Journal of the Korean Physical Society, Vol. 66, No. 4, February 2015, pp. 667∼671
Investigation of Internal Electric Fields in GaAs Solar Cell under Highly-concentrated Light Seoung Jun Lee, Hyun-Jun Jo, Mo Geun So, Chang Won Sohn, Im Sik Han, Jong Su Kim∗ and In-Ho Bae† Department of Physics, Yeungnam University, Gyeongsan 712-749, Korea
Sang Jun Lee and Sam Kyu Noh Korea Research Institute of Standards and Science (KRISS), Daejeon 305-340, Korea
Hyonkwang Choi and Jae-Young Leem School of Nano Engineering, Inje University, Gimhae 621-749, Korea (Received 1 December 2014, in final form 16 December 2014) The temperature and the excitation-intensity dependences of the junction electric fields in the GaAs p-i-n solar cell structure have been investigated by using photoreflectance (PR) spectroscopy. In the p-i-n solar cell structure, two different electric fields are observed. The fast Fourier transform (FFT) analysis implies that the two electric fields can be assigned to the p-i and the i-n interfaces. The strengths of the electric fields at the p-i and the i-n interfaces are 38 and 44 kV/cm, respectively. The electric fields gradually increase due to the temperature-dependent photovoltage effect with increasing sample temperature. With increasing excitation intensity, the electric field at the p-i interface gradually decreases due to the photovoltage effect caused by carrier screening while that at the i-n interface is insensitive to the light’s intensity. This abnormal behavior can be explained by the anisotropy carrier dynamics at the p-i and the i-n interfaces., The relation between the open-circuit voltage (VOC ) and the ideality factor in concentration photovoltaic (CPV) devices is discussed. PACS numbers: 78.66.Fd, 78.40.-q, 73.40.Lq, 73.50.Pz Keywords: Photoreflectance, Photovoltage, Solar cell DOI: 10.3938/jkps.66.667
I. INTRODUCTION
fill factor under very high concentrations have been reported in previous studies [5–7]. Generally, the internal electric field of a SC is a very important parameter because photo-generated electron-hole pairs can be efficiently separated by the junction’s electric field and can reach each electrode. For device fabrication, the internal electric fields of SCs are altered by the doping and the width of the depletion layer, and this alteration of the internal electric field can improve or degrade the efficiency of a SC. In case of a SC, the internal electric field is also reduced by the incident light’s intensity due to the photovoltage effect [8–10]. This photovoltage effect is improved with increasing the concentrated light. If we clearly understand the internal electric fields of SCs under high concentration, we can improve the conversion efficiency of CPVs. Photoreflectance (PR) spectroscopy is useful for investigating the internal electric fields [8–11]. The FranzKeldysh oscillations (FKOs) that appear above the bulk band gap contain information on the internal electric field. The period of the FKO is directly related to the electric field’s strength in a sample [8,10], and the shape
A GaAs solar cell (SC) has a high efficienciy due to the band gaps being around 1.4 eV and to the high crystalline quality [1–3]. Therefore, GaAs-based SCs have been often employed as concentrating photovoltaics (CPVs). Today’s best efficiency is 29.1% for a GaAs single junction under an AM 1.5 condition [1]. Because the photo-generated current of a SC is proportional to the solar flux absorbed, CPVs require a higher the concentration. For a long time, to improve the efficiency of CPVs, many researchers focused on the series resistance and the heat extraction [4–6]. However, many questions still need to be address and many problems still need to be resolve before using ultrahigh concentrations in commercial CPV systems. The characteristics of III-V compound semiconductor SC such as efficiency, external quantum efficiency (EQE), shunt resistance and ∗ E-mail: † E-mail:
[email protected] [email protected]; Fax: +82-53-810-4616
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Journal of the Korean Physical Society, Vol. 66, No. 4, February 2015
Fig. 1. (Color online) Band structure and electric field distributions of the p-i-n structure as a depth profile calculated by using the 1D Poisson equation at 300 K.
of the FKO indicates how many electric fields can exist in a SC. Recently, PR was proposed as a useful tool for quality assessment of multi-junction structures [12]. A photovoltage effect has some effect on the characteristics of the SC. The photo-generated carrier-induced screening of the interface electric field results in a reduction of the interface electric fields. Therefore, the solar cell efficiency can be affected by the photovoltage effect. Therefore, PR is employed to investigate the photovoltage effects for GaAs p-i-n solar cells. In this work, the internal electric fields of GaAs p-i-n SC as a function of the excitation intensity have been investigated at room temperature (RT) by using PR spectroscopy. Also, the temperature dependence of the internal electric fields is determined at temperatures from 25 to 300 K. The photovoltage effect in CPVs is discussed.
II. EXPERIMENTS AND DISCUSSION To investigate the effect of the light’s intensity on the junction’s electric fields in solar cells, we prepared a GaAs p-i-n junction solar cell grown by using molecular beam epitaxy (MBE). The p-i-n sample consists of a 200 nm n+ layer (2 × 1018 /cm3 ), a 250 nm unintended doped n layer (5 × 1015 /cm3 ), and a 200 nm p+ layer (2 × 1018 /cm3 ). We measured the p-n junction’s electric field strength for the SC structure by using a PR setup similar to that described previously [13]. PR measurements were performed using a laser diode of 637 nm wavelength as an excitation source, and the PR signals were detected by using a p-i-n Si detector. The probe’s light was a monochromatic beam obtained from a tungsten-halogen lamp dispersed through a monochromator. PR spectra were measured at temperatures ranging from 25 to 300 K. A closed-cycle He refrigerator was used to control the sample’s temperature. When no voltage is applied across the p-n junction,
Fig. 2. (Color online) (a) Photoreflectance (PR) spectrum and (b) fast Fourier transform (FFT) result for the p-i-n structure at 300 K.
the junction is in thermal equilibrium. Therefore, the Fermi energy is constant throughout the entire system. Figure 1 shows the energy-band structure and the interface’s electric-field depth profiles simulated by using the 1-dimensional Poisson equation for a SC structure in thermal equilibrium [14]. The red and the black lines are the conduction- and the valence-band depth profiles of the SC structure, respectively. The conduction- and the valence-band energies must bend because the relative positions of the conduction- and the valence-bands with respect to the Fermi energy change between the p and the n regions. The built-in potential barrier is formed by band bending and creates a built-in electric field. The blue line shows the built-in electric-field distribution in a SC structure. The electric field is created in the space charge region (SCR) by the separation of positive and negative space charge densities; therefore, the SCR is created in the interface (air-semiconductor or p-n junction). When the width of the intrinsic layer is longer than the SCR of the p-n junction, the interface of the p-n junction is separated into p-i and i-n interfaces, as shown in Fig. 1, and the electric field in the intrinsic layer is uniform. Three SCR; which are the surface and the p-i and the i-n interfaces, exist in our p-i-n SC. The electric field is affected by the width of SCR and the potential barrier height, which are changed by the donor and the acceptor impurity concentrations. The electric fields of the interfaces calculated by using the 1-dimensional Poisson equation are 600 (surface), 43.7 (p-i) and 43.7 (i-n) kV/cm, respectively. Figure 2 shows (a) the PR spectrum for a lowexcitation light intensity and (b) the fast Fourier transform (FFT) result for the FKO at RT. The PR spectrum consists of the GaAs band-to-band (Eg ) transition and FKOs due to the electric fields. The dielectric constant is changed by the material and the impurity doping in the semiconductor. The refractive index is a function of the dielectric constant. Light is dominantly reflected when the refractive indices of the two materials are dif-
Investigation of Internal Electric Fields in GaAs · · · – Seoung Jun Lee et al.
ferent from each other. Therefore, the probe beam of the PR measurement is reflected at the interface, which the dielectric constants are different from each other. The PR spectrum gives information not on the bulk’s electric fields but on the interface’s electric fields. Under a single electric field, the FKO takes the shape of a simple cosine, which decreases with increasing photon energy [8, 9]. Figure 2(a) does not show a simple cosine shape for the FKO, so we suppose that several FKOs are overlapped. The existence of several FKOs implies that not only several electric fields but also electron-heavy hole (e-hh) and electron-light hole (e-lh) transitions exist in our sample. To calculate and distinguish each electric field, We performed FFT analysis [10,15]. In Fig. 2(b), observing the frequency related to the surface’s electric field is difficult because a strong electric field has a longer period in the FKO result and a low frequency in the FFT result [10]. Therefore, we suppose that the electric fields at the p-i and the i-n interfaces, but not at the surface, can be observed in the FFT results. Figure 2(b) shows three dominant peaks. In the case of GaAs, two FKO frequencies in the FFT results can be expected when one uniform electric field exists in the sample. The two frequencies are due to the e-hh and the e-lh transitions, and the frequency ratio of e-hh to e-lh transitions should be 0.7915 due to the ratio of the effective masses [16]. When light is illuminated on a semiconductor with a built-in potential barrier, the barrier height (Vbi ) decreases due to the photovoltage (VP ) effect [17,18]. The temperature and the excitation-power dependences of the potential barrier height (Vbi ) are given by current transport theory. Generally, the built-in potential barrier (Vbi ) in a p-n junction is given by [17,18] Vbi = VF − VP with VP =
Jpc nkT ln + 1 , (1) q JS (T )
where VF is the Fermi-level pinning, k is the Boltzmanm constant, q is the electron charge, and n is the ideality factor. Jpc is the photo-induced current density, and Js (T) is the saturation current density. The VF is reduced as the Jpc is increased. The Jpc is proportional to the intensity of incident photons, and the penetration depth of incident photons (excitation laser) exponentially decreases from the surface. Therefore, the Vbi nearer to the surface is found to be low in the case of PR spectroscopy. According to the relation between heavy and light holes, the 47.6 and 59.6 eV−3/2 peaks of Fourier space are assigned to e-lh and e-hh transitions in the i-n junction, respectively, and the shoulder at 54.6 eV−3/2 and the 69.6 eV−3/2 peaks are assigned to e-lh and e-hh transition in the p-i junction, respectively. The calculated electric fields of the p-i and the i-n junctions are 38 and 44 kV/cm, respectively. The electric field of the p-i junctions is lower than that of the i-n junction. The electric field of the p-i junction from the FFT analysis is lower than the simulation result, as shown in Fig. 1, because the probe and the excitation beams in the PR
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Fig. 3. (Color online) Temperature dependences of (a) the PR spectra and (b) the electric fields.
setup decrease the electric field of the sample due to the photovoltage effect [8,10]. Also, the unintended diffusion of the dopant can modify the interface’s electric field, and the defects in the sample can decrease the internal electric field. In the case of a concentrated SC device, a highly-dense photon injection leads to an increase in the temperature due to the phonon process and to the heat caused by the resistivity of the SC. Therefore, the temperature of the SC increases gradually with increasing intensity of incident photons. This increase in the SC’s temperature affects the internal electric field of the SC. To investigate the effect of temperature on the internal electric fields, we analyzed the temperature dependence at temperatures from 25 to 300 K, and the PR spectra are shown Fig. 3(a). With decreasing temperature, the band-gap energy increases due to shrinkage of the lattice constant. The change in the period of the FKO with increasing temperature implies that the strengths of internal electric fields are altered, as shown in Fig. 3(b). Figure 3(b) shows the temperature dependence of the electric fields obtained from the FFT analysis. With increasing temperature, the electric fields gradually increase. In Eq. (1), the Vbi is a function of temperature (T ); therefore, the electric fields change with the temperature. The Js (T ) is also a function of T [19]. Considering the above relations, the Vbi of a SC increases in proportion to the temperature, and the result is in good agreement with the variation in the electric field [8,20]. The open-circuit voltage (VOC ) can be expressed as follows [20]; Jpc kT ln +1 , (2) VOC = q JS (T ) In a high-concentration condition (Jpc /JS (T ) 1), 1 is ignored, and the VOC increases due to the growth of Jpc . If the SC has good quality (low JS ), the VOC increases with increasing light intensity. In general, the temperature growth due to the high concentration decreases the open-circuit voltage (VOC ) because the band-gap energy
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Journal of the Korean Physical Society, Vol. 66, No. 4, February 2015
decreases. In addition, a high light intensity can generate a high thermal effect due to the introduction of heat. The increase in the SC’s temperature increases the internal electric field of the SC. In other words, the reduction of the electric field by the photovoltage effect is compensated for by the improvement caused by the thermal effect. Therefore, the electric field is saturated. Generally, the relation between the photovoltage (Vp ) and the photocurrent density (Jpc ) is given by [10] Jpc nkT ln = + 1 , (3) VP e JS
Fig. 4. (Color online) Electric fields as a function of the excitation intensity at 300 K.
is reduced [6, 21]. However, this effect can be ignored at low concentrations because the effect of the Jpc is stronger. To investigate the internal electric field for a high light intensity, we measured the excitation-intensity dependence of the PR spectra at 300 K, and the results are shown in Fig. 4. The electric field due to the e-hh is similar to that due to the e-lh across all excitation regions. These results imply that our decision for the e-hh and e-lh in above results is correct. While the excitation intensity increases to 400 mW/cm2 (4 suns), the electric field of the p-i junction gradually decreases due to the photovoltage effect, but the electric field in the i-n junction remains almost unchanged. In the PR measurement system, the carriers generated by the incident photons (excitation laser) produce the photovoltage effect, and photo-generated carriers exponentially decrease from the surface to inside the semiconductors. Therefore, the photovoltage effect is not uniform in depth. The electric field of the p-i junction, which is close to the surface, is strongly affected by the photovoltage effect, and the electric field of the i-n junction, which is far to the surface, is weakly affected. The electric field of the p-i junction is saturated at intensities above 800 mW/cm2 (8 suns). The reason for this saturation is as follows: With increasing light intensity, the photo-generated carriers can be accumulated on each side of the p-n junction, so the internal electric field gradually decreases. For a very high light intensity, we suppose that the number of accumulated carriers reaches equilibrium; then, the electric field of the p-i junction is saturated. The diffusion current of the photo-generated carriers is dominant compared to the recombination current at the saturation point of the internal electric field, so the ideality factor
where n is the ideality factor. The Vp increases with increasing Jpc under a high concentration condition, and the direction of Vp is opposite to the direction of Vbi . Therefore, the Vbi is reduced by increases in the Vp , and the VOC decreases. Not well-grown SC has a high n value, so the Vp decreases more. Therefore, the VOC is reduced as compared with that of a well-grown SC (ideal SC) under the same photocurrent condition. If Eq. (2) is considered, the VOC gradually increases with increasing light intensity; therefore, the VOC is altered by the photovoltage effect. In CPVs, the ideality factor (n) is an important characteristic.
III. CONCLUSION The temperature and the excitation-intensity dependences of the junction electric fields in the GaAs p-i-n solar cell structure have been investigated by using PR spectroscopy. In the p-i-n solar cell structure, the two different electric fields, which can be assigned to the p-i and the i-n interfaces, are obtained from the FFT analysis. The strengths of electric fields at the p-i and the i-n interfaces are 38 and 44 kV/cm, respectively. The electric fields gradually increase due to the temperaturedependent photo-voltaic effect with increasing sample temperature. With increasing excitation intensity, the electric field at the p-i interface gradually decreases due to the photovoltage effect caused by carrier screening while that at the i-n interface is insensitive to the light’s intensity. This abnormal behavior can be explained by the anisotropy carrier dynamics at the p-i and the i-n interfaces. In a high concentration, the photovoltage effect is compensated for by the increase in the carrier transport and the thermal effect; therefore, the electric field is saturated. In CPVs, the open-circuit voltage is strongly affected by the ideality factor.
ACKNOWLEDGMENTS This work was supported in part by a National Research Foundation of Korea grant funded by the
Investigation of Internal Electric Fields in GaAs · · · – Seoung Jun Lee et al.
Korean Government (NRF-2011-00111728 and NRF2013K2A2A2000881). This work was also supported by the Human Resources Development program (No. 20124030200100) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy.
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