III.
SOLID STATE PHYSICS
A.
SOFT X-RAY SPECTROSCOPY
has been proceeding
Construction
spectrograph
techniques
range
of 304
study
for the
employed
10-9-10
specimen
-
allow
10 mm Hg;
a
on
new ultra-high-vacuum
energy bands
of electronic
of the
operation
these pressures
surface free from contamination.
stainless
steel
is
it
and glass;
are
in
number
of
stainless
steel-to-glass
solids.
in
spectrograph
soft
X-ray
The
vacuum
in
at pressures
necessary
in
the
keep the
order to
The apparatus is built almost entirely
No
completely bakeable.
materials have been employed in the construction.
a
L. L. Isaacs
J. Silverman
R. Weber
Prof. G. G. Harvey
Dr. K. W. Billman
Dr. E. R. Pike
T. Higier
Prof. W. P. Allis
Prof. S. C. Brown
Prof. C. W. Garland
seals that
ferromagnetic
It has been possible to make
range
from 3 inches to 0.25 inch
diameter.
The conventional diffraction grating would be risky to bake.
A new dispersion system
has therefore been designed which makes use of the Einstein relation between the velocity of a photo-ejected electron and the photon causing the ejection. A (3Tr)/Z electron
spectrometer, which has been discussed previously (1), is used to analyze the photoelectrons. The photoelectric target for the soft X rays is a molecular beam. Magnesium is
being used in preliminary studies.
Students have completed thesis work on an electron-injection system for an Allen
type of multiplier for use with the spectrometer, and on the construction of an iron-free
magnet based on previous calculations (1).
The electron spectrometer and its detection system have operated in initial tests
according to calculations, and a resolution of 1 part in 1000 is expected. This may possibly be increased by electronic means, and it is hoped that such improvement will be
limited only by stray magnetic fields.
A
copper-beam
oven
has been
copper surface in high vacuum.
and we hope
that the
M-levels
developed
for the purpose
of laying
The band structure of this metal
may
also be
observed in
the
will
down a
be
free atoms
studied,
of the
beam.
E.
R. Pike, K. W. Billman
References
1. E. R. Pike, Focusing properties of a 3r/2 electron spectrometer for studies of
photoelectric emission excited by soft X rays, Quarterly Progress Report No. 53,
Research Laboratory of Electronics, M. I. T., April 15, 1959, pp. 13-19.
(III.
B.
SOLID STATE PHYSICS)
CYCLOTRON RESONANCE IN N-TYPE GERMANIUM AT LIQUID-HELIUM
TEMPERATURE
Measurement of cyclotron resonance in n-type germanium by exciting carriers with
a dc electric field has shown two advantages over the methods of exciting carriers with
light, or exciting carriers with the microwave electric field:
a.
There is only one sign for the carrier, and it is possible to check the theory of
cyclotron resonance developed by B. Lax (1) at lower w/v.
b.
This method is less noisy than microwave excitation, and higher densities can
be achieved than with the other two methods.
1.
Method of Measurement and Results
The work in this quarter was devoted to improving both the accuracy and the
interpretation of the measurements.
The magnetic-field values and the effective
mass parameters were measured in several samples of n-type germanium at magnetic
fields greater than 683 gauss for m
tron.
t
= 0. 08 me, where me is the mass of the free elec-
The theoretical (1) and experimental values are listed below for two samples.
Sample 1
m /m e
Theoretical
Experimental
B(l11)
0. 205
0.08
1610
E(011)
0. 189
710
0. 083
Sample 2
m"/m e
B(211)
E(01 1)
0. 358
>2700
>0. 32
0. 156
1220
0. 143
0.08
663
0. 078
Experimental studies were made to improve the accuracy of the ratio of microwave
power absorbed at each separate resonance determined by the magnetic field. It is
necessary to know n, the density of carriers, which is given by the relation
Idc = nelEdc; n i occurs in a product, and
.
was also measured separately from the
(III.
SOLID STATE PHYSICS)
Schematic drawing of equipment used in
cyclotron-resonance experiment.
Fig. III-1.
magnetoresistance at T = 4. 2"K.
It was found that p. decreases monotonically when Edc
is perpendicular to Bdc, which is in agreement with magnetoresistance theory (2), and
that p decreases for B < 1800 gauss when Edc and Bdc are parallel, and then remains
constant as B increases.
Figure III-1 shows the
equipment
used in the principal
cyclotron-resonance experiment.
Theory of Anisotropic Scattering
2.
In this investigation, the equation for the microwave conductivity of an electron in
germanium for anisotropic scattering time has been solved, and it was found that with
o/v ~ 10,
2
1
sin
the half-width of the
m* 2
0 mm
S
(vt-v), where
Vt
and
mt
m =
mt
m
cyclotron-resonance
absorption is
given by A = v t -
= 1/3
= 1/2
= 1/4
=1/12
1/2
1/3
1/4
1/12
0.9
0.8
0.7
,/W
=
0.20
St /1
H (211)
E ([O1)
.10
0.15
MAGNETIC
0.20
FIELD
0.25
0.30
=0.5
H(124)
0.6
E (210)
0.35
0.05
(WEBERS)
0.10
0.15
MAGNETIC
020
0.25
0.30
0 35
FIELD (WEBERS)
(b)
Fig. III-2.
Microwave power absorption versus magnetic field
for two magnetic-field orientations.
0.5
0.4
020
-t/W
=
x
0.3
H(211)
t/c
0.2
E(Oli)
0.1
0O
z 0.5
60
o
H(124)
0I
E (210)
0
-0 .I
-0.2
-0.2
0
0x x
-0.3
;
x
-0.4
-0
V//Vt :I
5,
= /2
: 1/2
-0.6
-0.6
1/3
-0.7
S1/4
./4
08.8
o .
i14~i
li
-0.9
0
0.05
0.i0
O.15
MAGNETIC
020
25
FIELD (WEBERS)
030
0.35
0.0
0.5
MAGNETIC
20
5
FIELD (WEBERS)
(b)
Fig. III-3.
Microwave frequency shift versus magnetic field for the
two magnetic-field orientations of Fig. 111-2.
030
,35
SOLID STATE PHYSICS)
(III.
Here,
0 is the angle that the B-field makes with the 111 direction.
Formulas for the frequency shift and power absorption were computed numerically
1
1
1 1
9
Plots of
with w = 23. 4 X 10 X 27.
, 4-' 3'
for o/v = 2. 5, 3, 4, 5, and for vp/vt =
microwave power absorption versus magnetic field (Figs. III-2 and III-3) have been made
with the aid of the following formula calculated for power absorption and frequency shift
of the resonant cavity containing germanium:
mt
M
2
V2
+
Vi
V
/M
V
+
2sin
bt2
1+
V
t
++
t
[V
i
t
2
2
2
Icos 2 0
Ve
sin 4 0
2
4
Vt
+
L
2
2
14
2
2
V
n
Vt
2
2
Wbt
cos
2 +2
2
2
t
2]
Y~
Vt
2
co
s4
+ f
t
t
V L'
sin
2
2
2
d sin
cos
sin
2
z 2
2 +
cos
cos
b sin
cos
W
2i
VI
2J
Yt
2
8
1
+
2
sin2
I
2?I
V
-h
Mt/I
t
1i
2
V tZ
2-
F
0
2 cos
2
t
i LL
2
?
2
+
+
"V
t
t
m
Mt
22
0 V- +
V
vt
L
2
V
I
2t+v
t
2
t
c sin
cos
t
2 sin2
1
cos 2 0
t
+
mtt
P
22
e E ac
mtv
2
cos 2 'bcos
2
sin2
Vt
2
2+
t
L'
t
sin2 i sin2
sin 0
2
bt
i,
4
1+
2
cos
sin2
-
V
O
2
i
1+
mt
t
t
..
.
S
v2t
,t,
22
nfafV E
bt
2 sin
,
2_
V
m
t
mt
ti
2
V
t,
,
m..
V
t
V tV
mt
I
I',
2
V
t
SV
2 sin2
2
Dbt
2
Vt
2
21+
,
m,c
t
"
2
V
ac
mtVt E0.
V
t
It
4
sin
0
S
V +
0
4
m
2
2m
2
t
mt
t
cos2
t
m
1
t2
t
t
t
t 2
t
cos
1+
V
t
The plots showed, first, that the power P can be represented by a simpler formula:
2
ne
ac m
P=1tvt
2
2
where a = sin i
1
1
lobi)
+ cos
2
/
i
m/m
i
+ (wb
, and v. = v-sin
1
. 2
4 mm*
2
(v-v ).
t
The plots also showed that at B = 3000 gauss, the difference in microwave power
absorption with isotropic scattering and anisotropic scattering can be as high as
80 per cent. Thus a reasonably accurate comparison of the power-absorption maxima,
B=700
B=3000
gives a good indication of whether or not the anisotropic scattering is an effective
mechanism.
T. Higier
(III.
SOLID STATE PHYSICS)
References
1. B. Lax, R. N. Dexter, A. F. Kip, and G. Dresselhaus,
electrons in silicon, Phys. Rev. 96, 222 (1954).
Effective masses of
2. L. Gold, Anisotropy of the hot electron problem in semi-conductors with spheroidal energy surfaces, Phys. Rev. 104, 1580 (1956).