Correspondence

Theory of the Orin necessary modification of Ridley’smodel.

Velocity The details of such rate limitations have not
Gunn Effect been worked out but one consequence that
Gunn [I] has recently discovered a new can be readily predicted is that thethreshold
kind of current oscillations a t microwave fieldwill increase with decreasing sample
frequencies, in n-type GaAs and InP. In his length, in order to accomplish the distribu-
paper, Gunn discusses several possibleex- tion change along the shorter available dis-
planations for these oscillations. Most of tance. This dependence, too, has been ob-
these explanations he rejects outright; about served.
the remainder he has serious reservations. HERBERT KROEMER
The purpose of this correspondence is to Varian Associates
point out that most, if not all, of the known Palo Alto, Calif.
properties of theGunn effect can be ex- EL EP E”
plained, a t least qualitatively, if it is as- REFERENCES
sumed that these semiconductors havea Fig. 1. [ l ] J. B. Gunn. “Iptabilities of current in 111-V
semiconductors. I B M J . Res. & Dm..vol. 8 . pp.
negative differential bulk conductivity 141-159;April 1964.
above the oscillation threshold field and that [ZI B. K. Ride; “Specific negative resistance in
solids.” Proc.’Phys. Soc., vol. 82. pp. 954-966;
the current oscillations are due to the pe- through the negative mobility range for a 1963.
riodic nucleation and disappearance of finite distance, near the electrodes. As [31 H. Krcemer. to be oublished.
141 W. Shocklev, ‘Negative resistance arising from
traveling space-charge instability domains, Shockley [4] has pointed out, such an over- transit time in semiconductor diodes Bell. Sys.
of the kind discussed by Ridley [2].1 simplified treatment of the boundary condi- Tech. J . , v d . 33, PP. 799-826; July. lb54.
Assume that the drift velocity vs field
behavior is characterized by a negative dif-
tions may lead to profound errors in prob-
lems of this sort. Some form of instability is,
t51 G. F. Day. personal communicatlon.
61 B. K. Ri,dey and T. B. Watkins. “The possibility
of negatlve resistance effects in semiconductors.”
therefore, likely to remain in these high-field Prw. Phys. Soc., zol. 78, PP. 293-304; 1961.
ferential mobility range as in Fig. 1. Ridley [’I] H. Ehrenreich. Band structure and electron
[2] has shown that acrystalcannot be cases, although it is not likely to have the transport of GaAs.” Phyr. Rm.,vol. 120, pp. 1951-
1963. December 1%0.
biased stably in that range but that it will form of strong coherent transit-time oscilla- 181 C. ,Hilsum, ‘Transferred electron amplifiers and
break up into domains of lower and higher tions. All of this is consistent with the work oaclllatms “ PRW. IRE. v d . 50. pp. 185-189;
February.’l%2.
fields, corresponding to the points L and V of Day [SI of this laboratory, who succeeded
in Fig. 1, and that these domains will travel in strongly attenuating existing oscillations
with a velocity equal to the drift velocity by increasing the field strength.
UL of the carriers. As one high-field domain Another refinement necessary in Ridley’s
moves out of the crystal a t the positive elec- model is the fact that space-charge limita-
trodea new domain gets nucleated a t or tions prevent the domain walls from being
near the negative end. In sufficiently short arbitrarily thin, particularly a t the electron-
samples only one nucleation center willbe depleted positive end of the high-fielddo-
active, leading to coherent oscillations, with main, where the space-charge density cannot
a frequency approximately equal to V L / L , exceed the donor space charge. For a suffi- RF Characteristics of Thin Dipoles
where L is the sample length. A detailed in- ciently low net donor density the domain
wall thickness exceeds the sample length In theabove paper 111 Mackand Reiffen
vestigation [3] shows that the frequency is give an analysis of scattering by dipoles
somewhat larger than this value and that it and no domains are possible. If one assumes
a difference between low and high fields of a whichis fundamentally in error,although
increases slowly with increasing voltage, in their results are approximately correct. I t
agreement with Gunn’s observations. few thousand volts per cm, this occurs when
the product of net donor density and sample is the purpose of this communication to call
The terminal current associated with attention to the correct formulation, and to
such domain travel oscillates between the length is less than a few times 1010 cm-’.
This was also observed by Day [SI. show to what extent the formulas of Mack
values corresponding to the valley velocity and Reiffen apply.
and to thethreshold value, also in agreement LVe wish to suggest that theorigin of the
negative differential mobility is Ridley and Theerror lies in the identification of
with the observations, if one assigns Gunn’s power “dissipated” in aThevenin equiv-
low current limits to the valley drift veloc- Watkins’ mechanism [6] of electron transfer
into the satellite valleys that occur in the alent circuit with reradiated power. A little
ity. thought shows that thiscannot generally
Such a field-controlled bulk-type nega- conduction bands of both GaAs and InP.
Gunn [ l ] has rejected this mechanism on the be true, since an open-circuited antenna
tive conductance cannot be stabilized by would then scatter no field. Also what
loading it with a sufficiently low impedance, grounds that the energy separation of the
satellite valleys would require electron tem- justification would one have for using the
in contrast tothe interface-type negative Thevenin equivalent over the Norton
conductance of a single Esaki tunnel diode. peratures of the order of 4000’K, while the
experimental electron temperature a t 80 per equivalent?This would give diametrically
It behaves essentially like a large number of opposite predictions as to reradiated power.
series-connected tunnel diodes. This isin cent of the threshold fieldis only of the
order of 400’K. However, thisargument In general, no identification of a power dis-
agreement with Gunn’s observation that it sipated in an equivalent circuit can be
is impossible to stabilize the current a t the overlooks the fact that the combined density
of states of the six (100) satellite valleys is made.
low value. The correct formulation for scattering
about 400 times that of the main valley [7].
According to Ridley’s simple model the Hilsum [8] has considered this fact and has by antennas was first given by Y. Y. Hu
domains, and thereby
the oscillations, estimated avelocity peak field of 3000 v/cm, for center-loaded dipoles [2], and this was
should disappear if fieldsinexcess of the an electron temperature a t this field of only later generalized to arbitrary antennas [3],
valley field are applied. However, Ridley’s about 670°K, and of only about 530’K a t [4]. The exact formulation for an antenna
model does not take into account the fact 80 per cent of the peak field, all values for loaded by an impedance Z L yields an echo
that, even in this case, the field must pass the already high lattice temperature of area [4].
373’K, with lower values for lower tempera-
tures.
Manuscript received October 14 1964. Such drastic changes in electron distribu-
1 Ridley himself hints at this pokibility in “Elec;
tric bubbles and the quest for negative resistance, tion are, of course, notinstantaneous in
N n v Scicnfisf. vol. 22. pp. 352-355; May, 1964. either time or space. This indicates a third Manuscript received June 23.1964.

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