ELECTRICAL PROPERTIES OF POLYCRYSTALLINE SILICON IN DARK

Transcription

1 CHAPTER III ELECTRICAL PROPERTIES OF POLYCRYSTALLINE SILICON IN DARK 3.1 INTRODUCTION A lot of attention is being focused on the electrical properties of PX-Silicon because of its application in integrated circuit devices and solar cells. The electrical properties of this material are determined by several factors such as GB states density, nature of GB states distribution, grain size and doping concentration [67]. In order to predict the performance of these devices, it is necessary to understand the physics of grain-boundaries. Grain boundaries can be considered to have a large density of intrinsic and extrinsic defects. These defects introduce interface states within the energy gap which acts as traps and recombination centers as discussed by Queisser [178], Werner [43] and Seager [71]. There is strong evidence that midgap states at silicon grain-boundaries are determined by extrinsic properties. On the other hand, band tail states seem to have intrinsic origin. Werner and Peisel [179] proposed that band tail states are related with the degree of disorders within the GB plane. Many energy distributions of trapping states such as δ-function, continuous, exponential, U-shaped and Gaussian were considered to explain the electrical properties of PX-Si material. Groot and Card [74] and McGonigal et al. [79] found that GB interface states density and energy distribution are temperature dependent. It has also established that the density of these states is determined by the duration and temperature of the treatment [180].

2 Several qualitative valuable models [15,17,50,54,55,71, ] have been proposed to explain the variation of carrier mobility and resistivity of this material with the grain size and doping concentration. These models have considered carrier-trapping at grain boundaries and have neglected the highly disordered nature of the grain boundary material. Mandurah et al. [34], Lu et al. [54], and Joshi and Srivastava [62] represented the effect of grain boundary material on the carrier transportation PX-Si by an additional potential barrier qφ across the grain boundary. To explain the electrical conduction in heavily doped polysilicon films, Mandurah et al. [33-35], and Negi and Joshi [122] have considered the combined mechanism of dopant segregation and carrier trapping at grain boundaries. As discussed in Chapter-II, these models have some inadequacies. It is observed that some of the existing theories could be able to explain the dependence of carrier mobility and resistivity of this material on doping density and temperature. In this Chapter an attempt is made to explain the variation of electrical properties of the PX-Si with doping density, temperature, and grain size and dopant species. Author s model is valid for Boron and Phosphorus doped PX-films over wide temperature, doping concentration and grain size range. 3.2 DOPANT SEGREGATION AT GRAIN BOUNDARY During high temperature processing some of the dopant atoms segregate to the grain boundaries where they are trapped and become electrically inactive. The remaining dopant atoms (N g ) are distributed uniformly within the grains. Mandurah et al. [33-34] have established that the number of atoms segregating to the grain boundaries (N gb ) is a strong function of grain size, dopant concentration and processing temperature T A. They proposed following 56

3 expression for average doping concentration within the grains (after considering dopant segregation at grain-boundaries). N g =N / {1+A exp (Q o / kt A )} (3.1) such that N = N g + N gb (3.2) where Q o is the dopant heat segregation, T A is the annealing temperature and A = AQ s / N Si. Here Q s (cm -3 ) is the density of segregation sites at the grainboundaries. N Si (cm -3 ) is the silicon bulk concentration and A is the entropy factor. The factor A has different values for different doping species. The values of parameters A, Q s and N i are taken from [34,35]. 3.3 POTENTIAL BARRIER IN GRAIN BOUNDARY DEPLETION REGION Present work assumes only acceptor like and donor like grain boundary states for n-type and p-type PX-Silicon respectively [71,104,110]. The most appropriate energy distribution of the mid gap interface states is the Gaussian type of energy distribution (see Chapter-IV). This energy distribution can be reduced to δ-function distribution. In this Chapter, to calculate the potential barrier height (qv g ), the localized grain boundary interface states (δ-function) model is considered. This model assumed that the grain-boundary interface states of density N gs (cm -2 ) are located in a narrow energy range at energy level E T above the intrinsic Fermi level E i. By using this model the following simple expression for qv g can be mentioned [54]. 2q N g W g = qn gs / {1 + 2exp (E F + qv g - E T )}, for N g > N * (3.3) and qv g = qn g [(d - δ) 2 / 8ε], for N g < N * (3.4) where N * is the critical doping density, E F is the Fermi level, d is the grain size and δ is the grain boundary width. If the doping concentration within the grains 57

4 (N g ) is known, the Fermi-level E F in the totally depleted and partially depleted grains can be determined by using the following equations: E F = E T - qv g + kt ln[{1/2 N gs /(d - δ) N g }-1], for N g N g * and n i exp(e F / kt) = N g /{1+ 2exp[(E A - E F ) /kt]}, for N g N g * (3.5) (3.6) Here E A is the acceptor impurity level within the forbidden energy gap [17]. This is given by E A = - E g (T) / N 1/3 (3.7) E g (T) is the energy gap of the material at temperature T. If there is no segregation of dopant species at grain-boundaries, then N = N g. The variation of energy gap of the semiconductor with temperature can be expressed [7] as, E g (T) = E g (o) αt 2 / (T + β). (3.8) 3.4 BAND GAP NARROWING The effective intrinsic carrier concentration (n i ) in heavily doped semiconductors depends upon band gap narrowing. The effective band gap narrowing, which includes all heavy doping effects, can be expressed by [186]. E g = c 1 ln [(N + c 2 ) / ] + c 3 (3.9) where c 1 =0.022 ev, c 2 = cm -3, c 3 = ev are the fitting parameters. The above formula is applicable when N cm -3. If heavy doping effects are considered the intrinsic carrier concentration at temperature T is given by n i = n i exp ( E g / 2kT). (3.10) 3.5 GRAIN BOUNDARY SCATTERING POTENTIAL BARRIER Many studies have demonstrated that the electrical properties of PX-Si of large grain size under high illumination levels [64,126] or in the high doping 58

5 concentration range at room temperature [34,35,62] cannot be explained satisfactorily without considering a scattering potential barrier qφ at the grainboundary. Like Mandurah et al. [34,35], Lu et al. [55], Joshi and Srivastava [62], and Negi and Joshi [122] models for carrier transport in PX-Si, in the present study author has represented grain boundary scattering effects by a rectangular potential barrier of width δ and height qφ. The width of barrier δ is assumed to be approximately equal to the width of the grain-boundary. Some studies have attributed the origin of the potential barrier qφ to the impurity scattering, phonon scattering and Coulombic scattering of the carriers at the grain-boundaries [56,57,187]. On the other hand there are some studies [33,34], which assumed that the origin of qφ is related to the energy gap of the GB material. Seager [71] predicted that GB material is not purely amorphous. There are many studies, which completely discards the amorphous region at the GB of PX-Si. On the other hand the study of Kato et al. [77] demonstrates that the GB s have amorphous like structures. Werner and Peisel [179] have predicted that the behavior of grain-boundaries in this material represents a two dimensional amorphous material. Das and Lahiri [73] have shown that in some cases GB material changes from disordered to polycrystalline phase. There are some studies [34,35,62], which assumed that the GB material is disordered in nature and it behaves as an intrinsic wide band-gap semiconductor (E g 1.32eV). Neither the exact nature of GB material nor the origin of the potential barrier qφ is clear. In the present work author considers that the origin of GB scattering potential barrier qφ is mainly related to the energy gap of the material. Author also assumes that the energy gap of the GB material is somewhat greater than 59

6 the energy gap of single crystal silicon within the crystallites. As a result of this the grain-boundaries form heterojunction with the grains. Considering the GB scattering effects, the effective potential barrier as seen by the carriers within the disordered GB region of a PX-Si is given by; qh = qv g + qφ, for 0 x δ/2 (3.11) where qh is the maximum energy from E vo to the top of the potential barrier (Fig. 3.1). Potential barrier qφ may be less or greater than qv g depending upon the doping concentration range, grain size and the temperature. At high doping levels (N > ), for Boron doped samples at room temperature and for large grain sizes, qv g << qφ. Hence under these conditions the above relation reduces to qh = qφ (3.12) In order to consider the effect of grain-boundaries on the electrical properties of PX-Si, the following assumptions have been considered: 1. The barrier height (qφ) is a function of dopant species, temperature and annealing temperature. It may be a function of grain size especially for phosphorous and arsenic doped samples. 2. The dependence of qφ on doping density is controlled by the segregation of dopant atoms to the grain-boundaries. 3. GB width is not a function of grain size, temperature, doping density, annealing temperature and dopant species. Note that in the existing models [34,35,62], qφ was assumed to be independent of grain size, doping species and annealing temperature. 60

7 Fig. 3.1 Energy diagram of p-type PX-Si grain (a) at zero bias (b) under bias conditions, showing different carrier transport components across the grain boundary. 61

8 Furthermore, in these models it was assumed that qφ is not affected by the segregation of dopant atoms to the grain-boundaries. 3.6 CURRENT-VOLTAGE RELATIONSHIP In the present work, for simplicity, we have assumed that the transport properties of PX-Si are one-dimensional and the grain boundaries (N b ) are perpendicular to the direction of current. In general, the voltage drop across a grain (V a ) is divided between the composite grain boundary region (V o ) and the grain (V c ) itself such that V a = V / N b = V o + V c (3.13) If V L, V R and V gb are the voltage drops across the depletion region on the left and right sides of the GB and the GB layer of width δ, respectively, then V o = V L + V R + V gb (3.14) If the applied voltage is much less than the height of the barrier in the depletion region (V o << qv g ), then V L = V R and qv gb can be calculated by using equations of [62,73]. Using one dimensional time independent W.K.B. approximation and Maxwell-Boltzmann statistics, the net current density (J) through the grainboundary resulting due to a small voltage can be expressed by qvg+qvgb/2 qh+qvgb/2 J = (A * T / k){[ f L (E) D 1 (E) de + f L (E) D 2 (E) de + f L (E) de] 0 qvg+qvgb/2 qh+qvgb/2 qvg-qvgb/2 qh-qvgb/2 - [ f R (E) D 1 (E) de + f R (E) D 2 (E) de + f R (E) de]} 0 qvg-qvgb/2 qh-qvgb/2 (3.15) where A * is the effective Richardson s constant, f L (E) and f R (E) are the probability distribution function for the occupancy of the energy level E by carriers to the left 62

9 and right sides, respectively and D 1 (E) and D 2 (E) are the transmission probabilities across the potential barriers qv(x) and q(h-v g ), respectively. The transmission probability D 1 (E) is given by D 1 (E) = exp[-{(4πδ / h) (2m * ) 1/2 (qh E) 1/2 + (qv g / E oo ) γ(α)}], for E < qv g. (3.16) where γ(α) = (1 - α) 1/2 + ln [{1-(1- α ) 1/2 }/ α 1/2 ], α = E / qv g, and E oo = (qh / 8π) (N g / m * ε). The transmission probability D 2 (E) is given by D 2 (E) = exp[-(4πδ / h) (2m * ) 1/2 (qh E) 1/2 ], (3.17) for qv g < E < qφ. By assuming that V o << φ, and using [34,62], the Eqn. (3.17) can be modified to D 2 (E) = exp[-{b 1 +c 1 (qv g E) + }], (3.18) where b 1 = (4πδ / h) (2m * ) 1/2 (qφ) 1/2 and c 1 = (2πδ / h) (2m * ) 1/2 (qφ) -1/2 However, the use of W.K.B. approximation for calculation of D 2 (E) and the Maxwell-Boltzmann statistics to calculate energy distribution of charge carriers are valid if the following conditions are satisfied [34]. qφ - kt (1 c 1 kt) -1 > e -1 and p * h 2 / (2πm * kt) 1/2 << 1. Thus, it can be noted that at very high doping levels or very low temperatures, the above conditions may not be satisfied. Further assuming that qv gb << qv g, the first component of current density J 1 (Thermionic Field Emission through the barrier qv g ) is given by 63

10 qv g J 1 = 2A * T 2 exp(-e F / kt) [(1/kT) D 1 (E) exp(-e / kt)de ] sinh (qv o /2kT) 0 (3.19) The second component of current density J 2 (TFES) resulting due to the thermionic emission of carriers over the potential barrier qv g and then tunneling through the grain-boundary barrier qφ can be expressed as J 2 = 2A * T 2 exp(-e F / kt) { [exp (-b 1 ) / (1 c 1 kt)] {exp (-qv g / kt) exp [(-qh / kt) + b 1 / 2]} sinh [{(1 + c 1 kt B) / (1+B)} (qv o / 2kT)]} (3.20) where B = δ / 4W g. Eqn. (3.20) is different from the corresponding equation adopted by Joshi and Srivastava [62], who assumed that qh is either equal to qφ or qv g. This is also different from the corresponding equation of Mandurah et al. [34] where qv g << qh and qh = qφ. The third component J 3 represents the Thermionic Emission (TE) of carriers over the total barrier height (E > qh) and is expressed by J 3 = 2A * T 2 exp (-E F / kt) exp (-qh / kt) sinh(qv o / 2kT) (3.21) As mentioned above components J 1 and J 2 of current represents the direct tunneling of carriers through the entire barriers extending from a to a, and -δ/2 to + δ/2 respectively. However, by the help of these components together with the third component J 3 we cannot explain the dependence of resistivity of PX-Si on temperature, especially in very low temperature range (T << 300K). This fact demonstrates that one more component of current must be considered 64

11 to overcome the above mentioned problem. In the present work we propose the following form of the fourth component J 4 of current. qv g J 4 = 2A * T 2 exp(-e F / kt) [(1/kT) D 4 (E) exp(-e / kt) de ] sinh (qv o /2kT) 0 (3.22) where D 4 is the transmission probability of the holes from valance band to the GB states (i.e. from x = -a to x = 0). The J 4 component is a two-step tunneling (TST) process [63], via the grain-boundary states (Fig. 3.1). This two step tunneling process is found to be more probable than a direct tunneling process through the entire barriers at low temperatures. In step 1 of this process, the carriers tunnel through half the barrier i.e. from a to 0, to the normally filled (donor type) grain-boundary states at x = 0. In step 2, we assume that these captured carriers (holes) are emitted to the top of the barrier (qv g ) at x = 0 by the thermionic emission process only. This two step process is analogous to that considered in MOS structures by Shewchun et al. [188]. Note that the TST process becomes significant only when the thermionic emission rate of charge carriers from GB states is much greater than the net tunneling rate of charge carriers through half the barrier extending from x = - a to 0. It is found that condition is satisfied when N gs cm -2 and the capture cross section σ =10-12 cm 2. We further assume that the transmission probability is D 4 (E) = exp[-{(1/f) (4πδ / h) (2m * ) 1/2 (qh E) 1/2 + (qv g /E oo ) γ(α)}], for E < qv g. (3.23) where f is the fitting parameter for PX-Si, the valve of this parameters is taken to be = 2 at room temperature for all doping species. It is important to mention that the expression for J 4 is totally different from the expression considered by 65

12 Rodder and Antonadis [63], who assumed no GB barrier qφ. Some studies [189] demonstrate that spatially inhomogeneous grain-boundaries in PX-Si materials may be the source of J 4 component. However, this concept cannot explain the dependence of electrical properties of PX-Si on temperature and illumination level [122]. If V o << 2kT/q then the J-V relation for PX-Si can be expressed as, J = (A * T q / k) exp(-e F / kt) {(1/kT) [ D 1 (E) exp(-e / kt) de ] 0 + [ [exp(-b 1 ) / (1 c 1 kt)][ exp(-qv g / kt) exp{ (-qh / kt) + b 1 /2]} qvg { (1 + c 1 kt B) / (1 + B) }] + exp(-qh/kt) qvg + (1/kT) [ D 4 (E) exp(-e/kt) de]} V o 0 (3.24) This equation can also be expressed as J = (A * T q/ k) exp(-e F / kt) {TFE + TFES + TE + TST }V o (3.25) In general all four conduction mechanisms occur in parallel; however J 3 component is dominant at high temperatures. In contrast to the existing models this relation is valid for Boron, Phosphorus and Arsenic doped PX-Si films with wide doping concentration range ( to cm -3 ), wide grain size range, wide temperature range (100 to 500K) and under small bias conditions (<10 mv). Furthermore, the present J-V relation is applicable not only for PX-Si but also for PX-GaAs material as discussed in Chapter- IV. 3.7 RESISTIVITY AND MOBILITY For small applied voltage the composite grain boundary barrier resistivity can be expressed by the following simple relation 66

13 ρ b = V o / J(2W g + δ ) = [(2πm * kt) 1/2 / q 2 (2W g + δ) p * ] [1 / (TFE +TFES + TE + TST)] (3.26) The average carrier concentration p * is given by p * = p(o)(1 - δ/d) kt [ 1 exp({ - (qv g + qφ) / kt}] / ( qv g + qφ) for N < N *, (3.27) and p * = p(o) [(1 - δ/d) (2W g /d){1 (kt/qv g ) + (kt/qv g ) exp({-(qv g /kt)}] for N > N * (3.28) where p(o) is the carrier concentration at the GB edge. The total resistivity ρ * of the PX-Si is given by ρ * = V a / J d = ρ b [(2W g + δ) /d] + ρ c [d (2W g + δ)] /d (3.29) Where, ρ c is the resistivity of undepleted part of the grain. This resistivity is equal to the resistivity of a single crystal of silicon. The effective carrier-mobility in PX-Si is expressed by µ * = 1 / (q p * ρ * ) (3.30) To explain the dependence of resistivity on temperature in very low temperature range, some workers [64,67] have considered variable range hopping of carriers in the GB defects by using two fitting parameters. However, the concept of hopping resistivity is not discussed in the present work because the hopping resistivity is found to be independent of doping density. 3.8 DISCUSSION The values of parameters used to compare theory with the experimental data [15,34,35,54,190] are listed in Table 3.1. It is assumed that N gs, E T and d 67

14 are not the functions of doping density and temperature. Figs. 3.2, 3.3, and 3.4 show the theoretical resistivity of Boron, Phosphorus and Arsenic doped polysilicon films versus the doping concentration for different values of grain size and temperature. From these plots we note that qφ is independent of doping density in case of Boron-doped samples but depends on doping density in case of Phosphorus and Arsenic doped samples at N > The change in qφ with N for these dopant species is shown in insets of Figs. 3.3 and 3.4. The change in qφ in the doping range N > at room temperature is attributed to the change in the nature of GB material due to segregation of dopant atoms to the GB. The incorporation of phosphorus atoms into the segregation sites at the GB leads to a more ordered system and hence reflects in the decrease of energy gap of GB materials or decrease in qφ. This prediction of present model is supported by Mandurah et al. [33,190], which demonstrates that the entropy factor A decreases with increasing segregation at grainboundaries. From Fig. 3.4 it is clear that qφ first increases with increasing dopant concentration up to cm -3 and then decreases rapidly (as observed in phosphorus doped samples) with increasing N. The increase in qφ with increasing N shows that the disordered region near the grain-boundaries increases. This disordered region results due to the arsenic clustering in the heavy doping range. This mechanism of arsenic clustering is observed in both heavily doped single crystals [191] and PX-Si [192] films. Consequently, qφ increases with N due to the mechanism of arsenic clustering. As doping density increases above cm -3, arsenic atoms diffuse to the GB, consequently qφ 68

15 decreases rapidly with increasing N. In this way present study demonstrates that both arsenic clustering and dopant segregation mechanisms may be responsible for the dependence of resistivity of As- doped PX-Si on the doping density. From above discussion it is very clear that qφ is a function of dopant species and dopant atom segregation mechanisms. It is also clear that qφ may be a function of grain size in Phosphorus and Arsenic doped films. From Fig. 3.2 we observe that resistivity of Boron-doped PX-Si film is a function of temperature. Our computations demonstrate that at temperature above the room temperature both qφ and the fitting parameter f are independent of temperature. On the other hand, the potential barrier qv g is found to vary with doping density and temperature in the intermediate doping density range (Fig. 3.5). In this way the present study predicts that the role of potential barrier qφ becomes very significant in the low and high doping density range. Fig. 3.6 represents the variation of resistivity of Boron-doped PX-Si as a function of temperature in low temperature range. In this case the Author finds that to fit the available experimental data [54] with the theoretical predictions, qφ and f remains constant with decreasing temperature at a fixed doping density. It is further observed that both the parameters qφ and f decrease with increasing doping density. The decrease in f with increasing doping density suggests that the role of J 4 component of current becomes very important. In other words the role of GB states near the band edge becomes appreciable in the low temperature and doping density range. The change in qφ and f with doping density in the low temperature range predicts that not only the nature of GB material changes but also the density and energy distribution of GB states changes. The possibility of change in qφ by phonon scattering processes seems 69

16 K Theory Single crystal Ref: [54] Ref: [54] Ref: [54] Ref: [15] Resistivity (Ohm-cm) K 417 K Doping Density N(cm -3 ) Fig. 3.2 Variation of resistivity of p-silicon at different temperature with doping density. Experimental points are culled from [15,54]. 70

17 Fig. 3.3 Variation of resistivity of n-silicon (Phosphorus-doped) at room temperature with doping density. Experimental points are culled from [190]. 71

18 Fig. 3.4 Variation of resistivity of n-silicon (arsenic doped) with doping density. Experimental points are culled from [35]. 72

19 0.3 Total Potential barrier qh(ev) K 344 K 417 K Doping Density N(cm -3 ) Fig. 3.5 Variation of Total Potential Barrier (qh) versus Doping Density N. 73

20 10 2 Theory Ref. [54] N=10 17 (cm -3 ) x / kt (ev -1 ) Fig. 3.6 Variation of resistivity at different temperature. Experimental points are culled from [54]. 74

21 to be negligible, because for a fixed doping density qφ is found to be independent of temperature The variation of average carrier concentration with doping density at different temperature is presented in Fig It is found that as the doping concentration increases the effect of grain size on p * decreases. For small grain sizes, p * is much less than N because in this case the grains get completely depleted of carriers. Present computations also indicate that the depleted grain is very sensitive to grain size and temperature. Fig. 3.8(a) shows the variation in the effective carrier mobility in PX-Si as a function of doping concentration at room temperature for different grain sizes. Our computed results agree reasonably well with the available experimental data [15,54]. It is observed that as grain size increases µ * increases and approaches the corresponding monocrystalline mobility asymptotically. It is also observed that the mobility minimum shifts towards the low doping level side on increasing the grain size. The abrupt decrease in mobility is a result of the increase in qv g near critical doping density. This plot shows that at high doping levels µ * approaches to its corresponding monocrystalline mobility µ c. The computed variation of µ * with N at different temperature is shown in Fig. 3.8(b). This shows that as temperature increases the mobility dip decreases and shifts towards the low doping level side. This is due to the lowering of the value of critical doping density N * and the decrease in the value of qv g. Present theory shows that whatever is the doping density above room temperature, the J 2 component of current density of p-type PX-Si is always comparable to the J 3 component, and J 4 component is insignificant (Fig. 3.9). This suggests that the role of GB states near the band edges becomes 75

22 insignificant at temperatures above the room temperature. On the other hand, J 4 component is found to be more significant than the other components below room temperature. As the temperature decreases the value of J 4 component increases. It is also observed that in very low temperature range the electrical properties of B-doped PX-Si are controlled by J 1 and J 4 components of current. However, near and below the room temperature the electrical properties of this material are controlled by J 2 and J 4 components. The dominance of the two step tunneling process (J 4 component) over other processes in low temperature range demonstrates that the presence of band tail states at the valance band edge of PX-Si grain-boundary with very small grain sizes, in addition to midgap interface states. A good agreement between present theory and available experimental data [54] predicts that the TST process of conduction is an important process in the low temperature range. The deviation between experimental and authors computed results may be due to the following reasons: (i) The use of δ-function approximation of GB trapping states is obviously an ideal assumption, hence an exact energy distribution of the trapping states must be taken into account, especially when TST process dominates over other conduction mechanisms. (ii) The interface states density N gs and interface states energy level E T are assumed to be independent of doping density and temperature, however these parameters vary with doping concentration, temperature, and doping segregation mechanisms. 76

23 3.9 CONCLUSIONS Author s electrical conduction model for PX-Si is valid for different dopant species under small bias condition. It is also valid over wide doping concentration, wide temperature and wide grain size ranges. The important features of the present model are: 1. The height of the rectangular potential barrier qφ at GB is mainly related to the disordered nature of the GB material. The energy gap of the GB material lies between the energy gap of single crystal Si and amorphous Si. The nature of this material is a function of dopant species, dopant density, dopant atoms segregation to the GB, temperature and annealing temperature. It is also found that the phonon scattering processes at the GB are less important. 2. The J 4 component is found to be more significant as compared to the other components below room temperature. This fact demonstrates that the TST process of conduction is very important in low temperature range. 3. At room temperature J 2 and J 3 components of current density are more significant than other components whatever the doping density is. 4. In As-doped samples both As-clustering and dopant segregation mechanisms are present, whereas in Phosphorous-doped samples only dopant segregation mechanisms is present. On the other hand in Borondoped samples no segregation and clustering mechanisms are present. 77

24 Average carrier concentration p*(cm -3 ) Ref: [54] Theory Doping density N(cm -3 ) Fig. 3.7 Variation of average carrier concentration with doping density. Experimental points are culled from [54]. 78

25 10 2 Effective mobility (cm 2 /V-sec) 10 1 Ref: [15] Ref. [54] 1220 A 230 A Doping Density N(cm -3 ) Fig. 3.8(a) Variation of effective mobility with doping density. Experimental points are culled from [15, 54] Effective mobility (cm 2 /V-sec) K 344 K 300 K Doping Density N(cm -3 ) Fig. 3.8(b) Variation of effective mobility with doping density at different temperatures. 79

26 J1 /J, J 2 / J, J 3 / J, J 4 / J J1/J J2/J J3/J J4/J Doping Density N(cm -3 ) Fig. 3.9 Variation of Different components of current density with N at room temperature for d= 230 Å. 80

27 Table 3.1 List of parameter values used in the calculation of PX-Si in dark. n i = cm -3 ε = F/cm Parameter B-doped B-doped P-doped As-Doped B-doped Ref:[54] Ref:[15] Ref:[190] Ref:[35] Ref:[54] Figs.- 3.2, Figs. - Fig Fig Fig , 3.7,3.8, 3.2, N gs (cm -2 ) N (cm -3 ) 10 18, , d (Å) δ( Å) qφ (ev) , 0.086, 0.09 E T (ev) f , 8, 25 81