Surface voltage and surface photovoltage - Dieter Schroder ...

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Surface voltage and surface photovoltage Q Q S + _ _ + _ + (a) p-type E c V SPV E c E i Φ E Fn E i E F E v E Fp E F E v (b) (c) Figure 8. (a) Device cross section showing the surface charge density Q and the semiconductor charge density Q S , (b) the band diagram in the dark and (c) the illuminated band diagram. carrier lifetime/diffusion lengths are so commonly measured is that they provide information about the low defect densities consistent with today’s integrated circuits. No other technique can detect defect densities as low as 10 9 –10 11 cm −3 in a simple, contactless room temperature measurement. In contrast to analytical techniques whose signals are usually proportional to impurity density, lifetime and diffusion length are inversely proportional to impurity density. Hence, analytical technique signals decrease while lifetime/diffusion length signals increase with decreasing impurity density. Further, the availability of commercial, clean room compatible equipment makes these measurements relatively simple. It is for these reasons that the IC community has adopted lifetime/diffusion length measurements as a ‘process cleanliness monitor’. The introduction of corona charge has extended the applicability of surface voltage/photovoltage characterization to many other measurements, mentioned above. Surface photovoltage is an attractive diffusion length characterization technique, because it is nondestructive and contactless, sample preparation is simple (no contacts, junctions, or high temperature processing required), it is a steady-state method and the equipment is commercially available. The concept of surface photovoltage can be understood with the band diagram in figure 8. Surface charge density Q induces an equivalent charge density in the semiconductor, Q S , with Q + Q S = 0 shown in figure 8(a). The semiconductor charge, in depletion, is provided by the ionized space charge density qN A W, neglecting electrons and holes in the space-charge region. The band diagram in the dark is shown in figure 8(b). When the sample is illuminated, the Fermi level splits into the quasi-Fermi levels E Fn and E Fp with the surface photovoltage equal to the splitting potential. The band bending is reduced as in figure 8(c). The sample is assumed to be homogeneous and is of thickness d, as shown in figure 9. One surface is chemically treated to induce a surface space-charge region as described earlier. The wafer can be homogeneous, or it can be in the form of a pn junction or metal–semiconductor junction. We will only treat the homogeneous case here. The surface with the induced scr is uniformly illuminated by monochromatic light of energy higher than the band gap, with the back surface kept in the dark. The light is chopped to enhance the signal/noise ratio using lock-in techniques. The wavelength is varied with a monochromator or a series of filters transmitting selected wavelengths. s r s 1 Φ(λ) V P V SPV p-Type (τ n , D n , L n ) 0 W d x Figure 9. Sample for SPV measurements. The black circles represent electrons and the open circles represent holes. Electron–hole pairs (ehps) are generated in both the spacecharge region (scr) and in the p-substrate by absorbed photons. The ehps generated in the scr are very quickly separated by the electric field with the minority electrons drifting to the surface. Those minority carriers in the quasi-neutral substrate, within approximately a minority carrier diffusion length of the scr edge, diffuse and drift toward the surface, establishing a surface potential or surface photovoltage relative to the grounded back surface. The surface photovoltage is proportional to the excess minority carrier density, n(W), at the edge of the scr, as described in more detail in appendix A. Light reaching the back surface produces an undesirable SPV signal that can be detected by its large amplitude, by a reversal in signal polarity over the SPV wavelength range or by a signal decrease with increasing illumination at the longer wavelengths. Equation (A4) in appendix A gives the excess carrier density. In principle, it is possible to extract the diffusion length L n from that expression for arbitrary W, d and α, the optical absorption coefficient. In practice this is difficult to do and several constraints are usually imposed on the sample to simplify data extraction. The undepleted wafer should be much thicker than the diffusion length and the scr width should be small compared to L n . The absorption coefficient should be sufficiently low for αW ≪ 1, but sufficiently high for α(d − W) ≫ 1. The diameter of the light should be larger than the sample thickness, allowing a one-dimensional analysis and low-level injection (excess carrier density (n) is lower than the majority carrier density p 0 ) should prevail. The assumptions d − W 4L n W ≪ L n αW ≪ 1 α(d − W) ≫ 1 n ≪ p 0 (16) allow equation (A4) to be simplified to (see appendix A) (1 − R) L n n(W) ≈ (s 1 + D n /L n ) (L n +1/α) . (17) R21
D K Schroder As is obvious from the boundary condition in the detailed derivation in appendix A, s 1 is the surface recombination velocity at the edge of the space-charge region, i.e., at x = W , not at the surface. The surface recombination velocity at the surface is s r as illustrated in figure 9. The excess carrier density at x = W is related to the surface voltage by the ‘law of the junction’ from pn junction theory n(W ) = n 0 (exp(qV S /kT) − 1) ≈ n 0 qV S /kT (18) for V S ≪ kT/q. The surface voltage is equal to the probe voltage, giving V P = kT (1 − R) L n q n 0 (s 1 + D n /L n ) (L n +1/α) . (19) The dimensions are shown approximately to scale in figure 10. Optically generated excess carriers diffuse and recombine. Because the electron and hole diffusion coefficients or mobilities differ, a Dember voltage is developed as a result of this mobility difference, given by [27] V b = kT ( ) (b − 1) q (b +1) ln (b +1)n 1+ (20) n 0 + bp 0 where b = µ n /µ p , with µ n and µ p the electron and hole mobilities. For p-type Si with b ≈ 3, p 0 ≫ n 0 and room temperature, equation (20) becomes ( V b = 0.013 ln 1+ 4n ) ≈ 0.013 4n . (21) 3p 0 3p 0 With n/p 0 typically 10 −6 –10 −4 , V b ≈ 1.7 × 10 −8 –1.7 ×10 −6 V, a voltage that is low compared to the surface photovoltage and is usually neglected. V S is proportional to n(W) for V S < 0.5kT/q. Typical surface photovoltages are in the low millivolt range, ensuring a linear relationship. D n and L n are assumed to be constant and over a restricted wavelength range, the reflectivity R can also be considered constant for bare surfaces. The surface recombination velocity s 1 is usually unknown. However, if n(W ) is held constant during the measurement, the surface potential is also constant, and s 1 can be considered reasonably constant. This leaves α and as the only variables. There are two implementations of the SPV method: (1) constant surface photovoltage and (2) constant photon flux density. In method (1), V P is held constant, implying n(W) is also constant. A series of different wavelengths is selected during the measurement with each wavelength providing a different α. The photon flux density is adjusted for each wavelength to hold V P constant, allowing equation (19) to be written as = n 0V P (s 1 + D n /L n ) (L n +1/α) = C 1 (L n +1/α) (22) (kT /q)(1 − R) L n where C 1 is a constant. Then is plotted against 1/α for constant V P . The result is a line whose extrapolated intercept on the negative 1/α axis ( = 0) is the minority carrier diffusion length L n , as shown in figure 11(a). The slope of such a plot is C 1 , containing the surface recombination velocity s 1 . While it W ≈ 0.5 µm 1/α (λ = 0.8 µm) 1/α (λ = 1.04 µm) L n (τ r = 100 µs) 0 100 200 300 400 500 600 700 x (µm) Figure 10. Cross section showing the various lengths for a 675 µm thick p-type wafer. Φ (normalized) 1/V P (normalized) 1 0.8 0.6 0.4 L n 0.2 s 1 = 1000 cm/s 0 -50 0 50 100 150 200 1 0.8 0.6 0.4 0.2 L n 1/α (µm) (a) s 1 = 1000 cm/s 0 -50 0 50 100 150 200 1/α (µm) Figure 11. Normalized SPV plots for (a) constant surface photovoltage (theory) and (b) constant photon flux density (points: data, lines: theory). (b) is difficult to extract s 1 from the other parameters contained in C 1 , it is possible to observe changes in s 1 by comparing SPV plots before and after a surface treatment that changes surface recombination. For the constant photon flux density implementation, we write equation (19) as 1 = n 0(s 1 + D n /L n ) (L n +1/α) = C 2 (L n +1/α) (23) V P (kT /q)(1 − R) L n where C 2 is a constant. A plot of 1/V P (normalized) versus 1/α gives L n as illustrated in figure 11(b), where both experimental data and theory are shown. V P changes during the measurement, hence surface recombination may vary during the measurement. However, the surface photovoltage variation is small and variations in surface recombination velocity are likely to be negligible. The condition W ≪ L n is generally satisfied for singlecrystal Si, but not necessarily for other semiconductors. For example, the diffusion length in GaAs is often only a few microns because radiative recombination dominates. Hence, diffusion length measurements, primarily used for Si to determine recombination centre densities, are less important R22
Page 1 and 2: INSTITUTE OF PHYSICS PUBLISHING MEA
Page 3 and 4: D K Schroder Vibrating Ref. Electro
Page 5: D K Schroder Figure 5. (a) Band dia
Page 9 and 10: D K Schroder (a) L n (µm) L n (µm
Page 11 and 12: D K Schroder φ s (V) 1 0.5 0 -0.5
Page 13 and 14: D K Schroder Φ (photons/sÂP 2 ) 4
Page 15 and 16: D K Schroder Appendix B. Sinusoidal

Surface voltage and surface photovoltage - Dieter Schroder ...

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