TEEE TRANSACTIONS ON ELECTRON DEVICES, VOL ED-18, NO. 3, MARCH 1971 recovery diode for pulse and harmonic 259 g time in junction diodes and junc- [(11) purities in semiconductors [12] See, for example, "Time domain reflecto [10]J. L. Moll and S. A. Hamilton, "Physical modeling of the step ard Company, Application Note b52 19(aetry, "Hewlett-Pack- Temperature in Gunn Diodes with Inhomogeneous Power Dissipation NILS O. JOHNSON, STUDENT MEMBER, IEEE, KJELL O. I OLSSON AND S. JORGE WILDHEIM Abstract-The output power of Gunn oscillators is limited by the under the assumption that the dissipation power density increased temperature which affects the velocity-field curve and is homogeneous throughout the diode volume. This assumption is certainly good for some cases, e. g, diodes tensity is more or less inhomogeneous, depending on the kind of operated in the LSA mode [6]. However, when diodes scillation mode. The present paper makes use of simple models of are operated in the usual transit-time dipole-domain the dipole domain mode and the accumulation mode in an analysis mode [6 and the transit-time accumulation mode [6] neous dissipation power density. The temperature the dissipation is much larger near the anode contact temperature dependence on diode dimensions and mounting is also than near the cathode contact [7]. In this paper simple is turned towards the heat sink than when the cathode is turned the operation are used to calculate the inhomogeneity of the ame way. This difference amounts to 150K for an accumulation dissipation. From this the temperature is calculated mode diode with 500K maximum temperature in the former case. Gunn diodes are typically mounted with only one con tact acting as an efficient heat sink. The present theor thus tells the difference in temperature when the diodes N HE Gunn diode is a solid-state microwave power are mounted with the cathode to the heat sink and with source with small dimensions. Today more than the anode to the heat sink. Obviously the temperature is 1-kW peak power is available from single diodes higher in the former case and the difference may be as under pulsed operation [1] but less than 1 W from Cw large as 40 K for domain mode diodes and 150K for diodes. The dissipation power density and the cor accumulation mode diodes when the maximum tem- nected temperature increase limit the production o perature with the anode to the heat sink is 500%K microwave power at high duty cycles. The allowable temperature of a diode has an upper limit. The contac HEAT CONDUCTION material is usually gold or silver alloys, which form an First we will give the equations by which the tem eutetic with GaAs at about 700 to 900K. The diode can perature is calculated from the dissipation power density thus be permanently damaged in this temperature re- P(=time average of the scalar product of electrical gion. The negative differential mobility in GaAs dis- field and current density). The geometry assumed appears at very high temperatures and there exists some shown in Fig. 1. The diode and the contact layer are evidence that it is too small to cause oscillations at assumed to be of circular shape when looked upon from a temperatures above 600 to 700K perature increase in diodes with different mountings ordinate a only. The heat conductivity of the heat sink is of GaAs. It is therefore ot received June 30, 1970 typically much larger than 6 ch Laboratory of Electronics, reasonable to approximate the heat How in the Gaas to be in the direction only. The equation of heat oratory of Electronics, tion then becomes(in the stationary state) niversity of Technology, Gothenburg, Sweden. He Chalmers university of Technology, Gothenburg, sweden. he is now +P(x) with STAL-LAV.I58 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL ED-18, NO. 3, MARCH 1971 [71 B. Lax a,:d S. F. Neustadter, “Transient response of a P-N recovery diode for pulse and harmonic generation circuits,” [SI R. H. Kingston, “Switching time in junction diodes and junc- ill] P. E. Gibbons, “Problems concerning the soatial distribution of junction, J. AppZ. Phys., vol. 25, 1954, p. 1148. Proc. IEEE, VO~. 57, July 1969, pp. 1250-1259. tion transistors,” Proc. IRE, vol. 42, May(1954, pp. 829-834. deep impurities in semiconductors,” Solid-State Electron., vol. [Uj J. 1,. Moll, S. ,f(rakauer, and R. Shen, P-hT junction charge￾storage diodes, Proc. IRE, vol. s!, 1962, p. 43. 13, 1969, p. 989. [lo] J. L. Moll and S. A. Hamilton, Physical modeling of the step [12] See, for example, “Time domain reflectometry,” Hewlett-Pack￾ard Company, Application Note 62, 1964. .. Temperature in Gunn Diodes with Inhomogeneous Power Dissipation Abstract-The output power of Gunn oscillators is limited by the increased temperature which affects the velocity-field curve and which may also permanently damage the diode or the metal contacts. The behavior of these oscillators indicates that the dissipation power density is more or less inhomogeneous, depending on the kind of oscillation mode. The present paper makes use of simple models of the dipole domain mode and the accumulation mode in an analysis of the inhomogeneous dissipation power density. The temperature increase caused by this dissipation power is then calculated. The temperature dependence on diode dimensions and mounting is also discussed. It is shown that the temperature is lower when the anode is turned towards the heat sink than when the cathode is turned the same way. This difference amounts to 150’K for an accumulation mode diode with 500’K maximum temperature in the former case. INTRODL-CTION T HE Gunn diode is a solid-state microwave power source with small dimensions. Today more than 1-kW peak power is available from single diodes under pulsed operation [l] but less than 1 W from CW diodes. The dissipation power density and the con￾nected temperature increase limit he production of microwave power at high duty cycles. The allowable temperature of a diode has an upper limit. The contact material is usually gold or silver alloys, which form an eutetic with GaAs at about 700 to 900’K. The diode can thus be permanently damaged in this temperature re￾gion. The negative differential mobility in GaAs dis￾appears at very high temperatures and there exists some evidence that it is too small to cause oscillations at temperatures above 600 to 700’K. A number of authors [2]- [5] have calculated the tem￾perature increase in diodes with different mountings Manuscript received June 30, 1970. Chalmers University of Technology, Gothenburg, Sweden. N. 0. Johnson is with the Research Laboratory of Electronics, K. 0. I. Olsson was with the Research Laboratory of Electronics, Chalmers University of Technology, Gothenburg, Sweden. He is now with Philips Teleindustri, Jakobsberg, Sweden. S. J. Wildheim was with the Research Laboratory of Electronics, Chalmers University of Technology, Gothenburg, Sweden. He is now with STAL-LAVAL Turbine Co., Finsping, Sweden. under the assumption that the dissipation power density is homogeneous throughout he diode volume. This assumption is certainly good for some cases, e.g., diodes operated in the LSA mode [6]. However, when diodes are operated in the usual transit-time dipole-domain mode [6] and the transit-time accumulation mode [6] the dissipation is much larger near the anode contact than near the cathode contact [7]. In this paper simple models of the domain mode and the accumulation mode operation are used to calculate the inhomogeneity of the dissipation. From this the temperature is calculated. Gunn diodes are typically mounted with only one con￾tact acting as an efficient heat sink. The present theory thus tells the difference in temperature when the diodes are mounted with the cathode to the heat sink and with the anode to the heat sink. Obviously the temperature is higher in the former case and the difference may be as large as 40’K for domain mode diodes and 150’K for accumulation mode diodes when the maximum tem￾perature with the anode to the heat sink is 500’K. HEAT CONDUCTION First we will give the equations by which the tem￾perature is calculated from the dissipation power density P( = time average of the scalar product of electrical field and current density). The geometry assumed is shown in Fig. 1. The diode and the contact layer are assumed to be of circular shape when looked upon from a direction perpendicular to the heat sink. The dissipation P is assumed to be a function of the longitudinal co￾ordinate x only. The heat conductivity of the heat sink is typically much larger than that of GaAs. It is therefore reasonable to approximate the heat flow in the GaAs to be in the x direction only. The equation of heat conduc￾tion then becomes (in the stationary state) dx \ dx/