A combination of experimental and modeling work is summarized in two areas: first, the calculation of excess free carrier and space charge distributions near contacts and their effects on device resistivity, and second, the characterization of a slow transient response (tau approx. 1 sec) in Ge:Be detectors which is due to trapping associated with Be(+) formation. In both cases, analytical models, based on continuity and rate equations, have been developed to enable the application of these findings to a wide variety of photoconductor materials

Haegel, Nancy M.

English

NASA Technical Reports Server

r t N90-21316
Near Contact Phenomena and Transient Effects in Far Infrared Photoconductors
Nancy M. Haegel
Department of Materials Science and Engineering
School of Engineering and Applied Science
University of California, Los Angeles
Abstract
This presentation summarizes a combination of experimental and modeling work in two areas:
first, the calculation of excess free carder and space charge distributions near contacts and their
effects on device resistivity, and second, the characterization of a slow transient response
(x -1 sec) in Ge:Be detectors which is due to trapping associated with Be + formation. In both
cases, analytical models, based on continuity and rate equations, have been developed to enable the
application of these findings to a wide variety of photoconductor materials.
I. Near-contact Behavior
The goal of this work was to model the distribution of excess free carriers and space charge in
the bulk material immediately adjacent to a heavily doped contact region. Figure 1 shows
schematically the distribution of free holes (p), ionized acceptors (NA'), electric field (E) and
potential (V) that might be expected as a result of the diffusion of carders due to the concentration
gradient and the resultant space charge. The object of the modeling was to determine the exact
extent and shape of the space charge region, as a function of material parameters such as doping,
compensation and mobility. Several attempts have previously been made to solve this problem
using numerical modeling, but diffusion in both cases was neglected in the space charge region
(1,2). This is not a good assumption, because the diffusion current plays a significant role in the
near-contact region.
A complete numerical solution, including both diffusion and drift components to the current,
has recently been completed (3), and this presentation is a summary of that work. Readers are
referred to the publication for a complete discussion of the problem. The distributions of free holes
( for p-type material), ionized acceptors and electric field are calculated by combining the continuity
equation, Poisson's equation and the current equation. The continuity equation, for the steady
state, can be expressed as
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25
https://ntrs.nasa.gov/search.jsp?R=19900012000 2020-03-19T23:17:53+00:00Z
lapE' + l.tp'E + D p" = 0 (1)
where l.t is the mobility of the free carri_'.ers.D it the. diffusion coefficient and the derivatives
represent spatial derivatives in one dimension. Since Poisson's equation and the current equation
can be used to express E and E' as a function of p, the final equation to be solved is a second order
differential equation in p. This has been solved using a finite difference technique (4). In this
work, we have used low field approximations and have not included the dependence of capture
cross section on electric field or the effects of velocity saturation. These are valid assumptions for
the low fields at which Ge detectors are usually operated.
The modeling parameters for this work are those appropriate for p-type Ge:Ga photo-
conductors operated under low photon backgrounds at 3.0 K. The boundary condition on both
sides was taken as a thin region (L = 0.25 _m) with an excess hole concentration of
1016-1018 cm-3.
Solutions as a function of device thickness are shown in Figure 2 for a 10 I.tm and 25 _m
thick layer of material with a contact at either side. In Figure 3, the effect of bias, on a 100 _m
thick layer, is shown. The results are for material with a Ga concentration of 2 x 1014 cm -3, with a
compensating donor concentration of 1011 cm-3. One sees that for the very thin layers, the
resistivity of the device would be dominated by contact effects, since the hole concentration is
determined by diffusion from the contact. Bulk resistivity values would not be obtained in an I-V
measurement of this type of structure. For the common thicknesses for current detectors,
however, (t > 0.5 mm) the contact should not have a significant effect on the I-V characteristic.
In Figure 4, the effect of varying the compensating donor concentration is seen. The space
charge region will extend much farther as the compensation ratio is decreased. Thus, one would
predict a contact effect on measured resistivity for thickness less than 200 t.tm for lightly
compensated material with ND = 10 cm -3. The critical thicknesses will be even less for donor
concentrations in the ranges of 1011-1012 cm-3, which are more common for Ge:Ga.
We have developed analytical expressions for the extent of the space charge region and the
excess cartier concentrations and have verified them with the numerical results. These expressions
are given in Figure 5. With these results, one can determine the effect of the contact in any
extrinsic photoconductor.
The calculation of the steady state space charge distributions near the contacts is a necessary
first step for further investigation of the transient response of the space charge region.
Experimental work is in progress in order to verify the modeling predictions. We will measure the
I-V characteristics and study the fundamental transport behavior of thin devices in the contact-
dominated regime.
26
Contact
P
N A-
E
V
Bulk" unbiased
i
X
X
X
Contact
P
N A-
E
V
Bulk • with bias
i
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Figure 1
27
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POSITION (gm)
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28
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Figure 3
29
(a) ND = 1012 cm-3
(b) ND = 1011 cm-3
(c) ND = 1010 cm "3
1°12 (a)
,o, \ NA --_
Z 10 4
Z_ (c)o(-) lo 0
o
20 40
POSITION (_m)
Figure 4
General Analytical Solutions: Si:X, GaAs:X ....
P+
,, ,, ,,
• _
Distance of zones
,. _x=_/_.l /
II. Ax =
III. Ax = E_
V = -_-+ kT £n
Figure 5
3O
II. Transient Phenomenon due to A + Formation in Ge:Be Photoconductors
A slow transient response to step function increases in photon flux, with a time constant on
the order of 0.1 - 1.0 sec, has previously been identified and documented in Ge:Be photo-
conductors operation under low photon backgrounds at temperatures of 2-3 K (5). A combination
of modeling and experimental work has shown that the transient response is due to the effect of the
formation of the overcharged Be acceptor center Be +. This presentation summarizes a study of this
phenomenon which has recently been published (6), and the reader should consult this reference
for a complete description of the work.
The photoconductive response to a step function in photon signal as a function of temperature
is shown in Figure 6. The transient response has a time constant which is significantly longer than
would be expected due to either the free carrier lifetime or the dielectric relaxation time in the
material. We believe that the slow transient response is due to hole trapping by neutral Be atoms to
form the overcharged acceptor Be +. Be can bind three or even four holes because of the four-fold
degeneracy of the top of the valence band, and the existence of Be + has been clearly established
experimentally (7).
The mechanism for the trapping phenomenon is shown in Figure 7. Development of the rate
equations for the process results in an equation for the time constant x' associated with Be +
trapping and equilibration of
[Be ]'t' = 'to _ e E/kT (2)
where xo is the free carder lifetime, Be is the Be concentration, Nv is the valence band density of
states and E is the Be + binding energy.
A plot of ['r.'/'t"° x T 3/2] will have a slope proportional to the binding energy of the Be + center.
This is shown in Figure 8. The value of 4.3 meV which is obtained from the data is in excellent
agreement with the 4.5 meV binding energy of Be +. The application of uniaxial stress, which
breaks the degeneracy of the top of the valence band and eliminates Be + formation, also eliminates
the slow transient response, as shown in Figure 9. This gives additional support to the assignment
of the mechanism as associated with Be + formation.
Equation 2 can be adapted and used to estimate the time constant for A + or D- trapping in any
photoconductor material as a function of temperature. Overcharged acceptor and donor centers
have been identified in a variety of photoconductor materials, including Ge:Ga, Ge:Be, Si:P, Si:B
and Si:As.
31
In summary,aslow transientresponse,with a timeconstanton theorder of 0.1 to 1.0 sec.
between 2 and 3 K, has been observed in the photocurrent of Ge:Be extrinsic photoconductors.
The activation energy of the transient phenomenon (4.3 meV) and its behavior under applied
uniaxial stress indicate that trapping due to the formation of Be + centers is responsible for the
dynamics of the photoresponse. An analytical model of transient photoconductivity in a unipolar
system, where the trapping mechanism is associated with BeO---_ Be +, gives good agreement with
the experimental results.
References
.
2.
3.
4.
5.
6.
o
J. E. Ludman and J. Silverman, Infrared Physics 17, 177 (1977).
R. M. Westervelt and S. W. Teitsworth, J. Appl. Phys. 57, 5457 (1985).
N. M. Haegel and A. M. White, Infrared Physics, in press, 1989.
A. M. White, Infrared Physics 25, 729 (1985).
N. M. Haegel and E. E. Hailer, Infrared Physics 26, 247 (1986).
N. M. Haegel, J. W. Beeman, P. N. Luke and E. E. Hailer, Phys. Rev. B., 39, 3677
(1989).
E. E. Hailer, R. E. MacMurray Jr., L. M. Falicov, N. M. Haegel and W. L. Hansen,
Phys. Rev. Lett. 50, 612 (1983).
Acknowledgements
The author gratefully acknowledges the collaboration of A. M. White, of RSRE in Malvem,
England, in the modeling work for near-contact space charge. J. W. Beeman, P.N. Luke and E.
E. Hailer of Lawrence Berkeley Laboratory have contributed to the characterization of the Be +
transient response, and their work and interest are also acknowledged. This work has been
supported in part by NSF Grant DMR -8809298. I am also pleased to acknowledge the generous
support of my research program by a Fellowship in Science and Engineering from the David and
Lucile Packard Foundation.
32
E
O
c_
2.5 K 2.6 K 2.7 K
0.5 SEC/DIV
E
O
(b)
2.8K
0.5 SEC/DIV [c) 0.5 SEC/DIV
2.9K
(d) 0.5 SEC/DIV (e) 0.5 SEC/DIV
Figure 6
PROPOSED MECHANISM:
Hole trapping by Be ° to form Be +
uJ
f---.
...J
optical
generation
recombination o/-
Be 24.5 meV
----_---- -- Be 4.5 meV
Ev
thermal thermal
generation generation
Haegel, Beeman, Luke and Hailer, Phys. Rev. B.,
(in press) Feb. 15, 1989.
Figure 7
33
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Figure 8
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0 dynes/cm 2
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TIME (s)
Figure 9
34
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5


Near contact phenomena and transient effects in far infrared photoconductors

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