*The strong nonlinearity of molybdenum disulfide (MoS _{2}) provides a basis for microwave and mmWave devices. Under natural conditions, MoS_{2} exhibits a strong third-order nonlinearity, and it demonstrates a second-order nonlinearity with applied voltage. Based on this unique electrical property, a voltage-controlled MoS_{2} frequency doubler is designed. With an input power of 20 dBm at 1 GHz, the output power is -27 dBm at 2 GHz. Experimental results are consistent with simulation demonstrating an excellent frequency doubling effect. Although this work was conducted at 1 GHz, MoS_{2} has unique advantages for higher frequency applications as well. This offers new possibilities for controlling the electrical properties of two-dimensional (2D) semiconductor materials.*

Studies have shown that 2D materials such as transition metal dihalides play an important role in optoelectronics due to their strong nonlinearities. MoS_{2} is a new type of 2D semiconductor material with an ultra-thin, layer-like structure. It not only has a controllable bandgap and a special hexagonal crystal structure but also possesses a strong electrical nonlinearity. In 2017, Säynätjoki et al.^{1} investigated the nonlinear properties of monolayer and multilayer MoS_{2}. It was shown that monolayer MoS_{2} has a strong optical nonlinearity; the third harmonic is 30x stronger than the second harmonic.

The nonlinear property of MoS_{2} can be used to make devices such as microwave frequency multipliers and mixers that have unique advantages in microwave and mmWave device applications. In 2019, Fang et al.^{2} used the nonlinearity of MoS_{2} to fabricate a microwave triplexer. The MoS_{2}-based triplexer, with an input power of 14 dBm and an input frequency of 0.75 to 1.1 GHz yielded an output power at the third harmonic of -27.1 dBm with a conversion loss of 41.1 dB, but the second harmonic effect was poor.

The nonlinear behavior of MoS_{2} changes with applied DC bias. Based on this property, the design described is of a frequency doubler using a stable 2H MoS_{2} semiconductor crystal.^{3,4}

Modeling of MoS_{2} is important for the simulation of nonlinear devices based on it. In this work, MoS_{2} is equated to a reverse parallel diode pair. Simulation shows that the model matches well with measured results and that the frequency doubling effect can be adjusted by changing bias voltage.

By applying bias voltage to both sides of the MoS_{2} crystal, the second harmonic output power is increased and the third harmonic output power is reduced. The proposed doubler has a compact structure with a simple fabrication process, making it suitable for the development of micro and nanodevices.

**DESIGN AND MODELING**

**MoS _{2} Frequency Doubler Design Overview**

The design takes advantage of the strong nonlinear microwave properties of MoS_{2}, which are suitable for nonlinear devices such as a frequency multiplier.^{5} The structure comprises a bandpass filter, a bias circuit and a microstrip gap of MoS_{2} (see **Figure 1**). The circuit is designed on an FR-4 substrate with thickness H = 0.8 mm and relative dielectric constant ε_{r} = 4.41. The microstrip line thickness is T = 0.35 μm and its loss tangent TanD = 0.02. The 50 Ω microstrip line width is 1.41 mm with a gap length of 0.35 mm. The MoS_{2} crystal is in the form of a tape sticker from Shenzhen Six Carbon Technology Company.

The bandpass filter eliminates clutter with a passband of 400 to 1200 MHz covering the operating band of 800 to 1100 MHz. DC is provided on both sides of the microstrip gap by bias networks to enhance second harmonic emission from the MoS_{2} and improve the frequency doubling efficiency.

**Modeling**

When metal is in contact with a semiconductor material (Schottky contact), a potential barrier, called a Schottky barrier, is formed at the metal-semiconductor junction.^{6,7 }The Schottky barrier controls the current and capacitance characteristics at the contact surface, which in turn affects the electrical properties of the Schottky semiconductor.^{8-10}

Based on the electrical conductivity of MoS_{2}^{11-14} and the relationship between multilayer MoS_{2} and monolayer MoS_{2},^{15} MoS_{2} can be equated to a nonlinear resistance and capacitance in parallel. The equivalent circuit based on the resistor-capacitor model tends to ignore the parasitic capacitance, resulting in a slight difference between simulated and measured results.

Schottky diodes are designed based on the physical properties of metal-semiconductor Schottky contacts, for which a diode model is proposed that can effectively describe the frequency doubling characteristics of MoS_{2} films. According to the theory of MoS_{2} Schottky contacts,^{16-18} the MoS_{2} Schottky junction is equivalent to a combination of a resistor and an anti-parallel diode pair. The Cu-MoS_{2} and MoS_{2}-Cu interfaces in the circuit form the reverse-connected Schottky diodes.

The I-V characteristic of a nonlinear device can be represented by:^{19,20}

Where u is the voltage u = V_{0} + u_{0} applied to the nonlinear device. Equation (2) is a series expansion of Equation (1):

Where α_{n} (n = 0, 1, 2…) is determined by Equation (3).

and V_{0} is the bias voltage.

MoS_{2} has a strong nonlinearity, with its odd-order harmonic signal output being greater than the value of its even-order signal output when V_{0} = 0.^{21,22} Consequently, the nonlinear characteristic of multilayer MoS_{2} without bias is represented by Equation (4).

When V_{0}≠ 0, the value of the even-order signal is increased and the value of the odd-order signal is attenuated. Therefore, the nonlinear characteristic of the MoS_{2} film is described by Equation (2) when a bias voltage is added, and the values are different with different bias voltages.

In summary, carrier conductivity is adjusted to obtain the greatest frequency doubling effect.^{23} The series-connected resistance represents the finite conductivity of the MoS_{2} crystals. A current path is formed between the semiconductor and the external circuit when a voltage is applied. The MoS_{2} circuit model can be equated to a resistor-diode model; the diode equivalent model simulates its nonlinear characteristics.

**SIMULATION**

The simulation circuit is shown in **Figure 2**. The simulation is carried out without and with bias voltage applied. Without bias, the simulation results are shown in **Figure 3**. The third harmonic output power is about -35 dBm, while the second harmonic output power is barely -50 dBm. When the bias voltage is 21 V, the simulation results are shown in **Figure 4**. The second harmonic output power is about -32 dBm, while the third harmonic output power is about -45 dBm. The simulation results of the MoS_{2} equivalent diode model show that by applying a bias voltage to its terminals, the third harmonic decreases and the second harmonic increases.