One of the dominant defects in a solar grade p-type wafer is an interstitial oxygen impurity....
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One of the dominant defects in a solar grade p-type wafer is an interstitial oxygen impurity. (a) Show an expression of the total recombination rate contributed from band-to-band recombination, SRH (trap-assisted (recombination, and Auger recombination. Assume there is one trap state of E, for the SRH recombination. Also, simplify the recombination rate in the low level injection condition and explain what the low level injection condition is. (b) Using MATLAB, OCTAVE or EXCEL calculate and plot the bulk effective lifetime in the injection level from 10¹4 to 10¹7 cm². For your calculation, assume Ec- Et= 0.41 eV, tn = 360 us, and tn/ tp = 10. Also, the wafer is p-type and the donor concentration is 5×10¹5 cm³. For the calculations of radiative and Auger reombinations, refer to the table below. (c) Now, consider surface recombination. A thickness of the p-type wafer thickness is 200 um, and the effective surface recombination is 10 cm/s. In the same way, calculate the effective lifetime and plot the result. Refer to the following relationship: Teff, effective lifetime, Tbulk bulk lifetime estimated in (b), W wafer thickness, S surface recombination velocity. TABLE 7.1 Recombination Coefficients. Semiconductor Temperature (K) Si Si Si Ge GaAs GaAs GaP InP InSb InGaAsP 300 300 1 Teff Tbulk W 1 2S + 77 300 300 300 300 300 300 300 Radiative Recombination Coefficient, B (cm³/s) 4.73 x 10-15 [10] 8.01 x 10-14 [10] 5.2 x 10-¹4 [5] 1.7 x 10-10 [8 S/R] 1.3 x 10-10 18 't Hooft] 5.4 x 10-14 [5] 1.6-2 x 10-¹¹ [7] 4.6 x 10-¹1 [5] 4 x 10-10 [8] Auger Recombination Coefficient, C (cm/s) C₁ = 2.8 x 10-31, C₂ = 10-31 [11 D/S] C₁+C₁=2-35 x 10-31 [11 B/G] C₁ = 8 x 10-¹2, C₂ = 2.8 x 10-³1 C₁ = 1.6 x 10-2, C, = 4.6 x 10-31 [6] C₁ = 5 x 10-30, 30, C₂ = 2x 10-30 [8 S/R] C₁ = 3.7 x 10-³1, C₂ = 8.7 x 10-30 [6] C+C, =8 × 10-29 [9] One of the dominant defects in a solar grade p-type wafer is an interstitial oxygen impurity. (a) Show an expression of the total recombination rate contributed from band-to-band recombination, SRH (trap-assisted (recombination, and Auger recombination. Assume there is one trap state of E, for the SRH recombination. Also, simplify the recombination rate in the low level injection condition and explain what the low level injection condition is. (b) Using MATLAB, OCTAVE or EXCEL calculate and plot the bulk effective lifetime in the injection level from 10¹4 to 10¹7 cm². For your calculation, assume Ec- Et= 0.41 eV, tn = 360 us, and tn/ tp = 10. Also, the wafer is p-type and the donor concentration is 5×10¹5 cm³. For the calculations of radiative and Auger reombinations, refer to the table below. (c) Now, consider surface recombination. A thickness of the p-type wafer thickness is 200 um, and the effective surface recombination is 10 cm/s. In the same way, calculate the effective lifetime and plot the result. Refer to the following relationship: Teff, effective lifetime, Tbulk bulk lifetime estimated in (b), W wafer thickness, S surface recombination velocity. TABLE 7.1 Recombination Coefficients. Semiconductor Temperature (K) Si Si Si Ge GaAs GaAs GaP InP InSb InGaAsP 300 300 1 Teff Tbulk W 1 2S + 77 300 300 300 300 300 300 300 Radiative Recombination Coefficient, B (cm³/s) 4.73 x 10-15 [10] 8.01 x 10-14 [10] 5.2 x 10-¹4 [5] 1.7 x 10-10 [8 S/R] 1.3 x 10-10 18 't Hooft] 5.4 x 10-14 [5] 1.6-2 x 10-¹¹ [7] 4.6 x 10-¹1 [5] 4 x 10-10 [8] Auger Recombination Coefficient, C (cm/s) C₁ = 2.8 x 10-31, C₂ = 10-31 [11 D/S] C₁+C₁=2-35 x 10-31 [11 B/G] C₁ = 8 x 10-¹2, C₂ = 2.8 x 10-³1 C₁ = 1.6 x 10-2, C, = 4.6 x 10-31 [6] C₁ = 5 x 10-30, 30, C₂ = 2x 10-30 [8 S/R] C₁ = 3.7 x 10-³1, C₂ = 8.7 x 10-30 [6] C+C, =8 × 10-29 [9]
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Steps Step 1 of 2 a Explanation Expression for Total Recombination RateThe total recombination rate Rtotal in a semiconductor can be expressed as the sum of the individual recombination ratesRtotal Rb... View the full answer
Related Book For
Fundamentals Of Momentum Heat And Mass Transfer
ISBN: 9781118947463
6th Edition
Authors: James Welty, Gregory L. Rorrer, David G. Foster
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