High speed graphene-silicon electro-absorption modulators for the O-band and C-band

The static electro-optical behaviour of the SLG EAM is defined by the relation between the absorption and graphene's Fermi level μ. Graphene's absorption is derived from the 2D complex optical conductivity ${\sigma }_{g}\left(\omega ,{\rm{\Gamma }},T,\mu \right)$, calculated from the Kubo formula.²⁾ This formula takes into account interband and intraband transitions, and it depends on the angular frequency ω, the charged particle scattering rate ℏΓ, the temperature T, and most importantly graphene's Fermi level μ. The latter can be shifted by sweeping the voltage V_g across the GOS capacitor,²⁾ according to

$$\begin{eqnarray}&&{V}_{g}=\displaystyle \frac{q\left({n}_{0}+{n}_{s}\right)}{{C}_{{\rm{GOS}}}}=\displaystyle \frac{q}{\pi {\left(\hslash {v}_{F}\right)}^{2}}\displaystyle \frac{{\mu }^{2}}{{C}_{{\rm{GOS}}}},\end{eqnarray} \tag{ 1 }$$

where q is the elementary charge, ℏ is the reduced Planck constant, v_F is the Fermi velocity of carriers in graphene and C_GOS is the capacitance of the GOS capacitor. The Fermi level μ is the sum of two contributions:

$$\begin{eqnarray}&&\mu ={\mu }_{0}+{\rm{\Delta }}\mu .\end{eqnarray} \tag{ 2 }$$

μ₀ is the initial Fermi level position due to the fixed number of charges n₀ (graphene's intrinsic doping), and Δμ is the Fermi level shift caused by the number of charges n_s accumulated on graphene when we apply V_g across the capacitor.

The static electro-optical behaviour of the SLG EAM as a function of applied voltage is mainly affected by two parameters: graphene's intrinsic doping (n₀) and the scattering rate ℏΓ. The intrinsic doping n₀ affects the position of minimum transmission as a function of applied voltage. Figure 2(a) shows the simulation, performed using Lumerical MODE Solutions, of the optical transmission as a function of gate voltage for a TE SLG EAM with 5 nm thick SiO₂ and 500 nm wide waveguide operating at 1560 nm, for neutral (n₀ = 0 cm⁻²) and p-doped (${n}_{0}=12\,\times \,{10}^{12}\,{\mathrm{cm}}^{-2}$) graphene, for scattering rate ℏΓ = 15 meV. For neutral graphene, the minimum is at 0 V, therefore switching between high transmission (on-state) and low transmission (off-state) requires ∼3.5 or ∼−4 V DC bias. For p-doped graphene, the minimum transmission point is shifted to negative bias. In this case, switching occurs between −2 and 2 V, which is compatible with current CMOS technology. The scattering rate ℏΓ, which is inversely proportional to the mobility μ,²⁴⁾ affects the ER of the modulator. As shown in Fig. 2(b), a lower scattering rate, implying higher graphene quality, results in higher ER for a given V_pp because graphene can reach full transparency. For example, a 75 μm long SLG EAM would show 0.5 dB higher ER for ℏΓ = 0.43 eV compared to ℏΓ=30 eV. In real applications, graphene's scattering rate is often more than 10 meV,²⁴⁾ resulting in a reduced ER and increased IL.

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The 3 dB frequency response of a SLG EAM is limited by the RC constant of the device, and can be explained using the equivalent electrical circuit in Fig. 1(b).

3.2.1. Device resistance

The device total resistance (R_tot) is the sum of graphene's contact and sheet resistance (R_graC and R_gra) and the Si contact and sheet resistance (R_SiC and R_Si). Graphene's resistance is affected by the scattering rate ℏΓ, which is proportional to the impurity density ${n}^{* }$, caused by local potential fluctuations and electron/hole puddles on the graphene layer.^25,26) Higher scattering rate corresponds to lower mobility and therefore higher resistance. When the mobility is higher (lower ℏΓ and ${n}^{* }$), the peak in graphene's resistance corresponding to the neutrality point is higher. As a consequence, the resistance experiences a more abrupt change when the gate voltage is increased or decreased to move away from the neutrality point.²⁴⁾ The values of R_graC and R_gra at a fixed DC voltage bias are also affected by graphene's intrinsic doping n₀. For n₀ = 0, graphene's resistance reaches its peak value at 0 V voltage bias, and decreases for increasing (or decreasing) voltage bias. When applying V_gate as indicated in Fig. 1(a), p-doped (n-doped) graphene shows a peak value at negative (positive) voltage bias due to the shift of graphene's charge neutrality point [Fig. 3(a)]. The resistance then decreases as the voltage increases (decreases). In case of p-doped graphene, there is therefore a low resistance region for voltage values around or greater than 0 V. The Si contribution to R_tot depends on the doping level of the three Si regions: contact, slab and waveguide areas. To properly estimate how the silicon doping impacts the resistance, we perform a process simulation using Sentaurus TCAD, which accurately emulates the real processing performed in the fab. Afterwards we extract the values of silicon resistance (R_Si and R_SiC) for the three doped regions together (contact, slab and waveguide) by performing a transient device simulation at different voltage values. Figure 3(b) shows the values of R_tot as a function of gate voltage for a 75 μm long device with p-doped graphene (mobility μ_c = 800 cm² V⁻¹ s⁻¹; R_graC = 880 Ω μm and R_gra = 340Ω/□at 0 V) and a waveguide width of 500 nm, for p-doped (p_wg = 1.9 × 10¹⁸ cm⁻³, p_slab = 3.2 × 10¹⁹ cm⁻³) and n-doped (n_wg = 2.3 × 10¹⁸ cm⁻³, n_slab = 2.7 × 10¹⁹ cm⁻³) Si. p-doped silicon exhibits higher sheet resistance than n-doped silicon, due to the lower mobility of holes compared to electrons. The variation of R_tot with gate voltage is influenced by the voltage-dependent behaviour of R_graC(V) and R_gra(V) only.

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3.2.2. GOS capacitance

The total GOS capacitance C_GOS is given by the series of graphene's quantum capacitance C_q, the oxide capacitance C_ox and the Si depletion capacitance C_Si:

$$\begin{eqnarray}&&\displaystyle \frac{1}{{C}_{{\rm{GOS}}}}=\displaystyle \frac{1}{{C}_{q}}+\displaystyle \frac{1}{{C}_{{\rm{ox}}}}+\displaystyle \frac{1}{{C}_{{\rm{Si}}}}.\end{eqnarray} \tag{ 3 }$$

Graphene's quantum capacitance is given by the following equation^27,28):

$$\begin{eqnarray}&&{C}_{q}=\displaystyle \frac{2{q}^{2}}{\hslash {v}_{F}\sqrt{\pi }}\sqrt{| {n}_{s}+{n}_{0}| }=\displaystyle \frac{2{q}^{2}}{{\hslash }^{2}{v}_{F}^{2}\pi }| \mu | ,\end{eqnarray} \tag{ 4 }$$

where μ is graphene's Fermi level as defined in Eq. (2). The quantum capacitance is characterised by a minimum when μ = 0 [Δμ = −μ₀, according to Eq. (2)] and it increases linearly for $| \mu | \gt 0$ [Fig. 4(a)]. For intrinsic (undoped) graphene, the Fermi level is at the Dirac point, μ₀ = 0 and therefore C_q = 0 for Δμ = 0 [Fig. 4(b)]. In p-doped (n-doped) graphene, μ₀ < 0 (μ₀ > 0) and, as a consequence, the minimum of C_q is located at Δμ = −μ₀ [Fig. 4(b)]. When graphene is not pristine, the additional impurity carrier density ${n}^{* }$ should be included in the calculation, The quantum capacitance becomes²⁶⁾

$$\begin{eqnarray}&&{C}_{q}=\displaystyle \frac{2{q}^{2}}{\hslash {v}_{F}\sqrt{\pi }}\sqrt{| {n}_{s}+{n}_{0}| +| {n}^{* }| }.\end{eqnarray} \tag{ 5 }$$

If we compare C_q with C_ox calculated for 5 nm of SiO₂ (Fig. 4), we see that the latter is significantly smaller for each value of μ away from the neutrality point. When $n* \,\gt \,0$, the minimum of the quantum capacitance increases and C_q becomes significantly higher than C_ox for any value of chemical potential, as shown by the dotted lines in Fig. 4. For this reason, when placed in series with C_ox, the contribution of C_q is minor.

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The analytical model used to calculate C_GOS as a function of applied voltage V_g is based on the MOS capacitor model,²⁹⁾ with the difference that for the GOS capacitor graphene's quantum capacitance C_q is included in the calculation. The voltage is applied on the graphene contact, while the silicon contact is grounded. In accumulation, when V_g < V_FB < 0 for p-doped Si and V_g > V_FB > 0 for n-doped Si, with V_FB being the commonly known flatband voltage of a MOS capacitor,²⁹⁾ the silicon layer is not yet depleted, so the quantities that play a role are C_q and C_ox. To calculate the amount of charges n_s accumulated on the graphene layer for each V_g < V_FB, we need to solve the following system

$$\begin{eqnarray}&&\left\{\begin{array}{l}{V}_{g}-{V}_{{\rm{FB}}}={Q}_{{\rm{acc}}}\left(\tfrac{1}{{C}_{{\rm{ox}}}}+\tfrac{1}{{C}_{q}}\right)={n}_{s}\left(\tfrac{1}{{C}_{{\rm{ox}}}}+\tfrac{1}{{C}_{q}}\right)\\ {C}_{q}=\tfrac{2{q}^{2}}{\hslash {v}_{F}\sqrt{\pi }}\sqrt{| {n}_{s}+{n}_{0}| +| {n}^{* }| }\hspace{30pt}(\mathrm{Eq}.\ 5)\end{array}\right.,\end{eqnarray} \tag{ 6 }$$

where Q_acc is the accumulation charge. The resulting equation for n_s is

$$\begin{eqnarray}&&\displaystyle \frac{q}{{C}_{{\rm{ox}}}}{n}_{s}+\left(\displaystyle \frac{\hslash {{v}_{F}}^{2}\sqrt{\pi }}{2q}\right)\displaystyle \frac{{n}_{s}}{\sqrt{| {n}_{s}+{n}_{0}| +| {n}^{* }| }}+\left({V}_{{\rm{FB}}}-{V}_{g}\right)=0.\end{eqnarray} \tag{ 7 }$$

Once the value of n_s for each V_g is known, we can calculate C_q through Eq. (4) and therefore the total accumulation capacitance ${C}_{{\rm{GOS}},{\rm{acc}}}={\left(\tfrac{1}{{C}_{{\rm{ox}}}}+\tfrac{1}{{C}_{q}}\right)}^{-1}$. Graphene's natural doping n₀ is considered in the calculation as an initial condition and it will automatically affect the position of graphene's charge neutrality point in the final result. In fact, n_s and n₀ in Eq. (4) are summed up before applying the absolute value, which is necessary to make a distinction between n-doped (n₀ < 0) and p-doped graphene (n₀ > 0). In inversion (V_g > V_T > 0 for p-doped Si and V_g < V_T < 0 for n-doped Si, where V_T is threshold voltage²⁹⁾) the silicon layer has reached maximum depletion and the quantities to be considered are C_q, C_ox and ${C}_{{\rm{Si}},\max }$. Equation (7) becomes

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{q}{{C}_{{\rm{ox}}}}{n}_{s}+\left(\displaystyle \frac{\hslash {{v}_{F}}^{2}\sqrt{\pi }}{2q}\right)\displaystyle \frac{{n}_{s}}{\sqrt{| {n}_{s}+{n}_{0}| +| {n}^{* }| }}\\ \quad +\,\left({V}_{g}-{V}_{{\rm{FB}}}-2{\phi }_{F}\right)=0,\end{array}\end{eqnarray} \tag{ 8 }$$

where the bulk potential ${\phi }_{F}$ takes into account the voltage drop due to ${C}_{{\rm{Si}},\max }$. The total inversion capacitance can be calculated as ${C}_{{\rm{GOS}},{\rm{inv}}}={\left(\tfrac{1}{{C}_{{\rm{ox}}}}+\tfrac{1}{{C}_{q}}+\tfrac{{W}_{{\rm{dep}},{\rm{\max }}}}{{\varepsilon }_{0}{\varepsilon }_{{\rm{Si}}}}\right)}^{-1}$, where ${W}_{{\rm{dep}},\max }$ is the maximum width of the depletion region in the silicon layer.

To calculate the total capacitance ${C}_{{\rm{GOS}},{\rm{dep}}}$ in depletion (${V}_{{\rm{FB}}}\lt {V}_{g}\lt {V}_{T}$ for p-doped Si and ${V}_{{\rm{FB}}}\gt {V}_{g}\gt {V}_{T}$ for n-doped Si), a different approach is necessary. The width of the depletion region in silicon W_dep has to be calculated for values of the surface potential ${\phi }_{s}$ ranging from 0 to $2{\phi }_{F}$. From W_dep, the depletion charge Q_dep and therefore the number of charges on graphene n_s can be calculated. The total GOS capacitance in depletion is given by ${C}_{{\rm{GOS}},{\rm{dep}}}\,={\left(\tfrac{1}{{C}_{{\rm{ox}}}}+\tfrac{1}{{C}_{q}}+\tfrac{{W}_{{\rm{dep}}}}{{\varepsilon }_{0}{\varepsilon }_{{\rm{Si}}}}\right)}^{-1}$. All the quantities that have been calculated as a function of ${\phi }_{s}$ can then be expressed as a function of the applied voltage through ${V}_{g}={V}_{{\rm{FB}}}\,+{\phi }_{s}-{Q}_{{\rm{dep}}}\left(\tfrac{1}{{C}_{{\rm{ox}}}}+\tfrac{1}{{C}_{q}}\right)$.

Throughout the calculation of C_GOS, the values of ${V}_{g}({n}_{s})$, and therefore ${V}_{g}(\mu )$, are extracted step by step, and are used to obtain graphene's absorption (and therefore transmission) as a function of the applied voltage V_g through Eq. (1), as shown in Fig. 2.

The results of the calculation of C_GOS for a GOS capacitor with p-doped silicon (${p}_{\mathrm{wg}}=1.0\,\times \,{10}^{18}\,{\mathrm{cm}}^{-3}$) for n-doped (${n}_{0}=-12\,\times \,{10}^{12}\,{\mathrm{cm}}^{-2}$), neutral (n₀ = 0 cm⁻²) and p-doped (${n}_{0}=12\,\times \,{10}^{12}\,{\mathrm{cm}}^{-2}$) graphene is shown in Fig. 5(b). As expected, graphene's quantum capacitance affects C_GOS only where C_q reaches its minimum [Fig. 5(a)]. This effect is clearly visible only when the GOS capacitor is in accumulation mode, and therefore C_GOS is higher. As a consequence, reducing C_q by reducing the impurity density ${n}^{* }$ would only have a small effect on C_GOS as a whole. In order to decrease C_ox, we could use an oxide with a lower permittivity or increase the oxide thickness. However, both solutions would increase the field necessary to accumulate charges on the capacitor plates in the whole range necessary to operate the device. In other words, the lower capacitance would allow to obtain a higher 3 dB frequency response, but the ER for the same voltage range would be significantly reduced. The device capacitance can therefore be optimised by focusing on how C_Si changes when varying the type and level of doping, and on how this affects C_GOS. Figure 6 shows the calculation of C_GOS performed for p-doped graphene (${n}_{0}=12\,\times \,{10}^{12}\,{\mathrm{cm}}^{-2}$) for different levels of p-type and n-type silicon doping. The capacitance in accumulation is not affected by the variation in silicon doping level. A reduction in capacitance is achieved in depletion for lower silicon doping, as expected due to the lower silicon depletion capacitance C_Si when the silicon doping is decreased. Due to this characteristic MOS behaviour, it is preferable to operate the device in depletion in order to obtain lower capacitance.

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To optimise the SLG EAM for high-speed operation, the 3 dB frequency response of the device has to be maximised. This figure of merit is limited by the device RC constant, therefore the total resistance and capacitance of the device have to be minimised in the desired operating region in order to obtain the lowest possible RC. In fabricated devices, graphene is most often p-doped, due to dangling oxygen bonds in the SiO₂ below and also due to environmental and polymer contamination during processing.^30,31) In terms of static electro-optical performance, as seen in Sect. 3.1, this means that the switching between on and off states takes place in the region between −2 and 2 V voltage bias. This region corresponds to the low resistance region in case of p-doped graphene, as shown in Fig. 3. In order to have low capacitance in the same voltage range, p-doped Si is preferable because it allows to operate the device in depletion for voltage bias higher than 0 V. As a result, when p-doped graphene is combined with p-doped silicon, the total RC is reduced in the region between 0 and 2 V. Likewise, in case of n-doped graphene, the situation would be reversed and the best choice would be a device with n-doped silicon operating at low reverse bias. This is better visualised in the example in Fig. 7. Figure 7(a) shows the values of C_GOS as a function of gate voltage for a 75 μm long device with p-doped graphene (${n}_{0}=12\,\times \,{10}^{12}\,{\mathrm{cm}}^{-2}$) and a waveguide width of 500 nm, for p-doped and n-doped Si (doping values in Table I). Using these values of C_GOS and values of R_tot from Fig. 3(b), the 3 dB frequency response is then extracted by simulating the electrical equivalent circuit in Fig. 1(b). Even though p-doped silicon exhibits higher sheet resistance than n-doped silicon, the considerably lower GOS capacitance of the EAM with p-doped silicon in the 0–2 V region allows to achieve a two-fold improvement in 3 dB frequency response at 0 V [Fig. 7(b)].

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Patterning graphene under the contact area, e.g. with holes, to increase the edge contact perimeter between graphene and the metal can lead to a significant reduction in graphene's contact resistance.³²⁾ Improved values of graphene contact and sheet resistance (${R}_{{\rm{graC}}}=100$ Ω μm and R_gra = 60 Ω/□) would allow to achieve a 3 dB frequency response of 17 GHz (18% improvement) at 0 V DC bias for a 75 μm long EAM and 25 GHz for a 25 μm long EAM. With reduced doping in the waveguide (${p}_{\mathrm{wg}}=4\,\times \,{10}^{17}\,{\mathrm{cm}}^{-3}$) this values could be further improved up to 23 and 31 GHz for L_device = 75 μm and L_device = 25 μm respectively.

We fabricated three samples with different type and level of doping in Si (summary in Table II). Sample A was fabricated with n-doped Si, with average carrier concentrations of n_slab = 2.5 × 10¹⁸ cm⁻³ and n_wg = 1.2 × 10¹⁸ cm⁻³ for the slab and the waveguide regions respectively. Sample B was fabricated using higher n-doping in the Si slab and waveguide regions than sample A (n_slab = 2.7 × 10¹⁹ cm⁻³ and n_wg = 2.3 × 10¹⁸ cm⁻³), with the purpose of reducing the total parasitic resistance without significantly impacting the GOS capacitance. Sample C was fabricated using p-doped Si ( p_slab = 3.2 × 10¹⁹ cm⁻³ and p_wg = 1.9 × 10¹⁸ cm⁻³). The characterisation of the samples was carried out under ambient conditions.

The three samples were first characterised by performing unbiased fiber-to-fiber transmission measurements on SLG EAMs with waveguides optimised for TE mode propagation (TE waveguides, W_wg = 500 nm) and with four different device lengths (L_device =  25, 40, 50 and 75 μm). The transmission scales linearly with the device length, and the extracted average and standard deviation values of absorption are 0.08 ± 0.01, 0.08 ± 0.01 and 0.05 ± 0.01 dB μm⁻¹ for samples A, B and C respectively.

We then performed biased fiber-to-fiber transmission measurements on the same EAMs, by sweeping the wavelength from 1510 to 1600 nm, while applying a DC bias ranging from −4 to 4 V. Figure 8(a) shows the extracted ER versus device length (L_device) for the three samples at the peak transmission wavelength of 1560 nm. The values of ER scale linearly with the device length, reaching up to 2.6 dB for Samples A and C and 3.8 dB for sample B for L_device = 75 μm. An example of the extracted transmission as a function of DC bias at 1560 nm for L_device = 75 μm is reported in Fig. 8(b). All three samples show minimum transmission of the modulation curve located at reverse bias. which indicates p-type doping in graphene. Sample B exhibits lower p-type graphene doping than the other two samples, which translates into the minimum transmission being shifted towards lower reverse bias. As a consequence, when the reverse bias on sample B is increased, graphene approaches again transparency, resulting in a more symmetrical transmission curve compared to the other two samples. The average and standard deviation values of modulation efficiency (${\rm{ME}}={\rm{ER}}/{L}_{{\rm{device}}}$) across the four devices at 1560 nm are 0.03 ± 0.01, 0.05 ± 0.01 and 0.04 ± 0.01 dB μm⁻¹ for samples A, B and C respectively. The higher modulation in sample B is attributed to higher mobility in graphene compared to the other two samples. This is confirmed by the values of graphene's mobility extracted from transfer length measurements (TLM) of graphene's electrical test structures fabricated on the same sample ($1610\,{\mathrm{cm}}^{2}\,{{\rm{V}}}^{-1}\,{{\rm{s}}}^{-1}$ for sample B and $1490\,{\mathrm{cm}}^{2}\,{{\rm{V}}}^{-1}\,{{\rm{s}}}^{-1}$ for sample C). The lower p-type graphene doping and the higher graphene mobility in sample B are attributed to sample-to-sample variations of graphene's properties, caused by uncontrolled variations in processing conditions.

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The electro-optical S₂₁ frequency response of the modulators was measured between 100 MHz and 30 GHz at DC bias ranging from 0 to 2 V with a vector network analyser, using −8 dBm RF power and a 50 Ω load resistor. Figure 9(a) compares the extracted 3 dB frequency response (${f}_{3{\rm{dB}}}$) of the three samples as a function of DC bias for L_device = 75 μm. Figures 9(b) and 9(c) compare the extracted R_tot and C_GOS from the fitting of the S₁₁ frequency response measured on the three samples, performed using the equivalent electrical circuit shown in Fig. 1(b). Among the n-doped samples, sample B exhibits the highest 3 dB frequency response at any forward voltage bias, with a maximum value of 8.9 GHz at 0 V DC bias for L_device = 75 μm. The decrease in R_tot (20% at 0 V DC bias) achieved in sample B with the higher doping in the slab and waveguide regions, counteracts the slight increase in C_GOS caused by the higher waveguide doping (13% at 0 V DC bias). This allows to improve the ${f}_{3{\rm{dB}}}$ from sample A to sample B at any forward voltage bias, e.g. with a gain of 2 GHz (29%) at 0 V DC bias (Table III). As expected from the theoretical analysis, the sample fabricated using p-doped Si (sample C) shows a substantial increase in 3 dB frequency response compared to sample B, with values up to 22.8, 21.6, 14.2 and 16.1 GHz at 0 V DC bias for L_device = 25, 40, 50 and 75 μm respectively (Table III). Even though the Si sheet resistance is higher, the lower C_GOS obtained by operating the device in depletion mode instead of accumulation mode allows to significantly reduce the total RC constant, and thus enhance the 3 dB frequency response at any forward voltage bias. The values of ${f}_{3{\rm{dB}}}$ decrease with higher device length, due to the increase in the total RC constant related to the 50 Ω load resistor (Table III).

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Table III.  Values of measured 3 dB frequency response (f_3dB) at 0 V DC bias on TE SLG EAMs for L_device = 25, 40, 50 and 75 μm. The ${{f}}_{3{\rm{dB}}}$ is higher for sample C (p-doped Si) and for smaller device lengths.

	Measured ${{f}}_{{\bf{3}}{\bf{dB}}}$ (GHz)
	L = 25 μm	L = 40 μm	L = 50 μm	L = 75 μm
Sample A	10.9	7.7	8.2	6.9
Sample B	12.9	10.6	9.6	8.9
Sample C	22.8	21.6	14.2	16.1

Despite the high 3 dB frequency response achieved with the sample with p-doped Si (sample C), the ER of the SLG EAMs remains limited when using TE-polarised light, with values ranging from 0.9 dB for L_device = 25 μm–2.6 dB for L_device = 75 μm. The performance with TE-polarised light can be improved by using an optimised waveguide thickness.^33,34) However, in our case this approach is not possible due to specific waveguide height requirements of the fab used to fabricate the substrate. Using waveguides optimised for TM mode propagation (TM waveguides) can increase the ER for a given device length, due to the bigger overlap between the TM optical mode and the graphene layer compared to TE when the waveguide thickness is 220 nm [see inset of Fig. 10(a)]. To maximise the overlap with graphene but still ensure mode confinement in the waveguide, we use a waveguide width of 750 nm.⁵⁾ Unbiased transmission measurements performed on sample C (p-doped Si) from 1510 to 1600 nm on SLG EAMs with TM waveguides, equivalent to the ones performed on TE waveguides, showed that graphene's absorption is 0.09 ± 0.01 dB μm⁻¹, which is 2.3 times higher than the 0.04 ± 0.01 dB μm⁻¹ measured on TE waveguides, in agreement with the value of 2.2 extracted from Lumerical MODE simulations. The ME of the four SLG EAMs is consistent across the measured C-band spectrum for both TE and TM devices [Fig. 10(b)]. The drawback in using TM waveguides comes from the wider waveguide width, which leads to higher sheet resistance and GOS capacitance, resulting in a 1.1–1.5 times lower 3 dB frequency response compared to TE waveguides (Fig. 11). Nevertheless, due to the low C_GOS at forward bias on the SLG EAMs with p-doped Si, TM waveguides exhibit 3 dB frequency response at 0 V DC bias of 20.7, 18.0, 15.7 and 14.2 GHz for L_device = 25, 40, 50 and 75 μm respectively.

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To demonstrate the broadband operation of graphene devices, we measured TM graphene-Si EAMs fabricated on sample C with exactly the same processing steps and cross section, but designed to operate in the O-band. We characterised four devices, with same lengths as the TM C-band devices demonstrated earlier (L_device =  25, 40, 50 and 75 μm) and waveguide width of 380 nm. Fiber-to-fiber transmission measurements from 1260 to 1330 nm, resulted in an average absorption across the four devices of 0.10 ± 0.01 dB μm⁻¹. The biased transmission measurements were performed sweeping the DC bias from −4 to 4 V and the wavelength from 1270 to 1320 nm. The average and standard deviation values of ME at the peak of the fiber grating couplers (1300 nm) across the four devices are 0.041 ± 0.005 dB μm⁻¹. The lower modulation efficiency compared to C-band TM devices is due to the higher energy of the photons in the O-band. As a consequence, it's necessary to apply a higher voltage in order to achieve full transparency in graphene, which may result in oxide breakdown. The extracted ME of the four TM O-band SLG EAMs is consistent across the O-band spectrum, as shown in Fig. 12(a). The 3 dB frequency response of the O-band SLG EAMs, extracted from electro-optical S₂₁-parameters measurements at 1300 nm wavelength, reaches values of 19.7, 20.3, 19.3 and 16.0 GHz at 1 V DC bias for L_device = 25, 40, 50 and 75 μm respectively [Fig. 12(b)].

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A summary of the performance of the C-band TE, C-band TM and O-band TM SLG EAMs on sample C is reported in Table IV for L_device = 75 μm. The FOM is defined as ER/IL and should therefore be as high as possible. The C-band TM EAM represents the best compromise between IL and ER, as shown by the high value of FOM, while also exhibiting a 3 dB frequency response of 14 GHz. Eye diagrams were measured on the C-band SLG EAM with p-doped Si (sample C), TM waveguide and L_device = 75 μm at 1560 nm using 2²³-1 PRBS, 2.5 V_pp, 14 dBm input optical power and a 50 Ω terminated probe. Open eye diagrams were generated from 5 Gb s⁻¹ up to 50 Gbit s⁻¹, thus demonstrating potential for high-speed data transmission using graphene technology. Examples at 10, 25 and 50 Gbit s⁻¹ are shown in Fig. 13(a). The large-signal ER and the signal-to-noise ratio (SNR) are reported in Fig. 13(b) as a function of bit rate. The dynamic energy consumption (${E}_{{\rm{bit}}}={{CV}}^{2}/4$) of the SLG EAM is calculated to be ∼112 fJ, while the static power consumption is < 10⁻⁸ mW, due to the low leakage current flowing through the GOS capacitor (< 10 pA).

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