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CW X-band GaAs microwave generators
Solid-State Electronics Pergamon Press 1966. pp. 281-282. Printed in Great Britain
CW X-Band GaAs microwave
Vol.
9,
represents
the expression
f = 50/v,
generators
(1)
where f is the frequency in GHz and V, is the critical voltage in V. Equation (1) corresponds to an electric field of 3300 V/cm and to a domain velocity of 1.5 x 10’ cm/set. Experiments are presently in progress to characterize such units more completely.
(Received 9 December 1965)
WE HAVE succeeded in generating coherent CW microwave oscillations at frequencies up to 12 GHz. The oscillations were produced in bulk gallium arsenide samples by means of the Gunn effect.(l) The devices were fabricated from single crystal n-type gallium arsenide with a resistivity of -2-S Q-cm and a mobility of N 4500 ems/V-sec. Slices of this material were oriented in the (100) direction, and reduced to the desired thickness (lo-150 p) by standard grinding and etching techniques. Rectangular samples were obtained by cleaving along the (110) directions. Pure tin contacts were applied to both sides of the gallium arsenide chips in an atmosphere of forming gas, and the samples were mounted in microwave packages. Typical d.c. I-V characteristics are shown in Fig. 1. The good ohmic character of the contacts is evident from the symmetry of the forward and reverse curves as well as from the similarity of the critical voltages and currents. The microwave characteristics of the units were measured in a tunable coaxial cavity and in an X-band cavity with a tuning range from 8.2 to 12.4 GHz. Frequencies of operation were determined with a spectrum analyzer. CW units were biased with a voltage-regulated d.c. power supply. In addition, pulsed measurements were carried out on several units using a Hewlett-Packard Model 214A pulse generator. The CW samples were observed to oscillate in room temperature ambient with no auxiliary cooling. Fundamental frequencies of these units ranged from 3.3 to 12.1 GHz. In Fig. 2, we show a plot of frequency vs. critical voltage for CW units as well as several pulsed units fabricated from the same material. Data are also shown for three pulsed units aa reported by GuNN,~) and for the CW results of QUIST and FoYT@). The solid line
FIG. 1. Forward and reverse I-V characteristic zero centre for sample ERC-47.
Critical
Voltage
with
Wok.)
Fro. 2. Frequency vs. critical voltage for CW and pulsed gallium arsenide Gunn oscillators. 281
NOTES
282
Acknowle&ements--Much of the authors experience in the field of solid state microwave generation was gained at the Raytheon Company’s Research Division, in Waltham, Massachusetts and they acknowledge the cooperation of their former colleagues. The authors also wish to express their appreciation for many valuable discussions with Dr. W. BERNARDof NASA’s Electronic Research Center.
characterized by the Seebeck coefficient S, the thermal conductivity k, the electric resistivity p, and the Thomson coefficient -r. According to the theoretical approach outlined by SUNDERLANDand BuRAK(~), the heat balance equation of the thermoelements is given by
W. D. STRAUB J.
A. AYER H. ROTH
National Aeror~utics and Space Administration Electronics Research Center 575 Technology Square Cambridge, Massachusetts References 1. J. B. GUNN, IBM J. Res. Develop, 8, 141 (1964). 2. T. M. QUIST and A. G. FOYT, Proc. Inst. Elect. Electron. Engrs. 53, 303(1965).
Solid-State
Electronics Pergamon Press 1966. pp. 282-285. Printed in Great Britain
Vol.
4 October 1965; in revisedform 1965)
8 November
IN A RECENT PAPER, SUNDERLAND and BUM(~) studied the influence of constant Thomson coefficients on the performance of power generators. The temperature distribution, power output, and thermal efficiency of a fully insulated thermoelement were expressed in analytical form. The condition of optimum performance, however, was not determined in the paper. The purpose of this work is to determine the effect of the Thomson heat on the optimized performance of a thermoelectric generator. Consider a thermoelectric generator consisting of an n-type and a p-type thermoelement with same lengths L and uniform cross-sectional area A. The hot junctions, x = L, are joined by a metal block maintained at a temperature Th and two cold junctions, x = 0, are maintained at a temperature T, with a load resistance R between them. The current carried by the thermoelement is I. The bulk properties of two thermoelements are
(1)
where x is the distance from the heat sink and the subscripts n and p correspond to the properties of the n-type and p-type elements respectively. The overall thermal efficiency is defined by equation (2) opposite, where S,, = S,(T) + Sn( T). The temperature gradient at the hot junction can be calculated from equation (1). The thermal efficiency can be expressed in the form given in equation (3) opposite, where E = pn/j&,, F = z/pk,/ppk,, and
AR
9,
The optimized performance of a thermoelectric generator with the Thomson effect (Received
(i = % P)
m= L(Fn + &Fip) is the ratio of the external to internal resistance. w = [,$,,/( dpDkp+ y’pnk,)]zTh is the dimensionless figure of merit. f = (Th - T,)/Th. The average value of the transport properties are defined as: Th PC =
pc(T)dT/(Th-
Tc)
(i =
P, n)
s
T, Th Kc =
&,, =
k( T)dT/( Th - Tc) f TO
[Sp(T)+&(T)ldT/(Ths TC
Tc)
The value of /3*(i = p, n) is given by ,!& = &L/krA For the purpose of simplification for numerical calculations, assume that the material properties can be approximated by the mean values of the
CW X-Band GaAs microwave
Vol.
9,
represents
the expression
f = 50/v,
generators
(1)
where f is the frequency in GHz and V, is the critical voltage in V. Equation (1) corresponds to an electric field of 3300 V/cm and to a domain velocity of 1.5 x 10’ cm/set. Experiments are presently in progress to characterize such units more completely.
(Received 9 December 1965)
WE HAVE succeeded in generating coherent CW microwave oscillations at frequencies up to 12 GHz. The oscillations were produced in bulk gallium arsenide samples by means of the Gunn effect.(l) The devices were fabricated from single crystal n-type gallium arsenide with a resistivity of -2-S Q-cm and a mobility of N 4500 ems/V-sec. Slices of this material were oriented in the (100) direction, and reduced to the desired thickness (lo-150 p) by standard grinding and etching techniques. Rectangular samples were obtained by cleaving along the (110) directions. Pure tin contacts were applied to both sides of the gallium arsenide chips in an atmosphere of forming gas, and the samples were mounted in microwave packages. Typical d.c. I-V characteristics are shown in Fig. 1. The good ohmic character of the contacts is evident from the symmetry of the forward and reverse curves as well as from the similarity of the critical voltages and currents. The microwave characteristics of the units were measured in a tunable coaxial cavity and in an X-band cavity with a tuning range from 8.2 to 12.4 GHz. Frequencies of operation were determined with a spectrum analyzer. CW units were biased with a voltage-regulated d.c. power supply. In addition, pulsed measurements were carried out on several units using a Hewlett-Packard Model 214A pulse generator. The CW samples were observed to oscillate in room temperature ambient with no auxiliary cooling. Fundamental frequencies of these units ranged from 3.3 to 12.1 GHz. In Fig. 2, we show a plot of frequency vs. critical voltage for CW units as well as several pulsed units fabricated from the same material. Data are also shown for three pulsed units aa reported by GuNN,~) and for the CW results of QUIST and FoYT@). The solid line
FIG. 1. Forward and reverse I-V characteristic zero centre for sample ERC-47.
Critical
Voltage
with
Wok.)
Fro. 2. Frequency vs. critical voltage for CW and pulsed gallium arsenide Gunn oscillators. 281
NOTES
282
Acknowle&ements--Much of the authors experience in the field of solid state microwave generation was gained at the Raytheon Company’s Research Division, in Waltham, Massachusetts and they acknowledge the cooperation of their former colleagues. The authors also wish to express their appreciation for many valuable discussions with Dr. W. BERNARDof NASA’s Electronic Research Center.
characterized by the Seebeck coefficient S, the thermal conductivity k, the electric resistivity p, and the Thomson coefficient -r. According to the theoretical approach outlined by SUNDERLANDand BuRAK(~), the heat balance equation of the thermoelements is given by
W. D. STRAUB J.
A. AYER H. ROTH
National Aeror~utics and Space Administration Electronics Research Center 575 Technology Square Cambridge, Massachusetts References 1. J. B. GUNN, IBM J. Res. Develop, 8, 141 (1964). 2. T. M. QUIST and A. G. FOYT, Proc. Inst. Elect. Electron. Engrs. 53, 303(1965).
Solid-State
Electronics Pergamon Press 1966. pp. 282-285. Printed in Great Britain
Vol.
4 October 1965; in revisedform 1965)
8 November
IN A RECENT PAPER, SUNDERLAND and BUM(~) studied the influence of constant Thomson coefficients on the performance of power generators. The temperature distribution, power output, and thermal efficiency of a fully insulated thermoelement were expressed in analytical form. The condition of optimum performance, however, was not determined in the paper. The purpose of this work is to determine the effect of the Thomson heat on the optimized performance of a thermoelectric generator. Consider a thermoelectric generator consisting of an n-type and a p-type thermoelement with same lengths L and uniform cross-sectional area A. The hot junctions, x = L, are joined by a metal block maintained at a temperature Th and two cold junctions, x = 0, are maintained at a temperature T, with a load resistance R between them. The current carried by the thermoelement is I. The bulk properties of two thermoelements are
(1)
where x is the distance from the heat sink and the subscripts n and p correspond to the properties of the n-type and p-type elements respectively. The overall thermal efficiency is defined by equation (2) opposite, where S,, = S,(T) + Sn( T). The temperature gradient at the hot junction can be calculated from equation (1). The thermal efficiency can be expressed in the form given in equation (3) opposite, where E = pn/j&,, F = z/pk,/ppk,, and
AR
9,
The optimized performance of a thermoelectric generator with the Thomson effect (Received
(i = % P)
m= L(Fn + &Fip) is the ratio of the external to internal resistance. w = [,$,,/( dpDkp+ y’pnk,)]zTh is the dimensionless figure of merit. f = (Th - T,)/Th. The average value of the transport properties are defined as: Th PC =
pc(T)dT/(Th-
Tc)
(i =
P, n)
s
T, Th Kc =
&,, =
k( T)dT/( Th - Tc) f TO
[Sp(T)+&(T)ldT/(Ths TC
Tc)
The value of /3*(i = p, n) is given by ,!& = &L/krA For the purpose of simplification for numerical calculations, assume that the material properties can be approximated by the mean values of the