mm) has a negligible effect on R. On the opposite, the SC layer with thickness typical for palm skin produces a significant impact

on the skin reflectance, leading to very low reflectance around 90 GHz and 60 GHz for $T^{sc} = 0.4$ mm and $T^{sc} = 0.7$ mm, respectively. For thicker SC ($T^{sc} = 1.2$ mm), the zone of low reflectance is observed already around 30 GHz.

These observations validate the conclusions derived in Sections V-B regarding the difficulties in choosing RSM parameters for palm skin with thick SC layer, as well as the assumptions of Section V-A regarding a negligible effect of thin SC on the reflectance of the head, torso, and forearm body sites.

## VI. APD DISTRIBUTION AND AUT LOADING IN PRESENCE OF DRY SKIN RSM

### A. APD DISTRIBUTION

In this section, we report simulated APD distributions for the homogeneous dry skin RSM (Fig. 4(d)) exposed to EMF emitted by reference antennas at 10 GHz, 30 GHz, 60 GHz, and 90 GHz placed at a separation distance of D = 2 mm, 5 mm, 10 mm, and 50 mm between the antenna under test (AUT) and skin surface. The two reference antennas used in this study are those defined in the IEC/IEEE standard [15], namely: (1) horn antennas loaded with a slot array and (2) cavity-backed dipole array antennas. The simulations are performed using the full-wave electromagnetic solver [29]. The APD distribution is reported in dBm/m² scale normalized to 0 dBm total radiated power (TRP) in free space.

Significant variations in APD distributions at the air/skin interface observed in Figs. 11–14 for different separation distances illustrate the challenge associated with APD evaluation for wireless devices operating in proximity to human body. For comparison, the power density distribution in free space for the same reference feeds can be found in [15], whereas the impact of the AUT and human body interaction on the APD is investigated in [4].

The data in Figs. 11–14 can be used as reference data for APD phantom design validation, as well as for the system check/calibration before APD compliance testing of 5G/6G wireless devices operating in the 6 and 100 GHz range [7].

### B. AUT LOADING

In this section, we report AUT loading ($S_{11}$) by the dry skin RSM for the reference feeds and separation distances considered above. The data are compared with $S_{11}$ in free space. A significant impact due to the presence of the body is observed for both feeds on the antenna matching and resonant frequency. Note that in user terminals, such as smartphones, the proximity of the body may additionally load active components, such as amplifiers, and/or activate proximity sensors used to trigger adaptive functions. Therefore, realistic performance conditions can only be reproduced in the presence of a phantom (e.g., reflectivity-based phantom [11], [12], [14]) that mimics the EM response of the human body.
## VII. CONCLUSION

In this paper, for the first time, the question of a universal Reference Skin Model (RSM) for APD evaluation above 6 GHz has been raised and answered through a systematic study over the EM response of a multi-layer body model versus tissue thickness over the range typical for human population at the body sites concerned the most by APD measurements during user exposure compliance testing of wireless devices (like smartphones) in typical 5G/6G use-case scenarios.

It was demonstrated that below 20 GHz skin reflectance can significantly vary as a function of ED and FA thickness. A large variation was also revealed between different body sites and the “typical” thin skin reflectance used in majority of earlier studies. In case of thin skin at head, torso, forearm (T < 0.02 mm), the impact of thin SC tissue on the reflectance from the skin surface was shown to be negligible. Comparison with the EM response of a homogeneous dry skin model revealed potential of the latter to be used as the universal RSM for APD evaluation in the entire 6 to 100 GHz range, balanced over different body sites.

The use of the dry skin model as RSM enables a simple and practical formulation of the phantom requirements. Additional advantages of the dry skin RSM for APD measurements are the following:

* It represents the well-characterized and reliable generic skin model, based on the analytical and experimental data elaborated by different research groups during the last decades, e.g., [10], [11], [12], [13], [14], [20], [23].

* It can be considered as representative of thin human skin (head, torso, forearm, etc., excluding palm) within the entire 6–100 GHz range. Between 6 and 20 GHz, it provides a moderate and conservative response, balanced for the selected body sites, while at higher frequencies, it mimics well the EM response of the anatomic multi-layer model.

* It is described by the analytical Cole-Cole model, which enables unique and easily reproducible definition of the RSM characteristics at any frequency. In particular, this allows calculation of reference data to validate the performance of an APD phantom at any frequency point within a DUT's operational bandwidth prior to use in APD compliance testing, which is important for evaluating system uncertainty.

* Finally, it facilitates computational dosimetry by reducing computational time and staircase errors, which are especially important when dealing with 3D shaped objects, like anatomic human models concerned by the compliance test scenarios.

In such a way, the proposed simple, yet reliable, analytical model represents a practical technology-agnostic definition of the APD phantom requirements, which can be used to harmonize the measurement and computational methodologies for APD evaluation above 6 GHz.

## ACKNOWLEDGMENT

The authors would like to thank the Mobile & Wireless Forum (MWF) for providing the reference antennas.

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