Correlation between performance characteristics of indoor photovoltaic devices and DC‐to‐DC up‐converters for low‐power electronic applications

Md Zunaid Baten, Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka 1205, Bangladesh. Email: mdzunaid@eee.buet.ac.bd Abstract This study presents a numerical analysis to correlate performance characteristics of indoor photovoltaic (PV) devices with those of DC‐to‐DC up‐converters designed for low‐ power electronic applications. A theoretical model based on self‐consistent solution of Poisson's equation and continuity equation under optical generation‐recombination conditions has been applied to design Cu2ZnSn(SSe)4‐based PV devices having type‐I and type‐II energy band profiles, such that they can operate with peak efficiencies of 12.6% and 14.1%, respectively, under illumination from an experimentally characterized white light‐emitting diode. Each PV device has been subsequently utilized as the input source of a Meissner oscillator‐based self‐driven DC‐to‐DC converter. Comparative analysis shows that in spite of the lower PV conversion efficiency, the PV device having higher short‐circuit current density results in a higher output efficiency of the converter circuit. Similar characteristic trends are obtained for a boost converter operating in a discontinuous conduction mode, whereas a continuous conduction mode of operation results in the opposite trend. The underlying reason behind such an observation has been traced back to the transient behaviour of the inductor current of the converter. The results of this study suggest close correlation between physics‐based design parameters of the PV device and output performance characteristics of the converter circuit.


| INTRODUCTION
The modern era has seen phenomenal advancements in the field of electronics, where the size of electronic devices has diminished significantly with the passage of time. Such advancements, accompanied by the incredible developments in the telecommunication sector, has made it possible for electronic devices coming from variegated sources to be cyberconnected such that they can form a complex network of 'things'-a paradigm popularly known as the Internet of Things (IoTs). The interconnected mesh of IoTs constitutes a cyber-physical system, which is considered to be the cornerstone of the ongoing fourth industrial revolution [1,2]. The remarkable advancement of IoTs and cyber-physical systems has resulted in a surge in the demand for reliable, nonexhaustible sources of energy supply, so that the constituent low-power electronic devices can operate reliably for long hours irrespective offrequent or sudden power-cuts, and at the same time maintain the lowest possible, if not zero, carbon emission. Conventionally, batteries of different kinds are utilized to power-up wired or wireless communication nodes, sensors, actuators and other low-power components of cyberphysical systems. However, irrespective of the technology, batteries need to be replaced over time and at the end of their limited life cycles, they pose significant threat to the environment in the form of electronic waste.
To overcome the shortcomings of conventional exhaustible sources of energy supply, efficient utilization of renewable energy resources is being considered as the most viable way forward. Energy harvesting by means of the photovoltaic (PV) energy conversion [3], thermoelectric generation [4] or motion sensing [5] is gaining a significant interest in this regard. Energy scavenging employing PV devices in particular has gained much prominence because of the higher efficiency and reliability of these devices compared to other sources, such as the piezoelectric vibrators or thermoelectric generators [6][7][8][9][10]. Thin-film PV devices designed and realized with different material systems, such as CIS, CIGS [11], GaAs, GaInP [12,13], CdTe [14], peroskvites [15] etc., have been reported to show promising characteristics in this regard. However, from a practical point of view, it is important to note that irrespective of the material system, output voltage of a single PV device is not high enough to drive a regular electronic device or an entire sensor node. So, energy harvesting only with a single PV device, no matter how attractive it sounds, will fail to meet the practical needs unless supplementary means are incorporated.
Utilization of power electronic driver circuits-comprising of BJTs, FETs or SCRs-appears to be the most logical approach towards fulfilling the requirements of low-power electronic loads, while being powered up by indoor PV devices. Though significant efforts have been invested on designing and developing indoor PV devices, it remains to be seen how solid-state physics-based design parameters of these devices are going to influence design considerations of DC-to-DC up-converter circuits to be used for driving lowpower electronic devices. This necessitates the need for device-circuit co-design, which is already an active domain of research in the study of novel materials and devices for next generation computing, neuromorphic and power-electronic applications [16][17][18][19]. Though such an approach has not been adopted in the field of indoor PVs, it is envisaged that there is significant scope of exploring the prospect of co-designing PV devices and the corresponding DC-to-DC up-converter circuits such that the requirements of low-power electronic loads are best served when the PV device is used in conjunction with its co-optimized driver circuit or vice versa. This study aims to investigate this untapped area of research in the overlapping fields of indoor PVs and low-power electronics, which altogether promises to be a highly prospective area of exploration in the burgeoning field of micro-energy harvesting for loTs and cyber-physical systems.
Here, physics-based design parameters of an indoor solidstate lamp operated PV device are correlated with performance characteristics of DC-to-DC up-converters operated in tandem with the PV device for driving low-power electronic components of IoTs. As the PV energy converter, we consider here a Cu 2 ZnSn(SSe) 4or CZTSSe-based PV device, which recently has been proposed as a low-cost, energy-efficient solution for indoor PV applications [20]. As for the power electronic driver, both conventional boost converters and a self-driven DC-to-DC converter based on the concept of the Meisnner oscillator have been considered. PV devices having type-I and type-II energy band profiles are respectively taken as inputs to the converter circuits and the corresponding performance characteristics of the converters have been evaluated based on numerical analysis. The results of this analysis suggest that output efficiency of the converter circuit can be enhanced by increasing the short-circuit current density of the PV device, even if it might degrade PV conversion efficiency of the latter. The underlying reason has been explained based on the discontinuous conduction mode of operation of the conventional boost converter, and also on the basis of transient characteristics of the converter circuits. The overall results of this study suggest that performance characteristics of powerelectronic converter circuits are strongly dependent on the physics-based design parameters of the PV device being used as the input source. This study thereby establishes a link between two different, yet closely related, areas of research related to the PV energy conversion technology, namely the solid-state device physics and power-electronics.

| NUMERICAL ANALYSIS OF PV SOURCES
Two CZTSSe-based PV devices having slightly different heterostructures have been considered as PV sources for driving low-power electronic loads in this study. Schematic diagrams detailing heterostructures of these devices, labelled as Device A and Device B respectively, are shown in Figure 1(a) and (b). As can be observed, both these devices comprise of the p-type CZTSSe absorber layer, the n-type CdS buffer layer and the n-type transparent conducting oxide layer. In Device A, ITO is placed on top of the n-type ZnO layer to form the n-contact, whereas in Device B an Al-doped ZnO residing over intrinsic ZnO buffer layer is used as the n-contact. Such choice of buffer layer causes the energy band diagram of Device A to be of straddling type, that is, of type-I in nature (Figure 1(c)). On the other hand, the energy band diagram of Device B is staggered (type-II) in nature, as has been shown in Figure 1(d). The performance characteristics of these devices have been evaluated considering irradiation by a commercially available 15W, 497 lumen white LED. The experimentally measured spectra of this LED, which is characterized to have a colour rendering index (CRI) of 75.74% and correlated colour temperature (CCT) of 6175 K, is shown in Figure 2(a).
To evaluate the performance characteristics of both Devices A and B under the considered indoor illuminating spectra, a theoretical model based on the numerical solution of the Poisson's equation and the continuity equation under optical generation-recombination conditions is considered [20]. Considering z-axis to be the direction of light propagation and carrier transport through the device (Figure 1 Here ɛ r (z) is the dielectric permittivity of the medium, q is the electron charge, N A (z) and N D (z) are the acceptor and donor concentrations, and n(z), p(z) are the free electron and hole densities, respectively. Upon solving Poisson's equations, the following continuity equations and drift-diffusion equations are solved iteratively in a coupled manner to obtain the electron and hole current densities, which are denoted as J n and J p , respectively.
Here, E F n and E F p are the electron and hole quasi-Fermi levels, which are estimated from the Boltzmann approximation of the Fermi-Dirac distribution function. The electron (μ n ) and hole (μ p ) mobility values, along with other material parameters used in this study, are shown in Table 1. These values have been taken from previous works reported in [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The electron (hole) recombination rates R n (R p )  (4) and (5) are calculated using the following relation considering band-to-band recombination under the steady state condition.
Here E g (z) is the material band gap, k is the Boltzmann constant, T is the operating temperature, N C (z) and N V (z) are effective density of states of the conduction and valence bands respectively, and r BB is the band-to-band recombination coefficient of the corresponding layer. To incorporate the effect of indoor illumination, electron (hole) generation rates, denoted as G n (G p ) in Equations (4) and (5), are calculated using the following relation: Here λ is wavelength of the incident light, α(λ) is the absorption coefficient of the material and ϕ 0 (λ) is the incident photon flux. Spectrally resolved reflectance (R(λ)) and absorptance (A(λ)) resulting from coherent or incoherent internal multiple reflections are calculated considering complex refractive index and total internal reflection in the semiconductor stack. It is to be noted that the numerical model described here is first validated with experimental results reported for the highest efficiency CZTSSe solar-cell [32].
Current density versus voltage (J − V) characteristics of both Devices A and B, calculated using the numerical model, are shown on the same plot in Figure 2(b) along with their figure of merits. As can be observed, under identical illumination conditions, Device A has a higher short circuit current density (J sc ) than does Device B However, the open circuit voltage (V oc ) of Device A is lower than that of Device B by about 0.17 V, which ultimately results in the higher efficiency of Device B The larger V oc of Device B arises from its specific nature of the energy band profile, which results in a relatively higher built-in field of about 6.6 � 10 8 V/cm at the junction. This is further evident from the non-equilibrium energy band diagrams shown in Figure 1(c) and (b), which clearly exhibit larger splitting between quasi Fermi levels in Device B than in Device A. Even though the relatively low electron and hole mobilities of intrinsic ZnO layer results in lower fill-factor (FF) of Device B, the enhancement of V oc more than compensates for this shortcoming, ultimately resulting in about 1.5% higher peak efficiency of Device B than that of Device A The two devices considered herein therefore represent two variants of a PV device having identical absorber material and slightly different conversion efficiencies. However, because of the differences in their energy band alignments, Device A attains its output efficiency primarily by a dint of high J s and Device B attains so by means of a relatively high V oc . From the viewpoint of device-circuit co-design, it is important to understand how such opposing attributes of the PV device having relatively close conversion efficiencies can influence output performances, and therefore design considerations of the DC-to-DC converter to be used for driving low-power electronic loads. Layer thickness (cm) 5 � 10 −6 (1 � 10 −6 ) 1 � 10 −6 (5 � 10 −6 ) 2.5 � 10 −6 (6 � 10 −6 ) 2 � 10 −4 (2 � 10 −4 )  (40) Hole mobility (cm 2 V −1 s −1 ) 40 (3) 3 (3) 40 (40) 10 (10) Band to band recombination 5 � 10 −07 (5 � 10 −07 ) 5 � 10 −06 (5 � 10 −06 ) 9 � 10 −08 (9 � 10 −08 ) 1 � 10 −09 (1 � 10 −09 ) Coefficient (cm 3 s −1 ) Abbreviations: CB, conduction band; VB, valence band.

| CORRELATION WITH DC-TO-DC CONVERTER PERFORMANCE
A self-oscillating power-electronic circuit, shown in Figure 3 (a), is considered as the DC-to-DC up-converter to drive lowpower electronic appliances designed based on energy harvested by the indoor-PV devices. The converter circuit is based on the topology of Meissner oscillator and has been reportedly used earlier for power-electronic applications [36][37][38]. Selfstarting DC-to-DC converters of similar topology have been reportedly used earlier for low-power electronic applications based on thermoelectric generators [37,38]. This study has explored design considerations of this converter while being utilized in conjunction with indoor-PV devices. For comparison and analysis purpose, a conventional DC-to-DC boost converter is also considered (Figure 3(b)). As can be observed, an additional driving circuit is required for switching the transistor element of the boost converter, whereas the oscillator-based circuit is self-driven and does not require any external circuitry to drive its switching element, namely the junction-gate field-effect transistor (JFET). The JFET shown in Figure 3 As has been shown in Figure 3(a) and (b), the CZTSSebased PV devices considered here are taken as inputs to both the self-driven converter and boost converter circuits. The equivalent circuit diagram of the PV devices is shown in Figure 3(c). To estimate the short circuit current (I sc ) and dark current (I dark ) of the equivalent circuit model, the cross-sectional area of both Devices A and B is taken as 1 cm 2 . This area results in peak output power density of 12−14.5 Wm −2 , which should be enough to drive micro-or milli-Watt rated power electronic devices and sensor nodes. To obtain I dark , dark current density ( J dark ) of each PV device is calculated using the relation: where k is the Boltzmann constant, T is the absolute temperature, q is the electronic charge, and V oc and J sc are the respective open circuit voltage and short circuit current density of the devices obtained from the numerical analysis described in Section 2. Though the J-V characteristics of Figure 2 Devices A and B are unequal, the present study intentionally excludes the effect of series and shunt resistance variation on driver circuit performances. For this reason, fixed series and shunt resistance values of R s = 0.72 Ωcm 2 and R sh = 621 Ωcm 2 , which are equal to the values reported for the highest efficiency CZTSSe solar cell [32], have been used in this study. Such consideration of identical R sh and R s for Devices A and B ensures that characteristic traits of the converter circuits will primarily be governed by the short circuit current density and open circuit voltage of the PV device being used as the input source.
To evaluate the output performance characteristics of the oscillator converter circuit of Figure 3(a), its output voltage (V out ) is simulated and plotted as a function of V oc while keeping the J sc values of the PV devices constant (Figure 4  (a)). On the other hand, in Figure 4(b), the dependence of V out on J sc is shown while keeping V oc fixed at the characteristic values of Devices A and B It is to be noted that the red and blue circles in these plots and also in subsequent plots denote the actual operating points of Devices A and B, respectively. As can be observed from Figure 4, the output voltage of the converter is positively correlated with both J sc and V oc . Consequently, even though Device B has a smaller J sc than does Device A, the former's higher value of V oc ultimately results in a V out comparable to what is obtained with Device A being used as the input source. Similar characteristics are observed in Figure 4(b), where, in spite of having a smaller V oc , the higher J sc value of Device A ultimately results in the converter circuit to give similar output voltages when Device A or B are used as the input sources. To understand how efficiency of the DC-to-DC converter (η os ) depends on V oc and J sc of the PV devices, η os is calculated as a function of V oc and J sc while keeping corresponding J sc and V oc values constant. The results shown in Figure 4(c) and (d) suggest that converter efficiency is expected to increase with J sc , whereas increasing V oc has less of an effect on η os . Consequently, the η os value obtained while Device A is being used as the input source is about 1.2% higher than what is attained with Device B as the input.
To better understand the numerical results shown in Figure 4, semi-analytical expression of the output voltage V out is derived based on the formalism and assumptions described in [39] for DC-to-DC converter operating in DCM. In this derivation, the series resistance of the inductor and the capacitor, as well as ON-resistance of the diode and JFET are ignored. In addition, for simplification of derivation, an equivalent inductance (L eq ) of the transformer is considered. Based on these considerations, when the JFET is OFF, the diode current (I D ) is given by: Under this condition, I D is related to the maximum inductor current (I max ) according to the following relation: where Here D 1 and D 2 are the duty cycles corresponding to decreasing and increasing inductor currents respectively, f is the frequency of operation, R and R out are the resistance values shown in the circuit Figure 3(a). The term V m is the output voltage of the PV device at its maximum power point. Comparing Equations (9), (10) and (11), we obtain: Under the DCM operation, the input and output voltages of the DC-to-DC converter are related by the following expression: Therefore, comparing Equations (12) and (13), the following dependence of converter output voltage on PV device output is obtained: ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi It is to be noted that V m is related to the PV device's open circuit voltage, short-circuit current and fill factor, which are all obtained from the numerical simulations described in Section 2. As can be observed from Figure 4, good agreement exists between numerical simulations and results obtained from the semi-analytical model described herein. It is obvious that the DC-to-DC converter output voltage and efficiency values are slightly overestimated if the series resistance and ON resistance of the inductor, capacitor, JFET and diode are ignored. Nevertheless, the results obtained from the simplified analytical model is found to be within ∼5% of the numerical calculations. Both the analytical model and numerical simulation results suggest that even though the PV device with higher open circuit voltage (appearing from type-II energy band diagram of the device heterostructure) results in a higher output voltage of the self-oscillating DC-to-DC converter operating in DCM, the higher short-circuit current density of the device having type-I energy band diagram ultimately results in a higher converter efficiency. This calls for careful consideration during device-circuit co-design, for low-power applications of indoor PV devices.
It is obvious that the numerical and analytical results described in Figure 4(a) are specific to the DCM operation of the DC-to-DC converter, which is the mode under which the self-oscillating converter circuit of Figure 3(a) invariably operates. To better understand the influence of the mode of operation on the overall output performances of the PV device connected DC-to-DC converter, this study evaluates the performance characteristics of the conventional boost converter (shown in Figure 3(b)) while it is operated in both continuous and discontinuous conduction modes [40]. These modes of operations are determined by the inductance (L) of the boostconverter circuit such that for DCM of operation, L is lower than a minimum inductance (L min ). Here L min is defined as: where D and f are duty cycle and frequency of operation of the converter circuit, respectively. Based on this calculation, inductance values of 7.5 and 25 mH have been utilized for DCM and CCM operations, respectively. As an oscillator-based converter invariably operates in DCM, for comparison purpose, the DCM-operated boost converter is designed such that it has duty cycle and frequency identical to that of the oscillator-based converter.
Output voltage of the boost converter operated in both CCM and DCM are shown in Figure 5(a) and (b) as a function of V oc and J sc, respectively, while keeping J sc and V oc constant. As can be observed, during the CCM operation, the device having a higher V oc (i.e. Device B) results in a higher V out . However, if the converter is designed to operate in DCM, the V oc has less of an effect on V out ; as a result, the output voltages obtained for Devices A and B are essentially the same. Similar characteristic trends are observed from the η boost versus V oc and η boost versus J sc relations shown in Figure 5(c)-(d), where η boost is output efficiency of the boost converter. While in the CCM, the converter efficiencies obtained for Devices A and B remain comparable. However, similar to the case of oscillator-based converter, during DCM operation, η boost tends to increase with J sc and it remains only weakly dependent on V oc . Consequently, in DCM, the boost converter operates with about 1.5% higher efficiency when the device having higher J sc (i.e. Device A) is used as the input source, even though the PV energy conversion efficiency of Device B is about 1.5% higher than that of Device A. Therefore, the results shown here suggest that output performance of the conventional boost converter operating in DCM closely resembles output characteristics of the oscillatorbased converter. ). As can be observed, during the CCM operation ( Figure 6(a)), the inductor current (I L ) always remains positive irrespective of whether Device A or B is used as the input source. This ensures that the diode appearing in the boost converter circuit remains conducting and there is build-up of voltage at the output. On the contrary, during the DCM operation, the inductor current becomes negative over several cycles (Figure 6(b)), causing the diode to impede the flow of current to the external load. The alternate conduction paths under such circumstances are the diode and parasitic shunt resistance appearing in the equivalent circuit model of the PV device. Consequently, both voltage build-up and efficiency of the CCM operated boost converter appear to be higher than those of the DCM operated one. It is noteworthy that the current I L tends to be less negative when Device A is used as the input source. This ultimately results in the higher conversion efficiency of the circuit when Device A is used as the input source, compared to the case when Device B is used as the input. Similar characteristic trends are observed from the transient response of the secondary inductor coil L 2 (Figure 3(a)) of the oscillator based converter circuit as well.
As has been shown in Figure 6(c), the inductor current I L becomes negative irrespective of Device A or B being used as the input source. However, similar to the case of the DCM operated boost converter, the current I L tends to decrease when Device B is used as the input instead of Device A. This trend is related to the characteristic resistance values of the PV devices, which are evaluated to be 13 and 21 Ω at the maximum power points of Devices A and B, respectively. However, the rise and fall time, as well as the time period and duty cycle of the transients are governed by elements of the DC-to-DC converter circuit, while the amplitude of the inductor current is observed to be significantly influenced by the characteristic resistance values of the PV devices. To further illustrate this aspect, inductor current of the self-oscillator based converter is calculated and plotted for different characteristic resistances of a PV device being used as the input source ( Figure 6(d)). As can be observed, a higher characteristic resistance of the PV device results in a smaller inductor current of the converter circuit. This is in accordance with the results shown in Figure 6(c), where the lower characteristics resistance of Device A results in a larger inductor current I L . Therefore, the intrinsic characteristics of Device A ultimately results in a higher output efficiency of the oscillator-based converter when it is used as the PV input source. Even though, Device B has a higher efficiency and open circuit voltage than does Device A, the former's lower J sc and higher characteristics resistance ultimately results in a lower efficiency of the self-driven converter, as well as of the DCM operated conventional boost converter. Therefore, the results of this work suggest that while designing the indoor PV devices employing CZTSSe as the absorber layer, type-I band alignment should be preferred over type-II band alignment, if the PV device is to be used as an input to a Meissner oscillator-based self-driven upconverter, or DCM operated boost converter for efficiently driving low-power electronic loads. Though the study presented here is based on PV devices of a specific thin-film material, the theoretical framework employed here can be extended to the PV devices of other material systems so that their figure of merits can be correlated to performance characteristics of DC-to-DC converters designed for driving low-power electronic components of IoTs and cyber-physical systems.

| CONCLUSION
In summary, performance characteristics of self-driven DCto-DC up-converters are evaluated taking as input CZTSSebased indoor-PV devices such that the overall assembly of PV device and converter can be utilized to drive low-power components of cyber-physical systems under indoor illumination conditions. Output characteristics of the PV devices having different band alignments are first evaluated employing a device physics-based numerical model. Conversion efficiency and output voltage of the converter circuit have been subsequently correlated with the short-circuit current density and open circuit voltage of these devices. Results of the analysis suggest that the efficiency of the converter can in fact be higher for a PV device of lower efficiency, provided its short-circuit current density is sufficiently high. Similar dependence is obtained for conventional boost converters operating in a discontinuous conduction mode, whereas a continuous conduction mode of operation results in the opposite characteristic trend. Transient analysis shows that the higher short-circuit current density of the PV device results in a lower negative current through the inductive path of the converter circuit, thereby enhancing overall efficiency of the converter. The observed correlation between the operation of the indoor PV device and DC-to-DC up-converters emphasize the need for the device and circuit co-design such that desired output characteristics can be attained while driving low-power components of IoTs and cyber-physical systems.