Third-order Nonlinear Dynamic Model for Electrical Characterization of Organic Light-emitting Diodes

1. Introduction

Organic light emitting diodes (OLEDs) are widely used in the displays of electrical devices including TV displays, mobile devices, and lighting. Moreover, OLEDs have received attention as next-generation displays because of their merits including low production costs, high durability, high efficiency, high flexibility, a lack of mercury, and emission without UV rays [1].

Therefore, research is actively being conducted into OLED light emission mechanisms. The main issues of light emission from an OLED include carrier injection, recombination, and transport processes [2]. These processes are closely related to the electrical characteristics of OLEDs. For this reason, electrical behavior prediction and analysis of electrical characteristics for OLEDs are important while studying the light emission mechanisms of OLEDs.

To understand the electrical characteristics of an OLED, Roy et al. analyzed the organic layer using a parallel RC circuit and evaluated the electrical properties employed in layer-by-layer self-assembled thin films [3]. Liao et al. reported the PN junction effects in an OLED [4]. Pitarch analyzed the SCLC (space charge limited conduction) effects occurring in an OLED [5]. Therefore, the extraction of parameters related to PN junctions and SCLC is a key process in the analysis of OLEDs.

To extract parameters, low-frequency impedance spectroscopy, steady-state I-V measurements, photo-detectors, and impedance meters are used [6]. However, each method only estimates a small number of parameters. Therefore, employing existing methods for estimating the important OLED parameters is costly and laborious, requiring separate sets of experiments and measurements. Moreover, as some measurements use linearization techniques, the measurement results can vary because of the DC biases.

To reduce the required effort and inaccuracy of existing estimation methods, we suggested the second-order nonlinear model for an OLED [7]. This model can be used for OLED’s electrical behavior prediction and parameter estimation based on the PN junction using a single data set. However, this model cannot be used to independently inspect each layer of an OLED because this model does not consider the electrical characteristics of an OLED’s layers (except for the emission layer).

This paper proposes a third-order nonlinear model, which considers the layer structure of an OLED and contains parameters related to the PN junction and SCLC. Trustregion (TR) algorithms and particle swarm optimization (PSO) algorithms are employed to estimate these parameters using a single set of measurement data. As a consequence, this nonlinear model efficiently provides in-situ characterization of the OLED parameters. All of the parameters related to the PN junction and SCLC are simultaneously estimated, which is demonstrated in our experimental results. Moreover, model parameters are used to estimate the physical characteristics of the layers of the OLED.

 

2. Structure of an OLED and Model

In this section, the structure of the OLED under test is explained. The third-order model suggested in this paper is also explained and is compared to the second-order model for OLEDs presented in our previous works. [7]

2.1 Structure of an OLED

An OLED consists of several thin layers of film: the cathode, electron injection layer (EIL), electron transport layer (ETL), emission layer (EML), buffer layer, hole transport layer (HTL), and p-type doped hole transport layer (p-HTL). The capping layer (CPL) surrounds the thin layers as depicted in Fig. 1.

Fig. 1.Structure of an OLED

Among the layers, ETL, HTL, and EML play important roles in the electrical and light emission mechanisms of an OLED. These layers are made of organic materials.

2.2 Structure of the third-order Model for OLEDs

The second-order nonlinear model suggested in [7] considers two electrical characteristics of an OLED, the PN junction and parasitic elements. In the second-order model, it is assumed that only the EML affects the parameters related to the PN junction since the EML has a similar structure to that of a PN diode. It is also assumed that the other layers only affect the parasitic elements. Therefore, the second-order model can be used to find only the electrical parameters related to the EML. Therefore, the second-order model cannot be used to find electrical parameters related to HTL or ETL, which is a drawback, because the HTL and ETL also play an important role in the light emission mechanism of OLEDs.

To evaluate the electrical mechanisms occurring in the ETL and HTL, the third-order model for OLEDs is developed. The third-order model is created by adding a parallel RC circuit that reflects the parameters related to the SCLC mechanism to the second-order nonlinear model. Since a parallel RC circuit is added, the structure of the third-order nonlinear model changes, as shown in Fig. 2.

Fig. 2.Equivalent circuit of an OLED

In Fig. 2, VOLED and IOLED denote the voltage across the OLED and current flow through the OLED, respectively. The parallel RC circuit, consisting of CPN and RPN, is an equivalent circuit for the PN junction. CPN and RPN are given by [8]

where VPN is the voltage drop due to the PN junction. n, k, and T are the ideality factor, Boltzmann constant, and absolute temperature, respectively. RPN0 and CPN0 are coefficients.

The parallel RC circuit consisting of CSC and RSC is an SCLC-equivalent circuit. CSC and RSC are given by [9]

where VSC is the voltage drop due to SCLC. l is a parameter that is determined by impurity concentration. RSC0 and CSC0 are coefficients. RP and CP are parameters representing parasitic resistance and capacitance, respectively.

Combining the equivalent circuits of the mechanisms occurring in the OLED, the differential equations of the model are as follows:

 

3. Parameter Estimation using the Model

The OLED analyzed in the paper is made by Samsung Display Co., Ltd.; it is a bottom-emitting device, i.e., light generated in EML radiates through HTL. H wever, the data sheet parameters are unknown. For measurement purposes, a resistor RL is connected in series with the OLED as shown in Fig. 3. The room temperature is 298K.

Fig. 3.Measurement circuit for the OLED

To create the overall circuit, VIN is applied, and VOLED is measured as the output. IOLED is given by

To estimate the parameters of the model, a two-stage estimation strategy is introduced. In this strategy, the parameters are divided into θ1 and θ2 which are given by

In the first stage, θ1 is estimated using the TR algorithm provided by Fontes et al. [10]. In the second stage, θ2 is estimated using the PSO algorithm provided by Schwaab et al. [11].

To allow estimation using only one data set, VIN is split into two parts. One part is a stepwise signal for measuring the static response of the OLED. The other is a pseudorandom binary sequence (PRBS) signal for measuring the dynamic response of the OLED. The PRBS signal is a sequence of pulse-width-modulated rectangular pulses, which has more frequency components than simple square waves [12]. The resulting VIN values are shown in Fig. 4.

Fig. 4.Input (Vin) used for model estimation

In Fig. 4, (a) shows the entire sequence of VIN ; (b) shows the first part (stepwise increase) of VIN, which is used for the estimation of θ1 ; and (c) shows the second part (PRBS) of VIN, which is used for the estimation of θ2.

3.1 Estimation of θ1

In the first stage of model parameter estimation, θ1 is estimated using the TR algorithm, which minimizes (11).

where is the steady steady state value of VOLED when the input VIN takes the rth value of the stepwise part, which is given by

with computed by (8); is the estimated value of with the parameter vector θ1 replaced by its estimate . Note that equation (12) results from setting the left-hand sides of (5)-(7) to zero.

Let denote the candidate estimate at the jth iteration for θ1. Then the improvement direction denoted by is given as follows:

where H and g are the Hessian matrix and the gradient of , respectively; D and Δ are the scaling matrix and a positive integer, respectively. If the constraint in (14) is satisfied, is updated using (15).

If the constraint in (14) is not satisfied, reduce Δ and recalculate (13) until (14) is satisfied. This iteration procedure is repeated until or j reaches a given maximum iteration number. The estimation results for θl are shown in Table 1.

Table 1.Estimation results for θl

3.2 Estimation of θ2

In the second stage of model parameter estimation, θ2 is estimated by the PSO algorithm using obtained in TABLE I. Let denote the ith candidate estimate for θ2 at the jth iteration, for 1 ≤ i ≤ M, where M is the number of candidate estimates at each iteration; the best estimate of the ith candidate is given by

where is the objective function defined as

and is the estimated value of VOLED(t) using (5)-(7) with θ2 replaced by its estimate while the value of θ1 is fixed to in Table 1. Then, the best estimate at the kth iteration is calculated using

Having obtained the estimate from for 1 ≤ j ≤ k at the kth iteration, is updated for the next iteration as follows:

where is a random number between 0 and , and is a random number between 0 and . and are pre-determined constants; in the estimation, and are 1.5. The value of resulting from (19) is further constrained to satisfy the following inequalities:

These constraints are given on the basis of the known physical characteristics such as the turn-on time of the device.

The best estimate at the (k + 1)th iteration is obtained using the same procedure as given above. This iteration procedure is repeated until the objective function converges. In this paper, the algorithm is stopped at the 16th iteration. Thus, the estimation result of the iteration procedure becomes the final estimate of θ2. the final estimate of θ2 is given in Table 2.

Table 2.Estimation results for θ2

 

4. Model Verification with Experimental Check

In this section, the validity of the model estimated in the previous section is demonstrated. The validity is confirmed using two methods. One method compares the dynamic and static characteristics of the OLED and the resulting model. The other method identifies whether the resulting model parameters accurately reflect the OLED’s physical characteristics.

4.1 Model verification with input-output data

The validity obtained by comparing the input-output relationship between the OLED and the resulting model identified in the previous section, is demonstrated here; both dynamic and static characteristics of the OLED are shown, to be consistent with the corresponding experimental data.

Static characteristics of the model are verified by comparing the I-V relationships of the OLED and the resulting model. I-V curve of the resulting model can be obtained analytically by solving the steady-state equations as shown in (12). These results are compared to the experimental data in Fig. 5, in which two curves are seen to be very close to each other.

Fig. 5.Static characteristics comparison result for the OLED (solid line) and the model (dotted line)

Note that the current is shown in log scale in the smaller figure and in linear scale in the larger figure. The maximum value of the residual is less than 7% of the current flowing into the OLED. Since the turn-on voltage of the OLED is roughly 3 V, the I-V relationship is compared when VOLED is larger than 2.5 V.

To verify the dynamic performance of the third-order model, the output of the resulting model is compared to that of the OLED. The comparison results obtained are shown in Fig. 6, in which the model outputs are seen to match the real-world data. Note that the PRBS signal applied in this experiment is different from the third-order model in Fig. 4, which is used in the parameter estimation. The maximum value of the residual is less than 5 % of the output of the OLED.

Fig. 6.Dynamic characteristics comparison result for the OLED (solid line) and the model (dotted line)

4.2 Model verification via analyses of the model parameters

OLEDs, which hae the same materials but with thickness of layers being different, are modelled in this section for the purpose of verifying the relation between the physical characteristics of OLEDs and the model parameters. Table 3 lists detailed thickness and brightness information for the OLEDs used in the experiment.

Table 3.Thickness/brightness comparison for the OLEDs

Brightness indicates the lighting power measured by the photodetector placed 5 cm away from the OLEDs when the voltage applied to the OLEDs is 4 V. Note that the OLED named Std is the one verified in the previous section; it has the highest lighting efficiency among the other OLEDs.

Low light emission efficiency of the OLED named M-HTL is caused by degradation of the thick HTL. Estimation results for several important model parameters of the OLEDs are shown in Table 4.

Table 4.Parameters comparison for the OLEDs

Comparing Std to M-HTL and M-ETL, we see that the thickness modification of HTL has little effect on the parameters of the estimated models. Whereas, thickness modification of the ETL affects the value of n of the model. Based on these results, we estimate that the sheet resistivity for holes in the HTL will be significantly smaller than the sheet resistivity for electrons in the ETL. This implies that the hole mobility of HTL is much larger than the electron mobility of ETL, which is confirmed by the well-known results of Park [13].

Comparing Std to M-EML, the value of Rp of the model for M-EML is larger than that of Std. Based on this result, we estimate that the power consumption ratio, not generating excitons but instead generates heat, will increase. Moreover, the sharp increase means that the ratio of traps, which does not affect the light emission mechanism, increases in the EML. These results match the lowest light emission efficiency of the M-ETL among the other OLEDs used in the experiments.

Based on these analyses, we have confirmed that several of the model parameters are useful to reveal the physical characteristics of an OLED. Specifically, the results of in Section IV. B confirm that the model can be used to determine the optimal thickness of the layers of the OLED using a simple experiment.

 

5. Conclusion

A novel third-order nonlinear model for an OLED was suggested; its parameters were estimated using the TR algorithm and the PSO algorithm. Experiments showed that the proposed nonlinear modeling method is effective when describing the dynamic and static behavior and estimating some of the physical characteristics of the OLED, which means that this model can be used to determine the optimal structure for an OLED in terms of light emission efficiency. Using a single set of experiments, it was possible to estimate all of the important parameters and characteristics of the OLED; this was in sharp contrast with conventional cases in which different experiments are carried out for the different characteristics of the device.

Further investigation will be conducted to reveal more closely the correlation between the model parameters and the device performance, such as determining the relationship between aging effects and the model parameters. It will also be necessary to develop a more efficient estimation scheme because the PSO algorithm employed in this paper is relatively slow.