584 IEEE TRANSACTIONS ON ELECTRON DEVICES, JUNE 1976

Correspondence _.

Saturation Velocity of Electrons in GaAs

Abstract-The saturation velocity of electrons in n-GaAs has been deduced from the ulE characteristic over a temperalure range 130-400 K. The experimental values are compared with those predicted by a model assuming the velocity to be limited by intervalley scattering in the (100) valleys. The agreement be- tween theory and experiment is very good if a value of 0.42n~o is used for the effective mass in the (100) valleys.

12 ,

40 50 60 70 80 90 100 110 120 130

E l e c t r i c Fie ld lkV/cml

Fig. 1. u/E curves showing extrapolations to higher fields, tempera- tures from top to bottom are 130,158,210,250,300,340,400 K.

I. INTRODUCTION GaAs is being increasingly used in both transferred electron

and IMPATT oscillator devices. In the design of these devi.:es, it is important to know the saturated electron drift velo'ity over the range of temperatures in which these devices might be expected to operate. Recent experimental curves of u ( E ) in GaAs have been published for a range of temperatures [l]. These curves show the electron velocity tending towards srku- ration at the highest values of electric field used (-85 kV/cm). The saturated velocity a t 400 and 450 K has been determi :led by Kramer and Mircea [2] from a comparison of the measured and calculated small-signal impedence of IMPATT devi ::es. An indirect measurement of the u(E) characteristic up t c 90 kV/cm has been made by Bastida e t al., [3] from the measured relation between the current and voltage in a Gunn diode u r - ing the transit of a domain. This measurement was, taken at room temperature. Measurements a t high fields have d s o been presented by Pokorny and Jelinek [4] and Riginos 151, both at room temperature. The values of the saturated drift velocity deduced from these previous measurements (see 3g. 2) do not agree with each other.

Theoretical u ( E ) curves [6], [7] in GaAs have not been avail- able to such high electric fields because of the uncertaint:? in the scattering mechanisms and the band structure away fmm the central minimum. Experimental results are given below which show the temperature variation of the saturated drift velocity. We present a theoretical estimate of this ve1o:ity based on the assumption that the velocity contribution co~nes solely from electrons occupying the (100) satellite valleys.

11. EXPERIMENT The velocity-field characteristic was determined by ];he

time-of-flight technique [l]. The samples used were epilapers of liquid phase GaAs on an n+ substrate. The layers were de- pleted of free electrons by reverse biasing a Schottky bartier formed at the surface of the layer. An ohmic contact was formed on the n+ substrate. A bunch of electrons creEted under the Au Schottky barrier by energetic electron bomlrrrd- ment drifted to the ohmic contact under the action of an ap- plied voltage. The motion of the electron bunch induced a d:ur- rent in the external circuit which persisted for a time T ec,ual to the bunch transit time across the epilayer. If the velocty- field characteristic has the form

Manuscript received December 22,1975; revised February 4,1956. The author is with the Natural Philosophy Department, University

of Strathclyde, Glasgow, G4 ONg Scotland.

TABLE I Constants A and B for the Curves of Fig. 1

Temp. ( O K 1 A lsicrnx10'81 r. I s / V X ~ C ~ ~ ~ I . - - __ .-

130

8.35 21 0 7.55 158 5.79

3w 9.1s 4.s93 250

-~

__-. - - -. .-

.- __ - 120-55kVicml 155-103kVicm!

8.5 6 . 2 7 4

3 3 R 4 9 . 7 1 ~

340 IZ0-5SkYkm!

12.3 155-113kVic1ni

9.91

_. . Z L i L 1

4 0 0 17.95 3.27 1

where A and B are constants and E the electric field, then the transit time T is given by

T =

= A l + B V

where V is the total voltage across the epilayer of thickness 1. Equation (2) indicates that the transit time is dependent only on the total voltage across the sample and not on the shape of the field profile when u ( E ) has the form given by (I).

A plot of T versus V yields a straight line from which A and B , and hence v(E) , can be determined. If the field variation across the layer is small, the velocity is simply given by

u ( E ) = - 1 T

where V E = -. 1

The u ( E ) characteristic was determined in the field range 30 kV/cm up to breakdown by finding the constants A and B. The u(E) characteristics thus determined at different temper- atures are shown in Fig. 1 for fields >40 kV/cm. Two of the r/V curves obtained were best approximated by two straight line sections, and values of A and B were obtained from each section. The constants A and B are shown in Table I. The ve- locity continues to decrease slowly with increasing electric field a t all temperatures used. Although the field variation across the sample was considerable (30 kV/cm in some cases),

CORRESPONDENCE 585

0

0 103 200 300 LOO 50G

Temperaturei°Kl

Fig. 2. Saturated drift velocity versus temperature. 0-present ex- periment; A-Pokorny and Jelinek [4]; +-Riginos [5]; X-Bastida et al. [3]; 0-Kramer and Mircea [2]; - - --Theory, m* = 0.35mo; _ _ Theory, m* = 0.42mo.

equations (3) and (4) could have been used for determining the u ( E ) curves a t high fields with little error because of the slow variation of v with E.

The u ( E ) curves are seen to be parallel to one another and tend towards a saturation velocity for the higher temperature curves. Avalanche breakdown, which occurs a t lower fields for lower temperatures, determined the highest field that could be tolerated. The lower temperature curves were extrapolated towards velocity saturation, assuming them to have the same shape as the higher temperature curves. A plot of the saturat- ed velocity so determined versus temperature is shown in Fig. 2.

111. THEORY Theoretical calculations of the u ( E ) characteristic [6j, [7]

are not usually taken to such high electric fields because of the uncertainty in the scattering mechanisms and the detailed band structure of GaAs away from the center of the Brillouin Zone. I t is generally assumed that equivalent intervalley scat- tering is the predominant mechanism in limiting the velocity in GaAs at very high electric fields [a]. If it is assumed that all of the electrons occupy the (100) valleys a t the very high elec- tric field values of interest here, then the velocity would be controlled entirely by equivalent intervalley scattering be- tween the (100) valleys. Intervalley scattering is identical in form [8], [9] to nonpolar optical phonon scattering, except for the value of some of the scattering parameters. Here we make use of an expression used by Nag [9] for nonpolar optical pho- non scattering. Using the fact that the carrier energy is much greater than the phonon energy (Le., the relaxation times ap- proximation is valid), the solution of the Boltzmann transport equation enables an expression for the current density as a function of electric field to be derived. This equation is

where

p ( E ) = 2 ( e E ) 2 T ~ T ,

3 m* kTL T~ momentum relaxation time constant T, energy relaxation time constant e electronic charge

E electric field m * effective mass TL lattice temperature k Boltzmann constant njj number of phonons with energy hwjj wjj phonon angular frequency associated with collision

process.

At very high electric fields the second tern1 in the square root bracket in ( 5 ) is negligible compared to p ( E ) . From ( 5 ) , a t -very high electric fields, we get an expression for the satura- tion velocity

where

njj = l/[exp (hwjj/kTL) - 11. On the assumption that all of the electrons occupy the (100)

valleys and that intervalley scattering is predominant, equa- tion (6) gives the saturated drift velocity as a function of lat- tice temperature. This equation is applicable to intervalley scattering as well as to optical phonon scattering. This is be- cause the short wavelength phonons associated with interval- ley scattering all have approximately the same frequency and are similar in characteristics to the long wavelength optical phonons. The assumption of the carrier energy >> hwjj used in the derivation of ( 5 ) i s equally applicable to both processes a t very high electric fields.

The theoretical saturated velocity is shown as a function of temperature in Fig. 2, for a phonon temperature hwjj/k = Tjj = 346 K and effective mass m* = 0.35mo (broken curve). These values for Tjj and m* are the ones used by Fawcett, Boardman, and Swain [6] in their Monte Carlo calculations of u/E. There is a degree of uncertainty in what value to use for m * ; assuming intervalley scattering, only a value of 0.42mo gives better agreement with the experimental results as shown in Fig. 2 (full curve). As Fawcett, Boardman, and Swain point out, this alteration in effective mass can be compensated for by a change in the intervalley deformation potential so that their calculated ulE curves are still in good agreement with the experimental results a t low fields.

IV. CONCLUSIONS We have presented experimental curves for the variation of

the saturated velocity of electrons in GaAs with temperature which should be useful for the design of hot electron devices such as IMPATT oscillators and Gunn diodes. Our curve is compared with other measurements in Fig. 2 and shows good agreement with the extrapolated values from the results of Bastida et al. [3] and Pokorny and Jelinek [4 ] . The saturation velocity agrees well with that calculated using a model which assumes intervalley scattering as being dominant in the (100) valleys, if an effective mass of m* = 0.42mo is used. The u ( E ) data presented here should also be useful for comparison with theoretical u ( E ) curves in the high field region.

REFERENCES [l] P. A. Houston and A. G. R. Evans, “Temperature dependence of

the high-field velocity of electrons in nGaAs,” Electron. Lett., vol.

[2] B. Kramer and A. Mircea, “Determination of saturated electron velocity in GaAs,” Appl. Phys. Lett., vol. 26, p. 623, June 1975.

131 E. M. Bastida e t al..’ “Indirect electron drift velocitv versus elec-

1, p. 210, May, 1975.

L ,

tric field measurements in GaAs,” Appl . Phys. Lett.,“vol. 18, p. 28,

[4] J. Pokorny and F. Jelinek, “Experimental nonsaturating velocity- Jan. 1971.

field characteristic of GaAs,” Proc. IEEE (Lett.), vol. 60, p. 457, Apr. 1972.

[5] V. E. Riginos, “Non-saturatin velocity-field characteristic of

Appl. Phys., vol. 45, p. 2918, July 1974. GaAs experimentally determine: from domain measurements.” J.

586 IEEE TRANSACTIONS ON ELECTRON DEVICES, JUNE 1976

[6] W. Fawcett, A. D. Boardmgn, and S. Swain, “Monte Carlo deter- mination of electron transport properties in GaAs,” J. Azys.

[7] J. G . Ruch and W. Fawcett, “Temperature dependence of the Chem. Solids, vol. 31, p. 1963, Sept. 1970.

transport properties of GaAs determined by the Monte Csrlo method,” J. Appl. Phys., vol. 41, p. 3843, Aug. 1970.

[8] E. M. Conwell, High Field Transport in Semiconductors. I+lew York Academic Press, 1967.

[9] B. R. Nag, Theory of Electrical Transport in Semiconductors. London: Pergamon Press, 1972.

Glass Envelope UV-Sensitive Flame Detectors

HOMER H. GLASCOCK, JR.

Abstract-The need for fast-response low-voltage flame sen- sors, able to operate for long periods in ambients presentirg a wide range of temperatures, prompted the construction amd testing of gas amplification UV-photosensitive detectors utilliz- ing 9741 glass envelopes and a variety of gas fills and electrode and getter materials.

Addition of 1 mole percent Hz to a He gas fill reduced the re- quired minimum time between counts for a given sensor ope rat- ing voltage without significantly changing the threshold volhge. All sensors with Hz additive ultimately became solar sensilive. Sensors performed well at temperatures as high as 350°C.

I. 1 NTRODUCTION

Geiger-Muller-type tubes responding to ultraviolet ( 1 JV) photons have been used as flame detectors for a number of years. A low operating voltage wide ambient tempern’xre range form of this device is discussed in [l]. This device re- quires external quenching of the discharge and is limited to counting rates less than 2 kHz.

Commercially available detectors have ultraviolet trans ?ar- ent glass envelopes and a fill of hydrogen gas. These detectors operate at high voltage (of the order of 800 to 1000 V), :fre- quently lose their solar blindness after operating for a w:>ile, and are limited in the maximum ambient temperature which can be used (probably because of gas release from the lube walls).

Hydrogen filled devices rapidly recover after a count. This allows high counting rates so that sufficient information lor a yes-or-no flame decision can be accumulated in a short time. In terms of operating a flame sensor, the practical minimum time between pulses is that value at which the sensor counting rate begins to increase significantly because of a memor:r ef- fect. This memory effect is due to any excited (or ionized) molecule which provides a free electron capable of initiating a new discharge in the process of being deexcited (or neutral- ized). Metastable atoms are primary offenders since they may yield ultraviolet photons long after the ions have beer. re- moved from the gas [2].

Rapid recovery depends upon the presence of a diatomic or polyatomic gas [3]. Choice of the gas is restricted by the fact that it must not adversely affect the cathode which in many applications should have a work function near 4.5 eV. Tho gas should not decompose at the highest temperatures ex:seri- enced by the sensor and the gas should not have metastable

Manuscript received January 5,1976; revised January 22,1976 The author is with Corporate Research and Development, General

Electric Company, Schenectady, NY 12301.

k 2 5cm - ,9741 GLASS

OLYBDENUM ANODE IGHT COLLECTOR

FERN1 CATHODE FN

BACK PLATE

Fig. 1. Glass envelope flame sensor (schematic).

states. These restrictions remove nearly all gases as candidates except hydrogen [a], [4]. While hydrogen has a rather high breakdown potential, satisfactory low voltage operation may be achieved if it is used as an additive to noble gases.

11. SENSOR ASSEMBLY The sensor envelope shown in Fig. 1, was formed from 9741

UV transmitting glass and a conventional vidicon stem made from FN glass. The cathode was in the form of a rod with its hemispherical end positioned about 1.3 mm from the molyb- denum anode so that light reflected from the anode impinged upon the cathode. Molybdenum is easy to fabricate into hemi- spheres, is relatively inert, and has a high reflectivity in the ul- traviolet. Cathodes were formed from tungsten, molybdenum, and tantalum which after cleaning, exhibited spectral re- sponses in good agreement with the literature values of their work functions.

Noble gas filled sensors were gettered with titanium, while aluminum and copper were used in detectors containing some hydrogen. The getter material was mounted on the back of the anode for radio-frequency heating and evaporation onto the tube wall. The mole percent gas mixtures used were (99.5 per- cent He + 0.5 percent Ar), (99 percent He + 1 percent Hz), and (99 percent Ne + 1 percent Hz). At 22OC, the minimum breakdown voltages of these compositions are very similar over the pressure range 10 to 150 torr.

111. SENSOR PERFORMANCE Glass envelope sensors with titanium getters employing

(99.5 percent He + 0.5 percent Ar) fill performed satisfactori- ly, but required larger minimum times between count than did the metal-ceramic variety, probably because of contaminating gas release from the glass envelope [l]. These sensors could be operated for a t least a few hours at 300°C with no ill effects. No long life tests were run. Operation at 4OOOC caused signifi- cant reduction in the operating voltage range. The threshold wavelength of sensors filled with this noble gas mixture were representative of the work function of the clean metal cath- ode.

Molybdenum and tungsten coil cathodes were found to per- form in a manner similar to rod cathodes. Use of a coil made it possible to keep the cathode warm in a cool ambient which can increase the operating voltage range by 50 percent or more without introducing significant thermionic background. The mechanism giving rise to this effect is not understood.

The performance of sensors filled with (99 percent Ne + 1 percent Hz) and (99 percent He + 1 percent Hz) gas mixtures were very similar. The (99 percent Ne + 1 percent Hz) mixture may be useful if loss of He by diffusion through the sensor en- velope proves to be important. Because of the relatively high light output in the visible region produced by the discharges in the Ne mixture it was possible to see .individual counts oc- curring. A1 proved to be superior to Cu as a getter in tubes containing Hz.

A representative glass flame sensor contained a tungsten rod cathode, a molybdenum anode, an aluminum getter, and a fill of 75 torr of (99 percent He + 1 percent Hz). Measure- ments made of 10-s response to a standard flame versus mini-