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Abstract
Perovskite quantum dots embedded composite film (PQDCF) exhibits strong photoluminescence emissions and is expected to be excellent down-shifting material for enhancing ultraviolet (UV) response of silicon devices. In this work, light conversion process is analyzed by combining the experiments with Monte-Carlo ray-trace simulation. Results show that external quantum efficiency (EQE) in the UV region was mainly determined by absorption loss and match of peak wavelength. Moreover, resolution was correlated with thickness and reabsorption. This conclusion provides a guideline for designing novel materials with enhanced UV sensitivity and an EQE of 28% is predicted. Our experimental results showed that the use of red emissive PQDCF achieved an EQE of 20%.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Silicon (Si) based charge coupled device (CCD) and complementary metal oxide semiconductor (CMOS) are most accessed imaging devices in modern optoelectronics due to their high reliability, large area array and superior uniformity [1–5]. However, the response of these devices usually covers the spectral region of visible (VIS) to near infrared (NIR) light [6–8]. Although the back illuminated device can expand the spectral response to UV region, the real application is still limited by the high cost [9–11]. The combination of luminescent down-shifting (LDS) materials with Si devices has been considered to be one of the lowest cost ways to achieve ultraviolet (UV) response [12–17]. The performance is strongly correlated with the down-shifting process, which was mainly determined by the luminescent materials. Very recently, perovskite quantum dots embedded composite film (PQDCF) are emerging as new-generation luminescent materials due to their superior high photoluminescence quantum yields (PLQY), high transparency in the longer wavelength and easy solution processability for device integration [18–21]. Recently, we demonstrated that the in situ fabricated green emissive PQDCF can enhance the UV response of Si photodiodes and image sensors [22]. External quantum efficiency (EQE) up to 15% at 290 nm was achieved with good resolution. To further optimize the performance, we analyzed the light conversion process of PQDCF coated silicon image sensor devices by applying Monte-Carlo ray-trace modeling.
As schematically described in Fig. 1, when the incident UV photons strike the PQDCF, various events are triggered [23–26]. In most of cases, the incident UV photons were absorbed by perovskite quantum dots (PQDs) and emitted as visible photons (vii). In the UV region, photon loss mainly includes the leaving from the surface of PQDCF (reflection of PQDCF (i), escape of photons from front (ii) and side (iii)), transmission through the PQDCF (iv), absorbed light without emission (v). In addition, the emitted visible photons can be reabsorbed by PQDs because of the overlap of the PL and absorption spectra (vi). There is also possibility that the reabsorbed photons reemit photons (viii). The EQE of PQDCF enhanced image sensor in the UV region was mainly determined by the ratio between visible photons reached to the device (ix) and incident UV photons as well as the device response to the visible photons. EQE, image resolution and response time are the most important parameters for image sensors. Because PQDCF has an average lifetime of 28-50 ns [22], PQDCF enhanced devices can response to UV light immediately. In the following, we mainly focus on the light loss and the influence of PQDCF on the EQE and image resolution.
Fig. 1 The illustration of the light conversion process in PQDCF enhanced image sensor. In the UV region, Photon loss comes from the reflection (i), front and side escape (ii,iii), transmission (iv), absorption (v), reabsorption (vi). Only the emitted visible photons (vii,viii) that reach the sensor (ix) contribute to the EQE. RP represents the diffusion radius of photons.
2. Model and methods
2.1. The Monte-Carlo ray-trace model
Monte-Carlo ray-trace model is a well-developed method to simulate the light conversion and transport processes [27–31], which calculate the probability of each photon. The simulation begins with the photons hitting the front surface of the PQDCF. Each incident photon is tracked until its fate is determined and the photon number of each fate is counted. The reflection and refraction are determined via Fresnel equation. The absorption is determined by the absorption coefficients and thickness of PQDCF according to Beer-Lambert law. The wavelengths of emitted photons are identical with the PL spectra of QDs. The ratio of the emitted photons to the absorbed photons depends on the PLQY of PQDCF. All visible photons of the emission by QDs are considered to be isotropically. According to the final fate of each photon, EQE is calculated to model the sensitivity, diffusion radius (RP) and modulation transfer function (MTF) are calculated to model the resolution. The details are described in the following.
2.1.1. EQE
For an image sensor with EQE denoted as EQEsensor(λ), firstly we calculate the number of photons reach the image sensor at each wavelength (n(λ)), then integrate n(λ) with the EQEsensor(λ) to derive the EQE of the PQDCF enhanced image sensor (EQEPQD_sensor).
where m(λ) is the number of incident photons at each wavelength and serves as an input parameter of our simulation.2.1.2. Diffusion radius
In the model developed by Geyer et al, a diffusion radius RP was adapted to characterize the resolution of LDS film [32]. In their work, RP was defined as the radius from the emitter within which P percent of the photons strike the detector for the LDS film with thickness H. If P close to 1, RP can be calculated as following Eq. (2)
In this work, we define the diffusion radius RP as the horizontal distance from the incident point on PQDCF to the striking point (see Fig. 1), which relates to the reflection, absorption, emission of PQDCF and EQE of image sensor.
Setting all incident photons converged on the same point of the front surface of PQDCF, firstly we calculate a photon number distribution function NPQDCF(x,y,λ) which represents the photon number density of reaching the image sensor at each wavelength per unit area. Then, the EQE of the image sensor (EQEsensor) is taken into account which means that only the photons of really inducing photovoltaic conversion can influence the resolution of the image sensor. We then model the constraint between P and RP as:
when calculating RP, the integral range is gradually expanded until the ratio of the response within RP to the total response reaches P.2.1.3. MTF
MTF is another common-used indicator to evaluate resolution in the imaging application. The MTF of the PQDCF enhanced image sensor contains two parts: the MTF of the image sensor and the MTF of the PQDCF. The MTF can be calculated through the Fourier transform of point spread function (PSF) and The PSF of the image sensor (PSFsensor) is generally a rectangular function of the pixel size [33–35]. In the Monte-Carlo ray-trace model, we develop the formula of the PSF of PQDCF by taking EQEsensor into account:
Then the MTF of the enhanced image sensor MTFPQD_sensor is derived:where the symbol “ℱ ” represents Fourier transform and the operator “| |” represents the magnitude.In this work, we proposed three assumptions to simply the simulation: (1) No light scattering occurs in the PQDCF because the sizes of QDs are as small as from 3 nm to 6 nm [22]. (2) Since the PL spectrum of QDs slightly varied with the excitation wavelength and excitation intensity, the PL spectrum is assumed to remain the same at different excitation wavelengths. (3) Photons are incoherent. The light intensity can be linearly superimposed by counting the number of photons.
2.2. Input parameters for simulation
The main input parameters for our simulation are:
- (1) Wavelength, angle of incidence, location (x and y coordinates) of each incident photon.
- (2) Absorption coefficient, PL spectrum, PLQY, refractive index and thickness of the PQDCF. These parameters were measured by applying optical spectroscopic measurements.
- (3) Length, width, pixel size, EQE of the image sensor.
3. Results and discussion
Figure 2(a) shows the absorption and PL spectra of a typical green emissive PQDCF with thickness of 2.5 μm. Figure 2(b) shows the corresponding refractive index at varied wavelengths. These data were used as input for simulation. As reported in our paper, the as-synthesized PQDCF have average PLQYs of 90% at 397 nm. Here the PLQYs from 397nm to the PL peak wavelength is assumed to be a constant value of 90%, which along the UV band are derived from the measured EQE of the PQDCF coated sensor and the absorption coefficients of PQDCF through the Monte-Carlo ray-trace model. The image sensor we used is a front-illuminated electron multiplying charge coupled device (EMCCD, provided by East China Institute of Optoelectronic Integrated Device. Its peak EQE is 45%@710 nm). The pixel size is 30 μm × 20 μm. Because the photosensitive area is 11.52 mm × 8.64 mm which is much larger than the thickness of PQDCF, the side-escape loss is neglected.
Fig. 2 (a) The absorption coefficients and normalized PL spectrum of the green emissive PQDCF. (b) The refractive index of the PQDCF and the polymer matrix polyvinylidene difluoride (PVDF).
3.1. EQE and photon loss
As shown in Fig. 3(a), the simulated EQE is plotted with the wavelength of incident light. Considered the influence of the coupling between PQDCF and the EMCCD, we measured the EQE of EMCCD coated with PVDF as input parameter throughout the simulations. It because the PQDCF is PVDF doped with perovskite quantum dots and they have similar refractive index. Since the EMCCD device does not respond to UV light in the wavelength of 240-400 nm, the EQE of PQDCF coated EMCCD in the wavelength less than 400 nm was mainly attributed to the down-shifting process of PQDCF. Because the green emissive PQDCF are transparent in the wavelength of 600-1100 nm, the detection of PQDCF coated EMCCD mainly originate from the Si sensor. The green emissive PQDCF coated EMCCD device achieved an experimental maximum EQE of 15% at the wavelength of 290 nm.
Fig. 3 (a) The EQE of the EMCCD coated with PVDF or PQDCF under different excitation wavelengths. (b) The photon proportions of different fates in the green emissive PQDCF.
By correlating the parameters of PQDCF and image sensor as input in Monte-Carlo ray-trace modeling, we analyzed the EQE and photon loss. Figure 3(b) presents the corresponding proportions of loss and emission to the incident photons. The photon losses are mainly attributed to the front loss, absorption loss and reabsorption loss in PQDCF. The front loss includes the reflection of PQDCF and the front-escape loss. The reflected photons from PQDCF are about 3.5%. The front-escape loss in the UV band is about 10.5%. The absorption loss is about 20% around 300 nm and increase to 47% at 240 nm, which is the main factor of photon losses and originates from the properties of polymer matrix, the defect of QDs, the influence of the residual precursors. It is noticed that an absorption peak occurs at 320 nm for the green emissive PQDCF, which is consistent with the absorption peak of PbBr2/PVDF. The reabsorption loss is about 6%, correlating with the overlap between the absorption and PL spectra. Because EMCCD device does not respond to light with wavelength less than 400 nm, the emitted photons that reach sensor determine the EQE in the UV region with a maximum ratio of 55% at 290 nm. These results suggest that the absorption and emission play dominant roles in the fates of photons. The EQE value can be further improved by better matching the PL emission peak of PQDCF and the maximum EQE value of EMCCD device or improving the original EQE value of EMCCD at 521 nm.
Because the spectral tuning is of the most importance for improving the EQE of the PQDCF enhanced EMCCD, we recently fabricated highly luminescent red emissive PQDCF with emission peak at 670 nm and PLQY of 60%-80% [36]. Figure 4(a) shows the UV-NIR absorption and PL spectra. The refractive index of the red emissive PQDCF is around 1.43. The experimental results show a maximum EQE of 20% at 330 nm was achieved for the red emissive PQDCF with measured PLQY of 70% at 397 nm. If the PLQYs of red emissive PQDCF increase to 90%, a maximum EQE of 28% is predicted in Fig. 4(b).
Fig. 4 (a) The absorption coefficients and normalized PL spectrum for the red emissive PQDCF. (b) The EQE of the EMCCD coated with red emissive PQDCF.
3.2. Resolution
Resolution is an important feature for imaging sensor device. For conventional Si based sensor device, the resolution is mainly determined by the pixel size. It has been known that the use of LDS layer induced optical crosstalk and may lead to the loss of image resolution. In this section, we analyzed the influence of the PQDCF on resolution of PQDCF enhanced EMCCD.
The diffusion radius (RP) was calculated according to Eq. (3) shown in Fig. 5(a). Incident photon wavelength of 290 nm was applied for simulation and the ratio of containing photon number (P) is set to 68% and 95% respectively. The simulation results show that diffusion radius (RP) is a monotonically increasing function of thickness (represented by H). The black solid line in Fig. 5(a) refers to the diffusion radius with P of 68% calculated by Eq. (2) proposed by Geyer et al [32]. The emitted photons with further propagation distance are more likely reabsorbed based on Beer-Lambert law. Because of the consideration of reabsorption, the diffusion radius is limited in our model compared with Geyer et al.
Fig. 5 (a) The diffusion radius with the excitation wavelength of 290 nm. (b) The diffusion radius with various excitation wavelengths and the thickness of the PQDCF is 2.5 μm. (c) The calculated MTF of PQDCF with different thickness, and the MTF of the bare EMCCD before spatial frequency first drops to 0. (d) since the pixel size (30 μm × 20 μm) is asymmetrical in the x and y directions, the MTF of this whole device in both directions is drawn separately with thickness of 2.5 μm.
Figure 5(b) plots the diffusion radius (RP) with different incident wavelengths at a thickness of 2.5 μm. It is noticed that the diffusion radius slightly varied in the UV region. The MTF of PQDCF was calculated according to Eqs. (4) and (5) at excitation wavelength of 290 nm. As shown in Fig. 5(c), MTF strongly relies on the thickness (H) of PQDCF. From Fig. 5(d), although the value of MTF is mainly determined the EMCCD device, it can be decreased with the incorporation of a thick PQDCF. If the thickness of PQDCF is much smaller than the pixel size of EMCCD device (30 μm × 20 μm), the resolution of PQDCF coated EMCCD device is only slightly varied.
3.3. The EQE and resolution influence of incident angle
Light is typically not incident perpendicularly to the surface of photodetector in the imaging applications. According to Fresnel’s equation, the reflectance of incident light at various angles is different. The light conversion process of PQDCF coated EMCCD device may be affected by the incident angle. We then calculated the EQE and MTF (Fig. 6) of the green emissive PQDCF at different incident angles.
Fig. 6 (a) The EQE corresponding to different incident angles and the proportion of front loss. The incident angle is the angle between incident light and normal vector of the front surface of PQDCF, the wavelength of incident photons was set to 290 nm. (b) The MTF of the green emissive PQDCF for different incident angles (10, 30, 60 degrees).
As shown in Fig. 6(a), the EQE are not sensitive to incident angle over 0 to 60 degrees. It because the increase of front loss is only 5% from 0° to 60°. From Fig. 6(b), for the spatial frequency less than 50 cycle/mm, the calculation curves of MTF almost coincide, which indicates that for imaging devices with pixel sizes above 20 μm, the influence of the PQDCF on MTF is almost the same at incident angles less than 60°.
4. Conclusion
In summary, we adapted the Monte-Carlo ray-trace model to analyze the down-shifting conversion process of PQDCF enhanced EMCCD. By comparing the simulation and experimental results, we discussed the main influence factors of EQE and resolution. It was found that the absorption loss and the match of peak wavelength are the main factors influenced EQE in the UV region. Based on the above conclusions, PQDCFs with high PLQY and low absorption loss in the UV waveband, high transparency in NIR regions, and suitable PL emission response wavelength of the image sensor are preferred to achieve high-sensitivity UV enhanced broadband Si image sensor. This conclusion provides a guideline for designing novel materials with enhanced UV sensitivity and an EQE of 28% is predicted for this EMCCD with peak EQE of 45%@710 nm. Our experimental results show that the use of red emissive PQDCF with PLQY of 70% achieved an EQE of 20% in UV region. Moreover, the resolution of PQDCF coated EMCCD are correlated with the thickness and reabsorption of PQDCF layer. The EQE and MTF of PQDCF coated EMCCD device are slightly varied with the angle change of incident light from 0 - 60 degrees. In all, our simulation results show that the performance of PQDCF coated EMCCD well fit the requirements of imaging applications.
Funding
National Natural Science Foundation of China (61722502).
Acknowledgments
The authors would like to thank Chuanxian Hu (Institute of Semiconductors, Chinese Academy of Science) and Wei Xue (Beijing Institute of Technology) for the kind assistance.
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