Quantitative Measurement of Local Carrier Concentration of Semiconductor From Displacement Current-Voltage Curve Using a
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Mat. Res. Soc. Symp. Proc. Vol. 591 02000 Materials Research Society
EXPERIMENT Figure 1 (a) shows a schematic diagram of TDM. The distance between the tip and the sample d(t) is given by d(t) - do + d, sinw t,
()
where do is the mean distance, d, is the amplitude of the vibration, and w is the vibration angular frequency. When the tip is vibrated with applying a d.c. tip voltage V, the external circuit current i(t) becomes
i(t) - it(t) + iD(t),
(2)
where iT(t) is the tunneling current and iD(t) is the displacement current. The tunneling current between a sample and a locally spherical tip with radius r is expressed as [7] iTrWtOC
Vr 2 exp[- 2cd(t)],
(3)
where d(t) is the distance between the tip and the sample, and K is the minimum inverse decay length for the wave functions in a vacuum. From eq. (3), iT(t) should be exponentially proportional to d(t). On the other hand, the displacement current depends on the surface carrier densities due to space charges, trapped carriers in surface states, and dipole moments, and iD(t) is given by (4)
t•(,)_ V X( ), dt
(b) Tip kmge
(a) Z-axie Pinez
Pk=~ i4Xs
V0)U
LoT-i pMp.
Disolacement Cuoeldt
Fig. 1. (a)Schematic diagram of TDM, and (b) Typical tip image.
202
where C(t) is the capacitance between the tip and the metal sample written as [4] C(t) - 4;rsor{0.93 - 1 rJ 2 Ind(1)1. 1
(5)
Here e. is the dielectric permittivity of a vacuum. From eq. (5), a metal sample by
iD (t)
is rewritten in case of (6)
Cos O) w(t)iD(t)" 4=°rV(2-d~•°s:
Figure 2 shows theoretical curves of d(t), iD(t), and iT(t). In Fig. 2, iD(t) and depend on the phase, and they are separated by utilizing phase difference as follows: iT(t) Amplified external circuit current signal is applied to two-phase amplifier which include 2 demodulators operating at .7/2 apart. When one demodulator phase is set as 0 rad in Fig. 2, iD(t) is canceled, and the effective tunneling current ID,(V) is separated. At the same time, the other demodulator phase is set as ;r/2, and the effective displacement current ID(V) is separated from tunneling current. The TDM apparatus is based on the ultrahigh-vacuum STM system (UNISOKU, USM-501). Modifications, e.g., electrical shields of the tip piezo, voltage sources for z-axis piezo, and programs for measurements have been made on it. The tip is vibrated by applying a sinusoidal oscillation voltage to z-axes piezo actuator control unit using a multifunction •15 synthesizer (NF, 1945). The vibrating frequency of the z-axis is 1120 Hz, which is Ri.o smaller than the resonance frequency (4 kHz) co of the piezo. The amplitude of the vibration
H
di is 0.74 nm. The mean distance d. is set
"
o
on the order of a few nm and is controlled by
using a constant tunneling current feedback mode of the STM system. The external circuit current i(t) under this experimental condition is on the order of fA to pA. The tip voltage V is applied using a d.c. voltage standard (YEW, 2553). A high-speed current amplifier (Keithley 428) is used for
1
0 0 ..
2 :03-1 -
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Frequency f=-
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