Small Molecule Based Organic Photo Signal Receiver for High‐Speed Optical Wireless Communications

Abstract The present work describes the development of an organic photodiode (OPD) receiver for high‐speed optical wireless communication. To determine the optimal communication design, two different types of photoelectric conversion layers, bulk heterojunction (BHJ) and planar heterojunction (PHJ), are compared. The BHJ‐OPD device has a −3 dB bandwidth of 0.65 MHz (at zero bias) and a maximum of 1.4 MHz (at −4 V bias). A 150 Mbps single‐channel visible light communication (VLC) data rate using this device by combining preequalization and machine learning (ML)‐based digital signal processing (DSP) is demonstrated. To the best of the authors' knowledge, this is the highest data rate ever achieved on an OPD‐based VLC system by a factor of 40 over the previous fastest reported. Additionally, the proposed OPD receiver achieves orders of magnitude higher spectral efficiency than the previously reported organic photovoltaic (OPV)‐based receivers.

time ( rise ) and fall-time ( fall ) of OPDs were determined by the time required to reach 90% of the maximum signal after light-on and 10% of the maximum signal after light-off, respectively. The response time of BHJ-OPD ( rise =3.2 sec,  fall =3.3 sec) was significantly faster than PHJ-OPD ( rise =13.7 sec,  fall =12.7 sec). Following an investigation of microsecond-level photoresponse of OPD receiver, devices were constructed to determine their effective mobility and charge recombination properties using transient photocurrent measurements under laser illumination. [9,33] The TDCF photocurrent transients measured without delay time are depicted in Figure S2b. The sample was kept at a pre-bias of 0.5 V during excitation and at a collection voltage (V coll ) of -3 V prior to collection. The effective mobility  TDCF of the OPDs was calculated from t 0 using Equation 6. In comparison to the mobility of PHJ-OPD, which is 3.0E-5 cm 2 /Vs, the mobility of BHJ-OPD is 3.6E-5 cm 2 /Vs.

= •
(1) , where is the thickness of the organic layer.
To determine the source of the difference in mobility between two device types, we analyzed the charge recombination dynamics using time-delayed TDCF measurements. [34] After a time delay of 300 ns to 20000 ns, transient photocurrent was measured and parameters relating to recombination dynamics were determined for each device by fitting the differential extracted charge (Q/t) plot to the collected charge amount (Q coll ).
because light can generate free charges through the BHJ layer, second-order recombination may be the primary recombination mechanism for BHJ-OPD. Although bimolecular recombination occurs throughout the OPD, BHJ-OPDs have a higher net charge mobility due to the suppression of background charge generation, and the average travel path for free charges is shorter in BHJ-OPD than in PHJ-OPD under a fixed electrical field. As previously stated, recombination coefficients derived from TDCF measurements with delay can adequately explain this phenomenon. The parameter for bimolecular recombination, k 2 , was greater for BHJ-OPD (1.7E-10 cm -3 /s) than for PHJ-OPD (1.9E-11 cm -3 /s). Furthermore, the parameter relating to first-order recombination (Q bg ) of BHJ-OPD (1.0E-9 C) was less than that of PHJ-OPD (2.3E-9 C).

Supplementary Note 3. Pre-equalizer circuit and response
The system's capability is limited by the organic photodiode's (OPD) -3dB bandwidth limitation of 1.4MHz at 4V reverse bias. Pre-equalization is frequently used to augment the visible light communication (VLC) system's limited bandwidth. On various order circuits, the analog pre-equalizer can be designed with a variety of shapes, slopes, and cut-off frequencies. In the current study, a simple first order pre-equalizer consisting of a resistor ( ) and ( ) a capacitor in parallel is used, as illustrated in Figure S3a. It is located between the arbitrary waveform generator and the light source, just before the transmitted signal lights are generated.
Additionally, the modulated alternating current (AC) components from AWG are distorted to the required shape via a pre-equalizer.
Three circuits with varying shapes and -3dB frequencies are evaluated here by varying the values of and , designated as , respectively. The frequency responses of OPD and each APEQ are depicted in Figure S3b. The response of APEQ1 is flat, and the -3dB bandwidth is extended to ~6 MHz with an ~18dB attenuation of the DC response. APEQ 2 has a lower response gain (almost -3dB) but a wider -3dB bandwidth (~7 MHz) than APEQ 1. APEQ3 exhibits an arched response with a -3dB point of ~7 MHz. Figure S3c illustrates BER measurements and eye-diagram insets at a data rate of 30 Mbps after applying each APEQ. Due to the limited bandwidth, 30 Mbps with APEQ1 cannot meet the FEC threshold. Although the signal-to-noise ratio is relatively high in comparison to others, the eye opening is unclear, as illustrated in the inset (i). While APEQ2 and APEQ3 both reduce response, the BER satisfying the threshold is obtained due to the larger -3dB bandwidth. Notably, the APEQ2 eye diagram (inset (ii)) is more distinct than the APEQ one eye diagram (inset (iii)). c) BER measurement with a data-rate of 30Mbps and eye-diagram at difference APEQ.

Supplementary Note 4. DCO-OFDM
Due to its high spectral efficiency, DC-biased optical orthogonal division multiplexing (DCO-OFDM) has been widely used to achieve the highest performance in optical wireless communication (OWC) systems. By applying DC bias to the optical OFDM signal in DCO-OFDM, the transmitted signal can be made unipolar, satisfying the requirements of both the intensity modulation (IM) and direct detection (DD) systems. Nonetheless, due to the high peakto-average power ratio (PAPR), it is difficult to maintain a positive signal. [49] However, the clipping process ensures not only a positive signal but also the full dynamic range of the light source, resulting in a higher signal-to-noise ratio (SNR). The clipped OFDM signal ( ) can be expressed with unclipped OFDM signal ( ): , where is [ ] , and ( ) denotes clipping noise. The signal is distorted by passing through the channel h(n) with the additive noise ( ). The received signal ( ) can then be expressed as: , where indicates a convolution operation.
Equations 5 and 6 express the SNR on each subcarrier in OFDM, where denotes the sub-carrier index. It can be defined as ( ), and , where ( ) denotes the channel impact, denotes the variance of the additive noise at the receiver, and denotes the variance of the clipping noise, respectively, as shown in Equation (5). Then, this can be organized as shown in Equation (6) with available and meaning an effect of additive noise and clipping noise.
Using this available SNR on each subcarrier, the capacity (C) of the DCO-OFDM can be derived with the maximum number of bits ( ) as: , where is the time duration of a single DCO-OFDM frame.
is the distance between subcarriers and means the subcarrier size for the Fourier fast transform (FFT). To mitigate interference between OFDM symbols, the number of redundant subcarriers, , is added to the pure OFDM signal for the cyclic prefix (CP). The total subcarrier size is expended in this case as . When the following inequation is satisfied, , converges to .
As a result, the can be estimated by Equation 8.
Particularly, the capacity of DCO-OFDM can be optimized by utilizing a channel adaptive bit and power loading scheme for high data rates. It determines the number of bits and the amount of power allocated to each subcarrier for M-level quadrature amplitude modulation (M-QAM) based on the channel condition. The level of QAM is simply calculated by = on subcarrier. Although this method adds complexity to the system, it enables the DCO-OFDM to perform better than in the fixed case. Using this method, the data-rate can be calculated according to the channel condition as: , where and denote over sampling rate and system sampling clock, respectively.   subset of the recurrent neural network (RNN) model that is capable of processing sequential data 40 . As illustrated in Figure S5, a single LSTM unit consists of an input gate ( ), a forget gate ( ), a cell candidate ( ) and an output gate ( ). Each gate has their own weights: input weight ( ), recurrent weight ( ) and layer bias ( ). Theses weights are updated depending on learning rate of each gate. Then, at the t step, the output of the input gate, forget gate, cell candidate, and output gate according to , , , are calculated as: , where is the current input. The cell state ( ) and hidden state ( ) are shared to the next LSTM unit to analyze the sequential relation of input data. These states on t th are calculated as: , where indicates the element-wise multiplication of vectors and is the previous cell state information. Initially, the forget gate determines whether or not to preserve information in the LSTM process. The input gate then determines the content to be updated in the cell. The cell candidate for the current cell state is determined. Following that, the cell state is updated using the results of the forget gate, input gate, and cell candidate, and the cell is passed to the following layer. Finally, the output gate calculates the output and sends it to the following layer as well. All steps in this process are influenced by the previous result of the output gate. Thus, the LSTM method can be used to treat a sequential data set containing severe ISI, such as a communication signal, in order to predict the original data and mitigate the problem. Bidirectional LSTMs (bi-LSTMs), in particular, which are structured with forward and backward LSTMs, can learn more efficiently.