Surface voltage and surface photovoltage - Dieter Schroder ...

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Surface voltage and surface photovoltage Probe φ s V s - V P p-type V P + + + Q Q S - - p-type t air E vac /q V, φ W M W S φ s E c /q φ = 0 E v /q x φ F V P φ s = V s (a) (b) Figure 3. Cross section and band diagram of a metal–air–semiconductor system with zero work function difference: (a) no surface charge, (b) with surface charge. V ox Q 1 V G φ s V G + + + + + ρ ox p-type 0 x 1 t ox x (a) (b) Figure 4. (a) MOS capacitor cross section showing a charge sheet Q 1 at x = x 1 and uniform charge ρ ox throughout the oxide; (b) the corresponding band diagram showing oxide and surface potentials. Let us now extend this example to a Kelvin probe held above a semiconductor covered with an insulator and a probe– semiconductor work function difference W MS leading to the negative probe potential V P = W MS in figure 5(a). Next consider oxide charge density ρ ox (C cm −3 ) and surface charge density Q (C cm −2 )asinfigure 5(b). These charges induce charge density qN A W in the semiconductor (indicated by the negative charges) and qn on the probe (indicated by the solid circles, representing electrons). The probe voltage, calculated with the same approach as used for MOS capacitors, is V P = V FB + V air + V ox + φ. (7) The flatband voltage in this case is V FB = W MS − t air t equ Q C equ − 1 C equ ∫ tequ t air x t equ ρ ox dx (8) where C equ is the equivalent capacitance and t equ the equivalent thickness given by C equ = C airC ox C air + C ox = ε 0 t equ t equ = t air + t ox /K ox . (9) Equations (7)–(9) show the probe voltage to be due to W MS , Q and ρ ox . A single measurement is unable to distinguish between these three parameters. Next we will consider the effect of light on the sample. For simplicity, we will use the bare sample in figure 6. Figure 6(a) shows the band diagram with surface charge density Q in the dark and in figure 6(b) the sample is strongly illuminated driving the semiconductor to the flatband condition and the probe potential approaches zero. Hence by measuring the surface voltage without and with light, we obtain the surface potential and hence the charge density from equation (4). To understand how this comes about, we must look at the flatband condition in more detail. The semiconductor charge density Q S for a p-type semiconductor in depletion or inversion is Q S =− √ 2kT K s ε 0 n i F(U S ,K) (10) where F is the normalized surface electric field, defined as [26] F(U S ,K)= [K(e −US + U S − 1) + K −1 (e US − U S − 1) +K(e US +e −US − 2)] 1/2 . (11) In this expression K = p 0 /n i (p 0 is the majority carrier density and n i the intrinsic carrier density), U s = qφ s /kT is the normalized surface potential, φ s the surface potential and the normalized excess carrier density ( = p/p 0 , where p = n is the excess carrier density). In the absence of excess carriers, i.e., in equilibrium, the last term in equation (11) vanishes. F is plotted versus φ s in figure 7 as a function of the normalized excess carrier density, produced by illuminating the device. The electric field is related to the charge density through equation (10). Constant charge implies constant R19
D K Schroder Figure 5. (a) Band diagram for φ MS ≠ 0, but zero charges, (b) φ MS ≠ 0, Q ≠ 0 and ρ ox ≠ 0. V P + + + - - - p-type V P ≈ 0 Light + + + p-type E Fn V P φ s E Fp E F (a) (b) Figure 6. (a) Band diagram with surface charge, (b) band diagram with surface charge and strong illumination. The black circles represent electrons. with V ox given by F 10 3 10 2 10 1 100 10 1 10 4 0 0.05 0.1 0.15 ∆ =0 0.2 Si, T=300 K V ox = Q/C ox =−Q S /C ox (13) where Q is the surface charge density and Q S the semiconductor charge density. The voltages in the dark and under intense illumination (φ S → 0) are given by V P,dark = V FB + V air + Q/C ox + φ s φ s (V) Figure 7. Normalized surface electric field, F , function versus surface potential as a function of normalized excess carrier density or light intensity. electric field or constant F . Hence as n increases, the surface potential decreases, because the locus of the F –φ s plot is along a horizontal line such as the dashed line. It is obvious from figure 7 that the surface potential decreases with increasing light-generated excess carriers. In the limit of intense illumination, φ s → 0 and the semiconductor approaches flatband. The probe potential is given by V P = V FB + V air + V ox + φ s (12) V P,light = V FB + V air + Q/C ox . (14) The charge density Q remains constant during the measurement, regardless of illumination, and the change in the surface voltage becomes 5. Applications V P = V P,dark − V P,light ≈ φ s . (15) 5.1. Minority carrier diffusion length A major application of SPV is the measurement of minority carrier diffusion length, even though the minority carrier diffusion length plays a negligible role in most integrated circuits (ICs) consisting of MOS devices. Then why measure the minority carrier diffusion length? The reason that minority R20
Page 1 and 2: INSTITUTE OF PHYSICS PUBLISHING MEA
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Page 7 and 8: D K Schroder As is obvious from the
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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