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The Schottky barrier cold cathode
Solid-State
Electronics
Pergamon
Press 1969. Vol. 12, pp. 945-954.
THE SCHOTTKY
BARRIER COLD
C. A. STOLTE, Hewlett-Packard
Printed
J. VILMS
Laboratories,
in Great Britain
CATHODE*
and R. J. ARCHER
Palo Alto, California
94304,
U.S..%.
(Received 30 April 1969)
Abstract-Cathodic vacuum emission from forward biased, rectifying contacts between n-type Gap, ZnSe and ZnS and thin Ag films covered with a monolayer of Cs agrees with a simple theory which assumes isotropic scattering of hot electrons on transmission through the interface between the semiconductor and the Ag. The maximum measured emission efficiency is 6 x 10 -3 per cent but at least 2 per cent is expected with further development. RBsume-L’emission cathodique a vide des contacts redresseurs directement polarises entre le ZnS, ZnSe et GaP de type n et les pellicules fines d’Ag couvertes d’une couche simple de Cs s’accorde avec une theorie simple qui presume l’eparpillement isotropique des electrons chauds dans la transmission a travers l’interface entre le semiconducteur et l’argent. Le rendement d’emission maximum mesure est de 6 x 10 - 3 pour cent mais on atteindra 2 pour cent dans de futurs modeles developpes. Zusammenfassung-Die Vakuumemission von als Kathode geschalteten gleichrichtenden Kontakten zwischen n-Typ Gap, ZnSe oder ZnS und dunnen Silberfilmen, die mit einer monoatomaren Cs-Schicht belegt sind, wird durch eine einfache Theorie erkllrt. Dabei wird vorausgesetzt, dass heisse Elektronen beim Durchtritt durch die GrenzAPche zwischen Halbleiter und Silberschicht isotrop getreut werden. Der maximale bisher beobachtete Emissionswirkungsgrad ist 6 x 10 - a Prozent, aber mindestens 2 Prozent sind hierfiir nach einer weiteren Entwicklungsarbeit zu erwarten.
1. INTRODUCTION
THE USE of a Schottky barrier at a metal-semiconductor contact to inject electrons through a thin metal film was first proposed by ATALLA and has been discussed by several authors,(2-4) and electron emission from such a structure has been reported.‘“*“) An experimental study of this device has been conducted using Ag contacts to various semiconductors with large Schottky barrier heights. Cs monolayers were used to lower the vacuum work functions of the thin Ag films. 2. THEORY OF THE COLD CATHODE The mechanism of cathodic emission in the metal-semiconductor cathode is represented in
Fig. 1, which depicts electron potential energy in different parts of the structure under normal operating voltages. When the diode is forward biased as shown, electrons are injected into the thin metal film. In the absence of scattering, these electrons remain at an energy slightly above the top of the Schottky barrier, and move ballistically through the metal film. If the metal-vacuum work function &, is lower than the Schottky barrier +B, and the metal film is thin enough for ballistic transit, a large fraction of the electrons can be emitted into the vacuum and collected at the anode. The hot electron current density over the forward-biased barrier is given byc7) JH = J,,,(exp(qvnlnW
* Work supported in part by the Air Force Cambridge Research Laboratory, Office of Aerospace Research, USAF, Bedford, Massachusetts under Contract No. F19628-68-C-0090.
945
- 1)
(1)
where K is Boltzmann’s constant, q is the electronic charge, T is the absolute temperature, I’, is the forward bias voltage, and n is a number close to 1.
C. A. STOLTE,
946
J. VILMS
and R. J. ARCHER where A4 = L?,-- Es = y$,- dn. Equations (4) are derived assuming:
(3) and
1. Maxwellian distribution of the electron momenta at x1 in the semiconductor; 2. negligible electron-phonon and other scattering in the region between x1 and x2; 3. isotropic elastic scattering into the positive half-sphere of momentum at the interface at
LA’ V@l.
.;$!p
v
A
FIG. 1. The Schottky barrier cathode under normal operating voltages, showing the variation of electron potential energy E as a function of distance x.
The saturation
current is given by
J sat = AT2 e-dB/kT
(2)
on the simplest theory, where A is the appropriate Richardson’s constant.(8) The cathodic emission current density, JA, is therefore given by
JA = JHf(s,$)
exp(-
3
(3)
where Wis the metal thickness, LB is the ballistic mean free path of the injected electrons in the metal, and f is given by
Assumption 3 was judged to represent best the nature of electron transport across an interface having a significant degree of irregularity on an atomic scale, which is the case for our devices. Assumption 2 probably leads to a slight overestimate of cathodic emission expected from a practical device. Important characteristics of the cold cathode are its emission efficiency 7, the energy spread of the emitted electrons, and the variation of emitted current with bias voltage on the Schottky barrier diode. The theoretical cathodic emission efficiency, for current transport, is given by (3) and (5) as
J.4 y=J= H
Max(E,,E,)
x exp( - E/kT)
x2; transmission coeffi4. a quantum-mechanical cient of unity at x2; 5. zero escape probability for electrons scattered in the metal; dependence of the escape 6. step-function probability at xa on the perpendicularly directed component of the electron energy; and 7. sufficiently large anode voltage to insure the absence of space charge for x > xa.
2kT+A$ 2E, dE
expt-2)
exp(-
3,
A+>0
(4)
where E is the electron energy in the metal. In the practical case of large values of I& and E,, (4) reduces approximately to
[I-(I-z)(Jz)]
e,p(-~)sbc
(6) The principal features of the device efficiency, as seen from (6), are that in the case of A+ > 0, the efficiency is a strong function of A# and T. For A+ < 0, the efficiency is almost independent of T and only slowly varying as a function of A$. In
THE
SCHOTTKY
BARRIER
general there are components of forward current other than electron emission over the barrier and correspondingly the measured efficiency is expected to be smaller than given by (6). Experimental values of the slope constant n greater than 1.1 indicate significant leakage contributions to the current. The emitted electrons have a narrow energy spread several kT wide and centered slightly above the larger of the two energies ES or E, as given by the integrand in (4). The barrier voltage dependence of JA is governed by the hot electron component JH of the barrier current density and is given by (1) and (6) as JA =
qJsat[exp(z) -11
(7)
where 77and Jsat are nearly independent of Va. The value of n is about 1.00-1.10 by either the emission or the diffusion theory of the Schottky barrier. 3. EXPERIMENTS
AND
RESULTS
Our choice of materials for the experimental devices was determined by the requirements of (1) control of semiconductor properties and processing, (2) Schottky b arrier heights comparable to or larger than vacuum work functions, (3) large ballistic mean free paths in the metal, and (4) inertness of the metal to Cs. Devices were fabricated
Contacting Probe
Header
OhmicConioct
FIG. 2. Schottky barrier diode structure employed cathodic emission experiments.
in
COLD
CATHODE
947
using Ag on n-type GaP, ZnSe, and ZnS, with the geometrical configuration depicted in Fig. 2, and were cesiated to lower the work function of Ag. The semiconductor samples were of single crystal material having an electron concentration of 1Ol6 - 1018 cm- 3. Established ohmic contacting methods were generally applied. The semiconductor surfaces were prepared by chemical etch-polishing techniques, developed with the aid of ellipsometric measurements of surface film thickness in addition to investigation of the electrical properties of Schottky barrier diodes formed on the surfaces. Either a Ag or a Pt contact stripe was evaporated in a high vacuum station after which the device was transferred to an ultrahigh vacuum chamber. Baking at 200-250°C for 6-16 hr was employed to obtain a base pressure of 10-ll-lO-lo Torr, after which the thin Ag film of 0.84 x 10e2 cm2 area was evaporated through a circular mask at a pressure of 1O-1o-1O-8 Torr. Cs was deposited from a low energy ion beam which allowed the deposition of controlled submonolayer amounts and a determination of the surface coverage of the metal.‘g) The vacuum work function was determined after each application of Cs by the photoemission technique. Cathodic emission measurements and evaluation of the Schottky barriers were performed in the ultra-high vacuum chamber, utilizing the evaporation mask, spaced about 0.15 cm from the sample, as the anode. Details of device preparation and experimental results for the three semiconductors are given below. (a) Gap-Ag experimental results Both vapor and melt grown materials were used. The vapor grown material, obtained from Bell Telephone Laboratories, Incorporated, had a carrier concentration of 3 x 1016 cmM3 and a Hall mobility of 160 cm2/V-set and the melt grown material supplied by Eagle-Picher Industries, Incorporated, had a carrier concentration of l-3 x 101scm-3andaHallmobilityof80cm2/V-sec. An alloyed Au-Sn ohmic contact was employed. An H,SO,-H202 etch was used in the chemical preparation of the GaP surfaces, giving an ellipsometrically determined surface film thickness in the range of 14-19A. Details of device fabrication for GaP and the other materials are also discussed in References 5, 10, 11 and 12.
948
C. A. STOLTE,
J. VILMS
and
R. J. ARCHER
Table 1. Device parameters and emission eficiency of Gap-Ag-Cs Sample
W-Q
n
dr-,(eV)
&(eV)
&(eV)
3 4 6 7
280 300 160 270
1.19 1.73 1.40 1.54
1.31 1.38 1.51 1.56
1.32 1.92 1.45 1.46
GaP No. 8
270
1.31
1.45
1.47
1.40 1.54 1.41 1.371.58 1.341.52
GaP GaP GaP GaP
No. No. No. No.
Table 1 summarizes the properties of the five Gap-Ag devices that were investigated. The first column gives the sample number and the second the thickness of the Ag film. The Schottky barrier properties obtained at the time of the cathodic
K
cold cathode
&(eV)
J*(A/cms)
?,,,=IAIIB
?,e”‘iLB
1.8
1.67 1.51 1.41 1.44
1.1 x10-Q 2.7~10-~ 5.9x10-G 9.2x10-’
4.3x10-10 2.3 x~O-~ 5.0x10-6 3.6x10-:
1.4x10-9 8.1 x10-’ 9.8x10-6 1.1 x10-6
3.5
1.39
1.5x10-’
1.3 x10-s
4.0 x 10 -5
measurements are given by the next five columns. The experimental slope constant, 11, of the forward I-V characteristic indicates the degree to which the current is ideal hot electron emission. The three standard measurements-saturation
18 (Amp)
FIG. 3. Variation of barrier current, Is, and emission current, Ia, as functions of applied barrier voltage, vTg, for cold cathode device GaP No. 8, as measured and after correction for series IR drop.
THE
SCHOTTKY
BARRIER
current, differential capacitance, and photoemission threshold-were used to measure the Schottky barrier heights. The barrier height derived from the I-V characteristics is calculated from (2) with Jsat determined from the intercept of the straight line defined by the highest I-V point, corrected for series IR drop, and a slope constant of 1.01. The 1,-v, characteristic of the Schottky barrier of GaP device Ko. 8 is shown in Fig. 3 as an example. Thebarrierheightfromcapacitanceisdetermined -from bc = Vat-AT/q+5
(8)
.where -V, is the voltage intercept of Ce2 vs. zapplied voltage and 5 is the Fermi level. An example is shown in Fig. 4. The value of $p, the photoemission threshold,
COLD
CATHODE
was determined by measuring the internal photoemission and fitting these data to a Fowler curve as illustrated in Fig. 5.(13) In Fig. 5, and in most cases, the data are fit by the sum of two Fowler curves having different +p values presumably owing to a patch effect. In these cases the values of K = Z&/K, are the ratios of efficiencies of the two responses. The value of the vacuum work function dv of the cesiated Ag film was determined, at the time of cathodic measurements, by measuring the photoemission of electrons from it into vacuum and fitting the yield data to a Fowler curve as shown, for example, in Fig. 6. The value of & increased with time. In the worst cases time constants were on the order of minutes (pressure - 10-r’ Torr) although stability of the order of a day was observed in one device. The effects of this instability were circumvented by repeated applications of
I i .I
1.0, t
0.9
1
-I 0.8
‘;
:07 zz
1
f :
0.6’
“u > 0.5
r
0.4 -
0
FIG. 4.
919
I
I
-0.5
-1.0 V&mts~
I
-1.5
I
- 2.0
1
-2.5
Differential capacitance-voltage characteristic for cold cathode device GaP No. 8.
C. A. STOLTE,
J. VILMS
and
R. J. ARCHER
-
t10-e
FIG. 5. Schottky barrier photoemissive yield vs. hv for cold cathode device GaP No. 8. Data points are experimental values; solid lines are the two theoretical Fowler curves which add to fit the data and have the values of the adjustment parameters indicated by arrows. sub-monolayer amounts of Cs between measurecathodic emission ments, and by performing measurements within minutes after applying Cs. Cathodic emission data are presented in the last three columns of Table 1. The d.c. cathodic emission current density, JA = IJO. x 10v2 cm2, was measured at room temperature with no significant heating due to diode current. An anode voltage of 30V was sufficient to produce saturation. IA/r, is the measured efficiency q,,, for the given device, IB being the Schottky barrier current. The value presented in the table is the maximum value obtained for each sample, measured immediately following cesiation to insure the lowest value of vacuum work function, and at a large value of IB to insure a minimum excess current contribution. The value of ymew’L~ is the efficiency adjusted to zero metal film thickness and is included to facilitate comparison of the results for different devices. An L, value of 24OA, appropriate for electrons of energy 1.40 eV? was assumed.‘r4’
1.3 t 1.5 @v
1.7
Photon
1.9
Eneqy(eV1
2.1
2.3
2.5
FIG. 6. Vacuum photoemissive yield vs. hv for cold cathode device GaP No. 8.
(b) ZnSe-Ag
experimental results
Al-doped, melt-grown ZnSe was obtained from Eagle-Picher Industries, Incorporated, and converted to low resistivity by heating in liquid Zn for 3-7 days. (r5) Typically the carrier concentration was 3x1016cm-3 and the Hall mobility 400 cm2/V-set for this material. The ZnSe contained stacking faults as revealed by preferential etching. A Ga-In alloy ohmic contact was applied, producing contact resistances on the order of 0.1 Q-cm2. The ZnSe surface was chemically prepared with a potassium dichromate-sulfuric acid etch followed by a cyanide rinse which gave an ellipsometric surface film thickness of about ISA. A total of four ZnSe-Ag devices were measured with the results shown in Table 2. The values in this table were derived by the same techniques as those for GaP in Table 1. The I-V characteristics of samples Nos. 5, 6 and 8 were not available; in an attempt to reduce the likelihood of front surface contamination by Ga-In, these samples had a large-area rectifying Pt back contact instead of an ohmic contact.
THE
--
-
Sample
SCHOTTKY
BARRIER
COLD
Table 2. Device parameters and emission eflciency of ZnSe-Ag-Cs 72
W(A)
&Se No. 1 ZnSe No. 5 ZnSe No. 6
300 300 300
3.0 -
ZnSe No. 8
850
-
+I-.v(eV)
&(eV)
&(eV)
1.25 -
1.53 -
1.47 1.20 1.221.47 1.351.55
-
-
In the case of ZnSe No. 8, the cathodic efficiency was measured at several different values of the work function by allowing the work function to relax and re-cesiating to lower the work function. The observed variation of the cathodic emission efficiency, vmeWILBas a function of the A+ measured for this sample is plotted in Fig. 7. These data were obtained at an I,-value which was sufficient to ensure that the excess current contribution to In was negligible. Figure 8 shows the variation of efficiency as a function of IB and illustrates a lowering of efficiency at small In-values due to excess Schottky barrier current.
K
&(eV)
951
CATHODE
cold cathode
Ja(A/cmZ)
~,=1,Jla
v,,,ew“B
2.0
1.35 1.40 1.37
7.1 x10-4 2.6x10-s 1.3 x10-7
6.0 x~O-~ 1.0x10-7 5.0x10-s
2.1 x10-4 3.5 x10-7 1.6x10-j
1.2
1.49
6.4~10-~
5.4x10-6
1.8~10-~
I
I
1
I
1
I
j
I
“I
I
I
1
10-e
IdIE
10-7
eL
lo-=
10-q
I
!
‘1
IO"
FIG. 8. Dependence of cathodic emission efficiency on barrier current; cold cathode device ZnSe No. 8.
(c) ZnS experimental results
10-I t.6’
I +.4
I t.2 A&v,
I
I
I
0
-.2
-.4
I
FIG. 7. Dependence of cathodic emission efficiency on barrier height difference for cold cathode device ZnSe No. 8.
Al-doped, melt-grown ZnS was obtained from Eagle-Picher Industries, Incorporated, and rendered conducting by heating in liquid Zn at 900°C for 3-7 days, after which the material had a carrier concentration in the range of 0.3-2x 1Ol7 crnb3 and a Hall mobility of 60-100 cm2/V-sec. The crystals contained stacking faults. Ga-In contacts were generally used and had ohmic contact resistances of about l-5 Q-cm2 on ZnS. The ZnS surface was prepared by etch-polishing in a bromine-methanol solution on a fiber pad with the sample held by a teflon fixture, and had an ellipsometric surface film thickness of 10-246.
/
C. A. STOLTE,
952
J. VILMS
and
R. J. ARCHER
Table 3. Device parameters and emission ejiciency of ZnS-Ag-Cs Sample
WA)
a
ZnS No. 1 ZnS No. 2
280 600
1.4 -
ZnS No. 3
400
ZnS No. 12 ZnS No. 16
&-y(eV)
Cc(eV)
+e(eV)
K
1.27 -
1.30
2.0
-
-
-
900
-
-
-
410
-
-
1.20 1.391.58 1.371.57 1.401.75 1.191.40
Cr(eV)
cold cathode Tlrne’V /LB
JA(A/cm2)
~,,=~~/IB
1.45 1.35
7.1 x10-s 6.5 x10-s
6.0~10-~ 5.5x10-s
1.9x10-s 6.7 x~O-~
1.4
1.50
7.1 x10-s
6.0x10-s
3.2 x~O-~
4.0
1.61
1.2x10-9
1.0x10-*
5.0x10-7
4.1
1.56
3.5 x10-s
5.8x10-a
3.6~10-~
Results for five ZnS-Ag samples investigated are given in Table 3. The barrier I-V data are not available for four of these due to deterioration of the ohmic contact during vacuum bake out. For ZnS, the barrier heights obtained during the cathodic emission experiments were significantly less than those obtained in the preliminary studies because of ZnS surface instability during vacuum bake-out or contamination at some point in the overall fabrication procedure. 4. DISCUSSION
1
OF RESULTS
The data support the model for the cold cathode and establish that the cathodic emission results from the injection of hot electrons into the metal. Field emission is ruled out because of the dependence of cathodic emission current on the applied anode voltage. The results from one such experiment are given in Fig. 9. The observed threshold at 1OV is caused by a cut-off field produced by the large difference in the work functions of the cesiated metal pad and the surrounding semiconductor. Further experimental investigation of the threshold using the photoemission from the metal substantiated this explanation. The complete saturation of the cathodic current with anode voltage is conclusive evidence that the devices do not operate by field enhanced electron emission. Theory predicts that the cathodic emission current should have the same barrier voltage dependence as the hot electron component of the barrier current. As indicated in Tables 1-3, the barriers used in this investigation had n values ranging from 1.19 to 3.0. These large n values are
,IB=5x10-4Amp VS'O.798Y
-r-i-
i _
3
!:/FIG. 9. Variation of cathodic emission current Ia as a function of anode voltage V, for two different biases on the Schottky barrier; cold cathode device ZnSe No. 1.
interpreted as a barrier current comprised of a hot electron current in parallel with an excess current which has a weaker voltage dependence. Typical curves, shown in Fig. 3, 1.4-v&? and 1,-V, illustrate the different voltage dependences of IA and In. The emission current, IA, has an n-value
THE
SCHOTTKY
BARRIER
of 1 .Ol in agreement with theory, and corresponding to the hot electron current, whereas the barrier current, In, has an n-value of 1.31. This rejection of the excess current component by the emission mechanism was observed in all of the samples investigated. The detrimental effect of excess current is to lower cathodic emission efficiency at low values of 1, as illustrated in Fig. 8. At sufficiently large values of barrier current, the excess current is not a significant portion of the total barrier current and does not lower the measured efficiency. The dependence of the emission current on temperature was indirectly observed. The theory predicts that in the case of &, > +n, the efficiency is proportional to eMA*jkT. An increase in anode current with time at large diode currents was observed in samples which had a fairly large A+, 0.2-0.3 eV, and in particular in those samples with a highly resistive back contact. For one sample with a barrier difference of 0.3 eV, the increase in anode current indicated a temperature rise of 50°C on the basis of the theory. Surface temperature measurement of the sample under the same conditions using an infrared detector indicated the temperature rise to be no greater than 60°C. The measured cathodic efficiency, TmeWiLB, adjusted to zero metal thickness, is plotted in Fig. 10 as a function of the measured A+. As seen in Tables 1-3, the values of r/s determined by the three techniques are in good but not exact agreement for any given device. The smaller value of +p was used for +B in establishing the value of A# at the indicated data points. This is justified on the assumption that the double Fowler fit results from a patch effect with two regions with different barrier heights, one characterized by the upper and the other by the lower value of $p. The latter would dominate the total hot electron current. The error bars indicate the range of A+ when both the &- and the lower +,-values for +n are used. The scatter in the data is due to the imprecision of the values of 4s and +v. Since both are about 1.5 eV, a 10 per cent error in measurement would result in an error in the difference as large as 0.3 eV. The best data for testing the dependence of efficiency on A+ are those shown in Fig. 7, where the values of A+ were determined on a single sample with all conditions constant except the
COLD
CATHODE
953
--I
A@(evl
FIG. 10. Dependence of cathodic emission efficiency on barrier height difference. Circles (0), squares (Cl), and triangles (A) give the maximum measured efficiency for the Gap-Ag-Cs, ZnSe-Ag-Cs, and ZnS-Ag-Cs devices, respectively; the dashed line (- - -) is the least squares line from Figure 7; the solid line (---) gives the theory, (6), evaluated for variable Ev, Ei = 8.9 eV, T = 298”K, and W = 0; and the dot-dash line (.-.-*-) is the alternative theory, (9), evaluated using W = 0 and m/m* = 5.
value of +v. The dashed line in Fig. 10 is the least squares line from Fig. 7. The solid line in Fig. 10 is the theoretically predicted T-A+ relationship of (6), using W = 0, variable E,, and Es = 6.9 eV composed of $B = 1.40 eV and EF = 5.5 eV.(16) The agreement between the predicted results assuming isotropic scattering at the metal-semiconductor interface and the data from Fig. 7 is good. The data from all samples agree fairly well with the theory, although the emission efficiency of the GaP devices appears to be systematically too low. If conservation of transverse momentum is assumed at the metal-semiconductor interface instead of isotropic scattering, i.e. specular rather
C. A. STOLTE,
954
than diffuse refraction, efficiency would be
q=
then
the
theoretical
exp(-fj[l-(1-z)
xexp( --A$/(;-l)kT)] (s)
(1 ,
Acknowledgements-The authors wish to thank M. M. ATALLA, T. 0. YEP, P. E. GREENE, and R. A. BURMEISTER,JR., for helpful discussions, and to acknowledge the technical assistance of J. P. GARRETT, H. LUECHINGER,J. LITTLE and G. S. PECK.
REFERENCES 1. M.
W
x exp k~
and R. J. ARCHER
J. VILMS
(9)
which is shown in Fig. 10 by the dot-dash line. The better agreement of the data with (6) indicates that electrons are scattered on transmission across the interface. 5. CONCLUSIONS The model of the Schottky diode cold cathode and the device potential are established by the agreement of the experimental results with the simple theory describing the operation of the device. The maximum experimentally measured efficiency, 6 x 10e3 per cent, is below that deemed practical for broad device application but was limited by the inability to produce a sufficiently high Schottky barrier. This is a temporary limitation that will be eliminated by further development. The results, Fig. 10, indicate that an efficiency as large as 2 per cent would be obtained with a barrier height of 1.7 eV, for example, and the easily obtainable vacuum work function of 1.5 eV. A cold cathode with this efficiency would be a useful emitter in high performance vacuum tubes particularly in the high frequency range, in cathode ray tubes where the predicted narrow energy spread of electrons and the absence of the control grid would yield further flexibility in design, and in other applications where power or background light and heat are to be minimized.
2.
3.
4.
5.
6. 7.
8. 9. 10.
11. 12. 13. 14. 15. 16.
M. ATALLA, U.S. Patent No. 3,121,809, February 18,1964(filed September 25,196l). H. HEFFNERand M. COWLEY, Consolidated quarterly status rep. No. 13, Solid-State Elec. Research, Stanford Electronics Laboratories, p. 73 (December, 1961). D. V. GEPPERT, U.S. Patent No. 3,150,282, September 22, 1964 (filed November 13, 1962), and Proc. IEEE 54, 61 (1966). L. S. LERNER and R. J. ARCHER, Air Force Cambridge Research Laboratory Report AFCRL-66479 TAngust, 1966). R. J. ARCHER, J. COHEN and J. VILMS, Air Force Cambridge Research Laboratories Report AFCRLI68-0302 (June, 1968). R. WILLIAMS and C. R. WRONSKI, Appl. Phq’s. Lett. 13, (7), 231 (1968). M. M. ATALLA, VortrGge der 2. MikroelektronikTaaun~ des “Internationalen Elektronik-Arbeitin Munchen, Oktober 1966, R. kre;ses- eV” Oldenbourg Verlag, Miinchen, Germany (1967), 138-145. F. A. PADOVANI, Solid-St. Electron. 12, 135 (1969). R. E. WEBERand L. F. CORDES,Rev. Scient. Instrum. 37, 112 (1966). R. J. ARCHER, J. COHEN and J. VILMS, Air Force Cambridge Research Laboratories Scientific Report No. 1, AFCRL-684122 (March, 1968). Ibid., Scientific Report No. 3, AFCRL-684447 (September, 1968). Ibid., Final Report, AFCRL-68-065 1 (December, 1968). R. H. FOWLER, Phys. Rev. 38.45 (1931). S. M. SZE, C. R. CROWELL, G. P. CAREY and E. E. LABATE, J. appl. Phys. 37 (7), 2690 (1966). M. AVEN and H. H. WOODBURY,Appl Phys. Lett. 1 (3), 53 (1962). C. KITTEL, Introduction to Solid State Physics, 2nd
ed. p. 250. Wiley, New York (1956).
Electronics
Pergamon
Press 1969. Vol. 12, pp. 945-954.
THE SCHOTTKY
BARRIER COLD
C. A. STOLTE, Hewlett-Packard
Printed
J. VILMS
Laboratories,
in Great Britain
CATHODE*
and R. J. ARCHER
Palo Alto, California
94304,
U.S..%.
(Received 30 April 1969)
Abstract-Cathodic vacuum emission from forward biased, rectifying contacts between n-type Gap, ZnSe and ZnS and thin Ag films covered with a monolayer of Cs agrees with a simple theory which assumes isotropic scattering of hot electrons on transmission through the interface between the semiconductor and the Ag. The maximum measured emission efficiency is 6 x 10 -3 per cent but at least 2 per cent is expected with further development. RBsume-L’emission cathodique a vide des contacts redresseurs directement polarises entre le ZnS, ZnSe et GaP de type n et les pellicules fines d’Ag couvertes d’une couche simple de Cs s’accorde avec une theorie simple qui presume l’eparpillement isotropique des electrons chauds dans la transmission a travers l’interface entre le semiconducteur et l’argent. Le rendement d’emission maximum mesure est de 6 x 10 - 3 pour cent mais on atteindra 2 pour cent dans de futurs modeles developpes. Zusammenfassung-Die Vakuumemission von als Kathode geschalteten gleichrichtenden Kontakten zwischen n-Typ Gap, ZnSe oder ZnS und dunnen Silberfilmen, die mit einer monoatomaren Cs-Schicht belegt sind, wird durch eine einfache Theorie erkllrt. Dabei wird vorausgesetzt, dass heisse Elektronen beim Durchtritt durch die GrenzAPche zwischen Halbleiter und Silberschicht isotrop getreut werden. Der maximale bisher beobachtete Emissionswirkungsgrad ist 6 x 10 - a Prozent, aber mindestens 2 Prozent sind hierfiir nach einer weiteren Entwicklungsarbeit zu erwarten.
1. INTRODUCTION
THE USE of a Schottky barrier at a metal-semiconductor contact to inject electrons through a thin metal film was first proposed by ATALLA and has been discussed by several authors,(2-4) and electron emission from such a structure has been reported.‘“*“) An experimental study of this device has been conducted using Ag contacts to various semiconductors with large Schottky barrier heights. Cs monolayers were used to lower the vacuum work functions of the thin Ag films. 2. THEORY OF THE COLD CATHODE The mechanism of cathodic emission in the metal-semiconductor cathode is represented in
Fig. 1, which depicts electron potential energy in different parts of the structure under normal operating voltages. When the diode is forward biased as shown, electrons are injected into the thin metal film. In the absence of scattering, these electrons remain at an energy slightly above the top of the Schottky barrier, and move ballistically through the metal film. If the metal-vacuum work function &, is lower than the Schottky barrier +B, and the metal film is thin enough for ballistic transit, a large fraction of the electrons can be emitted into the vacuum and collected at the anode. The hot electron current density over the forward-biased barrier is given byc7) JH = J,,,(exp(qvnlnW
* Work supported in part by the Air Force Cambridge Research Laboratory, Office of Aerospace Research, USAF, Bedford, Massachusetts under Contract No. F19628-68-C-0090.
945
- 1)
(1)
where K is Boltzmann’s constant, q is the electronic charge, T is the absolute temperature, I’, is the forward bias voltage, and n is a number close to 1.
C. A. STOLTE,
946
J. VILMS
and R. J. ARCHER where A4 = L?,-- Es = y$,- dn. Equations (4) are derived assuming:
(3) and
1. Maxwellian distribution of the electron momenta at x1 in the semiconductor; 2. negligible electron-phonon and other scattering in the region between x1 and x2; 3. isotropic elastic scattering into the positive half-sphere of momentum at the interface at
LA’ V@l.
.;$!p
v
A
FIG. 1. The Schottky barrier cathode under normal operating voltages, showing the variation of electron potential energy E as a function of distance x.
The saturation
current is given by
J sat = AT2 e-dB/kT
(2)
on the simplest theory, where A is the appropriate Richardson’s constant.(8) The cathodic emission current density, JA, is therefore given by
JA = JHf(s,$)
exp(-
3
(3)
where Wis the metal thickness, LB is the ballistic mean free path of the injected electrons in the metal, and f is given by
Assumption 3 was judged to represent best the nature of electron transport across an interface having a significant degree of irregularity on an atomic scale, which is the case for our devices. Assumption 2 probably leads to a slight overestimate of cathodic emission expected from a practical device. Important characteristics of the cold cathode are its emission efficiency 7, the energy spread of the emitted electrons, and the variation of emitted current with bias voltage on the Schottky barrier diode. The theoretical cathodic emission efficiency, for current transport, is given by (3) and (5) as
J.4 y=J= H
Max(E,,E,)
x exp( - E/kT)
x2; transmission coeffi4. a quantum-mechanical cient of unity at x2; 5. zero escape probability for electrons scattered in the metal; dependence of the escape 6. step-function probability at xa on the perpendicularly directed component of the electron energy; and 7. sufficiently large anode voltage to insure the absence of space charge for x > xa.
2kT+A$ 2E, dE
expt-2)
exp(-
3,
A+>0
(4)
where E is the electron energy in the metal. In the practical case of large values of I& and E,, (4) reduces approximately to
[I-(I-z)(Jz)]
e,p(-~)sbc
(6) The principal features of the device efficiency, as seen from (6), are that in the case of A+ > 0, the efficiency is a strong function of A# and T. For A+ < 0, the efficiency is almost independent of T and only slowly varying as a function of A$. In
THE
SCHOTTKY
BARRIER
general there are components of forward current other than electron emission over the barrier and correspondingly the measured efficiency is expected to be smaller than given by (6). Experimental values of the slope constant n greater than 1.1 indicate significant leakage contributions to the current. The emitted electrons have a narrow energy spread several kT wide and centered slightly above the larger of the two energies ES or E, as given by the integrand in (4). The barrier voltage dependence of JA is governed by the hot electron component JH of the barrier current density and is given by (1) and (6) as JA =
qJsat[exp(z) -11
(7)
where 77and Jsat are nearly independent of Va. The value of n is about 1.00-1.10 by either the emission or the diffusion theory of the Schottky barrier. 3. EXPERIMENTS
AND
RESULTS
Our choice of materials for the experimental devices was determined by the requirements of (1) control of semiconductor properties and processing, (2) Schottky b arrier heights comparable to or larger than vacuum work functions, (3) large ballistic mean free paths in the metal, and (4) inertness of the metal to Cs. Devices were fabricated
Contacting Probe
Header
OhmicConioct
FIG. 2. Schottky barrier diode structure employed cathodic emission experiments.
in
COLD
CATHODE
947
using Ag on n-type GaP, ZnSe, and ZnS, with the geometrical configuration depicted in Fig. 2, and were cesiated to lower the work function of Ag. The semiconductor samples were of single crystal material having an electron concentration of 1Ol6 - 1018 cm- 3. Established ohmic contacting methods were generally applied. The semiconductor surfaces were prepared by chemical etch-polishing techniques, developed with the aid of ellipsometric measurements of surface film thickness in addition to investigation of the electrical properties of Schottky barrier diodes formed on the surfaces. Either a Ag or a Pt contact stripe was evaporated in a high vacuum station after which the device was transferred to an ultrahigh vacuum chamber. Baking at 200-250°C for 6-16 hr was employed to obtain a base pressure of 10-ll-lO-lo Torr, after which the thin Ag film of 0.84 x 10e2 cm2 area was evaporated through a circular mask at a pressure of 1O-1o-1O-8 Torr. Cs was deposited from a low energy ion beam which allowed the deposition of controlled submonolayer amounts and a determination of the surface coverage of the metal.‘g) The vacuum work function was determined after each application of Cs by the photoemission technique. Cathodic emission measurements and evaluation of the Schottky barriers were performed in the ultra-high vacuum chamber, utilizing the evaporation mask, spaced about 0.15 cm from the sample, as the anode. Details of device preparation and experimental results for the three semiconductors are given below. (a) Gap-Ag experimental results Both vapor and melt grown materials were used. The vapor grown material, obtained from Bell Telephone Laboratories, Incorporated, had a carrier concentration of 3 x 1016 cmM3 and a Hall mobility of 160 cm2/V-set and the melt grown material supplied by Eagle-Picher Industries, Incorporated, had a carrier concentration of l-3 x 101scm-3andaHallmobilityof80cm2/V-sec. An alloyed Au-Sn ohmic contact was employed. An H,SO,-H202 etch was used in the chemical preparation of the GaP surfaces, giving an ellipsometrically determined surface film thickness in the range of 14-19A. Details of device fabrication for GaP and the other materials are also discussed in References 5, 10, 11 and 12.
948
C. A. STOLTE,
J. VILMS
and
R. J. ARCHER
Table 1. Device parameters and emission eficiency of Gap-Ag-Cs Sample
W-Q
n
dr-,(eV)
&(eV)
&(eV)
3 4 6 7
280 300 160 270
1.19 1.73 1.40 1.54
1.31 1.38 1.51 1.56
1.32 1.92 1.45 1.46
GaP No. 8
270
1.31
1.45
1.47
1.40 1.54 1.41 1.371.58 1.341.52
GaP GaP GaP GaP
No. No. No. No.
Table 1 summarizes the properties of the five Gap-Ag devices that were investigated. The first column gives the sample number and the second the thickness of the Ag film. The Schottky barrier properties obtained at the time of the cathodic
K
cold cathode
&(eV)
J*(A/cms)
?,,,=IAIIB
?,e”‘iLB
1.8
1.67 1.51 1.41 1.44
1.1 x10-Q 2.7~10-~ 5.9x10-G 9.2x10-’
4.3x10-10 2.3 x~O-~ 5.0x10-6 3.6x10-:
1.4x10-9 8.1 x10-’ 9.8x10-6 1.1 x10-6
3.5
1.39
1.5x10-’
1.3 x10-s
4.0 x 10 -5
measurements are given by the next five columns. The experimental slope constant, 11, of the forward I-V characteristic indicates the degree to which the current is ideal hot electron emission. The three standard measurements-saturation
18 (Amp)
FIG. 3. Variation of barrier current, Is, and emission current, Ia, as functions of applied barrier voltage, vTg, for cold cathode device GaP No. 8, as measured and after correction for series IR drop.
THE
SCHOTTKY
BARRIER
current, differential capacitance, and photoemission threshold-were used to measure the Schottky barrier heights. The barrier height derived from the I-V characteristics is calculated from (2) with Jsat determined from the intercept of the straight line defined by the highest I-V point, corrected for series IR drop, and a slope constant of 1.01. The 1,-v, characteristic of the Schottky barrier of GaP device Ko. 8 is shown in Fig. 3 as an example. Thebarrierheightfromcapacitanceisdetermined -from bc = Vat-AT/q+5
(8)
.where -V, is the voltage intercept of Ce2 vs. zapplied voltage and 5 is the Fermi level. An example is shown in Fig. 4. The value of $p, the photoemission threshold,
COLD
CATHODE
was determined by measuring the internal photoemission and fitting these data to a Fowler curve as illustrated in Fig. 5.(13) In Fig. 5, and in most cases, the data are fit by the sum of two Fowler curves having different +p values presumably owing to a patch effect. In these cases the values of K = Z&/K, are the ratios of efficiencies of the two responses. The value of the vacuum work function dv of the cesiated Ag film was determined, at the time of cathodic measurements, by measuring the photoemission of electrons from it into vacuum and fitting the yield data to a Fowler curve as shown, for example, in Fig. 6. The value of & increased with time. In the worst cases time constants were on the order of minutes (pressure - 10-r’ Torr) although stability of the order of a day was observed in one device. The effects of this instability were circumvented by repeated applications of
I i .I
1.0, t
0.9
1
-I 0.8
‘;
:07 zz
1
f :
0.6’
“u > 0.5
r
0.4 -
0
FIG. 4.
919
I
I
-0.5
-1.0 V&mts~
I
-1.5
I
- 2.0
1
-2.5
Differential capacitance-voltage characteristic for cold cathode device GaP No. 8.
C. A. STOLTE,
J. VILMS
and
R. J. ARCHER
-
t10-e
FIG. 5. Schottky barrier photoemissive yield vs. hv for cold cathode device GaP No. 8. Data points are experimental values; solid lines are the two theoretical Fowler curves which add to fit the data and have the values of the adjustment parameters indicated by arrows. sub-monolayer amounts of Cs between measurecathodic emission ments, and by performing measurements within minutes after applying Cs. Cathodic emission data are presented in the last three columns of Table 1. The d.c. cathodic emission current density, JA = IJO. x 10v2 cm2, was measured at room temperature with no significant heating due to diode current. An anode voltage of 30V was sufficient to produce saturation. IA/r, is the measured efficiency q,,, for the given device, IB being the Schottky barrier current. The value presented in the table is the maximum value obtained for each sample, measured immediately following cesiation to insure the lowest value of vacuum work function, and at a large value of IB to insure a minimum excess current contribution. The value of ymew’L~ is the efficiency adjusted to zero metal film thickness and is included to facilitate comparison of the results for different devices. An L, value of 24OA, appropriate for electrons of energy 1.40 eV? was assumed.‘r4’
1.3 t 1.5 @v
1.7
Photon
1.9
Eneqy(eV1
2.1
2.3
2.5
FIG. 6. Vacuum photoemissive yield vs. hv for cold cathode device GaP No. 8.
(b) ZnSe-Ag
experimental results
Al-doped, melt-grown ZnSe was obtained from Eagle-Picher Industries, Incorporated, and converted to low resistivity by heating in liquid Zn for 3-7 days. (r5) Typically the carrier concentration was 3x1016cm-3 and the Hall mobility 400 cm2/V-set for this material. The ZnSe contained stacking faults as revealed by preferential etching. A Ga-In alloy ohmic contact was applied, producing contact resistances on the order of 0.1 Q-cm2. The ZnSe surface was chemically prepared with a potassium dichromate-sulfuric acid etch followed by a cyanide rinse which gave an ellipsometric surface film thickness of about ISA. A total of four ZnSe-Ag devices were measured with the results shown in Table 2. The values in this table were derived by the same techniques as those for GaP in Table 1. The I-V characteristics of samples Nos. 5, 6 and 8 were not available; in an attempt to reduce the likelihood of front surface contamination by Ga-In, these samples had a large-area rectifying Pt back contact instead of an ohmic contact.
THE
--
-
Sample
SCHOTTKY
BARRIER
COLD
Table 2. Device parameters and emission eflciency of ZnSe-Ag-Cs 72
W(A)
&Se No. 1 ZnSe No. 5 ZnSe No. 6
300 300 300
3.0 -
ZnSe No. 8
850
-
+I-.v(eV)
&(eV)
&(eV)
1.25 -
1.53 -
1.47 1.20 1.221.47 1.351.55
-
-
In the case of ZnSe No. 8, the cathodic efficiency was measured at several different values of the work function by allowing the work function to relax and re-cesiating to lower the work function. The observed variation of the cathodic emission efficiency, vmeWILBas a function of the A+ measured for this sample is plotted in Fig. 7. These data were obtained at an I,-value which was sufficient to ensure that the excess current contribution to In was negligible. Figure 8 shows the variation of efficiency as a function of IB and illustrates a lowering of efficiency at small In-values due to excess Schottky barrier current.
K
&(eV)
951
CATHODE
cold cathode
Ja(A/cmZ)
~,=1,Jla
v,,,ew“B
2.0
1.35 1.40 1.37
7.1 x10-4 2.6x10-s 1.3 x10-7
6.0 x~O-~ 1.0x10-7 5.0x10-s
2.1 x10-4 3.5 x10-7 1.6x10-j
1.2
1.49
6.4~10-~
5.4x10-6
1.8~10-~
I
I
1
I
1
I
j
I
“I
I
I
1
10-e
IdIE
10-7
eL
lo-=
10-q
I
!
‘1
IO"
FIG. 8. Dependence of cathodic emission efficiency on barrier current; cold cathode device ZnSe No. 8.
(c) ZnS experimental results
10-I t.6’
I +.4
I t.2 A&v,
I
I
I
0
-.2
-.4
I
FIG. 7. Dependence of cathodic emission efficiency on barrier height difference for cold cathode device ZnSe No. 8.
Al-doped, melt-grown ZnS was obtained from Eagle-Picher Industries, Incorporated, and rendered conducting by heating in liquid Zn at 900°C for 3-7 days, after which the material had a carrier concentration in the range of 0.3-2x 1Ol7 crnb3 and a Hall mobility of 60-100 cm2/V-sec. The crystals contained stacking faults. Ga-In contacts were generally used and had ohmic contact resistances of about l-5 Q-cm2 on ZnS. The ZnS surface was prepared by etch-polishing in a bromine-methanol solution on a fiber pad with the sample held by a teflon fixture, and had an ellipsometric surface film thickness of 10-246.
/
C. A. STOLTE,
952
J. VILMS
and
R. J. ARCHER
Table 3. Device parameters and emission ejiciency of ZnS-Ag-Cs Sample
WA)
a
ZnS No. 1 ZnS No. 2
280 600
1.4 -
ZnS No. 3
400
ZnS No. 12 ZnS No. 16
&-y(eV)
Cc(eV)
+e(eV)
K
1.27 -
1.30
2.0
-
-
-
900
-
-
-
410
-
-
1.20 1.391.58 1.371.57 1.401.75 1.191.40
Cr(eV)
cold cathode Tlrne’V /LB
JA(A/cm2)
~,,=~~/IB
1.45 1.35
7.1 x10-s 6.5 x10-s
6.0~10-~ 5.5x10-s
1.9x10-s 6.7 x~O-~
1.4
1.50
7.1 x10-s
6.0x10-s
3.2 x~O-~
4.0
1.61
1.2x10-9
1.0x10-*
5.0x10-7
4.1
1.56
3.5 x10-s
5.8x10-a
3.6~10-~
Results for five ZnS-Ag samples investigated are given in Table 3. The barrier I-V data are not available for four of these due to deterioration of the ohmic contact during vacuum bake out. For ZnS, the barrier heights obtained during the cathodic emission experiments were significantly less than those obtained in the preliminary studies because of ZnS surface instability during vacuum bake-out or contamination at some point in the overall fabrication procedure. 4. DISCUSSION
1
OF RESULTS
The data support the model for the cold cathode and establish that the cathodic emission results from the injection of hot electrons into the metal. Field emission is ruled out because of the dependence of cathodic emission current on the applied anode voltage. The results from one such experiment are given in Fig. 9. The observed threshold at 1OV is caused by a cut-off field produced by the large difference in the work functions of the cesiated metal pad and the surrounding semiconductor. Further experimental investigation of the threshold using the photoemission from the metal substantiated this explanation. The complete saturation of the cathodic current with anode voltage is conclusive evidence that the devices do not operate by field enhanced electron emission. Theory predicts that the cathodic emission current should have the same barrier voltage dependence as the hot electron component of the barrier current. As indicated in Tables 1-3, the barriers used in this investigation had n values ranging from 1.19 to 3.0. These large n values are
,IB=5x10-4Amp VS'O.798Y
-r-i-
i _
3
!:/FIG. 9. Variation of cathodic emission current Ia as a function of anode voltage V, for two different biases on the Schottky barrier; cold cathode device ZnSe No. 1.
interpreted as a barrier current comprised of a hot electron current in parallel with an excess current which has a weaker voltage dependence. Typical curves, shown in Fig. 3, 1.4-v&? and 1,-V, illustrate the different voltage dependences of IA and In. The emission current, IA, has an n-value
THE
SCHOTTKY
BARRIER
of 1 .Ol in agreement with theory, and corresponding to the hot electron current, whereas the barrier current, In, has an n-value of 1.31. This rejection of the excess current component by the emission mechanism was observed in all of the samples investigated. The detrimental effect of excess current is to lower cathodic emission efficiency at low values of 1, as illustrated in Fig. 8. At sufficiently large values of barrier current, the excess current is not a significant portion of the total barrier current and does not lower the measured efficiency. The dependence of the emission current on temperature was indirectly observed. The theory predicts that in the case of &, > +n, the efficiency is proportional to eMA*jkT. An increase in anode current with time at large diode currents was observed in samples which had a fairly large A+, 0.2-0.3 eV, and in particular in those samples with a highly resistive back contact. For one sample with a barrier difference of 0.3 eV, the increase in anode current indicated a temperature rise of 50°C on the basis of the theory. Surface temperature measurement of the sample under the same conditions using an infrared detector indicated the temperature rise to be no greater than 60°C. The measured cathodic efficiency, TmeWiLB, adjusted to zero metal thickness, is plotted in Fig. 10 as a function of the measured A+. As seen in Tables 1-3, the values of r/s determined by the three techniques are in good but not exact agreement for any given device. The smaller value of +p was used for +B in establishing the value of A# at the indicated data points. This is justified on the assumption that the double Fowler fit results from a patch effect with two regions with different barrier heights, one characterized by the upper and the other by the lower value of $p. The latter would dominate the total hot electron current. The error bars indicate the range of A+ when both the &- and the lower +,-values for +n are used. The scatter in the data is due to the imprecision of the values of 4s and +v. Since both are about 1.5 eV, a 10 per cent error in measurement would result in an error in the difference as large as 0.3 eV. The best data for testing the dependence of efficiency on A+ are those shown in Fig. 7, where the values of A+ were determined on a single sample with all conditions constant except the
COLD
CATHODE
953
--I
A@(evl
FIG. 10. Dependence of cathodic emission efficiency on barrier height difference. Circles (0), squares (Cl), and triangles (A) give the maximum measured efficiency for the Gap-Ag-Cs, ZnSe-Ag-Cs, and ZnS-Ag-Cs devices, respectively; the dashed line (- - -) is the least squares line from Figure 7; the solid line (---) gives the theory, (6), evaluated for variable Ev, Ei = 8.9 eV, T = 298”K, and W = 0; and the dot-dash line (.-.-*-) is the alternative theory, (9), evaluated using W = 0 and m/m* = 5.
value of +v. The dashed line in Fig. 10 is the least squares line from Fig. 7. The solid line in Fig. 10 is the theoretically predicted T-A+ relationship of (6), using W = 0, variable E,, and Es = 6.9 eV composed of $B = 1.40 eV and EF = 5.5 eV.(16) The agreement between the predicted results assuming isotropic scattering at the metal-semiconductor interface and the data from Fig. 7 is good. The data from all samples agree fairly well with the theory, although the emission efficiency of the GaP devices appears to be systematically too low. If conservation of transverse momentum is assumed at the metal-semiconductor interface instead of isotropic scattering, i.e. specular rather
C. A. STOLTE,
954
than diffuse refraction, efficiency would be
q=
then
the
theoretical
exp(-fj[l-(1-z)
xexp( --A$/(;-l)kT)] (s)
(1 ,
Acknowledgements-The authors wish to thank M. M. ATALLA, T. 0. YEP, P. E. GREENE, and R. A. BURMEISTER,JR., for helpful discussions, and to acknowledge the technical assistance of J. P. GARRETT, H. LUECHINGER,J. LITTLE and G. S. PECK.
REFERENCES 1. M.
W
x exp k~
and R. J. ARCHER
J. VILMS
(9)
which is shown in Fig. 10 by the dot-dash line. The better agreement of the data with (6) indicates that electrons are scattered on transmission across the interface. 5. CONCLUSIONS The model of the Schottky diode cold cathode and the device potential are established by the agreement of the experimental results with the simple theory describing the operation of the device. The maximum experimentally measured efficiency, 6 x 10e3 per cent, is below that deemed practical for broad device application but was limited by the inability to produce a sufficiently high Schottky barrier. This is a temporary limitation that will be eliminated by further development. The results, Fig. 10, indicate that an efficiency as large as 2 per cent would be obtained with a barrier height of 1.7 eV, for example, and the easily obtainable vacuum work function of 1.5 eV. A cold cathode with this efficiency would be a useful emitter in high performance vacuum tubes particularly in the high frequency range, in cathode ray tubes where the predicted narrow energy spread of electrons and the absence of the control grid would yield further flexibility in design, and in other applications where power or background light and heat are to be minimized.
2.
3.
4.
5.
6. 7.
8. 9. 10.
11. 12. 13. 14. 15. 16.
M. ATALLA, U.S. Patent No. 3,121,809, February 18,1964(filed September 25,196l). H. HEFFNERand M. COWLEY, Consolidated quarterly status rep. No. 13, Solid-State Elec. Research, Stanford Electronics Laboratories, p. 73 (December, 1961). D. V. GEPPERT, U.S. Patent No. 3,150,282, September 22, 1964 (filed November 13, 1962), and Proc. IEEE 54, 61 (1966). L. S. LERNER and R. J. ARCHER, Air Force Cambridge Research Laboratory Report AFCRL-66479 TAngust, 1966). R. J. ARCHER, J. COHEN and J. VILMS, Air Force Cambridge Research Laboratories Report AFCRLI68-0302 (June, 1968). R. WILLIAMS and C. R. WRONSKI, Appl. Phq’s. Lett. 13, (7), 231 (1968). M. M. ATALLA, VortrGge der 2. MikroelektronikTaaun~ des “Internationalen Elektronik-Arbeitin Munchen, Oktober 1966, R. kre;ses- eV” Oldenbourg Verlag, Miinchen, Germany (1967), 138-145. F. A. PADOVANI, Solid-St. Electron. 12, 135 (1969). R. E. WEBERand L. F. CORDES,Rev. Scient. Instrum. 37, 112 (1966). R. J. ARCHER, J. COHEN and J. VILMS, Air Force Cambridge Research Laboratories Scientific Report No. 1, AFCRL-684122 (March, 1968). Ibid., Scientific Report No. 3, AFCRL-684447 (September, 1968). Ibid., Final Report, AFCRL-68-065 1 (December, 1968). R. H. FOWLER, Phys. Rev. 38.45 (1931). S. M. SZE, C. R. CROWELL, G. P. CAREY and E. E. LABATE, J. appl. Phys. 37 (7), 2690 (1966). M. AVEN and H. H. WOODBURY,Appl Phys. Lett. 1 (3), 53 (1962). C. KITTEL, Introduction to Solid State Physics, 2nd
ed. p. 250. Wiley, New York (1956).