Microwave Absorption by Light-induced Free Carriers in Silicon
T. Sameshima and T. Haba
Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan
E-mail address: tsamesim@cc.tuat.ac.jp
Keywords: free carrier absorption, carrier density, carrier mobility, effective lifetime,
photo-induced carrier, recombination velocity

Abstract.
Microwave absorption caused by free carrier was investigated using an equipment of the
9.35-GHz-microwave interferometer and a numerical analysis program. Free carrier absorption
caused by light-induced carriers was investigated for silicon samples coated with
100-nm-thermally grown SiO2 layers as well as SiOx layers deposited by the evaporation
method. The effective minority carrier lifetime and the recombination velocity at SiO2/Si wereanalyzed in the case of photo-induced carrier generation with 532-nm-light illumination. The
effective minority carrier lifetime was increased from 360 to 540 μs and the recombination
velocity was decreased from 78 to 30 cm/s by 1.3x106-Pa-H2O vapor heat treatment at 260oC
for 3h for light illumination at 0.315 mW/cm2 in the case of thermally grown SiO2/Si becauseof passivation of SiO2/Si interfaces. They were markedly increased from 30 to 380 μs and from1300 to 60 cm/s by the H2O vapor heat treatment in the case of vacuum evaporated SiO2/Si,
respectively. Light-induced free carrier absorption was also observed for sample of a pnjunction formed by boron doping at a surface region by ion implantation followed by laser
irradiation with no passivation layers.

Introduction
Non-destructive and non-contact measurement method of electrical properties ofsemiconductor is attractive as monitoring samples during the device fabrication process. Free
carrier optical absorption effect is sensitive in microwave region. Free carriers insemiconductors respond to the incident electrical field of microwave on the order of GHz andcomplex refractive indexes can change so that transmissivity changes with the density of free
carriers [1,2]. Analysis of photo-induced carrier properties is also important for photovoltaic
devices such as solar cells. Measurements of microwave photoconductive decay [3] andquasi-steady-state photoconductance [4] have been widely used for measurement of the photo
induced minority carrier lifetime.
In this paper, we report a precise analysis of photo-induced carrier properties in silicon using
the microwave free carrier absorption effect. We present an equipment of microwave
interferometer developed for sensitive detection of free carrier absorption. The density of photo
induced carrier in silicon caused by light illumination is reported. We discuss changes in theeffective minority carrier lifetime induced by surface passivation by high pressure H2O vapor
heat treatment. Moreover, we also report light-induced free carrier absorption for sample of a pnjunction formed by boron doping at a surface region.

Experimental

Equipment: Figure 1 shows a schematic
equipment of the free carrier absorption
measurement system [5]. The 9.35-GHz
microwave
wasemittedbyafield-effect-transistor-(FET)-type oscillator.
Its intensity was modulated at a frequency of
1 kHz. The microwave was introduced usinga waveguide tube. It was symmetrically split
into two branches by a T-type waveguide.
There was a 1-mm gap each branch formeasurement of sample wafers, which wereinserted in the gaps A and B, respectively.
The microwaves transmitted through thesamples were combined using another Fig.1 Schematic equipment of microwave freeT-type waveguide, as shown in Fig.1. The carrier absorption measurement system
intensities of the sum IA+B and difference
IA-B of the microwaves in the two branches were detected by high-speed-diode rectifiers and thesignals were amplified by 1-kHz-lock-in amplifiers. The transmissivity of the sample A is
obtained as,
TA =

EA

2

E B0

2

= 2

I A+ B + I A− B
−1
I0

(1),

where I0 is a value of TA+B when there were no samples in the two gaps. The detection accuracyof the present system in the transmissivity was ±0.1%. A thin light scattering plate was inserted
into the gap A facing to the samples as shown in Fig. 1. A laser light at 532 nm was introduced
using optical fibers to the light scattering plate, which gave uniform illumination of the green
light to the samples. The intensity of the laser light was controlled from 0 to 3.27 mW/cm2 at
the sample surface.
Sample fabrication: In order to investigate surface effect on photo-induced carriers, fourkinds of samples were fabricated using p-type silicon wafers with resistivity ranging 22~23.5
Ωcm and a thickness of 625 μm. The surfaces of every silicon wafer were coated with
100-nm-thick SiO2 layers by the thermally grown method at 1100oC at first. The silicon wafer
coated with as-thermally grown SiO2 layers was used at the gap B as reference. The same kindof silicon wafer coated with thermally grown SiO2 layers was also inserted in the gap A andilluminated with 532-nm-green-laser light for photo-induced carrier measurement (sample 1).
Heat treatment in 1.3x106 Pa H2O vapor at 260oC for 3h was also applied to the samples toreduce the density of defect states localized at SiO2/Si interface (sample 2) [6]. In order toinvestigate low temperature surface passivation, SiOx films were also deposited at room
temperature on the top silicon surface by the vacuum evaporation of powdered SiO at a basepressure of 4x10-4 Pa after removing the thermally grown SiO2 layer by buffered HF solution at
the top surface and still keeping the thermally grown SiO2 at the rear surface (sample 3). Heat
treatment in 1.3x106 Pa H2O vapor at 260oC for 3h was also applied to the samples (sample 4).
The optical reflectivity at 532 nm was measured at the surface of samples.
A sample with a pn junction was fabricated in n-type silicon wafers with a resistivity of 70
Ωcm. Boron atoms were implanted with a density of 3x1013cm-2 and at 30 keV. They wereactivated by pulsed UV laser irradiation at 0.6 J/cm2. No surface passivation with oxide layers
was formed on the silicon surfaces
TheoryThe free carrier absorption effect is basically explained by the Drude theory [1,2]. Free
carriers in silicon vibrate according to the electrical field of the microwave. The vibration offree carriers causes a polarization, which induces change in the effective dielectric constant.
The effect of photo-induced carriers caused by illumination of green light was analyzed. The
complex dielectric constants are given as,⎛ε r = ε Si ⎜ 1 −⎝ω p12τ 12
ω p 2 2τ 2 2 ⎞−⎟1 + ω 2τ 12 1 + ω 2τ 2 2 ⎠⎛ω p12τ 1
ω p 2 2τ 2 ⎞+⎟⎜ ω (1 + ω 2τ 12 ) ω (1 + ω 2τ 2 2 ) ⎟⎝⎠ε i = ε Si ⎜

(2),

(3),

where τ1 and τ2 are the lifetimes of the majority carriers and minority carriers, respectively,
which are supposed to be given by the hole and electron carrier mobilities at the substrate
doping concentration, εsi is the dielectric constant of intrinsic silicon, ωp1 and ωp2 are the plasma
angular frequencies of the majority carriers and minority carriers, respectively, and εr and εi isreal part of the complex dielectric constant and the imaginary part of that of silicon, respectively.
ωp1 was 7x1011 rad/s in the present p-type silicon. It is much higher than the microwave
frequency. For crystalline silicon, the resistivity gives the carrier density and the carrier
mobility, because the relation between the carrier density and the carrier mobility has been welldefined [7] and the carrier life time is given by the carrier mobility.
Light illumination with an intensity of W per unit area gives a photon flux G=W/hv per unit
area, where h is the plank constant and v is the frequency of the green laser light. When thedensity of photo-induced carrier caused by photon flux G is enough lower than the density ofthe majority carriers par unit area, the photo-induced carrier density in-depth distribution
Nphoto(x) is given by carrier diffusion model for a steady state condition as,[8]D

d 2 N photo ( x )
dx

2

−

N photo ( x )

τb

=0

(4),

where D is the electron carrier diffusion coefficient, τb is the minority bulk carrier lifetime,
which is far different from the carrier lifetime τ and τ2 previously shown in eqs. (2) and (3).
Although τ and τ2 typically ranging from 0.07 to 0.2 ps, the minority carrier bulk lifetime ismuch longer because it is the time constant of carrier annihilation. The present silicon wafers
with the carrier concentration ranging from 6.0x1014~ 5.5x1014 cm-3 typically have an electron
minority carrier bulk life time of about 1 ms based on a precious literature.[9] Laser light at
532nm illuminated at the top surface is absorbed within the top 1μm depth because of the highabsorption coefficient of about 104 cm-1. We therefore place the boundary condition of carrier
generation and carrier recombination ratios as,DD

dN photodx(5),= − S2 N photo ( d )

(6),

x =0

dN photodx= S1 N photo ( 0 ) − η (1 − r )G

x =dwhere S1 and S2 are recombination velocities of the two surfaces of silicon, η is the quantum
efficiency for photo carrier generation, which is assumed as 1 in this investigation, r is the
optical reflectivity of sample surfaces at green laser light, d is the thickness of the silicon wafer,
The eqs. (4)~(6) give the density of photo carrier Nphoto(x) as,
N photo ( x ) =x
2d − x⎛⎛ D⎞ − Dτ b ⎛ D⎞ − Dτ b ⎞
S
e
S
e
−
+
+
⎜
⎟
⎜
⎟
⎜
⎟
2
2
2d
⎟
⎛ D
⎞⎛ D
⎞ ⎛ D
⎞⎛ D
⎞ − Dτ b ⎜⎝ ⎝ τ b
⎠
⎝ τb
⎠
⎠
− S2 ⎟ ⎜+ S1 ⎟ − ⎜− S1 ⎟ ⎜+ S2 ⎟ e
⎜
τ
τ
τ
τ
b
b
b
b
⎝
⎠⎝
⎠ ⎝
⎠⎝
⎠

η (1 − r )G(7).

The total photo induced minority carrier density per unit area n is obtained by integration of
Nphoto(x) from 0 to d as,

⎛

⎞
⎟
d
⎜
⎟
⎛ D
⎛ D
⎞ − Dτ b ⎞⎝⎠− S2 + ⎜+ S2 ⎟ e
n=
⎟
2d ⎜
⎟
⎛ D
⎞⎛ D
⎞ ⎛ D
⎞⎛ D
⎞ − Dτ b ⎜⎝ τ b⎝ τb⎠⎠− S2 ⎟ ⎜+ S1 ⎟ − ⎜− S1 ⎟ ⎜+ S2 ⎟ e
⎜
τ
τ
τ
τ
⎝ b
⎠⎝ b
⎠ ⎝ b
⎠⎝ b
⎠

η (1 − r )G Dτ b ⎜ 1 − e

−

d
Dτ b

(8).

In the present case, the electron minority carrier diffusion coefficient D is 36 cm2/Vs. We also
assume that the both surfaces coated with thermally grown SiO2 have a same quality with asame minority carrier recombination velocity.
The calculation program confirmed that the detection accuracy 0.1% of the present
microwave equipment allowed us to observe change in a photo carrier density per unit area of
5x1010cm-2. It means that the present measurement and analysis system has a possibility ofinvestigation of photo-induced carrier behavior in a low injection condition. The photo induced
minority carrier density per unit area n gives the effective minority carrier lifetime τeff as,n = η (1 − r )Gτ eff(9),where carrier annihilation rates at the surfaces and in the silicon bulk are reciprocally
represented by τeff, which corresponds to the effective minority carrier lifetime obtained byconventional equipments [3,4]. When τb is given, S1 and S2 as well as Nphoto(x) can beanalyzed using eqs (7) and (8).
Results and discussion

Transmissivity of 9.35-GHz-microwave isdetermined by the optical interference effectcaused by spatially distribution of Fresnel
coefficient. Figure 2 shows transmissivity ofsilicon wafers with different resistivity as afunction of substrate thickness. The transmissivity
changed periodically with the substrate thickness
in the case of 10000 Ωcm because of change inphases between microwaves incident at the top
and reflected from the rear surfaces. The
transmissivity decreased as the resisistivity
decreased because free carrier optical absorption
became important. There was a substantial
absorption for the sample with a thickness of 625
μm at 23 Ωcm and the transmissivity was 27%.
Figure 3 shows the transmissivity as a functionof the intensity of 532-nm light illumination for
four kinds of silicon samples. Solid triangles
show transmissivity for the sample with both
surfaces coated with thermally grown SiO2 layers.
Open triangles show transmissivity after
high-pressure H2O vapor annealing of the sample
with both surfaces coated with thermally grown
SiO2 layers. Solid circles show transmissivity forthe sample with the top surface coated with SiOx
layers. Open circles show transmissivity after
high-pressure H2O vapor annealing of the sample
with the top surface coated with SiOx layers. The
transmissivity monotonously decreased as thelight intensity increased from 0 (dark field) to
3.27 mW/cm2 for every sample. This is becauseof free carrier absorption by photo-induced

Fig.2: Transmissivity of silicon wafers withdifferent resistivities as a function ofsubstrate thickness.

Fig.3: Transmissivity as a function of theintensity of 532-nm light illumination for
four kinds of silicon samples.

carriers. The sample with the both surfaces coated with thermally grown SiO2 andhigh-pressure H2O vapor annealed showed the highest decrease in transmissivity from 27.1 to21.6% as the light intensity increased from 0 to 3.27 mW/cm2. On the other hand the sample
with as-deposited SiOx layer on the top surface showed the lowest decrease in transmissivity
from 26.5 to 24.5%.
Figure 4 shows the effective minority carrier
lifetime (a) obtained by the results of Fig.3 andthe surface recombination velocity (b) when theelectron minority carrier bulk lifetime wasassumed to be 1 ms. The sample treated withhigh-pressure H2O vapor annealing of siliconwith the both surfaces coated with thermallygrown SiO2 had highest effective minority carrier
lifetimes ranging from 400 to 540 μs for the lightintensity ranging from 0.315 to 3.27 mW/cm2. On
the other hand, the sample with the both surfaces
coated with thermally grown SiO2 before
high-pressure H2O vapor annealing had aneffective minority carrier lifetime ranging from
260 to 360 μs. High-pressure H2O vapor heat
treatment increased the effective minority carrier
lifetime because of passivation of thermallygrown SiO2/Si interfaces. The sample
as-deposited SiOx layer on the top surface had Fig.4: Effective minority carrier lifetime
low effective minority carrier lifetimes, whichmarkedly increased from 30 to 180 μs as the light (a) and recombination velocity (b) as aintensity increased from 0.315 to 3.27 mW/cm2. function of the intensity of 532-nm light
It indicates that as-deposited SiOx/Si interface illumination.
had substantial defect states which reduced theeffective minority carrier lifetime. The effective minority carrier lifetime was increased byhigh-pressure H2O vapor annealing to 250 to 380 μs similar to that of sample coated withthermally grown SiO2 layers. This indicates that high-pressure H2O vapor heat treatment
effectively passivated SiOx/Si interfaces.
The sample treated with high-pressure H2O vapor annealing of silicon with the both
surfaces coated with thermally grown SiO2 had the lowest recombination velocity ranging from25 to 45 cm/s, which was almost constant for the light intensity ranging from 0.315 to 3.27
mW/cm2. On the other hand, the sample with the both surfaces coated with thermally grown
SiO2 had the recombination velocity ranging from 65 to 90 cm/s. High-pressure H2O vapor
heat treatment achieved passivation of thermally grown SiO2/Si interfaces by reduction of therecombination velocity. The sample as-deposited SiOx layer on the top surface had a highrecombination velocity, which markedly decreased from 1300 to 200 cm/s as the light intensity
increased from 0.315 to 3.27 mW/cm2. It indicates that as-deposited SiOx/Si interface hadsubstantial defect states which caused serious recombination of photo-induced carriers. The
recombination velocity was decreased by high-pressure H2O vapor annealing to 60~90 cm/s
similar to that of sample coated with thermally grown SiO2 layers.
Figure 5 shows the transmissivity as a function of the intensity of 532-nm light illumination
for boron doped samples. The transmissivity decreased from 36.4 to 35.3% as the lightintensity increased from 0 to 3.27 mW/cm2 when the laser light was irradiated to the boron
doped top surface. The density of photo-induced carrier increased to 4.0x1011 cm-2. However
no change in transmissivity was observed when the laser light was irradiated to the rare surface.
Dashed lines are a calculated transmissivity when the recombination velocities were 0 cm/s forthe boron doped surface and 30000 cm/s for the rear surface. Good agreement between
experimental and calculated transmissivities means that the pn junction decreased therecombination velocity because of formation of potential barrier. Heavily boron doped regions
decreased electron density at the top surface and decreased recombination probability.

5. Summary
We reported free carrier absorption in orderto analyze electrical properties of silicon. A
9.35-GHz microwave interferometer wasconstructed by waveguide tubes with having
two narrow gaps for measurements of siliconwafers. We also developed a numerical analysis
program including free carrier opticalabsorption and the optical interference effect inorder to calculate the microwave transmissivity.
Free carrier photo absorption caused byphoto-induced carriers was experimentallymeasured and numerically analyzed for
625-μm-thick silicon samples coated with Fig.5 Transmissivity as a function of the
100-nm-thermally grown SiO2 as well as SiOx intensity of 532-nm light illumination forlayers deposited on the top-surface by the boron doped samples. Dashed lines are aevaporation method.
The 532-nm lighttransmissivity
whenthe
illumination ranging 0.315 to 3.27 mW/cm2 calculated
recombination
velocity
is
0
cm/s
at
the
boron
decreased the transmissivity owing to free
carrier absorption caused by photo-induced free doped surface and 30000 cm/s at the rearcarriers. The present equipment detected surface.
photo-induced minority carrier density per unit
area above 5x1010cm-2. The effective minority carrier lifetime was analyzed. It increased from360 to 540 cm/s for illumination at 0.315 mW/cm2 by 1.3x106-Pa-H2O vapor heat treatment at
260oC for 3h in the case of thermally grown SiO2/Si because of passivation of SiO2/Si
interfaces. It markedly increased from 30 to 380 μs by the H2O vapor heat treatment in the caseof SiOx layers deposited at the top surface. The recombination velocity was analyzed when theminority carrier bulk lifetime was assumed to be 1 ms. It was decreased from 78 to 30 cm/s
for illumination at 0.315 mW/cm2 by 1.3x106-Pa-H2O vapor heat treatment at 260oC for 3h inthe case of thermally grown SiO2/Si because of passivation of SiO2/Si interfaces. It wasmarkedly decreased from 1300 to 60 cm/s by the H2O vapor heat treatment in the case of SiOx
layers deposited at the top surface. Formation of pn junction by 3x1013-cm-2-boron doping in
a 70-Ωcm-n-type silicon reduced the surface recombination velocity and caused a density ofphoto-induced carrier of 4.0x1011 cm-2 at 3.27 mW/cm2 light illumination.

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