Effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-CdxHg₁₋xTe
The dependence of the conversion depth in CdxHg₁–xTe alloys subjected to ion-beam milling (CMT) on alloy composition and treatment temperature is studied both experimentally and theoretically. It is shown that in compositionally homogeneous crystals the dependence is defined by internal electric fie...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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| Zitieren: | Effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-CdxHg₁₋xTe / I.I. Izhnin, V.V. Bogoboyashchyy, K.R. Kurbanov, K.D. Mynbaev, V.M. Ryabikov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 1. — С. 53-59. — Бібліогр.: 19 назв. — англ. |
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irk-123456789-1199652017-06-11T03:04:40Z Effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-CdxHg₁₋xTe Izhnin, I.I. Bogoboyashchyy, V.V. Kurbanov, K.R. Mynbaev, K.D. Ryabikov, V.M. The dependence of the conversion depth in CdxHg₁–xTe alloys subjected to ion-beam milling (CMT) on alloy composition and treatment temperature is studied both experimentally and theoretically. It is shown that in compositionally homogeneous crystals the dependence is defined by internal electric fields, which affect the diffusion of charged intrinsic defects that arise as a result of the treatment. The results of calculations of the effect of the potentials of the p-n junction formed by ion-milling on the conversion depth fit well both the original experimental data and those taken from the literature. The data obtained confirm the validity of the diffusion model of the formation of the excessive mercury source in CMT subjected to ion-beam milling, which was proposed by the authors earlier. The results gained allow one to precisely predict and control the conversion depth in CMT crystals and epitaxial layers subjected to ion milling for p-n junction fabrication. This makes the results presented in the paper useful in CMT infrared detector technology. 2005 Article Effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-CdxHg₁₋xTe / I.I. Izhnin, V.V. Bogoboyashchyy, K.R. Kurbanov, K.D. Mynbaev, V.M. Ryabikov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 1. — С. 53-59. — Бібліогр.: 19 назв. — англ. 1560-8034 PACS: 73.61Ga, 61.72Vv, 61.80.Jh, 66.30Jt http://dspace.nbuv.gov.ua/handle/123456789/119965 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The dependence of the conversion depth in CdxHg₁–xTe alloys subjected to ion-beam milling (CMT) on alloy composition and treatment temperature is studied both experimentally and theoretically. It is shown that in compositionally homogeneous crystals the dependence is defined by internal electric fields, which affect the diffusion of charged intrinsic defects that arise as a result of the treatment. The results of calculations of the effect of the potentials of the p-n junction formed by ion-milling on the conversion depth fit well both the original experimental data and those taken from the literature. The data obtained confirm the validity of the diffusion model of the formation of the excessive mercury source in CMT subjected to ion-beam milling, which was proposed by the authors earlier. The results gained allow one to precisely predict and control the conversion depth in CMT crystals and epitaxial layers subjected to ion milling for p-n junction fabrication. This makes the results presented in the paper useful in CMT infrared detector technology. |
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| author |
Izhnin, I.I. Bogoboyashchyy, V.V. Kurbanov, K.R. Mynbaev, K.D. Ryabikov, V.M. |
| spellingShingle |
Izhnin, I.I. Bogoboyashchyy, V.V. Kurbanov, K.R. Mynbaev, K.D. Ryabikov, V.M. Effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-CdxHg₁₋xTe Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Izhnin, I.I. Bogoboyashchyy, V.V. Kurbanov, K.R. Mynbaev, K.D. Ryabikov, V.M. |
| author_sort |
Izhnin, I.I. |
| title |
Effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-CdxHg₁₋xTe |
| title_short |
Effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-CdxHg₁₋xTe |
| title_full |
Effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-CdxHg₁₋xTe |
| title_fullStr |
Effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-CdxHg₁₋xTe |
| title_full_unstemmed |
Effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-CdxHg₁₋xTe |
| title_sort |
effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-cdxhg₁₋xte |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119965 |
| citation_txt |
Effect of internal electrical field on compositional dependence of p-n junction depth in ion milled p-CdxHg₁₋xTe / I.I. Izhnin, V.V. Bogoboyashchyy, K.R. Kurbanov, K.D. Mynbaev, V.M. Ryabikov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 1. — С. 53-59. — Бібліогр.: 19 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT izhninii effectofinternalelectricalfieldoncompositionaldependenceofpnjunctiondepthinionmilledpcdxhg1xte AT bogoboyashchyyvv effectofinternalelectricalfieldoncompositionaldependenceofpnjunctiondepthinionmilledpcdxhg1xte AT kurbanovkr effectofinternalelectricalfieldoncompositionaldependenceofpnjunctiondepthinionmilledpcdxhg1xte AT mynbaevkd effectofinternalelectricalfieldoncompositionaldependenceofpnjunctiondepthinionmilledpcdxhg1xte AT ryabikovvm effectofinternalelectricalfieldoncompositionaldependenceofpnjunctiondepthinionmilledpcdxhg1xte |
| first_indexed |
2025-07-08T16:59:25Z |
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2025-07-08T16:59:25Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 1. P. 53-59.
PACS: 73.61Ga, 61.72Vv, 61.80.Jh, 66.30Jt
Effect of internal electrical field on compositional dependence of p-n
junction depth in ion milled p-CdxHg1–xTe
I.I. Izhnin1, V.V. Bogoboyashchyy2, K.R. Kurbanov3, K.D. Mynbaev4, V.M. Ryabikov5
1 R&D Institute for Materials SRC "Carat", 202 Stryjska Str., 79031 Lviv, Ukraine
2 Kremenchuk State Polytechnical University, 20, Pershotravneva Str., 39614 Kremenchuk, Ukraine
3 Institute of Economy and New Technology, 24/37, Proletarska Str., 39600 Kremenchuk, Ukraine
4 Ioffe Physico-Technical Institute, St.Petersburg, 194021 Russia
5 JSC Pure Metals, 3, Zavodska Str., 27500 Svitlovodsk, Ukraine
Abstract. The dependence of the conversion depth in CdxHg1–xTe alloys subjected to
ion-beam milling (CMT) on alloy composition and treatment temperature is studied both
experimentally and theoretically. It is shown that in compositionally homogeneous
crystals the dependence is defined by internal electric fields, which affect the diffusion of
charged intrinsic defects that arise as a result of the treatment. The results of calculations
of the effect of the potentials of the p-n junction formed by ion-milling on the conversion
depth fit well both the original experimental data and those taken from the literature. The
data obtained confirm the validity of the diffusion model of the formation of the
excessive mercury source in CMT subjected to ion-beam milling, which was proposed by
the authors earlier. The results gained allow one to precisely predict and control the
conversion depth in CMT crystals and epitaxial layers subjected to ion milling for p-n
junction fabrication. This makes the results presented in the paper useful in CMT infrared
detector technology.
Keywords: CdxHg1–xTe, ion-beam milling, conductivity type conversion.
Manuscript received 01.12.04; accepted for publication 18.05.05.
1. Introduction
Ion-beam milling (IBM) of narrow bandgap p-CdxHg1–xTe
(CMT) alloys is currently an approved technique for p-n
junction fabrication in CMT infrared detector technology
[1, 2]. The method is based on the phenomenon of the
formation of a thick surface layer with n-type
conductivity in an undoped p-type CMT crystal with
~ 1016 cm−3 Hg vacancies subjected to IBM [3]. It is
commonly accepted now that deep p- to n-type
conversion under IBM is due to the diffusion of
excessive interstitial Hg atoms generated under ion
milling. However, the exact mechanisms of defect
interaction in the converted layer and the effect of
external plasma are still under debate [4]; formation
mechanism of the source of the excessive mercury is not
understood either. Some authors believe that the
interstitial Hg atoms come from a layer etched from the
crystal surface during IBM. However, according to [5],
in reality the sputtered atoms originate only from the
depth of the first 2 – 3 atomic layers, which comprises a
layer not thicker than 1 nm. Authors of Ref. [1] believed
that about 0.02 % of mercury atoms released from the
crystal lattice as a result of IBM are first implanted in
the crystal down to the depth of 1 μm, and then move
further via plasma-stimulated diffusion. Quite a different
mechanism was suggested in Refs [6 – 8]. There, the
generation of excessive mercury was explained using the
mechanism based on the well-known model of a
“thermal spike” [9]. According to [6 – 8], at the spot
where the ion interacts with the surface, a microscopic
melt area is formed. This area very quickly crystallizes,
forming quite a few point defects in the cation sublattice.
These defects annihilate with each other, however, some
quick interstitial mercury atoms penetrate into the bulk
of the crystal, where they diffuse via relay mechanism
and interact with Hg vacancies and acceptor dopant
atoms, causing conductivity type conversion. The very
top CMT surface layer of 5 – 7 nm in thickness contains
a lot of defects, is depleted with Hg and thus, has p-type
conductivity.
Major features of p-n junction formation in CMT
subjected to IBM have been recently reviewed in [4].
Several conclusions were made there. First, it is noted
that in the majority of the IBM experiments the p-n
junction depth l appears to be proportional to the square
root of irradiation dose divided by the concentration of
the excessive tellurium (or Hg vacancy concentration in
case of homogeneous CMT) in the bulk of the crystal. At
the same time, in Refs [1, 10] where conversion was
studied in CMT epitaxial layers with a cap protective
layer, l depended on this relation linearly.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
53
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 1. P. 53-59.
Fig. 1. The dependence of the IBM-induced increase in the
electron concentration at 77 K, reduced to a sample area, on
the time of the storage at 300 K for the samples: 1 – P17-1, 2 –
P22-1.
Fig. 2. The dependence of the IBM-induced increase in the
electron concentration, reduced to a sample area, for the
sample P18-1 after storage, on the thickness of the removed
layer.
Secondly, a number of experiments revealed a
complex two-layer structure of the converted n-type
layer. In CMT with x = 0.2 after IBM, the top (surface)
layer up to 3 μm in thickness demonstrated the high
electron concentration (1017...1018 cm−3 at 77 K) with the
mobility of the order of about 104 cm2V−1s−1. The inner
layer was homogeneous with the electron concentration
and mobility of about 1015 cm–3 and 105 cm2V−1s−1,
respectively. According to [1], the top layer comprises a
0.5…1 μm-thick radiation-damaged layer and a
2…3 μm-thick second layer, in which the electron
concentration decreases exponentially from the surface.
Actually, radiation-induced damages, such as dislocation
loops located at ~ 50 nm below the surface have been
observed in CMT after IBM by transmission electron
microscopy [11].
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Yet another feature of IBM-induced conversion in
CMT, according to [4], was a strong dependence of the
conversion depth l on the alloy composition x. While in
narrow bandgap CMT with x = 0.2 l may reach hundreds
of micrometers [12], it quickly decreases with x
increasing, so at x > 0.4 the conversion takes place only
in a very thin surface layer [4]. This observation is
especially important since in modern CMT technology it
became a custom to cap free CMT surface with a thin
(~1 μm) wider bandgap protective layer [1, 4]. A drastic
decrease of l in CMT capped with such a layer has been
observed experimentally in [13].
The drastic decrease of l with increasing x is difficult
to interpret, if one believes that a source of Hg atoms is
the layer milled by the ions from the surface. In contrast
to this, the effect of x on l can be easily understood,
when a drift of charged interstitial mercury in electric
field originating at the interface between the very top
p-type defect layer and converted n-type layer is
considered, according to the model suggested in [6 – 8].
As the strength of the field increases with x increasing,
the conversion depth should decrease.
In this work, we report on experimental studies of the
conversion depth dependence in CMT under IBM on the
alloy composition, and correlate the experimental results
with those of theoretical calculations that model the
effect of the internal electric field on the process of
conversion at different temperatures. Calculations were
performed within the frames of the model [6 – 8]. The
results obtained confirm experimentally the validity of
the diffusion mechanism of Hg source formation in
CMT subjected to IBM, as proposed in [6 – 8].
2. Experiment
We have studied homogeneous single-crystal vacancy-
doped p-type CMT wafers with x = 0.16…0.28. The
crystals were grown using elemental Hg, Cd, and Te
with 6N class of purity at “Pure metals” factory
(Svitlovodsk, Ukraine) by vertical-directed
crystallization with replenishment from the solid phase.
They were doped with In, which ensured n-type
conductivity of the wafers with concentration
ND - NA ≈ 3⋅1014 cm−3 after IBM or low-temperature
annealing at Hg-saturated conditions. After the growth,
the wafers were annealed at 410 °C in Hg vapors to
obtain p-type conductivity with the mercury vacancy
concentration of 1016 cm−3. The vacancy concentration
was determined by measuring the hole concentration at
77 K. The measurements comprised investigations of
field dependences for the Hall coefficient and
conductivity, as well as processing the experimental data
using the Mobility Spectrum Analysis (MSA) method
[14] with consideration for the degree of vacancy
ionization at 77 K as depending on their concentration
and alloy composition [15, 16]. Parameters of the
samples are given in Table.
IBM milling was performed with Ar+ ions possessing
the energy 500 eV, ion current density j = 0.2 mA/cm2
and treatment duration t = 200 s. The temperature of the
samples during IBM was either 293 K (water cooling of
sample holder) or 345…350 K (no cooling).
The p-n junction depth was determined either by
measuring the Hall coefficient and conductivity of the
54
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 1. P. 53-59.
Sample parameters
Sample x
p77·10–16,
cm–3
[VHg]·10–16,
cm–3
Р16-1 0.202 1.47 1.30
Р17-1 0.162 2.40 2.30
Р18-1 0.206 1.21 1.04
Р19-1 0.212 1.31 1.22
Р20-1 0.242 0.78 0.71
Р21-1 0.228 1.16 1.12
Р22-1 0.276 0.64 0.72
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Fig. 3. The calculated dependence of the reduced conversion
depth on the alloy composition for T = 293 K (1) and 345 K
(2). Points designate experimental data from: 3 – this work, 4 –
Ref. [4].
samples with step-by-step chemical etching, or using
scanning electron microscopy in electron beam induced
current mode. To ensure time relaxation of IBM-induced
defects after the IBM, the samples were stored for two
months at room temperature. During the storage, the
Hall coefficient and conductivity of the samples were
periodically measured in various magnetic fields, and
being based on these data the electron and hole
concentrations at 77 K were determined using the MSA
method. Fig. 1 demonstrates an IBM-induced increase in
the concentration of electrons ΔNS with the mobility
~ 105 cm2V−1s−1, as measured at 77 K and reduced to a
sample area. The data are given for samples P17-1 and
P22-1 that represent the specimens with the lowest and
highest alloy composition x, respectively. It is seen from
the figure that the initial ΔNS value did not depend on x
and comprised ∼ 1014 cm−3; this value corresponds to
that typical of a radiation-damaged layer. With the
storage time tst increasing, ΔNS was decreasing as
τ+ st11 t with τ ∼ 103…104 s, and reached saturation
at tst > 103…104 min. Such behavior of ΔNS corresponds
to donor disintegration by a 3rd-order reaction. The fact
of n+ layer relaxation was confirmed by the results of
electrical measurements with step-by-step chemical
etching, performed with the crystals after the storage.
Fig. 2 shows the dependence of ΔNS on the thickness of
a chemically etched layer for the sample P18-1. It is seen
that the damaged layer after ~105 min of storage retained
only ∼ 1 – 2 % of the initial donor concentration; at the
same time, ΔNS did not exceed the value 3⋅1012 cm−2 in
the bulk of n-layer.
The measured values were used to calculate the p-n
junction depth lr reduced to the vacancy concentration
[VHg]0 = 1016 cm−3 and the ion fluence Φ 0 = 1018 cm−2:
,
][ Hg
Φ
Λ=
V
llr (1)
where Λ = Φ0 / [VHg]0 = 1 m is a characteristic ratio;
Φ = jt/e.
The experimental data are shown in Fig. 3. It is seen
there that the junction depth increases with temperature
increasing and decreases with x increasing.
3. Modeling
The proposed in this work model proceeds from the
assumption of the diffusion nature of excessive mercury
source as suggested in [6 – 8]. According to [5], CMT
etching with ions possessing ~ 1 keV energy sputters
only 2 to 3 atomic surface layers. Thus, the energy
imparted to a crystal by ions is mostly transferred into
heat [6], which leads to the formation of a microscopic
melt area, i.e., a thermal spike of Vmin ~ 10−19 cm−3 in the
volume and with the length L within the limits 5 to 7 nm.
Due to the very small value of Vmin, melt crystallization
and thermal relaxation of the thermal spike last less than
10−12 s [6]. Thus, after cooling down, the spike area
contains quite a few (N0 ∼ 1022 cm–3 [6]) non-
equilibrium defects, the majority of them being doubly
ionized mercury interstitials (HgI
⋅⋅) and vacancies (VHg″),
as well as neutral vacancy complexes, most probably
bivacancies (WHg
×). During relaxation of these defects
by means of mutual annihilation, which lasts trel ~ 10−9 s
[8], some interstitials penetrate from the defect layer into
the crystal bulk, thus forming a diffusion source of
excessive mercury at the external border of the
conversion layer. The interstitials further diffuse from
this source into the bulk of the crystal and annihilate
with mercury vacancies, causing p-to-n conductivity
type conversion.
Due to the fact that mercury atoms move from the
thermal spike area into the crystal, as well as to
preferential mercury evaporation during IBM of CMT
[5], the defect layer, which is the very thin surface layer
with the thickness L = 5…7 nm, is strongly depleted
with mercury. According to [8], 98 % of this mercury
deficiency exist in the form of neutral mercury
bivacancies, which interact with HgI
⋅⋅ much weaker than
ionized single vacancies VHg″. The maximum mercury
55
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 1. P. 53-59.
deficiency δ0 in the defect layer is reached when this
layer becomes impermeable for HgI
⋅⋅. This condition is
reached when δ0 = 1019 cm−3. Therefore, the defect
layer contains 0.02δ0
(i.e., ~ 2⋅1017 cm−3)
uncompensated VHg″, which define its p-type
conductivity [6, 8]. As a result, a p-n junction occurs at
the interface between the defect layer and the conversion
one. Electric field of this junction hinders HgI
⋅⋅ from
penetrating into the crystal.
As the defect layer is impermeable for HgI
⋅⋅, the
etched-out region (the top 1 nm of the layer [5]) cannot
act as a source of HgI
⋅⋅. Hence, the inner part of the
defect layer with a thickness of reltDI ≈ 1 nm, where
DI is the diffusion coefficient of HgI
⋅⋅ in the bulk of the
sample at the milling temperature. The average HgI
⋅⋅
concentration in the source is [8]:
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
δ
+
π
=
0
0
0 1ln
4
N
reD
jSc
wI
I . (2)
Here S is the effective area of the thermal spike
cross-section; N0 is the initial concentration of HgI
⋅⋅ in a
thermally relaxed thermal spike, r w = a / 2 is the
caption radius for HgI
⋅⋅ on a neutral Hg bivacancy, and
a = 0.648 nm is the CMT crystal lattice parameter.
To calculate the conversion depth as a function of
CMT characteristics and IBM parameters, let us consider
a semi-bounded crystal with a flat surface. The
coordinate z will be directed along the inner normal to
the surface, while the reference point z = 0 will coincide
with the interface between the defect layer and the
conversion one. If so, the surface of the crystal is located
at z = –L, where L is the thickness of the defect layer,
and the interface between the conversion layer and the p-
type “core” of the crystal is located at z = l. Within the
frames of the above listed assumptions, the density of
the diffusion flux of Hg at z = l according to [8] is
( )
1
0 B
0Hg
2
exp
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡ ϕΔ
= ∫
l
II dz
Tk
ze
cDJ ; (3)
subject to l >> r0, where r0 is the Debye screening
length. Here Δϕ = ϕ(z) – ϕ (0); ϕ is an electric field
potential of the structure.
The conversion depth l as a function of IBM duration
t can be calculated considering the conservation law for
the amount of matter at the inner boundary of the
conversion layer z = l, which appears as [6]:
Δtr dl = JHg dt, (4)
where Δtr is the density of caption centers for HgI
⋅⋅ in an
initial CMT crystal. In particular, in homogeneous
vacancy-doped CMT crystals Δtr = [VHg″]. Upon
integration of the Eq. (4) considering (2, 3), we get the
following equation:
( ) ( )
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
δ
+
Δπ
Φ
=⎥⎦
⎤
⎢⎣
⎡ ϕΔ
−∫
0
0
tr0
1ln
4
2exp N
r
Sdz
kT
zezl
w
l
. (5)
Solving the Eq. (5) requires to calculate the
distribution of the potential ϕ in the structure. At l >> r0
and (4π / 3)NIr0
3 << 1, where NI is the charged center
concentration in the diffusion region, it can be found on
the basis of the one-dimensional Poisson equation in the
continuous approximation:
( Npne
dz
d
S
−−
ε
π
=
ϕ 4
2
2
) . (6)
with N = ND – NA .
As the thickness of the defect layer L is of the order
of the screening length, we calculated ϕ by solving (5)
numerically. According to the above listed estimations
for the vacancy concentration in the defect layer, we
assumed that N = 4⋅1017 cm−3 at –L < z < 0. The donor
concentration in the conversion layer (z > 0) was taken
as N = 1 ⋅1015 cm−3, which is a typical value of N in
such an experiment. Since the HgI
⋅⋅ concentration in the
conversion layer is small (∼ 1012…1013 cm−3 [6 – 8]),
these defects were not considered in (5). In accordance
to [6], we assumed that L = 6 nm. The presence of the
damaged layer and top n-layer enriched with donors was
neglected as a first approximation. A possible influence
of these layers will be discussed below.
The electron and hole concentration in (6) were
calculated as
( )∫
∞ −
ε⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛ +−ϕ−ε
+ε=
0
1
exp1 d
kT
EFeNn C
e ; (7)
⎟
⎠
⎞
⎜
⎝
⎛ −+ϕ
−=
kT
EFeNp V
V exp . (8)
The density of states Ne (ε) was calculated using the
well-known formula:
( ) ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ ε
+⋅⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ ε
+ε
π
=ε
gg
e
e EE
mN 2112
32
23
h
; (9)
where
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+Δ
⋅+⋅+γ−
=
g
g
g
p
S
e
E
E
E
E
mm
0
0
2
11
3
2
[17].
We assumed that Ep = 17.3 eV; γS = 0.5 [17];
Δ0 = 0.96 eV [18]. Here γS is a parameter that allows for
the effect of remote bands similar to the Luttinger
parameters; 22
02 hPmEp = . Calculations were
performed using the empirical data from [19] for the
density of states inherent to heavy holes NV:
56
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 1. P. 53-59.
Fig. 4. The calculated dependence of the potential difference of
the defect layer field (1, 2) and of the potential of a varyband
protective layer (3, 4) on the composition of the protective
layer in CMT structure with x = 0.2 at T = 293 K (1, 3) and
345 K (2, 4).
Fig. 5. Temperature dependence of the conversion depth,
reduced to the vacancy concentration 1⋅1016 cm−3 and ion
fluence 1⋅1018 cm−2, in narrow bandgap CMT subjected to
IBM. The points show experimental data from Ref. [12] for
vacancy-doped CMT (x = 0.21) with the hole concentration
1⋅1016 (1) and 5⋅1015 cm−3 (2) at 77 K. Line 3 presents the
results of calculations by the formula (12) for x = 0.20.
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
++⎥⎦
⎤
⎢⎣
⎡
π
=
2
21
23
2
B 1
2
2
T
T
T
TTkmN hh
V
h
; (10)
where T1 = 334 K and T2 = 594 K are fitting parameters
with the temperature dimensionality, mhh = 0.40m0 is
the effective mass of heavy holes at ε = 0.
The bandgap value as a function of the
temperature and alloy composition was calculated using
the interpolation formula from [19]:
Eg (x,T) = –0.3098 + 1.9409x –0.7351x 2 +
+ 0.7061x 3 + 6.345⋅10−4T(1 –2.195x +
+ 0.309x 2 + 0.343x 3) eV. (11)
According to [19], (11) accounts for the temperature
dependence of Eg better than other formulae, since it
correctly considers the dependence of pre-exponential
factor α0 on Eg, temperature and population of states in
the conduction band in Urbach’s rule.
4. Results and discussion
Eq. (5) was solved in [6 – 8] for conductivity type
conversion in compositionally uniform CMT subjected
to IBM. According to obtained solution, the conversion
depth is given as
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ ϕΔ
−
ΔΛ
Φ
=
kT
e
ll exp
tr
0 ; (12)
where
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
δ
+
π
Λ
=
0
0
0 1ln
2
N
r
Sl
w
. (13)
Here Δϕ = ϕ(l) – ϕ(0) is the potential difference
between internal (z = l) and external (z = 0) boundaries
of the conversion layer.
It is seen that the factor l0 defined by (12) and (13) is
independent of the mercury interstitial diffusion
coefficient DI, because the HgI
⋅⋅ concentration in the
diffusion source, according to (2), is inversely related to
DI. Hence, l0 does not depend on the diffusion
coefficient of HgI
⋅⋅, and therefore, on the temperature.
The dependence of l0 on the alloy composition is
determined by its dependence on S and should be,
therefore, weak. Thus, the dependence of l on T and x is
generally determined by the last (exponential) factor in
(12). Assuming, according to the estimations of [6], that
S ∼ 10−13 cm−3, N0 ∼ 1022 cm–3, and δ0 ∼ 1019 cm−3, we
can assess l0 as ~ 155 μm.
Fig. 4 (curves 1 and 2) presents the calculated value
of Δϕ = ϕ(∞) – ϕ(0) as depending on x for
compositionally homogeneous CMT at T = 293 and
345 K; these temperature values correspond to the two
applied IBM techniques, namely, with cathode water
cooling and without cooling, respectively. It is seen that
Δϕ > 0, therefore, the electric field at the interface
between the defect layer and the conversion one hinders
the diffusion of positively charged HgI
⋅⋅ atoms into the
crystal. When x value is big, Δϕ increases with x almost
linearly. When x < 0.28, this dependence gets weaker
with x decreasing. With temperature increasing, Δϕ
decreases, and the conversion depth l increases.
The calculated conversion depth l in vacancy-doped
CMT is presented in Fig. 3. For calculations, we
assumed that Φ = 1 ⋅1018 cm–2 and ΔTe = 1 ⋅1016 cm–3, so
l = lr. It is seen from the figure that the values of lr
calculated according to the proposed model agree well
with those experimentally observed, if the factor l0 in
(12) is assumed to be l0 = 143 μm. We should like to
emphasize that the l0 value obtained by fitting was very
close to l0 ≈ 155 μm derived theoretically. This strongly
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
57
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 1. P. 53-59.
supports the validity of the proposed conversion
mechanism. Therefore, it is the dependence of Δϕ on
alloy composition that most probably determines the l(x)
dependence in compositionally uniform CMT.
The calculated dependence of the reduced conversion
depth l r , as defined by (1), on the temperature is given in
Fig. 5 (curve 3). The calculations were performed for
CMT with x = 0.2 under the assumption that
l0 = 143 μm. Fig. 5 (points 1 and 2) also demonstrates
the values of l r calculated using (1) on the basis of
experimental data [12] for two CMT crystals with the
vacancy concentration 1⋅1016 cm−3 (1) and 5⋅1015 cm−3
(2) subjected to IBM at the temperatures 130, 170, 230
and 330 K, and ion fluence Φ = 4 .5 ⋅1018 cm−2. It is
obvious that, in this case, the calculated values agree
well with the experimental data, too. The fact that
experimentally derived values of l r exceed those
obtained by calculations by the factor of ~ 1.5, can be
explained by higher IBM current density in [12]
(0.6 mA/cm2). Such current density causes strong
thermal effects that mask the pure phenomenon.
We should like to emphasize that in our model the
dependence of l on temperature is explained solely by
the variation of the potential ϕ with T, while in [12] this
dependence was related to the temperature dependence
of the diffusion coefficient of interstitial mercury. In our
model, according to (12) and (13), l does not depend on
this diffusion coefficient.
The results presented in this paper do not account for
the effect of the damaged layer and/or top n-layer with
the high donor concentration. Generally speaking, these
layers may affect the conversion via their effect on the
potential of the electrostatic filed and by capturing
mercury interstitials on radiation-induced defects.
Under the assumption that the potential of the top
n-layer complies with the Poisson equation in the
continuous approximation (6), the potential difference
ϕN for electrons in the top n-layer and in the bulk of the
conversion layer is about (2 – 3)kBT/e at N ∼ 1017 cm−3,
and it can strongly affect the conversion depth l.
However, in reality the effective eϕN value should be
substantially smaller due to the strong non-uniformity in
the potential of the top n-layer of the range of few kBT,
and mercury interstitials can selectively migrate along its
valleys. This non-uniformity is caused by two factors.
The first of them is high density of dislocations in the
damaged layer (∼ 1013 cm−2 [11]); these dislocations
strongly polarize the medium by their elastic field due to
deformation reciprocal action. The second one is
insufficient screening of the donor potential at
NI ∼ 1017 cm−3; in this case (4π / 3)NIr0
3 ≈ 1, and the
continuous approximation (6) is not valid for the n-layer.
In this situation, the effective value of eϕN is determined
not by the average value of the potential, but rather by its
values along the real paths of HgI
⋅⋅ migration. For the
reason, the potential of the damaged layer affects the
conversion depth at l > > 1 μm very scarcely.
The other option for the effect of the top n-layer is
the caption of non-equilibrium HgI
⋅⋅ on neutral radiation-
induced defects in this layer. The fact that it is by this
mechanism the top n-layer is formed is favored by the
deep relaxation of its conductivity (see Fig. 1). For this
relaxation, the observed variation of the carrier
concentration with time is best explained by the reaction
of neutralization of a doubly ionized donor by free
electrons: 2e′ + D ⋅⋅→ D×.
In such a system, on one hand, one might observe a
specific relay mechanism of acceleration of HgI
⋅⋅
diffusion, since when a free charged defect gets in the
n-layer, it decreases the energy of already captured
defects of the same charge sign, and stimulates the
dissociation of complexes on the distance of the order of
r0. This phenomenon can only weaken the effect of the
top n-layer on the conversion depth. On the other hand,
the caption of HgI
⋅⋅ on radiation-induced defects
decreases the flux of HgI
⋅⋅ in the depth of the conversion
layer, which is equivalent to the decrease of the effective
rate of HgI
⋅⋅ generation by the rate of surface drain
generation. However, the amount of the interstitial
mercury atoms captured on radiation-induced defects
(~ 5⋅1013 cm−2, see Fig. 1), is of the same order as that of
the atoms captured on the vacancies in the bulk of the
conversion layer; hence, the latter effect can account
only for a non-crucial l0 renormalization.
5. Conclusions
The diffusion model of the formation of the excessive
Hg source in CMT crystals subjected to IBM, proposed
by the authors [6 – 8], explains all the basic features of
the dependence of the conversion depth on the IBM
temperature and alloy composition both quantitatively
and qualitatively. This is true in relation to both
compositionally homogeneous CMT crystals and for the
samples with a wide bandgap protective layer. The
major factor, which defines these dependences, is an
electric field located at the interface between the p-type
defect layer and the n-type conversion layer, as well as
in the varyband region of the structures. The p-n junction
field weakens the flux of Hg atoms from the source into
the crystal, while the varyband region field enhances it.
At small irradiation doses, the drift of charged interstitial
Hg in the varyband region field leads to the linear
dependence of the conversion depth on the ion dose,
while the slope of this dependence becomes inversely
proportional to the initial Hg vacancy concentration. The
results presented in this work allow one to precisely
predict and control the conversion depth in CMT crystals
and epitaxial layers subjected to IBM, which is
important to modern CMT-based photodetector
technology.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
58
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 1. P. 53-59.
6. Acknowledgments
These investigations were partly supported by the
Ministry of Education and Science of Ukraine.
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© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
59
Abstract. The dependence of the conversion depth in CdxHg1–xTe alloys subjected to ion-beam milling (CMT) on alloy composition and treatment temperature is studied both experimentally and theoretically. It is shown that in compositionally homogeneous crystals the dependence is defined by internal electric fields, which affect the diffusion of charged intrinsic defects that arise as a result of the treatment. The results of calculations of the effect of the potentials of the p-n junction formed by ion-milling on the conversion depth fit well both the original experimental data and those taken from the literature. The data obtained confirm the validity of the diffusion model of the formation of the excessive mercury source in CMT subjected to ion-beam milling, which was proposed by the authors earlier. The results gained allow one to precisely predict and control the conversion depth in CMT crystals and epitaxial layers subjected to ion milling for p-n junction fabrication. This makes the results presented in the paper useful in CMT infrared detector technology.
Fig. 2. The dependence of the IBM-induced increase in the electron concentration, reduced to a sample area, for the sample P18-1 after storage, on the thickness of the removed layer.
Fig. 3. The calculated dependence of the reduced conversion depth on the alloy composition for T = 293 K (1) and 345 K (2). Points designate experimental data from: 3 – this work, 4 – Ref. [4].
Fig. 4. The calculated dependence of the potential difference of the defect layer field (1, 2) and of the potential of a varyband protective layer (3, 4) on the composition of the protective layer in CMT structure with x = 0.2 at T = 293 K (1, 3) and 345 K (2, 4).
Fig. 5. Temperature dependence of the conversion depth, reduced to the vacancy concentration 1(1016 cm−3 and ion fluence 1(1018 cm−2, in narrow bandgap CMT subjected to IBM. The points show experimental data from Ref. [12] for vacancy-doped CMT (x = 0.21) with the hole concentration 1(1016 (1) and 5(1015 cm−3 (2) at 77 K. Line 3 presents the results of calculations by the formula (12) for x = 0.20.
Under the assumption that the potential of the top n-layer complies with the Poisson equation in the continuous approximation (6), the potential difference (N for electrons in the top n-layer and in the bulk of the conversion layer is about (2 – 3)kBT/e at N ( 1017 cm−3, and it can strongly affect the conversion depth l. However, in reality the effective e(N value should be substantially smaller due to the strong non-uniformity in the potential of the top n-layer of the range of few kBT, and mercury interstitials can selectively migrate along its valleys. This non-uniformity is caused by two factors. The first of them is high density of dislocations in the damaged layer (( 1013 cm−2 [11]); these dislocations strongly polarize the medium by their elastic field due to deformation reciprocal action. The second one is insufficient screening of the donor potential at NI ( 1017 cm−3; in this case (4( / 3)NIr03 ( 1, and the continuous approximation (6) is not valid for the n-layer. In this situation, the effective value of e(N is determined not by the average value of the potential, but rather by its values along the real paths of HgI(( migration. For the reason, the potential of the damaged layer affects the conversion depth at l>>1 (m very scarcely.
References
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