1 Introduction

MEMS (microelectromechanical systems) is a fabrication technology by which a microfabricated miniature electromechanical structure can be added to an integrated circuit (IC) [1]. These devices have both mechanical and electronic parts, with size ranging from a few micrometers to millimeters. Their functions include sensing, control, and execution at micro scale, and have the ability to impact macroscopic domains [2]. However, the conventional power supplies used with MEMS have disadvantages. For example, chemical batteries have low energy density and short lifetime, solar cells cannot work properly in conditions without steady illumination [3], and fuel cells or other devices using fossil fuels, must replenish the liquid fuel supply while eliminating byproducts formed inside the electronics [4]. Under these conditions, nuclear micro batteries, especially betavoltaic batteries, have become promising candidates to supply power to MEMS. A nuclear battery has very high energy density (the total energy content per unit mass): approximately 10² to 10⁴ times higher than that of chemical or fossil fuels [5], while the power density is lower than that of conventional batteries. Based on semiconductor technology, some kinds of nuclear batteries can be miniaturized and integrated easily. Considering the long lifetimes of isotopes, and the spontaneity and stability of the decay process, such batteries can serve well under extreme conditions for many years. Generally, the domains of operation of a nuclear battery include long duration, no maintenance, low power, and high-energy power supply.

The first nuclear battery was made by Mosely in 1913, which directly used the charges of beta particles (electrons) to derive a current [6]. Subsequently, the first study of a betavoltaic battery was conducted in 1951, by Ehrenberg [7]. This was followed by the first betavoltaic battery (fabricated by Rappaport in 1953) using ⁹⁰Sr/⁹⁰Y with a semiconductor junction. The efficiency obtained was 0.4% [8]. Since the 1960s, several experiments involving betavoltaic batteries have been carried out, some of which were used in pacemakers [9][10]. However, considering the high cost and the toxicity of the contaminating isotope ¹⁴⁶Pm, the nuclear batteries used in pacemakers were replaced with safer lithium-ion batteries [11]. In the 1990s, due to the continuous development of MEMS, betavoltaic batteries eventually became a major alternative among micro power sources. Various radioisotopes, semiconductors, and energy converting structures have been simulated and tested to gain additional output power. The candidate isotopes include ¹⁴⁷Pm [9], ³⁵S [12], ³H [13], ⁶³Ni [3][14], ⁹⁰Sr [11], and ¹⁴C [15]. The two main energy converting structures are PN junctions and Schottky devices. With a planar conversion structure, a large portion of the energy is wasted because of the angular distribution of emitted particles. Therefore, a nonplanar structure is utilized to increase the contact area between the source and the energy converting portion. This has enabled the used of additional energy [16]. More recently, betavoltaic batteries with nanostructures have also been proposed. One of thse batteries uses one-dimensional ZnO nanowires, and by applying a sandwich structure, the betavoltaic device achieved excellent electrical performance. With a source radiating 10 mCi ⁶³Ni/Ni, the open-circuit voltage, short-circuit current, and effective energy conversion efficiency was 2.74 V, 18.4 nA, and 27.92%, respectively [17].

The development of the semiconductor industry has also played an important role in promoting betavoltaic battery research. In the 1950s, although Si was the first candidate energy converting material because of its technical maturity, its conversion efficiency was relatively low and it was vulnerable to radiation damage (the radiation threshold is ~200–250 keV; see [18]). Since then, a variety of semiconductors have been extensively researched. One of the main research achievements is the determination that the limit of conversion efficiency is a function of the bandgap [19]; specifically, that a betavoltaic battery using wide-bandgap semiconductors has higher conversion efficiency. Meanwhile, the open-circuit voltage and short-circuit current have also become higher, and new conductors are more radiation tolerant [20]. Consequently, third-generation semiconductors have become the focus of more recent research. SiC [3] [20][21][22] and GaN [23][24], in particular, are the most popular objects of research utilizing both Monte Carlo simulation and experimental methods. However, the growth of both materials is expensive and occurs at high temperature; therefore, a lower-cost semiconductor is preferred. Until now, there have been many studies about PN junction or Schottky diode-based betavoltaic batteries individually, but studies comparing electrical properties using these two structures on the same semiconductor are very few. Tarelkin et al. compared different metals in a Schottky barrier betavoltaic battery [25] and Rahmani compared Si-based PN junctions and Ni/Si Schottky barriers [26]. The performance of Schottky diodes is determined by the properties of the metal and the semiconductor; therefore, to obtain an extensive view of the comparison, the Schottky contact should be formed using the same semiconductor with different metals. Thereafter, different Schottky diodes and PN junctions can be comparable. Unfortunately, such an extended comparison is still lacking. For an advanced material, the doping method may not be mature enough, but this comparison is necessary to determine the potential performance of different devices and to find the best possible technology for fabricating betavoltaic batteries. Moreover, although it is well known that radioisotopes decay incessantly, the influence of time on the performance of betavoltaic batteries has not been explored. In fact, the decay process impacts the electrical performance profoundly, especially for isotopes with gaseous products (i.e., ³H), cascade decays (i.e., ⁹⁰Sr-⁹⁰Y), obvious density changes (i.e., ¹⁴⁷Pm), or short lifetimes (i.e., ³⁵S). In this paper, a cost-effective third-generation (i.e., wide bandgap) semiconductor (ZnO) was utilized as the energy converting material of a betavoltaic battery. PN junctions and Schottky diodes with different metals were also used as energy converting structures, and ⁶³Ni was selected as the beta source. To utilize fully the energy produced, the doping concentrations were modulated to match the depletion width and energy deposition range. According to the decay formula of ⁶³Ni, we analyzed the factors that influence the self-absorption effect and energy deposition. Using the Monte Carlo method, the time-related self-absorption process of the source and energy depositions were explored. Finally, the time-related electrical properties for all the devices designed in this work were obtained and compared.

2 Research Status on the Properties and Fabrication of ZnO Devices

ZnO is a material with great potential for use in the semiconductor industry. It is a direct bandgap semiconductor with a wide gap (3.37 eV) and is among the third-generation semiconductors (with SiC and GaN). Because of its excellent properties, it has been applied as a piezoelectric material, in varistors, transmittance conductive oxide film, fluorescent material, and in many other applications [27]. The direct and wide band gap enables optoelectronic applications in the blue/UV region, and for excitonic-effects-based optical devices, its high exciton binding energy makes it a favorable candidate. In comparison with GaN, the growth of ZnO is much easier. The large and high-quality ZnO bulk substrate is commercially available [28]. Moreover, by applying the homoepitaxial growth method, ZnO can be grown on native substrates, which can reduce the defect concentration and enhance film quality. In contrast, for GaN there are no native substrates. This means that a ZnO-based device of high quality could surpass the efficiencies obtained using GaN-based devices. Moreover, ZnO can be grown at much lower temperature, and the wet chemical etching method is available for it, which mean that the processing, design, and integration of electronic and optoelectronic devices would be more flexible [29]. For a betavoltaic battery, the conversion structure must work for a long time in radiation, therefore the radiation resistance of a material is of great importance. In fact, radiation damage is one of the major factors leading to degradation of betavoltaic batteries [30][31], but the extraordinary radiation hardness of ZnO can meet this challenge easily. Under bombardment from high-energy electron flux, no permanent defects are formed in the ZnO lattice [27], which result surpasses those with other common semiconductor materials, including Si, GaAs, CdS, and GaN. This indicates that ZnO devices would be very suitable for space applications [27] [29]. In addition, ZnO is inexpensive, nontoxic, has high breakdown strength, and good chemical stability, which make it a favorable semiconductor for use in radiation tolerant electronics [28].

Two electronic devices important for betavoltaic batteries are PN junctions and Schottky diodes, of which the former has been thoroughly researched. The devices used as the energy converting structure of a nuclear battery should have high performance and long-term stability because they would operate for a long time in radiation. Often, wide bandgap semiconductors suffer from doping asymmetry problems, which means that a semiconductor can be doped to achieve one type easily, but to obtain a contrary type is rather difficult. ZnO can easily be doped to achieve n-type, but creation of p-type ZnO has remained a challenge for years. In spite of many difficulties, researchers have succeeded in using various dopants and different growth techniques to grow p-type ZnO and even a ZnO homojunction. All these achievements now make it possible to fabricate ZnO-based betavoltaic batteries [32]. Moreover, the fabrication of ZnO homojunction diodes has also evolved in positive ways, adding to the potential for fabricating ZnO-based nuclear batteries. At present, well-maintained p-type ZnO films show no obvious degradation after a year [33]. By adding ZnMgO asymmetric double barriers, the homojunction performance can be enhanced substantially [34][35]. A series of novel and simpler fabrication methods have also been reported recently. By employing a surface pulsed laser irradiation method, p- and n-type ZnO can be fabricated with only one dopant in a single layer of NZO film [36]. A simple and controllable method at low temperature and in aqueous solution was also put forward, to create an Sb-doped ZnO (SZO)/ZnO film-based homojunction [37]. The wet chemistry method has also been utilized to fabricate ZnO homojunctions that show high rectification ratios [38].

In the mid-1960s, the study of ZnO-Schottky contacts was initiated. In comparison with ZnO homojunctions, the research on understanding and control of Schottky contacts on ZnO are relatively mature, especially for n-type ZnO. Experimental results show that Au, Ir, Pt, Pd, and Ag are the main metals used to provide Schottky contact on n-type ZnO, and the Schottky barrier height and ideality factor varies with different chemical treatments on a surface. The Schottky barrier height and ideality factor are usually within the range 0.4–1.2 eV and 1.0–3.57, respectively. Ideally, to get clean ZnO-metal contacts, the surfaces should be prepared under clean conditions. However, for a long time, several studies had not considered this; hence, the reported barrier heights were inconsistent. Even now, there is still no predictable method [39]. For p-type ZnO, Pd is suitable to form a Schottky contact [40], but generally, this research is still in its infancy. In short, ZnO has definite potential as a commendable energy converting material for use in betavoltaic batteries.

3 Principles for the Use of Schottky Devices and PN Junctions in Betavoltaic Batteries

Schematic diagrams of PN junction and Schottky device-based betavoltaic batteries are shown in Fig. 1. PN junctions play an extremely important role in electronic and optical applications. By joining together n- and p-type semiconductors, a PN junction is formed at the interface. Because of the existence of a concentration gradient, electrons diffuse into the p-region and holes diffuse into the n-region. An electric field that counteracts the diffusion can be created and this electric field can also sweep away mobile charges and obtain a space-charge region [41]. The movable charge carriers can hardly exist in this region; hence, this region is referred to as the depletion region. In fabricating semiconductor devices, there are metallization techniques by which to form Schottky and Ohmic contacts. A Schottky contact is formed using a metal and a semiconductor, and has a rectifying function similar to that of a PN junction [42]. By selecting the proper metals and doping concentration, a potential energy barrier between metal and semiconductor can be formed, analogous to that of a PN junction.

Fig. 1Full-screen View

Schematic diagrams of betavoltaic batteries: (a) PN junction-based and (b) Schottky device-based

When beta particles are emitted into a semiconductor, their energy will produce electron-hole pairs by ionization or transform the energy to heat. Electron-hole pairs can be produced either inside or outside the depletion region. In the depletion region, there is an electrical field that can separate electron-hole pairs, after which the charge carriers will be driven to produce current. However, outside the depletion region, there are no electrical fields to separate the electron-hole pairs, and instead, most of the charge carriers will recombine or become trapped by defects. Some charge carriers can drift into the depletion region, where they become part of the cell current [43].

4 Choice of Isotope and Corresponding Time-Related Behavior

Usually pure beta emitters are utilized for betavoltaic batteries, because beta particles are easier to shield than is gamma radiation; thus, the most common isotopes considered are ³H, ³⁵S, ⁶³Ni, ¹⁴⁷Pm, and ⁹⁰Sr. Among these isotopes, gaseous ³H is inconvenient to store and load, and its energy is relatively low (average β energy 5.682 keV). The ¹⁴⁷Pm source has relatively short half-life (approximately 2.62 a), which is unsuited to long-term, no-refill situations. Moreover, the ¹⁴⁷Pm used in betavoltaic batteries usually contains the impurity ¹⁴⁶Pm, which is toxic and emits energetic gamma rays (0.75 MeV). The half-life of ³⁵S is only 87.37 d, even shorter than that of ¹⁴⁷Pm. The strontium isotope (⁹⁰Sr) and its product ⁹⁰Y emit high-energy beta particles (average β energy: 195.8 keV for ⁹⁰Sr and 933.7 keV for ⁹⁰Y). However, to utilize fully the energy released, the device would have to be large and would undergo serious radiation damage. For these reasons, ⁶³Ni is preferred for its solid state, moderate energy (average β energy 17.425 keV), and relatively long half-life (101.2 a). However, for an actual solid-state source, the beta particles can be absorbed by the source itself (the self-absorption effect), which is inevitable. This effect may cause a rise in temperature, energy waste, and performance degradation. Moreover, the source decays continuously, which results in decrease of the radioactivity and changes the components in the source. Consequently, the regular pattern of the self-absorption effect is also changed. By choosing the proper level of radioactivity, the self-absorption effect can be reduced. In this work, the impact of time on the self-absorption effect was also taken into consideration.

The MCNP5 code was utilized in this work, and the number of particles in all the simulating processes was 10⁷. In this simulation, a 1×1 cm rectangular source with changeable height was used as the energy depositing model, and the self-absorption rate $\eta$ was defined as:

where $P_{\text{in}}$ is the deposition power in the source, and $P_{\text{total}}$ is the total power. Fig. 2a depicts the surface radioactivity and self-absorption rate at initiation, in relation to thickness. With increasing thickness of the source, there is less increase of the surface power, while the self-absorption rate can be very high (approaching 100%). This means that the extra thickness of the source makes no contribution to increase in the surface power. At 2.00337 μm, the surface power is almost unchanged, and the self-absorption rate is comparatively low; thus it was chosen as the proper thickness. The relevant absolute radioactivity, surface power, and self-absorption rate was 0.101121 Ci, 3.38845 μW, and 67.470%, respectively.

Fig. 2Full-screen View

Time-related self-absorption rate changes: (a) Initial and (b) In 200 years

The decay formula of ⁶³Ni is ${}_{\text{28}}{}^{\text{63}}\text{N}\text{i}\to {}_{\text{29}}{}^{\text{63}}\text{C}\text{u}+e^{-}+{\overline{\nu }}_{\text{e}}$. Eventually, the ⁶³Ni source changes into a mixture of ⁶³Ni and ⁶³Cu. In this process, the product ⁶³Cu is also solid, and there are no other reactions that cause decrease in the radioactivity. For the 2.00337 μm ⁶³Ni source mentioned above, the changes of time-related surface power and self-absorption rate are shown in Fig. 2b. As time goes by, the surface power-decline approximately follows the exponential decay law, while the self-absorption rate rises slightly. This is because ⁶³Ni and its decay product ⁶³Cu have almost the same density, and the difference in their atomic numbers is very small, which means it has little effect on the regular pattern of surface power decrease. The rise of the self-absorption rate is caused by a rise in the average electron number.

5 Choice of Metals for Schottky and Ohmic Contacts

For this work, n-type ZnO was selected to obtain the theoretical electrical behavior of Schottky devices because the fabrication of n-type ZnO is easier, and there are more studies about Schottky barriers on n-type ZnO. The influence of the surface state is neglected in the simulation. Theoretically, when a metal is brought into intimate contact with a semiconductor, whether it is an Ohmic or Schottky contact is defined by the work function of the metal and electron affinity of the semiconductor [39]. This can be expressed by the Schottky-Mott rule [44]:

This form is only available for Schottky barriers formed on n-type semiconductors, where ${\varphi }_{\text{B}}$ is the Schottky barrier height, which is defined as the difference in electrical potential between the Fermi energy of the metal and the band edge where the majority carrier resides. The term ${\varphi }_{\text{m}}$ is the metal work function, which is the energy needed to move an electron from the Fermi level to vacuum. Here, χ is the electron affinity of n-type ZnO (4.1 eV), which is the difference in potential between the conduction-band edge and the vacuum level. The densities, work functions of metals, and ideal Schottky barrier heights are presented in Table 1. To form a Schottky contact, the Schottky barrier height should be larger, and the doping concentration should be lower, than in the conduction band or valence band density of states. For n-type ZnO, metals with higher ${\varphi }_{\text{m}}$ are appropriate (i.e., Au, Pd, Ni, and Pt) and the conduction band density of states limits the doping concentration.

Table 1 can also be used to select metals to produce electrodes. Another metal-semiconductor contact, namely the Ohmic contact (which has relatively low contact resistance to the semiconductor bulk or series resistance), is appropriative for fabricating electrodes. In an actual Ohmic contact with gratifying performance, there should not be obvious performance degradation of devices, and the voltage drop should be negligible in relation to the drop across the device’s active region. An ideal Ohmic contact is formed when the barrier is zero, and in this condition the carriers are free to flow in or out of the semiconductor to ensure that the contact has minimum resistance [39]. For an n-type ZnO, the work function of the selected metal should be close to or smaller than the electron affinity of ZnO. It can be seen that Al, Ag, and Ti have relatively low work functions, indicating that they are adequate for this kind of contact. To form an Ohmic contact on ZnO with low contact resistivity, increase of the ZnO surface doping concentration is beneficial, along with reducing the Schottky barrier height. By applying these two methods, the barrier width becomes very thin, and the carriers are able to tunnel through.

6 Energy Deposition

The simulation model is presented in Fig. 3. ZnO bulk (1×1×0.5 cm³) was utilized for energy deposition. In this model, a layer of 200 nm is presented that refers to the dead layer (in which the deposited energy cannot be utilized). This includes the p-type region for the PN junction and metal layer for the Schottky diodes. The source was set on the bottom surface of the dead layer, and all particles were vertically incident. The energy deposition at initiation (time zero) in the dead layer and effective area (from the upper surface of the metal layer/p-type ZnO layer to the area of stratification) are presented in Fig. 4a. For all kinds of devices, more than 99% of the energy was deposited 6 μm from the upper surface of the source to the stratification area; therefore, the effective area was set. To utilize fully the energy produced, the width of the depletion layer was set at the same thickness as the effective area, which was 5.8 μm. Within the dead layer, the energy deposition remained almost unchanged throughout the simulations. Fig. 4b shows the change of time-related energy deposition, which has a slight downward trend in both the effective area and the dead layer.

Fig. 3Full-screen View

(Color online) Energy deposition model

Fig. 4Full-screen View

(Color online) Energy deposition in each device: (a) At initiation (time zero) and (b) Time-related energy deposition with effective area of 5.8 μm

The energy deposition comparisons of Schottky diodes and PN junctions are also shown in Fig. 4. In the dead layer, energy deposition takes the order E_Pt > E_Au > E_Pd > E_Ni > E_ZnO, while in the effective area, the situation is completely opposite. Clearly, from the energy deposition point of view, Ni is the most suitable metal for a Schottky diode among these four metals because it has relatively lower density (shown in Table 1). This leads to less energy deposited in the metal itself and more in the effective area. Moreover, a ZnO homojunction has the most energy deposition in the effective area among all these devices because ZnO has the lowest density (5.6 g/cm³).

7 Analyses of Built-in Potential and Depletion Width in Schottky Diodes and PN Junctions

In a betavoltaic battery, electron-hole pairs are separated by the potential built into the depletion region. To exploit the beta source energy, the depletion width and the energy deposition range should be well matched. The depletion width can be changed by adjusting the doping concentrations. For Schottky diodes, the built-in potential is given by the following relation [20]:

where V_t is the thermal voltage, and V_t = 0.0259 V at ambient temperature. Here, $N_{\text{c}}$is the conduction band effective density of states, and N_D is the doping concentration of n-type ZnO (cm^-3).

At zero bias, the depletion width is given by [20]:

where ${\epsilon }_{\text{s}}$ is 8.75, the relative permittivity of ZnO, ${\epsilon }_0$ is the vacuum permittivity, and $q$ is the electron charge.

In equilibrium condition, the built-in potential for PN junctions is given by the following relation [45]:

Here, $N_{\text{A}}$ and $N_{\text{D}}$ are doping concentrations of the p and n-types (cm^-3). At normal atmospheric temperature, they approximate the carrier intensities, and $n_{\text{i}}$ is the intrinsic carrier concentration.

The depletion width of a PN junction can be calculated using [45]:

Theoretically, the intrinsic carrier concentration can be expressed by:

The term E_g is the band gap of ZnO, and $N_{\text{c}}$ and $N_{\text{v}}$ are effective state densities of the conduction and valence bands, which can be calculated using

$N_{\text{c}}=2\frac{{\left(2\pi m_n^{*}{k}_{0}T\right)}^{3/2}}{h^3}$ and $N_{\text{v}}=2\frac{{\left(2\pi m_{\text{p}}^{*}{k}_{0}T\right)}^{3/2}}{h^3}$, where $m_{\text{n}}^{\text{*}}$ and $m_{\text{p}}^{*}$ indicate the effective masses of electrons and holes, k₀ indicates the Boltzmann constant, and T is the absolute temperature. In ZnO material, $m_{\text{n}}^{\text{*}}$ and $m_{\text{p}}^{*}$ are 0.27 m₀ and 0.64 m₀, respectively [46]. It was determined that $N_{\text{c}}$ = 3.52×10¹⁸ cm^-3, $N_{\text{v}}$ = 1.28×10¹⁹ cm^-3, and n_i = 3.74×10^-10 cm^-3. These equations are only adequate for non-degenerate semiconductors (N_D << N_c and N_A << N_v). Thus, for ZnO material, N_D and N_A should be no more than 1×10¹⁸ and 5×10¹⁸ cm^-3, respectively. The $m_{\text{n}}^{*}$ and $m_{\text{p}}^{\text{*}}$ selected here are a little different from those in our previous work, because we had to match the universally acknowledged value of the effective Richardson’s constant of ZnO [46] (that is, 32 A cm^-2 K^-2 while $m_{\text{n}}^{\text{*}}$ = 0.27 m₀). These differences led to small changes in the values of $N_{\text{c}}$ and $N_{\text{v}}$; nonetheless, the doping concentration ranges for non-degenerate semiconductors remained the same.

In this work, the depletion width was 5.8 μm. For Schottky diodes, the relationships of V_bi and W versus N_D are shown in Fig. 5a. With increase in the doping concentration, the built-in potential increases slightly while the depletion width decreases substantially. For the PN junctions, N_D was set at 10¹⁶ cm^-3, and the relationships of V_bi and W versus N_A are shown in Fig. 5b. These resemble the regular pattern of a Schottky diode. The selected doping concentrations and built-in potentials are listed in Table 2.

Fig. 5Full-screen View

Relations between built-in potential, depletion width, and doping concentration: (a) Pt/ZnO Schottky contact and (b) PN junction (with N_D set as 10¹⁶ cm^-3)

8 Electrical Performance Simulations

In the following calculations, it was assumed that the electron-hole pairs in the depletion region are completely collected, and that outside this region, none of them are collected. With these assumptions, the short-circuit current can be expressed by the following equation [45]:

where CE(n) is the collection rate of electron-hole pairs in layer n of the sample, E(n) is the deposition energy in layer n, A is the absolute radioactivity, q is the electron charge, and E_e-h is the average ionization threshold. In Section 6, we obtained the energy deposition in the depletion region, E(n), and according to the condition above, the relevant CE(n) was 1.

In our previous work, we used an empirical equation to estimate E_e-h because the universally acknowledged value was not presented [47]:

where E_g is the band gap and E_e-h as achieved was 9.9 eV.

To evaluate device quality, reverse saturation current is often utilized. If a device has low reverse saturation, it has fine quality. For Schottky diodes, the density of a reverse saturation current (A/cm²) can be expressed by [20]:

where A^* is the effective Richardson’s constant. For ZnO, the universally acknowledged value is $m_{\text{n}}^{\text{*}}$ = 0.27 m₀, A^* is 32 A cm^-2 K^-2. For PN junctions, it can be determined by [47]:

where k₀ indicates the Boltzmann constant.

The open-circuit voltage can be obtained by the following formula:

where $n$ is the ideal factor. In this work, it is considered to be 1, which indicates an ideal PN junction or Schottky device. Here, $J_{\text{sc}}$ is the short-circuit current density.

One of the key parameters that evaluates the performance of a betavoltaic battery is the fill factor (FF). A battery with higher fill factor has output power that comes closer to its theoretical maximum, thus its efficiency is higher. The definition of the fill factor is the ratio of the maximum output power (P_m) to the product of the relative open-circuit voltage (V_oc) and the short-circuit current (I_sc):

To evaluate the fill factor, an empirical equation can be utilized [47]:

where v_oc = V_oc / (k₀T/q).

The definition of maximum output power is as follows [47]:

In this work, we used the device converting efficiency to evaluate the total performance of the betavoltaic battery, which can be defined as below [48]:

where P_source is the surface power of the source.

9 Results and Discussion

According to Eqs. (10) and (11), the short-circuit current densities are constants without time-related changes, in theory. The short-circuit current density for a ZnO-based PN junction and for Pt, Au, Pd, and Ni/ZnO Schottky diodes is 4.65055×10^-52, 4.32989×10^-20, 4.91208×10^-11, 2.26936×10^-11, and 7.12622×10^-12 A/cm², respectively. These current densities indicate that the PN junction has the best quality among all these devices, while the Pt/ZnO Schottky device has the best quality among the Schottky devices.

Time-related electrical properties of the PN junction and of Schottky diodes are presented in Fig. 6(a)-(e). At the start (time zero), the ZnO-based PN junction has the highest open-circuit voltage, short-circuit current, fill factor, maximum output power, and conversion efficiency (up to 2.64452 V, 0.10259 μA, 94.5366%, 0.25647 μW, and 7.584%, respectively). These are much higher than with other Schottky devices. The reason is that the PN junction has very low reverse saturation current density, which leads to relatively higher V_oc according to Eq. (12). Meanwhile, the density of ZnO is lower than all the Schottky metals mentioned above, leading to more energy deposition in the effective area. Among these Schottky diodes, the Pt/ZnO device has the highest V_oc, P_m, FF, and η due to its highest ${\varphi }_{\text{m}}$, which leads to the highest ${\varphi }_{\text{B}}$ and lowest J₀. In addition, the Ni/ZnO device has the largest I_sc because Ni has the smallest atomic number and density among all the selected metals, which lead to the most energy deposition in the effective area.

Fig. 6Full-screen View

(Color online) Time-Related Electrical Properties: (a) V_oc, (b) I_sc, (c) FF, (d) P_m, and (e) Conversion efficiency

All the electrical properties (in a battery) decline as time goes by. The declines of I_sc and P_m follow the exponential law, while the declines of V_oc, FF, and η show approximately linear patterns. Among all the electrical properties, the decline of P_m is the most evident. Hence, P_m was selected to evaluate the validity of the battery concept. Taking the ZnO-based PN junction as an example, in 200 years the decline rates of V_oc, I_sc, P_m, FF, and η would be 1.365, 75.189, 0.065, 75.544, and 0.748%, respectively. While for Pt, Au, Pd, and Ni/ZnO Schottky diodes, the decline of P_m becomes more evident (76.523, 81.589, 80.636, and 79.862%, respectively). Thus, from the viewpoint of long-term service, Pt/ZnO and Ni/ZnO Schottky devices are more suitable than PN junctions, whereas Au/ZnO and Pd/ZnO Schottky devices are less adaptable. A Pt/ZnO Schottky diode could be utilized in devices that need high V_oc and P_m, and a Ni/ZnO Schottky diode would be more suitable for devices needing higher electric current.

In short, irrespective of whether the time factor is considered or not, PN junctions have the highest V_oc, I_sc, P_m, FF, and η (that is, the best electrical performance) among all the competitors discussed here. Regardless of long-term radiation damage, PN junction-based devices also have the longest active period. Nevertheless, Schottky diodes have their own advantages. The fabrication of Schottky diodes requires only one type of extrinsic semiconductor, which is very convenient for semiconductors with asymmetry doping problems (i.e., for GaN and ZnO obtaining n-type semiconductors is easier, while for diamond it is easier to get p-type ones). Compared with PN junction-based devices, Schottky diodes offer additional choices of state-of-the-art semiconductors, and the manufacturing processes are simpler. When fabricating Schottky diode-based betavoltaic batteries, the radiation source is in contact with the metal layer of the Schottky diode, which makes it less susceptible to radiation damage. In contrast, with a PN junction, the semiconductor lattice is prone to displacement due to radiation damage, because the radiation source is in direct contact with the semiconductor. All of these advantages indicate that Schottky diodes are a good alternative to PN junction-based betavoltaic batteries.

10 Conclusion

In summary, Schottky contacts using different metals for n-type ZnO and ZnO-based PN junctions were utilized as energy converting structures for betavoltaic batteries, with 0.101121 Ci ⁶³Ni as the selected beta source. Based on Monte Carlo simulations, the time-related self-absorption rate and electrical properties of a number of devices were obtained and compared. For a ⁶³Ni source, the self-absorption rate showed a slightly upward trend as time went by. The optimal doping concentration for Schottky diodes was N_D = 1.9765–3.57447×10¹³ cm^-3, and for PN junctions it was N_A = 8.44×10¹³ cm^-3 while N_D = 10¹⁶ cm^-3. Generally, the electrical performance of PN junctions is better than that of Schottky diodes. Among all the kinds of Schottky diodes discussed here, Pt/ZnO has the highest maximum output power, and Ni/ZnO has the greatest short-circuit current. Taking long-term service into consideration, Pt/ZnO and Ni/ZnO are the most suitable among the Schottky diodes. A Pt/ZnO Schottky diode could be utilized in devices needing high open-circuit voltage and maximum output power, while a Ni/ZnO Schottky diode would be more suitable for devices needing greater electrical current. Although its electrical performance is relatively inferior, the ZnO based Schottky diode has its own advantages, including easier fabrication, independence of p-type ZnO, and more resistance to radiation damage. Therefore, they still are considered viable alternatives to PN junctions as the energy converting structures of betavoltaic batteries.