Numerical analysis of the short-circuit current density in GaInAsSb thermophotovoltaic diodes

Infrared Physics & Technology 52 (2009) 152–157

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Numerical analysis of the short-circuit current density in GaInAsSb thermophotovoltaic diodes Xincun Peng, Xin Guo, Baolin Zhang *, Xiangping Li, Xiaowei Zhao, Xin Dong, Wei Zheng, Guotong Du State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, 2699 Qianjin Street, Changchun 130012, PR China

a r t i c l e

i n f o

Article history: Received 12 January 2009 Available online 16 June 2009 PACS: 84.60.Jt 85.60.Bt 85.60.Dw 78.66.Fd Keywords: GaxIn1xAs1ySby Thermophotovoltaic Diodes Short-circuit current

a b s t r a c t In this paper, a simulation and analysis on the short-circuit current density (Jsc) of the P-GaSb window/PGaxIn1xAs1ySby emitter/N-GaxIn1xAs1ySby base/N-GaSb substrate structure is performed. The simulations are carried out with a fixed spectral control filter at a radiator temperature (Trad) of 950 °C, diode temperature (Tdio) of 27 °C and diode bandgap (Eg) of 0.5 eV. The radiation photons are injected from the front P-side. Expressions for minority carrier mobility and absorption coefficient of GaxIn1xAs1ySby semiconductors are derived from Caughey–Thomas and Adachi’s model, respectively. The P-GaxIn1xAs1ySby emitter with a much longer diffusion length is adopted as the main optical absorption region and the N-GaxIn1xAs1ySby base region contribute little to Jsc. The effect of P-GaSb window and P-GaxIn1xAs1ySby emitter region parameters on Jsc is mainly analyzed. Dependence of Jsc on thickness and carrier concentration of the window are analyzed; these two parameters need to be properly selected to improve Jsc. Contributions from the main carrier recombination mechanisms in the emitter region are considered; Jsc can be improved by suppressing the carrier recombination rate. Dependence of Jsc on the carrier concentration and layer thickness of the emitter P-region are also analyzed; these two parameters have strong effect on Jsc. Moreover, adding a back surface reflector (BSR) to the diode can improve Jsc. The simulated results are compared with the available experimental data and are found to be in good agreement. These theoretical simulations help us to better understand the electro-optical behavior of GaxIn1xAs1ySby TPV diode and can be utilized for performance enhancement through optimization of the device structure. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Quaternary alloys, GaInAsSb, have attracted much interest in the technology of choice for present and future thermophotovoltaic (TPV) diodes, because they have the advantage of the versatility in obtaining alloys with a large range of energy gaps from 0.296 eV (4.2 lm) to 0.726 eV (1.7 lm) when lattice matched to commercially available GaSb wafers [1–3], which covers the typical wavelength range of TPV diodes with low temperature (800–1700 °C) radiators [4]. Most of the recently reported GaInAsSb diodes are in the range of 0.5–0.55 eV [1–3]. The optimal radiator temperature, when considering 95–97% reflection of all below-bandgap photons, is 950 °C [4]. 0.53 eV GaInAsSb-based TPV systems have shown more than 19% radiant heat conversion efficiency using refractive spectral control in a TPV system with radiator and diodes temperature at 950 °C and 27 °C, respectively [5]. The short-circuit current density (Jsc) is one of the most important characteristics for determining the output power density (Pout) * Corresponding author. Tel.: +86 431 85168 240x8113; fax: +86 431 85168 240. E-mail addresses: [email protected] (X. Peng), [email protected] (B. Zhang). 1350-4495/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2009.06.003

and the energy conversion efficiency (gdio) of a TPV diode [5–7]. Jsc is primarily dependent on the incident photon flux density (F(k)) and the internal spectral response (SRInt(k)) of the PV diode [6]. Thus, it is necessary to have a thorough understanding of the effects of these parameters to design and fabricate optimal TPV diodes. The numerical simulations of TPV diodes are particularly useful to accomplish such a task. However, most of the published research does not deal with this problem. Therefore, a numerical analysis on Jsc of a GaxIn1xAs1ySby-based TPV diode is presented in this paper. For a TPV system with a fixed radiator temperature, F(k) is determined by the performances of the spectral control system [5,7]. The internal spectral response (SRInt(k)), therefore Jsc, is affected by the TPV diode parameters such as the absorption coefficient (a), minority carrier mobility and recombination lifetime, surface or interface recombination velocities (S) and thickness (d) of the absorption layer and the reflectance of back surface reflector (BSR). In this work, the absorption coefficient of GaInAsSb alloy is calculated using Adachi’s model [8,9], the carrier mobility is calculated using Caughey–Thomas model [10–13] and the recombination rates for the main recombination mechanisms (e.g. the

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Fig. 2. Electron and hole mobility of GaxIn1xAs1ySby versus doping concentration at 300 K for several compositions.

Fig. 1. Schematic cross-section of the simulated Ga0.8In0.2As0.18Sb0.82 TPV diode.

radiative, Auger, and Shockley–Read–Hall recombination) are calculated by some semi-empirical formulas. Based on these material parameters, the short-circuit current density of a 0.5 eV Ga0.8In0.2As0.18Sb0.82-based TPV diode is simulated using onedimensional (1-D) numerical photovoltaic cell simulation software PC-1D [14], and then the effects of the device parameters on Jsc are discussed. 2. Methodologies and assumptions This section summarizes the methodologies and assumptions for calculating the related material parameters of GaxIn1xAs1ySby and for analyzing the short-circuit current density of a GaxIn1xAs1ySby-based TPV diode. We present only the simulation results for GaxIn1xAs1ySby alloy with 0.8 as the composition of x and 0.82 of y, which lattice matched to GaSb substrate, and the corresponding bandgap energy (Eg) equal to 0.5 eV [2,3]. Fig. 1 shows the cross-sectional structure of the GaxIn1xAs1ySby TPV diode investigated in this paper, which consists of the P+-GaSb window and contact layer, 0.5 eV Ga0.8In0.2As0.18Sb0.82-active P–N junction, N-type GaSb substrate, back surface reflector (BSR) and ohmic contact. The incident radiation photons are from the front P-side. The optimum temperature of the radiator for this TPV diode is Trad = 950 °C based on other’s works [4,7]. 2.1. Material parameters of Ga0.8In0.2As0.18Sb0.82 The minority carrier mobilities of P-type and N-type Ga0.8In0.2As0.18Sb0.82 are calculated by Caughey–Thomas empirical formula [10]:

lhe;hi ðNÞ ¼ lmin;he;hi þ

lmax;he;hi  lmin;he;hi

ð1Þ

 / 1 þ NhA;Di =Nref ;he;hi he;hi

In Eq. (1), the carrier mobility (lhe;hi ) is taken as a function of the semiconductor doping concentration N hA;Di at 300 K. lmax and lmin are the saturated values that mobility reaches for very low and high doping densities, respectively. Nref and / are the related fitting parameters. According to Mathiesen’s rule, lmax and lmin of the GaxIn1xAs1ySby alloys could be calculated with its binary compound mobility using Eq. (A4) in Ref. [15]. The other two parameters are obtained directly by linear interpolation of known binary data using the Eq. (A1) in Ref. [16]. The parameters in Eq. (1) for binary alloys that are relevant to GaxIn1xAs1ySby alloys are taken from Refs. [11–13] and summarized in Table 1. Fig. 2 shows the electron and hole mobility of GaxIn1xAs1ySby alloy at room temperature. Lines correspond to values calculated in this work, and selected mobility experimental data represented in Fig. 2 by symbols are taken from Ref. [17]. The calculated results agree well with the experimental data. The absorption coefficient a(k,T) of semiconductor can be calculated using the formula [9]:

8" #1=2 91=2 1 = 4p < ½e1 ðk; TÞ2 þ e2 ðk; TÞ2 2  e1 ðk; TÞ aðk; TÞ ¼  ; 2 k :

ð2Þ

where k is the photon wavelength, T is the material temperature. e1(k,T) and e2(k,T) are the real and imaginary parts of the dielectric function, respectively. In this work, the constants e1(k,T) and e2(k,T) for GaxIn1xAs1ySby are calculated using Adachi’s model dielectric function (MDF) [8,9]. In this model, e1(k,T) and e2(k,T) are calculated from the joint density of state functions at various critical-point energies in the Brillouin zone and indirect bandgap transitions, as

Table 1 Summary of parameters used in the Caughey–Thomas model for calculating the electron and hole mobilities at room temperature for binary alloys that are relevant to GaxIn1xAs1ySby alloys. Materials

Carriers

lmax (cm2/Vs)

lmin (cm2/Vs)

Nref (1017 cm3)

ø

Ref.

GaSb

Electron hole

5650 875

1050 190

2.8 9

1.050 0.65

[12]

GaAs

Electron hole

9400 491.5

500 20

0.6 1.48

0.3940 0.38

[11]

InSb

Electron hole

78,000 750

5000 100

0.7 6

0.7 0.6

[13]

InAs

Electron hole

34,000 530

1000 20

11 1.1

0.32 0.46

[11]

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Fig. 3. Absorption coefficient of GaxIn1xAs1ySby versus radiation wavelength at 300 K for various compositions.

shown by Adachi [8,9]. In this paper, the critical-point energies for calculating the dielectric function of GaxIn1xAs1ySby alloys are interpolated from known binary and ternary data using the Eq. (A3) in Ref. [16], whereas other parameters are obtained directly by linear interpolation of known binary data using the Eq. (A1) in Ref. [16], the related binary and ternary alloy data from Refs. [8,18]. Fig. 3 shows the absorption coefficient a of GaxIn1xAs1ySby alloy at 300 K as a function of radiation wavelength for several compositions. Lines correspond to values calculated from this work and selected absorption experimental data, represented as symbols, are taken from Refs. [19–20]. Comparing the shape of the calculated absorption coefficient with the measured data in Fig. 3, the calculated results agree well with the experimental data. The main carrier recombination mechanisms that affect the performances of GaInAsSb-based TPV diode are the radiative, Auger, bulk and surface/interface Shockley–Read–Hall (SRH) recombination. The formulas and related parameters for simulating the recombination rates in PC-1D for Ga0.8In0.2As0.18Sb0.82 are summarized in Table 2. The radiative coefficient (B) is calculated by using

Fig. 4. Dependence of minority carrier diffusion length in P- and N-type Ga0.8In0.2As0.18Sb0.82 and GaSb materials on majority carrier concentration.

Eq. (23) from Ref. [15], and the photo-recycling factor (u) is the calculated results taken from Ref. [5]. The parameters related to the bulk SRH and surface/interface recombination are the experimental data taken from Ref. [21–23]. In the low-level condition, the relation between minority carrier Auger coefficient (C) and lifetime (sA) could be expressed as sA = 1/(CN2), where N is the material doping concentration. The minority carrier Auger lifetimes (sA) for all compositions of GaxIn1xAs1ySby alloys as a function of doping concentration have been calculated by Tian et al. in Ref. [16]. So, the value of C can be calculated by the known sA; the calculated results for Ga0.8In0.2As0.18Sb0.82 are shown in Table 2. 2.2. Short-circuit current density of TPV diode The value of short-circuit current density (Jsc) can be assumed equal to photo-current density (Jp) and given by equation [6]:

J sc ¼ q

Z

km

FðkÞSRInt ðkÞ dk

ð3Þ

0

Table 2 Summary of recombination parameters for Ga0.8In0.2As0.18Sb0.82 alloy at room temperature. Recombination Radiative

Recombination rates   RRad ¼ uB np  n2i

Auger

   RAug ¼ C n n þ C p p np  n2i ðnpn2i Þ

Bulk SRH

RSRH ¼ sSRHe ðpþni ÞþsSRHh ðnþni Þ

Surface/interface

ð Þ RSRV ¼ Se ðpþni ÞþSh ðnþni Þ Se Sh npn2i

Parameters

Ref.

B = 7.22  1011 cm3/s u = 4 (zero back reflectance) u = 40 (Ideal BSR)

[5,15]

CP = 2  1028 cm6/s CN = 1  1027 cm6/s sSRHe = sSRHh = 0.1–1 ls

[15,16] [21–23]

Se/Sh 6 2000 cm/s (passivated by GaSb window) Se/Sh P 106 cm/s(without surface passivation)

[21–23]

a

CP and CN represent the Auger coefficients for P- and N-type Ga0.8In0.2As0.18Sb0.82, respectively; bSe and Sh are the surface recombination velocities for P- and N-type Ga0.8In0.2As0.18Sb0.82, respectively.

Table 3 Basic parameters for Ga0.8In0.2As0.18Sb0.82-based TPV diode. Basic parameters

P-GaSb window Emitter P-region Ga0.8In0.2As0.18Sb0.82 Base N-region Ga0.8In0.2As0.18Sb0.82 N-GaSb substrate a

S is the surface/interface recombination velocity.

Trad = 950 °C, Tdio = 27 °C, u = 4, sSRH = 0.1 ls, RBSR = 0% Carrier concentration n/p (cm3)

Thickness H (lm)

Sa (cm/s)

1018 1017 1017 1017

0.2 5 0.5 300

106 2000 2000 106

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where km is the wavelength corresponding to the semiconductor bandgap (Eg) and SRInt(k) is the internal spectral response of the TPV diode. F(k) is the spectral photon flux (number of incident photons/cm2/s per unit bandwidth) of the incident radiation that was absorbed by TPV cell. The expression for F(k) in the wavelength range of k < km could be written as:

FðkÞ ¼ eeff ðkÞUB ðkÞ ¼ eeff ðkÞ

2pc k4 ðehc=ðkkT rad Þ  1Þ

ð4Þ

where h, k, c and Trad are Plank’s constant, Boltzmann’s constant, the speed of light and the TPV radiator temperature, respectively; UB(k) is the spectral photon flux of the TPV radiator, which could be assumed as blackbody and follows Plank’s law; eeff(k) is the effective cavity emissivity that characterizes the performance of the spectral control in TPV system, which is mainly determined by the radiator emissivity, reflectance and absorbance of the optical filter, and the top electrode coverage rate of the TPV diode. The value of eeff(k) is taken as 0.78 based on the best reported spectral control system performance for GaInAsSb-based TPV system [5,7]. With the fixed F(k) by the above model, the short-circuit current density of a 0.5 eV Ga0.8In0.2As0.18Sb0.82-based TPV diode (device structure as seen in Fig. 1) was simulated using one-dimensional (1-D) numerical photovoltaic cell simulation software PC-1D, based on the carrier transport, Poisson, and carrier continuity equations for electrons and holes [14]. Since F(k) is fixed, we focus on SRInt(k).

3. Results and discussion The numerical simulations have been performed on 0.5 eV Ga0.8In0.2As0.18Sb0.82-based TPV diode (device structure is shown in Fig. 1) operated at 27 °C using PC-1D version 5.9. The basic device parameters of the investigated TPV diode are listed in Table 3. The minority carrier diffusion length (Le,P/Lh,N) is an important parameter in determining the carrier collection efficiency and SRInt(k) of a TPV diode. In fact, SRInt(k) can be improved by increasing the minority carrier diffusion length [6]. The calculated dependence of Le,P/Lh,N on the majority carrier concentrations for GaSb and Ga0.8In0.2As0.18Sb0.82 at 300 K by PC-1D is shown in Fig. 4. Based on the calculations in Section 2, le,P  lh,P, so Le,P  Lh,N. Thus, it is appropriate to choose P-type Ga0.8In0.2As0.18Sb0.82 as the main optical absorption material to improve the collection efficiency of the photon-generated carriers and then the value of SRInt(k) and Jsc. The incident photons are mainly absorbed in emitter P-region, only a few are transmitted to base N-region, which contributes very little to Jsc. In the following discussion, we will focus on the effect of top window and emitter P-region parameters on Jsc. Fig. 5a shows the internal spectral response (SRInt) of the Ga0.8In0.2As0.18Sb0.82 TPV diode for different window layer thicknesses (dW). Lines represent the simulated results for the device structure, and the parameters are shown in Table 3. The experimental data with the similar device structure are taken from Ref. [1], the simulated results agree well with the experimental data. Fig. 5b shows the dependence of Jsc on dW for different carrier concentrations (pW) of window layer. The non-passivated top P-GaSb window layer has the high front surface recombination rate and the low carrier collection efficiency, reducing dW leads to more of the incident photons transmitted into the emitter region, which has a higher carrier collection efficiency with the front surface passivated by window. Thus, SRInt(k) and Jsc increase with decreasing dW as observed in Fig. 5. Decreasing carrier concentration (pW) improves the carrier diffusion length and the carrier collection efficiency in the window, resulting in suppressed effect of dW on Jsc in Fig. 5b. However, Jsc decreases with decreasing pW in the low dW range. The inset of Fig. 5b shows the schematic equilibrium en-

Fig. 5. (a) Simulated internal spectral response at different window layer thicknesses (dW) compared to the experimental data reported by Wang et al. [1]; (b) simulated Jsc versus dW for different carrier concentrations (pW) in window layer.

ergy-band diagram of P-GaSb window/P-Ga0.8In0.2As0.18Sb0.82 emitter for different values of pW, for pW = pE = 1017 cm3, the P-GaSb window layer creates a downward energy-band bending and a minority carrier accumulative layer of P-Ga0.8In0.2As0.18Sb0.82 emitter region at the interface due to the type-II energy-band alignment, which increases the minority carrier recombination rate at the interface. Increasing pW leads to the upward energyband bending and decreases minority carrier recombination rate at the interface, resulting in increase in Jsc as shown in Fig. 5b. Fig. 6a–d presents the effect of the emitter P-region recombination parameters on SRInt(k), by keeping the other parameters in Tables 2 and 3 constant. The Auger recombination is primarily determined by the semiconductor energy-band structure, effective mass and temperature [16], which can be assumed as constant for a fixed semiconductor and temperature. The radiative recombination is related to the bandgap, effective mass, photo-recycling factor and temperature [15]. The calculated Auger coefficients for Ga0.8In0.2As0.18Sb0.82 are CP = 2  1028 cm6/s and CN = 1  1027 cm6/s at 300 K, respectively, and radiative coefficient is B = 7.22  1011 cm3/s without considering the photo-recycling effect and would be smaller if considered. From Fig. 6a and b, the SRInt(k) is not sensitive to CP in the range of 1030 < CP < 1027 or B in the range of 1012 < B < 1010; the high SRInt(k) (near 100%) can be obtained for both the above two parameter ranges. The SRH and surface recombination due to electronic defect states near the center of the bandgap are mainly determined by the density of the bulk deep energy defect and surface state, respectively. From Fig. 6c and d, SRInt(k) is suppressed by the decreased sSRHe or the increased Se. The bulk and surface quality of the semiconductor was improved by improving the material growth, and the surface

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Fig. 6. Simulated dependence of the internal spectral response on the various emitter P-region recombination parameters. During the variation of a single parameter, others taken from Tables 2 and 3 are fixed. (a) Variation of the Auger coefficient (CP), (b) variation of the radiative coefficient (B), (c) variation of the electron SRH lifetime (sSRHe), and (d) variation of the surface recombination velocity (Se).

passivation process can suppress the SRH and surface recombination, respectively. Fig. 7 shows the dependence of the individual recombination mechanism (in emitter P-region) determined Jsc and the total Jsc on the P-region carrier concentration (pE) for various recombination parameters, by keeping other parameters constant in Tables 2 and 3 . From the formulas for the Auger and radiation recombination rats in Table 2, increasing the carrier concentration (pE)

Fig. 7. Simulated dependence of the individual recombination mechanism determined Jsc and the total Jsc on the emitter P-region carrier concentration (pE). (Jsc)Aug, (Jsc)Rad, (Jsc)SRH and (Jsc)SRV are the Auger, radiative, SRH and surface recombination determined short-circuit current density, respectively; (Jsc)Total1, (Jsc)Total2 and (Jsc)Total3 are the total short-circuit current density for the device parameters taken from Tables 2 and 3 except for the recombination parameters given in the figure.

leads to increase in RAug and RRad, resulting in decrease in (Jsc)Aug and (Jsc)Rad as observed in Fig. 7, the much more rapid decrease in (Jsc)Aug is coursed by the higher ordered cubic function RAug to carrier concentration. The (Jsc)SRH and (Jsc)SRV are not sensitive to pE at high sSRHe and low Se values, respectively, while both are decreasing with pE at low sSRHe and high Se values, respectively. These results also correlate with the formulas calculated for RSRH and RSRV in Table 2, in which RSRH and RSRV become increasing functions to carrier concentration with decreasing sSRHe and increasing Se, respectively. Decreasing sSRHe or increasing Se decreases SRInt(k), resulting in decrease in Jsc. Fig. 8a shows the Jsc versus P-region thickness for different carrier concentrations, Jsc appears as a peak with varying dE and the peak gets higher and tends to get a higher value of dE with lowering pE. dE should be smaller than Le,P for obtaining the high collection efficiency of the photon-generated carriers; however, a thicker P-region can fully absorb the incident photons. The optimum dE is achieved for the maximal Jsc in Fig. 8a. Decreasing the P-region carrier concentration improves Le,P, resulting in increase in Jsc, which coincides with the results shown in Fig. 7. Meanwhile, the P-region thickness needs to be adjusted to obtain maximal Jsc. Increasing the P-region thickness can increase the photon absorption but decrease the carrier collection. A more efficient way to increase the photon absorption is by adopting a back surface reflector (BSR), which let the above bandgap photons double pass the active P–N junction. Fig. 8b presents the dependence of Jsc on the emitter P-region thickness (dE) for different RBSR (the fraction of the above bandgap photons reflected from BSR) values. Increasing RBSR can increase Jsc, and the maximal Jsc tends to be obtained at lower dE with increasing RBSR.

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Jsc. By appropriate combination of the aforementioned parameters, the performance of the device can be improved.

Acknowledgments The authors are grateful to Photovoltaics Special Research Centre, University of New South Wales, Australia, for their free-shared PC-1D program. This work was supported by National Natural Science Foundation of China under Grant No. 60676040.

References

Fig. 8. Jsc versus the emitter P-region thickness (dE) at: (a) different P-region carrier concentrations (pE) and (b) different RBSR values, with the condition that the other parameters in Table 2 are kept constant.

4. Conclusions In this paper, the numerical analysis of the short-circuit current (Jsc) in the P-GaSb window/P-Ga0.8In0.2As0.18Sb0.82 emitter/NGa0.8In0.2As0.18Sb0.82 base/N-GaSb substrate structure TPV diode is performed by using the quasi-one-dimensional numerical photovoltaic cell simulator PC-1D. The radiation photons are injected from the front P-side. The minority carrier mobility and the absorption coefficient are incorporated using Caughey–Thomas and Adachi’s model, respectively. The P-GaxIn1xAs1ySby emitter with the much longer diffusion length is adopted as the main optical absorption region, and the N-GaxIn1xAs1ySby base region contributes little to Jsc. The effect of P-GaSb window and PGaxIn1xAs1ySby emitter on Jsc is mainly analyzed. Reducing the window thickness leads to more of the incident photons absorbed in the emitter region with the higher carrier collection efficiency, resulting in increase in Jsc. Increasing the carrier concentration of the window layer leads to the upwards energy-band bending and the decrease in minority carrier recombination rate of the emitter region at the interface, and then Jsc improved. The minority carrier recombination mechanisms in the emitter region have the strong effect on Jsc, and it shows that the recombination needs to be suppressed to improve Jsc. The SRH and surface recombination can be suppressed by improving the material growth and the surface passivation process, and the Auger and radiative recombination can be suppressed by reducing the carrier concentration. In addition, the emitter P-region thickness has an important effect on Jsc. Moreover, a back surface reflector (BSR) applied to the diode can improve the

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