Minority Carrier Diffusion Length and Mobility-Lifetime Product of Carriers in Ag Doped and Undoped nc-cds Thin Films 5.

Transcription

1 5 Minority Carrier Diffusion Length and Mobility-Lifetime Product of Carriers in Ag Doped and Undoped nc-cds Thin Films 5.1 Introduction The important factor influencing the performance of devices is the behaviour of charge carriers in thin films. Thus, it is important to study and understand the charge transporting behaviour in thin films. This chapter concentrates on the quantitative measurement of the transport parameters like minority carrier diffusion length (L), mobility-lifetime (μτ) product of charge carriers and recombination lifetime (τ) of carriers in undoped and Ag doped nc-cds thin films. Both, the mobility and lifetime are important parameters which determine transport and recombination of charge carriers. The minority carrier diffusion length, L, is the average distance a carrier can move from point of generation until it recombines. Higher diffusion lengths are indicative of materials with longer lifetimes, and is therefore an important quality to consider with semiconductor materials. The diffusion length is closely related to the collection probability. The mobility-lifetime product of charge carriers, μτ, with units of cm /V, represents the average carrier drift length per unit field and is an important figure of merit for charge-collecting devices including photovoltaics [1] and photodetectors [, 3]. In this study, Steady-State 116

2 Photocarrier Grating (SSPG) technique is used to investigate both the minority carrier s L and μτ in nc-cds thin films. Steady-State Photo-Conductivity (SSPC) is used to investigate the majority carrier μτ in nc-cds thin films. Several techniques are used for direct measurement of L in semiconductor materials. Surface photovoltage (SPV) is one of these technique [4, 5]. SPV used a naturally existing depletion layer at the surface to generate photovoltage on illumination. The SPV generated with monochromatic radiation of different wavelengths of the given intensity is measured and L is determined from the plot of the surface photovoltage vs. the absorption coefficient. The method has a severe limitation that it is valid only if the thickness of the sample is three times or larger than the diffusion length [6, 7]. Recently, a Laser Beam Induced Current (LBIC) method [8] has been reported for determining L in Si wafers. The method was applied under low level injection condition and was found to be valid if thickness of the wafer was larger than 4L. Following these considerations, SSPG has evolved as one of the direct method to measure L of the investigated thin film semiconductors [9], to understand the effects of microstructure on the minority carrier properties. Keeping in view, the success of utilizing the SSPG technique for many materials such as hydrogenated amorphous and nanocrystalline silicon films [10] and devices [11], we have adopted this technique to find the minority diffusion length in thin films of undoped and Ag doped nc-cds. The SSPG method is based on the carrier diffusion under the presence of a spatial sinusoidal modulation in the photogeneration rate G, which induces a so-called photocarrier grating. From photocurrent measurements at different grating periods, the diffusion length can be determined by an analysis that assumes ambipolar transport and charge neutrality [1]. 5. Description of the Steady State Photocarrier Grating (SSPG) Concept SSPG technique was suggested by Ritter, Zeldov and Weiser named RZW hereafter, in 1986 [13, 14]. The experimental setup of SSPG is shown in Fig..1 (Chapter ). The principle of SSPG technique involves creating interference in the photoconductor material from two coherent beams of unequal intensity I1and I. Basically the two beams originate from splitting one laser beam with wavelength λ. When the two beams I1 and I are incident on the semiconductor, they suffer 117

3 refraction according to Snell s law. The angle between the two beams changes from θ in air to θ in the semiconductor with refractive index ns. The wavelength changes from λ to λ where λ = λ nair/ns (Fig. 5.1 (A)). According to plane wave interference theory, the two light beams interfere and form a varying light intensity pattern, as seen in Fig. 5.1 (B). Fig. 5.1 (A) Sketch of the interference experiment with two plane waves from the laser beams I1 and I. (B) Schematic of the interference fringes between coplanar electrodes. The parallel planes of constant photon flux are perpendicular to the air semiconductor interface. The analysis of the plane-wave interference for weak absorption in z direction results in a photogeneration-rate pattern G(x, y, z) according to [13]: G(x, y,z) 0.5 x G(x) (G1 G ) 0 (G1G ) cos (5.1) x G(x, y,z) G(x) (G1 G ) 1 A cos (5.) where G1 and G refer to the photogeneration rate resulting from beam I1 and I alone, A refers to the photocarrier grating amplitude. The grating period Ʌ in Eq. (5.1) is given by [13]: (5.3) sin ( / ) 118

4 for which it is noted that the only angle θ between the two beams in air enters in this equation. For weak absorption in which the generation rate is almost constant in the z direction there is only an x dependence in G(x). The RZW analysis suggests to exploit two conditions of the laser-beam arrangement at a given Λ: one measurement under coherent conditions with current density jll (Λ, I1+I) and one measurement under incoherent conditions with current density j (Λ, I1+I). RZW also suggested that a lock-in technique may be used with relative measurement to the current density with one beam only, with j1 (Λ, I1). A parameter β is defined given by [10]: j (,I1 I) j1 (,I1) U j (,I I ) j (,I ) U (5.4) where Ull and U are lock-in amplifier measurements under coherent and incoherent conditions. For a number of positions that relate to different grating periods, Λ, the β parameter is determined by measuring Ull and U. RZW related this β parameter with the ambipolar diffusion length, L, according to the relation [14]: U U 1 (1 4 L / ) (5.5) L 1 L 1 (5.6) where d 0, is a fit parameter ( ), with the Rose coefficient defined as the power law exponent in the photoconductivity versus light intensity dependence, d is the ratio between dark and total current under illumination and 0 is the grating quality factor which describes the reduction of the fringe visibility and is between zero and unity. The visibility of fringes is influenced by several factors like the partial coherence between the two beams, light scattering, and mechanical vibration averaged over some time constant [10]. 119

5 5.3 Minority-Carrier and Majority-Carrier Mobility-Lifetime Products The diffusion length, L, is related to diffusion coefficient, D, and recombination life-time, τr, by the relation [10]: L k T B e e h h D R (5.7) e ee h h where kb is the Boltzmann s constant, T the temperature, e the elementary charge, μe (μh) the electron (hole) mobility and τe (τh) the recombination life-time of electron (hole). We can associate either the electrons or the holes with the majority and minority carriers. Writing (μτ)min = μminτmin and (μτ)maj = μmajτmaj with the free carrier mobilities μmin and μmaj and the free-carrier recombination life-times τmin and τmaj embraces the respective mobilities and lifetimes. The Eq. (5.7) can be written as: L k T ( ) e ( ) B maj min (5.8) maj ( ) ( ) min For the case that (μτ)maj (μτ)min, Eq. (5.8) takes the form [15]: ( e ) min L (5.9) k BT The steady-state photoconductivity, σph, can be written in terms of generation rate, G, as [16]: eg[( t) ( t) ] (5.10) ph maj min where symbols have their usual meaning. For the case that (μτ)maj (μτ)min, Eq. (5.10) takes the form: ph ( t) maj (5.11) e G By Eq. (5.9) and (5.11), one can determine the mobility life-time product of majority and minority carrier. 10

6 5.4 Results and Discussion In order to extract the diffusion length, L, from β by using Eq. (5.5), the following conditions should be fulfilled: (i) (ii) (iii) The applied biasing voltage should be in the Ohmic region of I-V curve and the β parameter should be independent of the applied voltage to ensure that the diffusion prevails over drift. The variation of the photocurrent with varying applied voltage for all the samples is found to be symmetric and linear up to 100 V, indicating the Ohmic behavior of the contacts. The electric field dependence of β parameter for all samples has been plotted in Fig. 5.. Even though contacts are Ohmic for the electric fields of up to 150 V cm -1 for I-V measurements, the β parameter values are independent of the electric fields only up to 15 V cm -1, thereafter they become field dependent for higher electric fields and the transport is not diffusion controlled any more. For each sample, measurements of the β parameter for different grating period Ʌ are carried out in low electric field 100 V cm -1, where the β parameter values are constant and satisfy the applied electric field condition minimal critical electric field given by Ec= (kbt/e)(1/l) [17]. E E c, where Ec is the The necessary condition for the material to be in the lifetime regime, the dielectric relaxation time τdiel should be much shorter than the common carrier recombination lifetime τ. The dielectric relaxation time is given by τdiel = ε0 ε /σph. Here ε0 is F/cm and ε the dielectric constant of the material. The estimated value of ε for nc-cds thin film from the transmission data is The common carrier recombination lifetime is given as, τ = (τe τh) / (τe + τh) and has been calculated by using the values of τe and τh which are listed in Table 5.1. The ratio τ /τdiel has been calculated and it is found to be greater than unity for all samples; therefore the necessary condition for ambipolar transport in the lifetime regime is fulfilled [18, 19]. Surface recombination effects must be considered for an accurate determination of diffusion length, L. For all the studied samples L << 1/α, the effect of surface recombination is thus small and hence, it can be neglected when determining the L values [14]. 11

7 Fig. 5. The electrical field (E) dependence of experimental β-values for nc-cds, nc- CdS:Ag 1% and nc-cds:ag 5% thin films at 300 K. Experimental results of the photocurrent ratio, the β parameter versus the grating period Ʌ, are shown in Fig. 5.3 for nc-cds, nc-cds:ag 1% and nc-cds:ag 5% thin films. The β values change strongly for all the samples and become negative for the grating period higher than 0.5 μm. The variation in β parameter is not only controlled by diffusion length, L, but also the grating quality parameter φ as defined in Eq. (5.5) [0]. For this reason, diffusion length, L, and φ are obtained simultaneously using the nonlinear fit of Eq. (5.5) to the experimental data. The best fit results of β are shown in Fig. 5.3 as full lines. As theoretically expected, for the lower grating period values (Ʌ < L), the grating disappears and the β parameter approaches to unity for all the samples. The calculated values of diffusion length, L, and φ are listed in Table 5.1 for undoped and silver doped nc-cds samples. The value of diffusion length, L, is also obtained from the variation of versus /(1 ), known as the Belberg s plots [1]. Fig. 5.4 shows the Belberg plots for our samples obtained from the experimental β values at different grating period Ʌ. A straight line has been obtained from the best fit to data points using Eq. (5.6) for each sample, which confirms that the measured length for each case is the ambipolar diffusion length []. 1

8 Fig. 5.3 Typical variation of β versus grating period Ʌ for nc-cds, nc-cds:ag 1% and nc-cds:ag 5% thin films. The symbols represent the experimentally measured values and the full lines are the fits to Eq. (5.5). Fig. 5.4 The Balberg plots of nc-cds, nc-cds:ag 1% and nc-cds:ag 5% thin films obtained from the β parameter and grating period Ʌ. The solid lines are the best fit to data using the Eq. (5.6). 13

9 The calculated values of diffusion length LBelberg from the intercept of the Belberg plot are listed in Table 5.1. The calculated values of diffusion length, L, with best fit of data points of Fig. 5.3 to Eq. (5.5) and from the intercept of Belberg plot show nearly similar results. The good agreement between the two evaluations is good indicator that the measurements are reliable even though the diffusion length is short. Fig. 5.5 The intensity dependence of photoconductivity for nc-cds, nc-cds:ag 1% and nc-cds:ag 5% thin films. Intensity dependence of steady state photoconductivity has been studied on undoped and Ag doped nc-cds thin films for getting information regarding the nature of recombination process. The plots of ln IPh versus ln F are shown in Fig It is clear from the figure that lux-ampere curves for all samples are linear indicating that the photoconductivity (σph) follows a power law with intensity (F) i.e Ph F (5.1) According to Rose [3], the value of lies between 0.5 and 1.0 can be justified by assuming the existence of continuous distribution of trap states in the gap. In our samples, the value of lies between 0.5 and 1.0 indicates that a continuous distribution of localized states exists in the mobility gap and the resulting recombination will be bimolecular in nature where the recombination rate of electrons 14

10 is proportional to the number of holes. Values of for nc-cds, nc-cds:ag 1% and nc-cds:ag 5% thin films are listed in Table 5.1. Table 5.1 A summary of SSPC and SSPG results for nc-cds, nc-cds:ag 1% and nc- CdS:Ag 5% thin films at 300K. Sample α 10 4 (cm) -1 (cm -3 s -1 ) γ G 100 (μτ) e 10 ⁷ (cm /V) L (nm) L Balberg (nm) Φ (μτ) h 10 ¹⁰ b 103 τ e (cm /V) (ms) τ h (μs) nc-cds nc-cds: Ag 1% nc-cds: Ag 5% The μτ with units of cm /V, is the average length a carrier moves per unit field, and is therefore an important figure of merit for charge collecting devices; it is directly proportional to the quantum yield [3] and the conversion efficiency [1] in photodetectors and solar cells, respectively. The higher mobility-lifetime product increases the diffusion length, L, and leads to an increased short-circuit current in cell; higher carrier mobilities are desirable in such applications. For the investigation of majority and minority carrier mobility-lifetime product in undoped and Ag doped nc- CdS thin films, the SSPC and SSPG techniques are used. The temperature dependent steady state photoconductivity is measured for nc- CdS, nc-cds:ag 1% and nc-cds:ag 5% samples in the temperature range from 00 K- 340 K. The SSPC is dominated by the majority carrier transport. Hall measurements show that all films are n-type in nature i.e. electrons are the majority carriers in these films. From the steady state photoconductivity, the majority carriers (electron) mobility-lifetime products can be evaluated. The relation (5.11) for the majority carriers (electron) can be written as: ( t) e ph eg (5.13) 15

11 where G denotes the photo-carrier generation rate defined as G = α N0 e d (α is the absorption coefficient evaluated from transmission spectra and N0 is the photon flux). The temperature dependent electron mobility-lifetime product for nc- CdS, nc-cds:ag 1% and nc-cds:ag 5% thin films in the temperature range 00 K K is shown in Fig The calculated value of (μτ)e for nc-cds, nc- CdS:Ag 1% and nc-cds:ag 5% samples corresponding to 300 K are tabulated in Table 5.1. Fig. 5.6 Temperature dependence of the majority carriers mobility-lifetime product for nc-cds, nc-cds:ag 1% and nc-cds:ag 5% thin films. The estimated value of (μτ)e product, increases slightly for low Ag doping and it increases up to one order of magnitude for higher Ag doping. The increase in (μτ)e product upon doping is related to the shift of the Fermi level position. The parameter b [= (μτ)e/(μτ)h] defined as the ratio of mobility-lifetime product of electrons and holes is taken as a measure for the Fermi level position [1, 4]. The b parameter increases after Ag doping indicating that the Fermi level shift towards the conduction band (Table 5.1). The thermal occupation of any distribution of recombination centers in the band gap will change when the Fermi level shifts and the density of centers that capture majority carriers is greatly reduced by the change in thermal occupation. If the Fermi level is close to the conduction band, most defects will be thermally occupied 16

12 by electrons and inaccessible to excess electrons, thus leading to a large electron lifetime and the large mobility-lifetime product [5]. The diffusion length, L, values obtained from the best fits to data of Fig. 5.3 are used to calculate the minority carrier (hole) mobility-lifetime products using the Einstein relation (5.9). The calculated values of (μτ)h are shown in Table 5.1. It is clearly seen that majority carrier (μτ)e products are higher than the minority carrier (μτ)h products, for all undoped and Ag doped nc-cds thin films, indicating electron dominated transport. The calculated values of diffusion length, L, and (μτ)h for nc-cds:ag 1% are slightly less than nc-cds sample and they increase for nc-cds:ag 5% sample. From the calculated values of (μτ)h product, it is clear that the (μτ)h product is not so much affected by the Fermi level shift, but its values vary according to the variation in grain size as shown in XRD and SEM results. In general, the grain boundaries introduce allowed energy levels in the band gap of a semiconductor and act as an efficient recombination centres for the minority carriers. This effect is important in minority carrier devices, such as photovoltaic solar cells and it is expected that some of the photogenerated carriers to be lost through recombination on the grain boundaries. Typically, the efficiency of the device will improve with increasing grain size [6]. The literature values of mobility-lifetime product for bulk CdS are cm /V [7] and cm /V [8] for electrons and holes, respectively. The measured value of (μτ)e product is slightly higher and of the same order for nc-cds and nc-cds:ag 1% as the bulk value. For nc-cds:ag 5% sample, the measured value of (μτ)e product is higher up to an order of magnitude as compared to the bulk value. On the other hand, the measured (μτ)h product is lower than the bulk value by two order of magnitude for all the samples. The bulk value of τe and τh for CdS is 0.5 ns and 1. ns, respectively (calculated by using bulk values of mobility and mobility-lifetime product of electrons and holes, respectively). For comparison, we estimate the carrier recombination time by dividing the measured mobility-lifetime product by measured electrons and holes mobility from TOF technique in our samples. The calculated values of τe and τh are listed in Table 5.1. The carrier lifetime enhance significantly in our samples as compared to bulk CdS. In solar cells and photodetectors, higher lifetime of the carriers minimizes the recombination and maximizes the charge collection, which is desirable [9]. 17

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