Large-area and bright pulsed electroluminescence in monolayer semiconductors

Transition-metal dichalcogenide monolayers have naturally terminated surfaces and can exhibit a near-unity photoluminescence quantum yield in the presence of suitable defect passivation. To date, steady-state monolayer light-emitting devices suffer from Schottky contacts or require complex heterostructures. We demonstrate a transient-mode electroluminescent device based on transition-metal dichalcogenide monolayers (MoS2, WS2, MoSe2, and WSe2) to overcome these problems. Electroluminescence from this dopant-free two-terminal device is obtained by applying an AC voltage between the gate and the semiconductor. Notably, the electroluminescence intensity is weakly dependent on the Schottky barrier height or polarity of the contact. We fabricate a monolayer seven-segment display and achieve the first transparent and bright millimeter-scale light-emitting monolayer semiconductor device.

The time dependent luminescence decay in 2D materials can be calculated using a recombination model for 2D excitonic systems presented in our previous work: where 〈N(t)〉 is the exciton concentration as a function of time (t), τr is the exciton lifetime, and Cbx is the biexcitonic recombination rate [3][4][5] . Solving this differential equation yields: where the boundary condition, 〈N(0)〉, is the initial exciton concentration. From Supplementary Equation 2, we can then calculate the PL QY during quasi-steady-state operation as a function of initial exciton density. The modeled values are in excellent agreement with quasi-steady-state QY measured using a pulsed laser with varying repetition rates as shown in Supplementary Fig. 15.

Supplementary Note 2. AC frequency dependence.
EL spectra measured with f ranging from 100 kHz to 10 MHz are shown in Supplementary   Fig. 3a and the spectral shape was observed to be f independent ( Supplementary Fig. 3b). The EL intensity per cycle shows minimal frequency dependence because 1/f is much larger than the EL decay time constant (~ 8 ns, Supplementary Fig. 2). This shows that the device can be operated at frequencies as high as 10 MHz, and is ultimately limited to a modulation frequency of 125 MHz corresponding to the EL decay time constant. This is the fastest electrically modulated light emitting device reported for TMDCs 6 . (1) (2)

Supplementary Note 3. Current components during AC transient.
The total gate current (Ig,total) in a two-terminal t-EL device can be described by Supplementary semiconductor, the mechanism can be similarly explained, and we obtain larger EL during the -Vg to +Vg transient relative to the +Vg to -Vg transient.

Supplementary Note 5. Gate oxide characterization.
To verify the gate oxide quality as well as to directly measure Cox, capacitance vs.
frequency measurements were performed on devices fabricated on 50 nm SiO2/Si substrates as shown in Supplementary Fig. 21 over a frequency range of 1 kHz to 1 MHz. The measured capacitance of 5.1 pF is consistent with the calculated value of 6.91 pF. Furthermore, the measured impedance vs. frequency is in excellent agreement with the expected impedance of a direct capacitor (which is given as Xc = (2πfCox) -1 , where Xc is the reactance of the gate capacitor).
Furthermore, from DC measurements the leakage currents are below the noise level (pA range) of the measurement setup, and indicate that the device has a purely reactive impedance.

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The EL internal efficiency of the t-EL device can be extracted from the ratio of the total number of emitted photons per cycle to the steady-state electron (n0) and hole (p0) concentrations: Here T is the time period, L is the length of the device, R is the radiative recombination rate and β is the fraction of steady-state carriers which undergo recombination during a Vg transient. The value of (n0+p0) can be calculated using Supplementary Equation 6. During a -Vg to +Vg transient (total change of 2Vg), the net voltage dropped at the Schottky source contact is equal to the sum of the barrier heights to electrons and holes (φBn + φBp = Eg). Thus, To achieve steady-state carrier densities, sufficient voltage must be applied to enable large band bending and thus achieve significant tunneling through the Schottky barriers. As such this equation is only valid for sufficiently high Vg, which is shown in Supplementary Fig. 13. The integral in the numerator is equal to the total number of photons emitted per cycle. The internal efficiency is unity when the PL QY is 100% and all of the steady-state carriers undergo recombination (β = 1).
Practically, due to the finite slew rate of the AC source and a finite radiative recombination rate, a fraction of the steady-state carriers exit the semiconductor through the source contact without recombining (β ≠ 1). The external efficiency is given by: where ηext is the light extraction efficiency. This is calculated using (4n 2 ) -1 where n is the refractive index of the medium, as well as the optical interference from the Si substrate with a 50 nm SiO2 layer. The enhancement factor for Si/SiO2 is experimentally determined to enhance the lightoutcoupling by 1.6× for WSe2 and 2× for WS2.

Supplementary Methods
Three independent approaches were used to verify the system calibration, and are discussed in detail in our previous work. 3 In the first approach, the wavelength of the spectrometer was calibrated using Ar and Kr lamps (Newport) as reference. The instrument function versus wavelength of the system was obtained by measuring the response of a Lambertian light source generated under the objective through the illumination from a temperature-stabilized lamp (ThorLabs SLS201) onto a diffuse reflector surface. The system efficiency was calibrated by measuring the response of the 514 nm laser focused on the diffuse reflector. In the second approach, we cross-calibrated using a silicon photodiode which was able to acquire a fraction of the PL but is independent of the optical path of objective. In the third approach, the calibrations were performed using a sample with a known QY close to 100% (Rhodamine 6G in methanol). These three approaches were in good agreement with each other (<15% error).