Measurement of electron phonon scattering in insulators by photoinjectio

Spicer, W. E.

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NASA QUARTERLY STATUS REPORT #3
for Period Ending 31 (January 1969
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GRANT ; NGR-05-020-066
Principal Investigator
W. E. Spicer
Stanford University
Stanford, California
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I. INTRODUCTION
W. R. Spicer
In Part II of this report, a summary is given of the method developed
to measure electron-phonon scattering in insulators by photoinject.on. This
is closely related to prevent charging in insulating films by photoinject-
ing electrons into 'the films from a metal substrate while photocurrent is
being drawn from the insulator. These studios of alkali halides are part
of the over-all program to study alkali halides and their alloys.
In the third section of the report, a description is given of new
techniques developed in the Kramers-Kronig analysis of optical reflectivity
data. This work was done as part of the study of the silver halides.
A
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4Page 2
II. HOT ELECTRON TRANSPORT IN THE ALKALI HALIDES: LITHIUM FLUORIDE
T. H. DiStefano
Hot electron scattering is being studied in the alkali halides by the
technique of photoeinject on. l ' 2 in the photoinjection experimeirt, developed
by the author, electrons are photoemitted from the substrate of an insulat-
ing thin film, through the film itself, and into vacuum. The scattering
properties of the film can be determined from the energy distribution of
those electrons which have propagated through the film.
The major scattering mechanism in the alkali halides is due to inter-
action with the longitudinal optical phonon. Since the energy gain or loss
in each collision is small, the motion of the electron is well modeled by
the random wal"i process. For more than a few scattering events, the random
walk reduces to diffusion with a characteristic length, X. which is 1/,V(3-
times the average path length t,.3
	 a
The energy of the longitudinal optical phonon is largely independent
of the phonon wavelength in the alkali halides. Thus, in each collision the
.
electron will either gain or lose energy YfW 	 The probability of energy gain
and of energy loss in each scattering event is,
n
Prob. (gain) = 2n + 1
+1n
Prob. (loss) = 
n + 1
(phonon absorption)
(phonon emission)
where, n = -	 1
XWp/KT - 1
e
On the average, a stream of electrons moving through the crystal will lose
energy Ae in each collision:
cPage 3
Kwp
Qe = 
2n + 1
Since the hot electron motion is essentially a random walk, the average
number of these collisions made in diff"s ing a distance L is N(L)
N(L) ^	 (L ) 2 .
And, by this elementary model, the average energy loss suffered by an
electron beam in traversing a crystal of length L is JOE. In the light
alkali halides at room temperature there is little chance of phonon absorption,
simply because there are not many excited phonon modes in the crystal, At
these temperatures there is a near certainty of a loss of energy WW  per
collision' which corresponds to the case for which n 0.
Now, it is seen that if the energy loss of a stream of hot electrons
were measured, then the scattering length of electrons of that particular
energy could be determined. The photoinjection experiment, which was de-
signed to measu re this loss of energy, has been tried and preliminary results
have been oh	 .ied for the case of LiF.
Electron transport; in LiF was studied by analyzing the energy distri-
bution of a beam of electrons which has propagated through a thin film of
the material. Hot electrons were photoemitted from the substrate of the film
into the film itself; the energy distribution of the electrons transmitter,'
through the film and into vacuum were measured by the standard photoemission
v
techniques . 4 Photoexcitation in the substrate was produced by light which
has propagated through the alkali halide at less than the band gap energy.
The highest energy photon which will pass through an insulator of band
d
energy Eg is, of course, Eg . These photons can excite electron^ in the
metallic substrate to an energy of Eg above the Fermi energy. For most
r
i
Page 4
metal-insulator interfaces, the conduction band of the insulator lies about
four volts above the Fermi level in the metal. Thus, this technique can in-
ject electrons into the insulator with kinetic energies ranging from zero to
E  - 4 eV. For a film of CsX on copper the yield is similar to that of the
copper below the band gap of the CsX; however, the threshold of the copper
has been lowered by the CsI coating which causes it to have a higher yield
than the yield for pure copper. At Photon energies greater than the threshold
of 6.5 eV ::or the CsI, photoemission from the Csl itself dominated the yield.
By a careful selection of the substrate material, the stream of in-
jected electrons has been made to be quite monoenergetic. This was ac-
complished by exciting electrons from just below the Fermi level to the con-
duction band statesof the metal substrate. Yttrium was chosen for its
exceptionally high density of filled 4d  states, as well as for its low
work function. Eastman has found s that electrons photoemitted from this
band have an energy spread of only .4 eV, which is narrow enough to provide
an excellently monoenergetic source of electrons.
Xnitially, there was some difficulty in obtaining a clean surface of
yttrium because of its high chemical activity and its affinity for hydrogen.
However Y any metal with the low work functir%n necessary to inject electrons
high into the conduction band of the insulator deposited on itself would be
very electropositive, and hence chemically active.
A solid substrate of yttrium was tried and found to be unsatisfactory.
This substrate was polished with 207o anhydrous nitric acid in glycerine, sus-'
pended in kerosene; the more usual polishing techniques  were unsuccessful.
Transfer to the photoemission apparatus pas done in dry nitrogen. The solid
sample yielded abysmally poor results after being heat cleaned in a vacuum
c
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Y
n
Page 5
of 10
-g
 Torr. After being heat cleaned in 10 microns of hydrogen and then
heat, cleaned in vacuum, this solid sample gave the poor photoemission results
shown in Fig. 1.
Vacuum evaporated yttrium yielded photoemission energy distribution
curvos which were comparable to those of Eastman. The yttrium was evaporated
at 11500C from a prefired tantalum boat. At this temperature the tantalum
acts as a getter, as well as being completely insolvable in the yttrium.7
The results shown in Fig. 1 indicate that this yttrium provides a well-resolved
peak of injected electrons, with a width of less than a volt. This peak
from the yttrium is identifiable in the energy distributions of electrons
photoinjected through alkali halide thin films. In the preliminary results
for LiF, using yttrium as a monochromatic source, the scattering lengths
found vary from 95 4to 120 1^ for electrons with kinetic energies in the
range 5 eV to 10 eV.
References
1. T. H. biStefano and W. E. Spicer, APS Bulletin 13, 	 403 (1968).
2. T. 11. Distefano, NASA Annual Report (NGR-05-020-066'), May 1968.
3. S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).
4. W. E. Spicer, C. N. Berglund, Rev. Sci. Instr. 35, #12, 1665-1667 (1964).
5. D. Eastman, private communication.
6. B. Love, THE RARE EARTHS, Spedding and Daane, ed., (Wiley & Sons, Inc.,
New York, 1961), p. 215.
7. C. E. Lundin, THE RARE EARTHS, Spedding and Daane, ed., (Wiley & Sons,.
Inc., New York,, 1961), p. 266.
I
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rPage 3a
0 SO 1 1 d Y.
He4t CIC4nfd
to G00 °C
©	 ©	 D Solid Y
Heat Cleartd
to !000X ihl0 ,p HZ.
7	 O !U.
Photoemission from Solid Yttrium
w7	 (p
	 -5	 - t-	 '-3	 -2-	 - 1	 0 eV.
Photoemission Through LiF Films on Clean Yttrium
Fig. 1
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111. EFFECTS OF ME EXTRAPOLATION OF VIE REFLECTANCE
ON T11E OPTICAL CONSTANTS DETERMINED BY THE
KRAMERS-KONIG ANALYSIS
Robert S. Dauer
A. Introduction
If the complex normal ,incidence reflectivity r 
= I r+ e 18 is known, then,
all the optical properties can be determined from the Fresnel equation and
the definitions of the constants. Further, if the reflectance R = I r1 2 is
known at all photon energies E then the phase of the reflectivity at energy
E0
 is determined uniquely by the Kramers-Kronlg transform)
0 (E ) ^ 1	 d1n) rI0	 G	 dE
E + E
1n I	 'I dE,
E - E0
(1)
Since the reflectance cannot be measured over an infinite photon energy
range, the data must be extrapolated in some manner in the unknown regions.
The necessity of using an extrapolation of the data requires an examination
of the uniqueness of the calculated optical constants in the region of
measurement.
This question has been studied by calculations of 0 using the re-
flectance data of White and Straley2 for AgCl. The Kramers-Kronig integral,
Eq. (1), was performed using 'this laboratory's computer program  which was
modtf ied to allow for the calculation to be performed using a high energy
extrapolation which leads to the best agreement between the calculated 1rW
energy optical constants and known values in this region. In these calcula-
tions on AgCl, the phase shift was fit to zero in the transparent region
(0 through 3.0 eV). Though calculated for a specific set of data and
mPa go 7
fitting criterion ) the results reported below should be characteristic of
the calculation as performed using this laboratory's computer program.3
B. High Energy Extrapolation
The integral of Eq. (l) is performed by considering the reflectant. 	 .s
plotted on a log-log scale and straight lines drawn between the data points.4
The solution for the contribution to 8 froib each of these straight lines
is known exactly. 4 'Thus ) a natural extrapolation to high energies which is
continuous with the last measured value is
R= Rf (E ) -A) Ef s E Em	 (2a)
where R  is the reflectance at the highest energy of measurement) Ef ►
Being a straight line on a log-log scale ) this extrapolation is uniquely
specified by one point )
 Rm) calculated using Eq, (2a) at energy Em.
In performing the calculation of @(ED ) ) Em will be the largest energy
in the numerical integration. Thus ) in the calculation we are implicitly
assuming that the contribution to 6 for energies greater than Em is zero.
From	 inspection of Eq. (1) it is seen that this is equivalent to having
assumed a constant reflectivity from Em to infinity. Therefore ) the numeri-
cal method inherently assumes
R Rf (Em) -A = Rm constant) E z Em .	 (2b)
_f
There are thus two adjustable parameters in the choice of such an
extrapolation: A and Em .	 It is found that variation of either of these
quantities while the other is,held fixed affects the magnitude but not the
position of optical constant structure in the region of measurement. One
cPage 8
criterion that can be used in choosing the parameters is to obtain a fit of
the calculated optical constants at low photon onen-gies to known values,
If A is chosen to satisfy this fitting criterion )
 then it is found that
different choices of Em will lead to different "optimun, values for A. For
B
the AgC1 data used  in which Ef 21.1 eV ) the absorption coefficient a is
the same for all pairs of Em and corresponding "optimum" A at photon energies
below 15 eV if Em is reasonably (at least 50%) larger than Ef.
To obtain a more accurate knowledge of the optical constants in the
high energy region of measurement )
 a second criterion must be used in choosing
the extrapolat`on, 5
 If the measured R is decreasing at high energies ) a
reasonable choice is to require that the slope of the reflectance be con-
tinuous at Ef , Using this criterion ) the error in the optical constants
can be estimated :,Mr a given R slope discontinuity. It is found that f'or
all slope discontinuities
Aaf a! L AS
	 (S)
where Qaf is the percent deviation of of at E  9wom the corresponding value
calculated with reflectance having a conti.nuou:; slope at E  and AS is the
percent discontinuity in the slope of the reflectance at Ef.
The error of the optical const,,z&5- its a mAximum at Ef . It is found
that the error in a at an energy E is given aprraoximately by
Aa N Aar f (E ) 8, 6' E s E f	 (4)
f
As can be seen from Eq„ (2a), the slope of the extrapolation at E 
depends only on A. Thus ) using our second criterion of R slope continuity)
A can be chosen unambiguously. Then Em can be varied to satisfy the fitting
cPage 9
criterion at low photon energies. The computer program used for these cal-
culations is currently being modified to perform this. In addition, the
high energy errors of the other optical constants are being studied.
C. Conclusions
Except for energies near the end of the measurement range, the optical
constants calculated by a Kramers-Kronig analysis of a set of reflectance
data are insensitive to the extrapolation of the data to high photon energies
when the extrapolation is chosen to make a few low energy calculated optical
constants agree with known values. This very significant conclusion is furthe
substantiated by calculations of the optical constants of amorphous Ge by
T. M. Donovan using this program. 6 By fitting 8 to zero over the very nar-
row transparent region, tae. i-e,Sulting value for the index of refraction at
zero frequency was well within one percent of the measured value for
amorphous Ge. 1.4 addition,	 the calculated e 2 at the absorption edge fit
the measured val,uee quite well. Because of the reliability of the optical
constants calculated in this manner, the Kramers-Kronig transform is a use-
fpj check of the measured reflectance data. In the case of AgCl, 7 low
photon energy negative dips in the calculated a,k, and e 2 lead to an ex-
amination of the reflectance data in the corresponding energy region. It
was found that by "smoothing" R in accordance with earlier measurements in 	 I
this region, the calculated optical constants no longer exhibited these
unphysical values. Thus, the Kramers-Klronig analysis revealed an error in
A
the experimental data.
cM
Page 10
By requiring the extrapolation to have the same slope as the measured
reflectance at the highest energy of measurement, an estimate of the error
of tY,- optical constants to this energy region is obtained. In addition,
the axtrapolation can be chosen unambiguously yielding more reliable high
energy optical constants.
References
1. E. L. Kreiger, D. J. Olechna, and D. S. Story, G. E. Technical Informa-
tion Series No. 63-RL-3458G.
2. J. J. White, III and J. W. Straley, J. Opt. Soc. Amer. 58, 759 (1988).
The reflectance data for AgCl was generously supplied by J. J. White, III.
3. The computer program used for the Kramers-Kronig analysis of an input
set of reflectance values was written in Algol 60 by J, L. Shay based
on Ref. ' l. It was translated into Fortran IV by D. H. Seib.
4. J. L. Shay, "Kramers-Kronig Analysis Using B5500 Computer," (unpublished).
5. It should be noted that since the optical constants depend on the energy
that specifies the extrapolation of the data, Em, the fo;,,m of the ex-
trapolation does not have zany physical significance.
6. T. M. Donovan, private communication, 1969.
7 For details, see R. S. Bauer, NASA Quarterly Status Report #1 (NGR-05-
020-06611 May 1968 through 31 July 1968, p. 2.
s'
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Measurement of electron-phonon scattering in insulators by photoinjection Quarterly status report, period ending 31 Jan. 1969

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