近代物理实验：反转恢复法测少子寿命（学习资料）_Analysis and Characterization of P-N Junction

IEEE TRANSACTIONS ON ELECTRON DEVICES AcKn IR Electron current incident on an electron-voltaic converte G.B. Shoop participated in the development of the I,= Current through the load of an electron voltaic the ac assembly of the batteries. J. Scott -Monck made the allium arsenide diodes and some of the silicon diodes. I The self-absorption limited electron current paport,who first conceived of this method of energy con- Io= Reverse saturation current of a diode. ss of a E. F. Pasierb, Jr, made the later silicon diodes. R. c. which would be emitted from the surface of a Hand designed the atomic battery assembly. P. Rap radioactive layer of semi-infinite thickne version, has provided helpful discussion 。 Short-circuit current of an electron-voltaic con- verter TABLE OF SYMBOLS Boltzmann's constant L. Diffusion length of electrons A, A'= Parameters used to describe the rate of de- L, Diffusion length of holes radation of semiconductors under electron ir- =q/ T. ao= Approximate self-absorption coefficient of Pm l47 "max Eleetron-voltaic conversion efficiency radiation q beta rays in cm tu= Radioisotope half-life. a/p Approximate absorption coefficient of Pm47beta T= Minority carrier lifetime rays in em /gm Minority carrier lifetime before electron ir- B Empirical constant to describe current voltage radiation relationship of a diode. Vmax Voltage across an electron-voltaic converter EB- Energy of an emitted electron under open circuit conditions EBsx Average energy of betas from a radioisotope. Vmp Voltage across an electron-voltaic converter at EBm Maximum energy of betas from a radioisotope a load which gives maximum power E. Energy gap of a semiconductor. Ionization energy required to generate and col- G Specific activity of a radioisotope in curies/gm lect an electron-hole pair in a diode. Analysis and Characterization of P-N Junction Diode Switching H. J. KUNOT, MEMBER, IEEE Summary--A new charge control model of a p-n junction diode Ⅰ NTRODUCTION is introduced in which the reverse current ig as well as the forward current IF are related to the charge Q stored in the base region by HE SWITCHING TIME of a semiconductor diode time constants Tg and Tp, respectively. The se switching is of great importance in computer circuit design transient is analyzed for normal switching operation where a con- Recently, in particular, development of very high exist, anrtent phase(storage phase )and a decaying current phase speed switching transistors made the switching time of current phase diodes much more significant than ever before. The switch equ ing time analysis of diodes have been carried out by some expressed in terms of measurable device para authors [1[8]. However, the switching tim he equations external circuit variables Ip and Ig; and an derived by most of the authors in the past, [1]-[41,[71, eter R. The proposed model is applicable to action diodes of [8), are expressed in terms of parameters which are ex- any type tremely difficult to measure and not practical for charac- ported. It is shown that the experimental results are in very good terizing the diode switching. It is, therefore, desirable for ent with the practical circuit design purposes to find new ways of characterizing the diode switching in terms of parameters s Received June 17. 1963 which can be measured simply 1968. Portions of this pa CON Con- In this paper the reverse switching transient is analyzed August, ational Cash Register Company, Electronics Division, Har and new diode switching time equations are derived thorne, calif. relating the reverse current ig as well as the forward Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03 47 from IEEE Xplore. Restrictions apply

IEEE TRANSACTIONS ON ELECTRON DEVICES January ACKNOWLEDGMENT I, = Electron curent incident on an electron-voltaic 6. B. Shoop participated in the development of the source deposition technique and performed the actual assembly of the batteries. J. Scott-Monck made the gallium arsenide diodes and some of the silicon diodes. E. F. Pasierb, Jr., made the later silicon diodes. R. C. Hand designed the atomic battery assembly. P. Rap￾paport, who first conceived of this method of energy con￾version, has provided helpful discussion. TABLE OF SYMBOLS Parameters used to describe the rate of de￾gradation of semiconductors under electron ir￾radiation. Approximate self-absorption coefficient of Pm14? beta rays in cm-l. Approximate absorption coefficient oiPm147 beta rays in cm2/gm. Empirical constant to describe current voltage relationship of a diode. Energy of an emitted electron. Average energy of betas from a radioisotope. Maximum energy of betas from a radioisotope. Energy gap of a semiconductor. Specific activity of a radioisotope in curies/gm. converter. = Current through the load of an electron voltaic converter. = The self-absorption limited electron current which would be emitted from the surface of a radioactive layer of semi-infinite thickness. = Reverse saturation current of a diode. = Short-circuit current of an electron-voltaic con- = Boltzrnann’s constant. = Diffusion length of electrons. = Diffusion length of holes. = q/kT. = Electron-voltaic conversion efficiency. = Electronic charge. = Radioisotope half-life. = Minority carrier lifetime. = Minority carrier lifetime before electron ir- = Voltage across an electron-voltaic converter = Voltage across an electron-voltaic converter at = Ionization energy required to generate and col￾verter. radiation. under open circuit conditions. a load which gives maximum power. lect an electron-hole pair in a diode. Analysis and Characterization of P-N Junction Diode Switching* a. J. KUNOt, MEMBER, IEEE Summary-A new charge control model of a p-n junction diode is introduced in which the reverse current iR as well as the forward current Zp are related to the charge Q stored in the base region by time constants 73 and T~, respectively. The reverse switching transient is analyzed for normal switching operation where a con￾stant current phase (storage phase) and a decaying current phase exist, and for overdriven switching operation where no constant current phase exists. New switching time equations are derived. The equations are expressed in terms of measurable device parameters Tp, TR, and Cj; external circuit variables ZF and IR; and an external circuit param￾eter R. The proposed model is applicable to p-n junction diodes of any type. Experimental results using various types of diodes are also re￾ported. It is shown that the experimental results are in very good agreement with the theory. * Received June 17, 1963; revised manuscript received August 20, 1963. Portions of this paper were presented at the WESCON Con￾vention, San Francisco, Calif., August, 1963. t National Cash Register Company, Electronics Division, Haw￾thorne, Calif. INTRODUCTION HE SWITCHING TIME of a semiconductor diode is of great importance in computer circuit design. Recently, in particular, development of very high speed switching transistors made the switching time of diodes much more significant than ever before. The switch￾ing time analysis of diodes have been carried out by some authors [1]-[8]. However, the switching time equations derived by most of the authors in the past, [I]-[4], [7], [8], are expressed in terms of parameters which are ex￾tremely difficult to measure and not practical for charac￾terizing the diode switching. It is, therefore, desirable for practical circuit design purposes to find new ways of characterizing the diode switching in terms of parameters which can be measured simply. In this paper, the reverse switching transient is analyzed and new diode switching time equations are derived by relating the reverse current iE as well as the forward Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03:47 from IEEE Xplore. Restrictions apply

196 Kuno: P-N Junction Diode switching Fig. k-Planar junction diode model current Ip to the minority carrier charge Q stored in the such that base region of the diode by the reverse and forward time constants Ta and Tp, respectively. The equations are ex- 60,0+9=gO. pressed in terms of measurable diode parameters, via Te, TR, and Ci, external circuit resistor R, and the forward Then we get to reverse current ratio IP/IR ag=0,0-Q ANALYsis oF SWITCHING OPFRATION Charge Equation Considering the junction capacitance C, as shown in Fig. 1, the total current i(t) Alowing into the terminal 1 In order to simplify the analysis, let us consider a is given by planar junction diode shown in Fig. 1. ( We do not lose generality by this simplification. )We shall also assume that the conductivity of the p-type material o, is much i(0=ir(,t+ at greater than that of the n-type material on, so that the hole current at the junction may be considered to be the i, (0, t)+C total current. The continuity equation in the n-type (base)region can be written in terms of the excess hole whe nsity as [8] P C (v)dvi where Thus we can relate the total current i(t) that flows into p(, t=P(, t-Po he terminal l to the charge Q()stored in the base region of the diode and the junction voltage V, by the following namely, the charge equation Q 十+C; 1) P(, t)=hole density Integrating this equation over the region <a <w Now let us consider the switching circuit shown in and defining the total charge stored in the base region Q Fig. 2. Initially, the switch S is in position 1, and the such that diode is forwardly biased and conducting current IF We shall assume that the switch s has been in position 1 Q(0=9, for a long time so that a steady state may be assumed the time t=0. Then the initial condition can be ob- we get tained by substituting steady-state condition do Q dt i, (0, t)-i,(w, t) Noting that the term Q/T, represents the recombination dQ rate in the base region where a w and that i,(w, t) represents the recombination rate at the boundary a =wo let us define the total recombination rate constant, tp to i, be subscript F is chosen since, for steady state, Q is related into(1) Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03: 47 from IEEE Xplore. Restrictions apply

1964. Kuno: P-N Junction Diode Switching 5 Fig. 1-Planar junction diode model. current IF to the minority carrier charge Q stored in the base region of the diode by the reverse and forward time constants rR and TF, respectively. The equations are ex￾pressed in terms of measurable diode parameters, vix., rP, T~, and Ci, external circuit resistor 8, and the forward to reverse current ratio IF,/IR. ANALYSIS OF SWITCHING OPERATION Charge Equation In order to simplify the analysis, let us consider a planar junction diode shown in Fig. 1. (We do not lose generality by this simplification.) We shall also assume that the conductivity of the ptype material a, is much greater than that of t,he n-type material o,, so that the hole current at the junction may be considered to be the total current. The continuity equation in the n-type (base) region can be written in terms of the excess hole density as [8] where = hole current P(x, t) = hole density P,(x) = hole density in thermal equilibrium. Integrating this equation over the region 0 _< x 5 w, and defining the total charge stored in the base region Q such that Q(t) = P \m P dx, -0 we get Noting that the term Q/T~ represents the recombination rate in the base region where 0 < x < w and that ip(w, t) represents the recombination rate at the boundary x = w, let us define the total recombination rate constant, TF,~ to IF by The subscript F is chosen since, for steady state, Q is related such that Then we get Considering the junction capacitance Cj as shown in Fig. 1, the total current i(t) flowing into the terminal 1 is given by where Vi = junction voltage Thus we can relate the total current i(t) tlhat flows into the terminal 1 to the charge Q(t) stored in the base region of the diode and the junction voltage Vi by the following, namely, the charge equation Initial Condition Now let us consider the switching circuit shown in Fig. 2. Initially, the switch X is in position 1, and the diode is forwardly biased and conducting current IF. (We shall assume that the switch S has been in position 1 for a long time so that a steady state may be assumed at the time t = 0-). Then the initial condition can be ob￾tained by substituting steady-state conditions i(O-) = IF into (1). Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03:47 from IEEE Xplore. Restrictions apply

TEEE TRANSACTIONS ON ELECTRON DEVICES Fig.sTeady state hole density distributions in the base region Fig. 2-Diode switching circuit. The initial hole density distribution can be found by At this time, the total charge in the base region is given by solving the diffusion equation. Typical steady-state dis- tributions are shown in Fig 3 Q(t,=9 P(a, t,)dx at t=t, Normal Switching Operation Noting that Q(t )is related to IR, let us define TR,re In normal switching operation, switching transient con- lating the minimum amount of charge remaining in the sists of constant current phase(storage phase) and de- base region which is required to support the reverse cur- caying current phase as shown in Fig. 4. Now suppose rent, such that that att=0 the switch S is quickly thrown from position 1 to position 2. Then the current starts to fow in the Q()= IRTR opposite direction. The maximum reverse current is Although it is not immediately obvious why the mini- limited, by the external resistor R, to mum amount of charge required to support the reverse V,-V V current is linearly related to the reverse current, the (3) justification is made empirically as shown in a later Then the stored charge Q starts to decay in a manner Substituting (8)into(4), and solving for the storage For0 t,, the hole density decays further, and current tarts to decay he stored charg With the initial condition given by(2), we can solve for gradient at z=0 necessary to support I g. Let us assume Q(0)and get that the reverse current ig(o is related to the charge Q(0), as we have defined TR, by the relationship Q(0=(I,+IxTp exp t)-IRTP Q(0= TRin(O (10 During the constant current phase, i.e., 0 t Ia=9 uEP-D, for 0<t<t,.(6) Considering the circuit shown in Fig. 2, the junction oltage V, is related to in by Att= t,, the hole density at the junction(r=0)becomes zero, and(6)become a Le Can et al, [51, and Moll et al. thus obtaining t,=T In (l+IriG (7) t correct, sinc orted by the hole density gradient at the junction as given by (7) Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03: 47 from IEEE Xplore. Restrictions apply

10 S IEEE TRANXAGTIONS ON ELECTRON DEVICES January h 0 W 0 W - I- I-x c-x - Fig. 3-Steady state hole density distributions in the base region Fig. 2-Diode switching circuit. of various types of diodes. The initial hole density distribution can be found by solving the diffusion equation. Typical steady-state dis￾tributions are shown in Fig. 3. Normal Switching Operation In normal switching operation, switching transient con￾sists of constant current phase (storage phase) and de￾caying current phase as shown in Fig. 4. Now suppose that at t = 0' the switch S is quickly thrown from position 1 to position 2. Then the current starts to flow in the opposite direction. The maximum reverse current is limited, by the external resistor R, to Then the stored charge Q starts to decay in a manner shown in Fig. 5. For 0 - IRTF. (5) During the constant current phase, Le., 0 t,, the hole density decays further, and current starts to decay, since the stored charge cannot keep the gradient at x = 0 necessary to support I,. Let us assume that the reverse current iR(t) is related to the charge &(t), as we have defined rR, by the relationship Ut) = TRiR(t) (10) where t > t,. Considering the circuit shown in Fig. 2, the junction voltage Vi is related to iR by thus obtaining t, = T~ In (1 + IF/IR), but their assumptions are LeCan et al., [5], and Moll et al., [6], assume that Q(t.) = 0, not correot, since the current.1, at t = t, is supported by the hole density gradient at the junctlon as given by (7). Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03:47 from IEEE Xplore. Restrictions apply

1964 no: P-N Junction Diode Switching 11 Fig. 4-Current and voltage switching characteristics of a diode Fig 5-Hole density distributions during the switching Fig. 6-Storage time 4, of a diode as a function of Ip/IR iRR 4=232+R (16) Differentiation of this with respect to time t gives 1+_8 d (12) Overdriven Switching Operation Then(1) becomes In normal switching operation, we have derived the expression for the storage time t, given by(9). It can be di ir=(TR+RC+-iR (13)seen that, as Is is inereased keeping Ir constant, t, de- creases and becomes zero when with the boundary condition given by( 8); i.e IRE-IE Let us define I we can solve for in(t) for t>t, We get Ro as the critical reverse current beyond which t, becomes zero, b.e., 1+ (17 i(6-1s(-(x+Z(-)·10 When i,>IRo, viz., overdriven switching, the charge Defining t, as the time that in takes to decay from I2 stored in the base region cannot support the reverse to 10 per cent of Ir as shown in Fig. 4, i.e current. Thus, the reverse current immediately starts to iR(n=0.1IN lo=I, (18) t, can be obtained from(14) as shown in Fig. 7, and assume that to is very gmall so tr (15) that the charge stored in the base region does not decay appreciably during this interval of time. Then the all Authorized icensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03: 47 from IEEE Xplore. Restrictions appl

1964 Kuno: P-N Junction Diode Switching 11 owt "(t) Fig. &Current and voltage switching characteristics of a diode. (cl t = tS (a) t > tg Fig. 5-HoIe density distributions during the switching. Fig. 6-Storage time t, of a diode as a function of IF/IR. Vj = - V, + iRR. Differentiation of this with respect to time t gives Then (1) becomes with the boundary condition given by (8); i.e., &(is) = IRTR we can solve for iR(t) for t > t,. We get 7 (12) Overdriven Switching Operation In normal switching operation, we have derived the expression for the storage time t, given by (9). It can be (13) seen that, as I, is increased keeping I, constant, ts de￾creases and becomes zero when TF TR 1, = --I,. Let us define IRo as the critical reverse current beyond which t, becomes zero, Le., I20 = - I,. TP TR (17) (14) When i, > IRO, vix., overdriven switching, the charge Defining tf as the time that iR takes to decay from I, stored in the base region cannot support the reverse to 10 per cent of I, as shown in Fig. 4, i.e., current. Thus, the reverse current immediately starts to decay to IRo. Let us define to such that iR(tf) = 0.1 I,, i,(t3 = IRO, (18) tf can be obtained from (14). as shown in Fig. 7, and assume that to is very small so (15) that the charge stored in the base region does not decay appreciably during this interval of time.3 Then the all 1+- I TF J or thus to, is very small compared with rg in most cases. This assumption is justifiable since the time constant RCi, Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03:47 from IEEE Xplore. Restrictions apply

IEEE TRANSACTIONS ON ELECTRON DEVICES January current flowing during the interval to may be considered Then(1)becomes to discharge the junction capacitance, and for the over- driven switching, where ts to, (1) reduces to iR(O=(TR+RC3+ -in(o-I,+rc, die (19) with the boundary condition ro>in(to=i the solution of (26)becomes Q(0=IPT, a constant for tIRO, switching transient were analyzed using the set-up shown n Fig. 8. Diodes tested are grouped into four general types: 1) germanium gold bonded, 2)germanium expitaxial 0 to, we have ig Ino and results show very good agreement with the switching characteristics given by(14),(22), and (27) TRiR t o(t AY工树篇 Fig. 7-Current switching characteristics of a diode overdriven in reverse directi Fig. 8--Set-up for diode switching test. Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03: 47 from IEEE Xplore. Restrictions apply

12 IEEE TRANSACTION# ON ELECTRON DEVICES January current flowkg during the interval to may be considered Then (1) becomes to discharge the junction capacitance, and for the over￾driven switching, where t > ix(to) = 1x0 Q(t) = Ip~p = constant for t IRo t %.e., 0 < t < to. At the end of the overdriven phase; Le., t = to, we have iR(tO) = IZO. (23) Substituting (23) into (22) and solving for to, we obtain to = h%,[ In (1 + 2) - In (I + ?)] (24) or 3- OVER-DRIVEN Fig. 7-Current switching characteristics of a diode overdriven in the reverse direction. with the boundary condition iR(tO) = the solution of (26) becomes and where t, is defined as the time required €or i, to decay from IBo to 10 per cent of IRO; i.e., i(tf) = 0.1 IRO. EXPERIMENTAL RESULTS Various types of diodes were selected for switching time measurement. Also, current waveforms during the switching transient were analyzed using the set-up shown in Fig. 8. Diodes tested are grouped into four general. I types: 1) germanium gold bonded, 2) germanium expitaxial mesa, 3) silicon planar, and 4) silicon diffused mesa. Fig. 9(a)-9(d) shows typical results of the storage time measurement of each group. IF was varied from 1 ma to 20 ma and IF/IR up to 100. It can be seen that each curve shows straight line relationship between t, and In (1 + IF/IR), as predicted by (9). The results also indicate that rF and rR are very constant over the wide range of IF and IE, as we have assumed. Fig. lO(a)-lO(b) shows typical switching transient characteristics observed with a sampling scope driving a X-Y recorder. Fig. 10(a) shows normal switching opera￾tion, and Fig. 10(b) overdriven switching operation. These results show very good agreement with the switching characteristics given by (14), (2.29, and (27). I 2.4 X 1 5M 500n POWER SUPPLY mTT￾PA- ~ S4MPLIUG TRIOGER SCOPE PROBE c yr DIODK 0-50v I m - - x-Y REMRDER Fig. 8-Set-up for diode switching test. Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03:47 from IEEE Xplore. Restrictions apply

1964 Kuno: P-N Junction Diode Switching 13 g (b) Diode H24001(Type 1).(b)Collector to base diod 10-g rent switching characteristics of a diode(H24001), theoretical (-) experimental 4 H numbers indicate National Cash Register Co. specification numbers Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03: 47 from IEEE Xplore. Restrictions apply

1964 Kuno: P-N Junction Diode Switching 4 6 810 20 Fig. 9Stprage time as a function of 1. -I- IF/I~ for various-types of diodes. (a) Diode H240014 (Type 1). (b) Collector to base diode of transistor 2N964 (Type 2). (c) Diode H250004 (Type 3). (d) Diode 1N914 (Type 4). Fig. 10-Theoretical and experimental current switching characteristics of a diode (H24001)4; theoretical (--), experimental (-). (a) Normal switching operation, (b) Overdriven switching operation. 4 N numbers indicate National Cash Register Co. specification numbers. Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03:47 from IEEE Xplore. Restrictions apply

IEEE TRANSACTIONS ON ELECTRON DEVICES J for preparing the manuseript, and the reviewers of these The proposed charge control model of diode assumes TRANSACTIONs for their constructive comments and re- linear relationships between Ir and Q, and between in commendations and Q, given by(2)and(10), respectively. The experi mental results show that Tp and TR are very constant; REFERENCES thus the assumption is justified. Analytical verification [1] R. Beaufoy and J. J. Sparkes, "The junction transistor as a may, however, be carried out by solving the diffusion Autom.Teleph. Elect.J.,vol. 13 quation for P(, () and integrating over the region (2) RE. bye 0≤x≤t, though it is a very complicated task devices, J, Appl. Phys., vol. 28, pp. 878-881; The good agreement of the experimental results with 3A. Ht Kingston, "Switching time on diodes and 834;May,19 reverse switching transient of p-n junction diodes of 4 iade KiRE The revere ancien vol. ED-8, pp any type by measuring Tr, Te, and Ci The proposed model may also be applied to collector- 16)C LeCan, K eart and C DeRuyter, "The Junction Transistor hing device,” Reinho base junction of a transistor to characterize the storage time of the transistor 6 PN n cha 43-53; ACKNOWLEDGMENt The author wishes to acknowledge V. Plage for his [8] E. L. Ste measuring techniues, S. Mitchell and Mrs. M. Lewis 9)iB T0 25, laboratory assistance, W. Meadows for developing many ill ook Co, Inc, New York, N. y f Transistors,"MeGraw- Impedance Characteristics of an AC MHD Generator' L J. KIJEWSKI, J. B. FANUCCI, AND N. NESSt Summary--A study is made of those parameters, associated with power to the load. This method is summarized by Steg the impedance of an ac mhd generator which affect the power and Sutton. DC generators have the disadvantage, for material in the region external to the plasma causes a significant certain applications, of requiring a dc-Ac converter increase in the power factor. An expression for the actual electrical The second approach, which is the one considered ower extracted from the generator, as determined by electrical herein, utilizes a traveling-wave type magnetic field, the impedance methods, is shown to be identical to the expression power being extracted by induction. The phase velocity derived by considering Lorentz forces on elements of the fluid for of the traveling magnetic field may be larger or less than the plasma velocity. In the former case, the plasma is ac- celerated; that is, electrical energy is converted into inter INTRODUCTION nal and kinetic energy. In the latter situation, the process HE INTERNAL and kinetic energy of a flowing is reversed; the behavior of this device is then analogous plasma in the presence of a magnetic field may to an induction generator. The induction generator is, of convert some of ita energy directly into electrical course, ac, and electrodes and converters are not required form. This process of energy conversion has been investi- The purpose of this paper is to investigate the various gated extensively of late and is known as"magnetohydro- parameters which affect the impedance characteristics of namie" power generat the traveling-wave MHD power generator, the primary There are two basic schemes for MHD power extraction. aim being to improve the power factor. In the paper of In the first scheme, electrodes are adjacent to the plasma. Bernstein et al., it was noted that for a generator which These electrodes are connected to a load resistance causing will deliver a sizeable power, the power factor is ex- a de current to fow through the circuit, thereby delivering Reecived June 17, 1963. This work was performed under Contr. ation, astronautics, vol, 5, pP 22 26: Agu et. Mod power gener- MHD generator by the Aeronautical System Divi- of Magnetohydrod ion, Wright-Patterson AFB, Ohi Mather, Eds, Columbia University Press f Defense Electronic Products, RCA, Moorestown, N.J. Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03: 47 from IEEE Xplore. Restrictions apply

14 IEEE TRANSACTIONS ON ELECTRON DEVICES January DISCUSSION The proposed charge control model of diode assumes linear relationships between IF and Q, and between iR and &, given by (2) and (lo), respectively. The experi￾mental results show that rF and 712 are very constant; thus the assumption is justified. Analytical verification may, however, be carried out by solving the diffusion equation for P(z, t) and integrating over the region 0 5 x 5 w, though it is a very complicated task. The good agreement of the experimental results with the theory indicates that proposed model can characterize reverse switching transient of p-n junction diodes of any type by measuring T~, rR, and Ci. The proposed model may also be applied to collector￾base junction of a transistor to characterize the storage time of the transistor. ACKNOWLEDGMENT The author wishes to acknowledge V. Plage for his laboratory assistance, W. Meadows for developing many measuring techniques, S. Mitchell and Mrs. M. Lewis for preparing the manuscript, and the reviewers of these TRANSACTIONS for their constructive comments and re￾commendations. REFERENCES [l] R. Beaufoy and J. J. Sparkes, “The junction transistor as B charge controlled device,” Autom. Teleph. Elect. J., vol. 13, pp. 310-327; October, 1957. [2] M. Byczkowski and J. R. Madigan, “Minority carrier lifetime in p-n junction devices,” J. Appl. Phys., vol. 28, pp. 878-881; [3] R. H. Kingston,,, “Switching time in junction diodes and junc￾August, 1957. [4] W. H. KO, “The reveme transient behavior of semiconductor tion transistors, PROC. IRE, vol. 42, pp. 829-834; May, 1954. diodes,” IRE TRANS. ON ELECTRON DEVICES, vol. ED-8, pp. 123-131; March, 1961. [SI C. LeCan, K. Hart and C. DeRuyter, “The Junction Transistor as a Switching Device,” Reinhold Publishing Corp., New York, [6] J. L. Moll, S. Krakauer, and R. Shen, “P-N junction charge N. Y.; 1962. [7] S. Y. Muto and. S. Wang, “Switching response of graded-base stored diodes,” PROC. IRE, vol. 50, pp. 43-53; January, 1962. P-N junction diodes,” IRE TRANS. ON ELECTRON DEVICES, vol. ED-9, pp. 183-187; March, 1962. [SI E. L. Steele, “Charge storage in junction diodes,” J. Appl. 191 L. B. Valdes, “The Physical Theory of Transistors,’’ McGraw￾Phy~., VO~. 25, pp. 916-918; July, 1954. Hill Book Co., Inc., New York, N. Y.; 1961. Impedance Characteristics of an AC MHID Generator* L. J. KIJEWSKI, J. B. FANUCCI, AND N. NESS? Summary-A study is made of those parameters, associated with the impedance of an ac MHD generator, which &ect the power factor. It has been found that the addition of a ferromagnetic material in the region external to the plasma causes a signislcant increase in the power factor. An expression for the actual electrical power extracted from the generator, as determined by electrical impedance methods, is shown to be identical to the expression derived by considering Lorentz forces on elements of the fluid for a particular approximation mentioned in the report. INTRODUCTION HE INTERNAL and kinetic energy of a flowing plasma in the presence of a magnetic field may convert some of its energy directly into electrical form. This process of energy conversion has been investi￾gated extensively of late and is known as “magnetohydro￾dynamic” power generation. There are two basic schemes for MHD power extraction. In the first scheme, electrodes are adjacent to the plasma. These electrodes are connected to a load resistance causing a dc current to flow through the circuit, thereby delivering No. AF33(616)-7913, sponsored by the Aeronautical System Divi- * Received June 17, 1963. This work was performed under Contr. sion, WrightrPatterson AFB, Ohio. ’ Defense Electronic Products, RCA, Moorestown, N. J. power to the load. This method is summarized by Steg and Sutton.’ DC generators have the disadvantage, for certain applications, of requiring a DC-AC converter. The second approach, which is the one considered herein, utilizes a traveling-wave type magnetic field, the power being extracted by induction. The phase velocity of the traveling magnetic field may be larger or less than the plasma velocity. In the former case,’the plasma is ac￾celerated; that is, electrical energy is converted into inter￾nal and kinetic energy. In the latter situation, the process is reversed; the behavior of this device is then analogous to an induction generator. The induction generator is, of course, ac, and electrodes and converters are not required. The purpose of this paper is to investigate the various parameters which affect the impedance characteristics of the traveling-wave MHD power generator, the primary aim being to improve the power factor. In the paper of Bernstein et al.,’ it was noted that for a generator which will deliver a sizeable power, the power factor is ex￾ation,” Bstronautics, vol. 5, pp. 22-25; August, 1960. 1 L. Steg, G. W. Sutton, “The prospects of MHD power gener- 2 I. B. Bernskin et al., “An electrodeless MHD generator,” in N. W. Mather, Eds., Columbia University Press, New York, N. Y.; “Engineering Aspects of Magnetohydrodynamics,” C. Manna1 and 1962. Authorized licensed use limited to: IEEE Xplore. Downloaded on December 15, 2008 at 03:47 from IEEE Xplore. Restrictions apply