A new analytical method of extraction of a diode series resistance from

current-voltage characteristics is proposed which takes into account dependence of the

series resistance on voltage (or current). The method supposes a presence of linear

section in the diode current-voltage characteristic plotted in semi-logarithmic scale. This

method is applied here to experimental data for silicon diode in which series resistance is

caused by freezing-out free current carriers into impurities at cryogenic temperatures.

Character of dependence of the base resistance on electric field in the base layer

determined in such way confirms hopping nature of silicon conduction under these

conditions

Borblik, V.L.

Shwarts, M.M.

Shwarts, Yu.M.

Semiconductor Physics Quantum Electronics & Optoelectronics

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 339-342.© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine339PACS 71.30.+h, 72.20.Ee, 85.30.KkA new method of extraction of a p-n diode series resistance from I-V characteristics and its application to analysis of low-temperature conduction of the diode baseV.L. Borblik*, Yu.M. Shwarts, M.M. ShwartsV. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine,41, prospect Nauky, 03028 Kyiv, UkrainePhone: +38(044)525-6292, fax: +38(044)525-7463*E-mail: borblik@isp.kiev.ua  Abstract. A new analytical method of extraction of a diode series resistance from current-voltage characteristics is proposed which takes into account dependence of the series resistance on voltage (or current). The method supposes a presence of linear section in the diode current-voltage characteristic plotted in semi-logarithmic scale. This method is applied here to experimental data for silicon diode in which series resistance is caused by freezing-out free current carriers into impurities at cryogenic temperatures. Character of dependence of the base resistance on electric field in the base layer determined in such way confirms hopping nature of silicon conduction under these conditions.Keywords: junction diode, series resistance, silicon, metal-insulator transition, low temperature, hopping conduction.Manuscript received 21.08.09; accepted for publication 10.09.09; published online 30.10.09.1. IntroductionThere exist many methods of series resistance extraction from current-voltage characteristics (CVC) of Schottky or p-n junction diode. Their description and comparison with each other one can find in papers [1-8] and references therein. But any of these methods is not applicable in the case if the series resistance varies with voltage (or current). Only paper [9] takes into account a base resistance modulation in Schottky diode but the method used in [9] is lengthy iteration procedure relative to the transcendental equation. We propose in this paper a simple analytical method suitable for p-n junction diode where the series resistance appears as a result of freezing-out current carriers into impurities at cryogenic temperatures.2. Experimental dataWe investigated silicon n+-p diodes with base doping level (by boron) which does not reach somewhat the critical concentration Nc for insulator-metal transition (Nc for p-Si is 41018 cm-3 [10]). Temperature family of CVC for one of these diodes (GPI-1025) at cryogenic temperatures is represented in Fig. 1. It is worthwhile to compare it (in the same temperature range and in the same scale) with CVC of the silicon n++-p+ diode (DT6-7) whose base is doped to the level which is somewhat higher than the critical concentration Nc (Fig. 2). In this case the diode series resistance is absent (negligibly small). Conduction of such the diode as it has been shown by us in [11] is realized by tunnel-recombination mechanism which is connected with localized electron states in the forbidden band [12]. The CVC are described by the dependence tUUI exp where 1tU is temperature-independent parameter related to tunneling through the barrier (equal to 80 V-1 in the given case).It is obvious of Figs 1 and 2 that at the base doping level which is somewhat lower than critical one, mechanism of conduction through the junction barrier remains practically the same; simply the series resistance Rs superimposes on it. Therefore CVC take the form tsUIRUII exp0 , (1)Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 339-342.© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine3401,0 1,2 1,4 1,6 1,8 2,0 2,2 2,410-1010-910-810-710-610-510-410-3GPI-102540 K 35 K6.5 K30 K25 K 20 K14 K9 K5K4.2 KI, AU, VFig. 1. Current-voltage characteristics of investigated silicon diode in cryogenic temperature region.where, however, parameter 1tU  (well defined in view of presence of linear sections in CVC) acquires weak temperature dependence remaining the same by the order of magnitude (from 70 to 100 V-1). Any of the methods of extracting Rs which considers Rs as constant does not give a result here. Therefore necessity of new method arises which would take into account dependence of Rs on U (or I).3. Differential method of extracting diode series resistance depending on voltage (or current)For more generality, let us consider CVC in the form  sIRUII  exp0 , (2)where nkTq  for classical current-conducting mechanisms (diffusion or generation-recombination; then 0I  is the saturation current, q is an electron charge, k is the Boltzmann constant, T is temperature, n is the ideality factor) and 1 tU  in our case. Representing equation (2) in the form  sIRUII 0ln (3)and considering α = const differentiate (3) with respect to U (traditional approach) dUdRIRdUdIdUId ss1ln, (4)then with respect to I dIdRIRdIdUIss1, (5)1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,410-810-710-610-510-410-3I, AU, VDT6-7Fig. 2. Current-voltage characteristics of the silicon diode with high doping level of the base in the same temperature range as in Fig. 1.and, finally, with respect to ln I (as in paper [1]) IddRIIRIddU ss lnln1 . (6)Equations (4) through (6) are linear differential equations for Rs. Any of them results in solution   minmin lnln11IIUUIRS , (7)where minU  and minI  are coordinates of any point (but best of the lowest one) of the linear section of CVC (see Fig. 3). In this point the boundary condition is set:   0, minmin UIRs .From (7) the expression for the voltage drop across the diode base follows as well  minmin lnln1 IIUUUbase  . (8)1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,410-1110-1010-910-810-710-610-5(Imin, Umin)I, AU, VFig. 3. Example of processing the typical current-voltage characteristic.Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 339-342.© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine3414. Application of the theory to the experimental dataShown in Fig. 4 are the values of Rs calculated by formula (7) plotted against baseU calculated by formula (8) in the temperature range 4.2 – 14 K. And similar calculation results for the temperature range 15 – 35 K are presented in Fig. 5. Note that at more low temperatures (Fig. 4), the diode base resistance at first increases and then exhibits exponential drop with the base voltage. At higher temperatures (Fig. 5) the base resistance decreases with the base voltage (after passing the maximum) non-exponentially.Though there exist the papers (see, for example, [13]) which predict increase of a diode series resistance at the expense of minority carrier injection, in our case reason is likely different. It appears to be connected simply with gradual transition from the situation wherep-n junction resistance is considerably greater than Rs (i.e. 0sR ), through the situation when p-n junction resistance becomes comparable with Rs, to the situation where Rs dominates in total diode resistance (maximum point). Subsequent decrease of Rs is its intrinsic variation with base voltage because of the electric field growth.0,0 0,2 0,4 0,6 0,8 1,0 1,210310410510610710814 K9 K6.5 K5 K4.2 KRs, OhmUbase, VFig. 4. Dependence of calculated diode series resistance on the base voltage in temperature range 4.2 – 14 K.0,0 0,2 0,4 0,6 0,810210310425 K35 K20 K30 K15 KRs, OhmUbase, VFig. 5. Dependence of calculated diode series resistance on the base voltage in temperature range 15 – 35 K.0 500 100010-810-710-610-510-410-314 K9 K6.5 K5 K4.2 K1/Rs , Ohm-1Eav , V/cmFig. 6. Comparison of electric-field dependences of the diode (closed symbols) and the testing resistor (open symbols) conductivity.It is worthwhile to compare dependence of the base conductivity 1sR  (when Rs decreases with the base voltage) on average electric field Eav in the base layer with the field dependence of conductivity for silicon testing resistor whose electric properties (conductivity type and doping) are equivalent to the investigated diode base layer. Such measurements have been carried out by us in paper [14] and they have established hopping nature of the testing resistor conductivity at low temperatures.Fig. 6 shows the results of such comparison: closed symbols – for the diode base conductivity, open symbols – for the testing resistor one. Both dependences (for each temperature) prove to be rather similar in their exponential portions. This gives evidence that in the diode, under injection conditions, conductivity of silicon doped below critical concentration keeps, at low temperatures, its hopping character.5. ConclusionSo, for the first time, there has been proposed an analytical method of extraction of a diode series resistance from the diode CVC taking into account dependence of the series resistance on voltage drop across the diode or across the diode base. Being applied to experimental data for silicon diode under conditions of freezing-out free carriers into impurities the method has allowed us to establish hopping nature of the diode base conductivity.References1. S.K. Cheung and N.W. Cheung, Extraction of Schottky diode parameters from forward current-voltage characteristics // Appl. Phys. Lett. 49 (2), p. 85-87 (1986).Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 339-342.© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine3422. T.C. Lee, S. Fung, C.D. Beling, and H.L. Au, A systematic approach to the measurement of ideality factor, series resistance, and barrier height for Schottky diodes // J. Appl. Phys. 72 (10), p. 4739-4742 (1992).3. V. Aubry and F. Meyer, Schottky diodes with high series resistance: Limitations of forward I-Vmethods // J. Appl. Phys. 76 (12), p. 7973-7984 (1994).4. M. Lyakas, R. Zaharia, and M. Eizenberg, Analysis of nonideal Schottky and p-n junction diodes –extraction of parameters from I-V plots // J. Appl. Phys. 78 (9), p. 5481-5489 (1995).5. V. Mikhelashvili, G. Eisenstein, V. Garber, S. Fain-leib, G. Bahir, D. Ritter, M. Orenstein, and A. Peer, On the extraction of linear and nonlinear physical parameters in nonideal diodes // J. Appl. Phys. 85 (9), p. 6873-6883 (1999).6. A. Kaminski, J.J. Marchand, and A. Laugier, I-Vmethods to extract junction parameters with special emphasis on low series resistance // Solid-State Electron. 43 (4), p. 741-745 (1999).7. C.-C. Liu, C.-Y. Chen, C.-Y. Weng, C.-C. Wang, F.-L. Jenq, P.-J. Cheng, Y.-H. Wang, and M.-P. Houng, Physical parameters extraction from current-voltage characteristic for diodes using multiple nonlinear regression analysis // Solid-State Electron. 52 (6), p. 839-843 (2008).8. W. Jung and M. Guziewicz, Schottky diode parameters extraction using Lambert W function // Mater. Sci. Eng. B (2009), doi:10.1016 /j.mseb.2009.02.013.9. A.I. Prokopyev and S.A. Mesheryakov, Fast extraction of static parameters of Schottky diodes from forward I–V characteristic // Measurement 37(2), p. 149 –155 (2005).10. P. Dai, Y. Zhang, and P.M. Sarachik, Critical conductivity exponent for Si:B // Phys. Rev. Lett.66 (4), p. 1914-1917 (1991).11. V.L. Borblik, Yu.M. Shwarts and M.M. 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A new method of extraction of a p-n diode series resistance from I-V characteristics and its application to analysis of low-temperature conduction of the diode base

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A new method of extraction of a p-n diode series resistance from I-V characteristics and its application to analysis of low-temperature conduction of the diode base

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Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)