Computation of Heterojunction Parameters at Low Temperatures in Heterojunctions Comprised of n-Type β-FeSi 2 Thin Films and p-Type Si ( 111 ) Substrates Grown by Radio Frequency Magnetron Sputtering

In this study, n-type β-FeSi2/p-type Si heterojunctions, inside which n-type β-FeSi2 films were epitaxially grown on p-type Si(111) substrates, were created using radio frequency magnetron sputtering at a substrate temperature of 560C and Ar pressure of 2.66 × 10−1 Pa. The heterojunctions were measured for forward and reverse dark current density-voltage curves as a function of temperature ranging from 300 down to 20K for computation of heterojunction parameters using the thermionic emission (TE) theory and Cheung’s and Norde’s methods. Computation using the TE theory showed that the values of ideality factor (n) were 1.71 at 300K and 16.83 at 20K, while the barrier height (φ b) values were 0.59 eV at 300K and 0.06 eV at 20K. Both of the n and φb values computed using the TE theory were in agreement with those computed using Cheung’s and Norde’s methods. The values of series resistance (Rs) computed at 300K and 20K by Norde’s method were 10.93Ω and 0.15MΩ, respectively, which agreed with the Rs values found through computation by Cheung’s method. The dramatic increment of Rs value at low temperatures was likely attributable to the increment of n value at low temperatures.


Introduction
At present, semiconducting iron disiliside (-FeSi 2 ) has received much attention for utilization in novel low-cost optoelectronic devices in part due to its various attractive physical properties [1][2][3].It has been reported that -FeSi 2 can be epitaxially grown on Si with 2-5% lattice mismatches [4].Furthermore, its composition consists of nontoxic elements (Fe and Si) [5].More importantly, it possesses high optical absorption coefficients (greater than 10 5 cm −1 at photon energies above 1.5 eV) [6,7] and a direct band gap of 0.85 eV corresponding to an optical telecommunication wavelength in the spectral range of near-infrared (NIR) [8,9].
Molecular beam epitaxy [10], ion beam synthesis [11], and reactive deposition epitaxy [12] have previously been utilized for growth of -FeSi 2 thin films.In order to grow -FeSi 2 , these methods require a postannealing procedure at temperatures of at least 800 ∘ C [13].Since the annealing procedure accelerates the diffusion of Fe atoms into the Si side, it is a potential cause for fabricated heterojunctions without rectifying action.Consequently, there is the occurrence of deep trap levels in the Si, which could act as leakage centers for the rectifying action [14].Hence, the growth of -FeSi 2 thin films at low temperatures is preferable.Previously, the authors utilized radio frequency magnetron sputtering (RFMS) for the growth of -FeSi 2 at low argon (Ar) pressure [15].Such low-pressure sputtering is effective for suppressing the diffused Fe atoms to the Si, whereas enhancing the kinetic energy of the grown species as the increased means free path is effective for -FeSi 2 film growth at low temperatures.The authors confirmed that the -FeSi 2 thin films grown by RFMS were epitaxially grown on p-type Si(111) substrates at a substrate temperature of 560 ∘ C. Furthermore, the ntype -FeSi 2 /p-type Si heterojunctions were fabricated and subsequently utilized as NIR photodiodes.Their photodetection properties exhibited obvious improvement at low temperatures.
As such, the aim of the present study was to further investigate the electrical characteristics of n-type -FeSi 2 /ptype Si heterojunctions grown using RFMS.Their forward and reverse dark current density-voltage (J-V) curves were measured as a function of temperature ranging from 300 down to 20 K.The values for heterojunction parameters such as ideality factor (n), barrier height (  ), and saturation current density ( 0 ) including the series resistance (  ) were computed using the thermionic emission (TE) theory and Cheung's and Norde's methods.Based on the totality of knowledge among the group members, this manuscript represents the first investigation of its kind for heterojunction parameters at low temperatures for n-type -FeSi 2 /p-type Si heterojunctions grown by RFMS using the aforementioned theory and methods.

Materials and Methods
-FeSi 2 layers were grown on Si(111) substrates by using FeSi 2 alloy targets.Before the growth of -FeSi 2 layers, the native oxide layer on the Si substrates was eliminated by immersion of the substrates in a diluted hydrofluoric acid (HF) solution and rinsing in deionized water.After cleaning, the Si substrates were immediately introduced to the inside of an RFMS system.The pressure inside the chamber was evacuated down to less than 10 −4 Pa.-FeSi 2 layers with a thickness of 300 nm were grown on p-type Si(111) substrates at a substrate temperature of 560 ∘ C for 10 hours.The sputtering pressure was maintained at 2.66 × 10 −1 Pa under Ar atmosphere, with RF power of 20 W tuned by using an RF automatching system performed for the discharge of Ar gas.In order to form front and back electrodes at room temperature after the growth of the -FeSi 2 layers on Si substrates, Pd and Al were grown using another RFMS system on the front Si substrate in a finger-shaped formation and on the entire back of the -FeSi 2 layer, respectively.
The crystallinity for the -FeSi 2 thin films was studied using X-ray diffraction (XRD; Rigaku RINT-2000/PC), while the surface morphology was investigated by Scanning Electron Microscope (SEM: Hitachi S-4700 Scanning Electron Microscope).The dark J-V curves as a function of temperature ranging from 300 down to 20 K for the present heterojunctions were measured under forward and reverse bias conditions by using a source meter (Keithley 2400).The thermionic emission (TE) theory and Cheung's and Norde's methods were utilized for computation of the heterojunction parameters, including the values of n,   ,  0 , and   .To evaluate the heterojunction parameters by TE theory, the  value was computed from the slope of the linear part obtained from the plot of ln  versus , while the   value was computed from the  0 value computed from the straight line intercept of the ln - at an applied bias voltage of 0 V.In addition, the group was made aware of the fact that the value of  0 for activation energy (  ) could be computed from the slope of the Arrhenius plot of ln  0 versus 1000/T.To evaluate the   value by Cheung's method, the relationships of d/d(ln )- and Cheung's function (()) [16][17][18] and  were plotted.Subsequently, the value for   was computed from the slope of these plots.To affirm the agreement and precision of the values for   and   , Norde's method was utilized, by which the relationship between Norde's function (()) [16,17,19] and  was plotted to compute   as well as   from the minimum point of ()- plot.

Results and Discussion
The XRD diffraction pattern for -FeSi 2 thin films grown using RFMS on Si(111) substrates at a substrate temperature of 560 ∘ C and Ar pressure of 2.66 × 10 −1 Pa is illustrated in Figure 1(a).The XRD pattern demonstrates a weak 404/440 diffraction peak as well as a strong 202/220 diffraction peak.These observed peaks are typical for epitaxial growth of -FeSi 2 thin films on Si(111) substrates.Figure 1(b) shows a pole figure pattern for the -440/404 peak.The grown -FeSi 2 films demonstrate the appearance of three epitaxial variants that are rotated by an angle of 120 ∘ with respect to each other.
Figure 2(a) displays an SEM micrograph for the surface of the -FeSi 2 thin films grown by RFMS on Si(111) substrates.It is clear that the -FeSi 2 thin films consist of a large amount of crystallites on the small side.Figure 2(b) illustrates a crosssectional SEM micrograph of the -FeSi 2 thin films, which clearly exhibited a sharp interface between the Si substrates and -FeSi 2 thin films.Furthermore, the grown -FeSi 2 thin films were uniform.
The J-V curves for the n-type -FeSi 2 /p-type Si heterojunctions grown by RFMS on a logarithmic scale as a function of temperature ranging from 300 down to 20 K under forward and reverse bias conditions in the applied bias voltage range of −1.5 to +1.5 V are displayed in Figure 3.All of the measurements were carried out in the dark.From particular consideration at room temperature, the fabricated heterojunctions exhibited a clear rectifying action similar to conventional p-n abrupt heterojunctions, which is due to the successful formation of a junction between -FeSi 2 thin films and Si substrates using RFMS at a substrate temperature of 560 ∘ C. Furthermore, this rectifying action evidently improved at lower temperatures.However, the -FeSi 2 /Si heterojunctions had a large leakage current at room temperature, which is likely because of the partially diffused Fe atoms in the depletion region of the Si sides acting as leakage centers for the carriers.This leakage current diminished at low temperatures as well.In addition, the J-V curves also showed linearity variation in a large voltage range, limited by the   effect at a high forward applied bias voltage.From consideration of the region of applied forward bias voltage ≤ 0.2 V, the forward current density exhibited a linear change with the applied bias voltage across the heterojunction.This can be described by means of the TE theory as the following relationship [20][21][22][23]: where  is the applied bias voltage across the heterojunction,  is the current density,  is the absolute temperature,  is Boltzmann's constant,  is the electron charge,  is the heterojunction ideality factor, and  0 is the saturation current density, which can be computed from the straight line intercept of the -axis of ln - at an applied bias voltage of 0 V.After the value for  0 is computed, the   value can be computed by the following equation: Based on (1) for the  value higher than 3/, the  value can be computed from the slope of the linear part of ln - as the following equation: Estimation of the  value following (3) can indicate the characteristics of the rectifying behavior in a junction.If it equals unity, the junction is ideal.Conversely, the junction is flawed if the value of  increases.In the case of the  value being equal to one, the transportation mechanism across the junction of the carrier is governed by a thermal diffusion process.If the  value is greater than one and lower than or equal to two, the transportation mechanism across the junction of the carrier is dominated by a generationrecombination (G-R) process.Besides, the transportation mechanism of the carrier is probably governed by a carrier tunneling process if the  value is greater than two [22].
Figure 4 illustrates a plot of  value versus the temperature for the present heterojunctions.By computation using (3), the  value at 300 K was 1.71 and remained nearly constant at a temperature ranging from 300 down to 120 K.As mentioned above, an  value greater than one and lower than two was suggestive of the transportation mechanism across the junction of the carrier being governed by a G-R process at the  -FeSi 2 /Si heterojunction interface [24].The existing defects in the -FeSi 2 layer might create deep energy levels in the bandgap, which could behave as recombination centers.At a temperature of 100 K, the  value was computed at 3.25 and increased to 16.83 at 20 K.When the  value was higher than two, the suggestion is that the transportation mechanism across the junction of the carrier in this range of temperature was governed by a tunneling process [24].This is likely due to the existing interface states at the interface of the -FeSi 2 /Si heterojunctions.The heterojunctions possess a large value for n, which is likely owing to the presence of a flawed contact behavior as well as the result of inhomogeneity and tunneling [25].When the values of  0 become known, the value for activation energy (  ) can be computed by the following relation [21,22,26]: Figure 5 illustrates an Arrhenius plot for ln  0 versus 1000/T.From the plot, the  0 value was 5.34 × 10 −4 A/cm 2 at room temperature and decreased to 9.93 × 10 −12 A/cm 2 at 20 K.The two regions indicate that there are two values for   in the present heterojunctions.The slopes for each region can compute the values of   .At 120-300 K, the recombination process is dominant with an   value of 0.24 eV, whereas the carrier tunneling process is dominant with an   value of 9.18 meV in temperatures below 120 K.
After the computation of the  0 value, the   value can be computed using (2).The inset of Figure 5 shows the plot of   versus temperature.At room temperature, the   value was 0.59 eV.This value decreased to 0.06 eV at 20 K. From the experimental results, the value of  increased and the value of   decreased at low temperatures.This is likely because of barrier height inhomogeneity, which may be attributable to the variation in thickness and composition of the interfacial layer as well as nonuniformity of the interfacial charges [27,28].
There are many methods to acquire the value of   .For the current study, the value for   was computed by using methods developed by Cheung.The equation by means of Cheung's method can be expressed as [18,23,28,29] where   ,   ,  * , and  are series resistance, barrier height, Richardson's constant of -FeSi 2 , and area of heterojunctions, respectively.
Based on (5), the relationship of dV/d(ln )-J was plotted on the left axis at (a) 300 K and (b) 20 K, as displayed in Figure 6.From this plot, / and   were computed from the -axis intercept and slope, respectively.In order to affirm agreement of the value for   by using (6), ()- on the right axis in Figure 6 was also plotted at (a) 300 K and (b) 20 K.The values for   and n  were computed from the slope and intercept point of the -axis, respectively.From the computations, the  values were 1.63 at 300 K and 16.13 at 20 K, while the   values were 0.54 eV at 300 K and 0.05 eV at 20 K.These values agreed with those computed from the TE theory.More importantly, the   values computed from the relationship of dV/d(lnJ)-J were 13.05 Ω at 300 K and 0.14 MΩ at 20 K. From the H(J)-J plot, the   values were 13.18 Ω at 300 K and 0.14 MΩ at 20 K.These results proved that the   values computed from the relationship of dV/d(ln )-J were approximately equal to those computed from the relationship of H(J)-J.The increasing R  values at low temperatures were likely due to the increment of  value at low temperatures.Besides, the current study utilized Norde's method to compute the R  value.The relationship based on Norde's method can be derived as [19,30] where  is bias voltage, J is the voltage-dependent forward current density, T is temperature, and  is the first integer higher than the  value.Both the   and   values could be computed by determining the minimum of ()- in the following equation: where ( 0 ) is the minimum of () and  0 is the corresponding voltage, and where  is the area of the heterojunctions and  min is the corresponding current density.
Advances in Materials Science and Engineering  The plots of ()- at temperatures of 300 K (red line) and 20 K (black line) are displayed in Figure 7. From the plot at 300 K, the values for ( 0 ) and  0 were 0.58 and 0.05 V, respectively.The values for ( 0 ) and  0 at 20 K changed to 0.06 and 0.26 V, respectively.Based on the computation using (8), the   values were 0.58 eV at 300 K and 0.07 eV at 20 K.In addition,   value computed by (9) was 10.93 Ω at 300 K and enhanced dramatically to 0.15 MΩ at 20 K.The results from computation using Norde's method were in agreement with those computed by the TE theory and Cheung's method.
The NIR light detection for n-type -FeSi 2 /p-type Si heterojunctions formed by RFMS was experimentally demonstrated in a previous study [15].Their light detection performance was unexpectedly degraded.In order to understand the causes of this degradation, junction parameters such as  and   were investigated in the current study.At room temperature, the junctions revealed a large reverse leakage current together with a weak response for NIR light irradiation [15].From the computation of the junction parameters, the  value was found to be >1 and ≤2 at room temperature.The implication is that the carrier recombination process was dominant in the transportation mechanism across the heterojunction interface [31].The presence of defects in -FeSi 2 thin films might generate deep energy levels in the bandgap, which could behave as recombination centers [31].For this reason, the weak response of NIR light was likely due to the recombination of photocarriers at the heterojunction interface, resulting from the presence of defects [32].Additionally, the estimated   value, which was 13.05 Ω at room temperature, might be attributed to the diffusion of Fe atoms into the Si side [33].The diffused Fe atoms generate deep trap levels in the depletion region, which produce the leakage current in the formed heterojunctions [33,34].Moreover, the NIR light detection was spoiled because the photogenerated carriers were trapped in the deep trap levels owing to the diffusion of Fe atoms [33,34].
At low temperatures, the ratio between the photocurrent and dark current was increased, which was probably due to the reduction of the reverse leakage current at low temperatures [15].This reduction of leakage current is attributable to the decreased carrier densities in the -FeSi 2 films at low temperatures [15,31,35].Unexpectedly, the photocurrent decreased along with the decrease of the leakage current at low temperatures [15].Based on the computation of the  value, this value increased to be >2 at low temperatures.This might imply that a tunneling process contributed to the carrier transportation mechanism [31].This is likely owing to the existence of interface states at the heterojunction interface [31].The existent interface states could behave as a trap center of photogenerated carriers [35], which would be the possible cause for the reduction of photocurrent at low temperatures.Additionally, we consider that the carrier tunneling process implies the appearance of spikes in conduction and valence bands owing to a heterojunction band offset as shown in Figure 8.These spikes prevent the flow of photogenerated carriers at the heterojunction interface.
The decreased photocurrent at low temperatures might be because the spikes that appear in conduction and valence bands are higher at low temperatures and they could behave as a barrier for the photogenerated carriers flowing at the heterojunction interface.It is expected that the spikes were enlarged at low temperatures owing to the Fermi levels of Si and -FeSi 2 layers approaching the center of the band gaps at low temperatures.Also, from the computation of the   , this parameter increased at low temperatures.This might be attributable to the low mobility of carriers in the -FeSi 2 thin films, which degrades at low temperatures [36].

Conclusions
Measurement and analysis were conducted on n-type -FeSi 2 /p-type Si heterojunctions grown by RFMS for the dark J-V curves as a function of temperature.Their heterojunction parameters were systematically computed using the TE theory, Cheung's method, and Norde's method.From computation using the TE theory, the value of  was 1.71 at 300 K and increased to 16.83 at 20 K, whereas the   value was 0.59 eV at 300 K and decreased to 0.06 eV at 20 K.The values for both  and   were approximately equal to those computed from Cheung's and Norde's methods.The values

2 )
Advances in Materials Science and EngineeringCurrent density (A/cm

Figure 3 :Figure 4 :
Figure 3: Semilogarithmic plot of the dark J-V curves of the present heterojunctions under forward and reverse bias conditions in the voltage range of −1.5 to +1.5 V at temperatures from 300 down to 20 K.

Figure 5 : 6 J
Figure 5: Arrhenius plot for log  0 versus 1000/T.The inset is a plot of the   value versus temperature.

Figure 7 :
Figure 7: Plots of F(V)-V at 20 K (left axis) and at 300 K (right axis).

Figure 8 :
Figure 8: Energy band diagram that indicates the spikes in conduction and valence bands for n-type -FeSi 2 /p-type Si heterojunctions.