Surface voltage and surface photovoltage - Dieter Schroder ...

D K Schroder
φ s
(V)
1
0.5
0
-0.5
t ox
= 9.2 nm
Depletion
Accumulation
-1
-1.5 10 -7 0 1.5 10 -7
Q (C/cm 2 )
Inversion
Figure 18. Surface potential versus charge showing the various
regions of the device. t ox = 9.2 nm. After Roy et al [43].
device is biased into accumulation or inversion, the oxide
thickness is given by
C ox = dQ t ox = K oxε 0
. (32)
dφ s C ox
This method is not subject to the poly-Si gate depletion effects
that affect conventional MOS-C measurements [45]. It is also
not affected by probe punchthrough and is relatively insensitive
to oxide pinhole leakage currents. Repeatability of 0.01 nm
has been demonstrated for 1.8 nm thick oxides [40].
5.5. Oxide leakage current
To determine oxide leakage current, usually known as gate
current in MOS devices, corona charge is deposited on the
surface of an oxidized wafer and the surface voltage is
measured as a function of time. The device is biased into
accumulation or inversion and the oxide leakage current is
related to the voltage through the relationship [46]
I leak = C ox
dV P
dt
⇒ V P (t) = I leak
C ox
t. (33)
When the charge density is too high, the charge leaks very
rapidly through the oxide by Fowler–Nordheim or direct
tunnelling and the surface voltage is clamped.
The deposited charge density is related to the oxide electric
field E ox through the relationship
Q = K ox ε 0 E ox = 3.45 × 10 −13 E ox (34)
for SiO 2 . Silicon dioxide breaks down at electric fields of
10–14 MV cm −1 .ForE ox = 12 MV cm −1 ,wefind the charge
to be 4.1 × 10 −6 Ccm −2 . Figure 19 is a plot of E ox versus Q,
clearly showing the electric field saturation at a charge density
of around 4.4 × 10 −6 Ccm −2 .
6. Frequency-dependent surface photovoltage
Most SPV measurements are made under dc conditions. It may
be that the incident light is chopped at a moderate frequency
(typically 500–600 Hz) for signal/noise enhancement through
lock-in techniques. However, there is information to be gained
by using ac-modulated incident light. For example, using
frequency-modulated light as the excitation source eliminates
the need to vibrate the Kelvin probe. The requirements on the
E ox (MV/cm)
0
-3
Accumulation
-6
Tunnel
-9 Regime
t ox
= 12 nm
-12
-6 10 -6 -4 10 -6 -2 10 -6 0
Q (C/cm 2 )
Figure 19. Oxide electric field versus surface charge for an oxidized
Si wafer. t ox = 12 nm. After Roy et al [43].
back contact can also be relaxed with a suitable capacitive
contact. As shown in appendix B, under such conditions,
the frequency-dependent minority carrier diffusion length
becomes
L n0
L n (ω) = √ (35)
1+jωτr
with L n0 the low-frequency value. The surface photovoltage is
measured versus the sinusoidally modulated input frequency.
The SPV equation becomes
V P (ω) = kT (1 − R) L n (ω)
(36)
q n 0 (s 1 + D n /L n (ω)) (L n (ω) +1/α)
with the frequency-dependent diffusion length L n (ω) given by
equation (35).
Nakhmanson originally put forth the theory for frequencydependent
SPV measurements [10]. It was later implemented
by Munakata et al who proposed [47] and later implemented
it with a flying spot scanner incorporating both blue and
infrared light sources [48]. The blue light, absorbed near
the surface, mainly characterizes the semiconductor near the
surface, while the infrared light probes deeper into the wafer.
By scanning the light beam, wafer maps can be generated
in a few minutes. The surface photovoltage depends on the
semiconductor band bending, which depends on the surface
charge density. Hence ac SPV measurements lend themselves
to surface charge density measurements [49].
In another version of ac SPV, the semiconductor surface
is depleted/inverted by chemically induced surface charges
and a sinusoidally modulated, low-intensity light generates
excess carriers. The carrier lifetime is determined from the
ratio of the real and imaginary SPV signals. Short-wavelength
light (λ = 0.4 µm) with high absorption coefficient ensures
carrier generation near the surface. Hence, the measured
lifetime is primarily determined by the oxide–semiconductor
interface, i.e., surface recombination, and is sometimes termed
the ‘surface lifetime’ [50].
In another commercial version, an oxidized wafer is
biased into inversion with pulsed light incident on the sample.
Optically generated minority carriers add to the inversion
charge, reducing the surface potential and space-charge region
width. The measured current I signal contains the relevant
parameters [51]. The slope of the I signal / versus plot gives
the surface lifetime. The signal also contains the substrate
doping density or resistivity, leading to contactless resistivity
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