CC BY
33
Electrical engineering
УДК: 621.382
Drach V.
VLADIMIR E. DRACH, Assistant Professor, EIU1-KF Department, Bauman Moscow State Technical University (Kaluga Branch). Bazhenov, 2, Kaluga, Russia, 248000, e-mail: drach@kaluga.org
Charge pumping technique for MOSFET nanoscale oxide characterisation: physical background and equipment (overview)
The article presents an overview of the charge pumping technique used to examine electrophysical characteristics of the MOSFET gate oxide. The required laboratory equipment and the hardware implementation of the charge pumping technique are discussed in the article. It has been demonstrated that, nowadays, the charge pumping technique has a sufficient accuracy to estimate the charge state of the gate oxide having a nanoscale thickness.
Key words: charge pumping, charge state, border traps, gate oxide, MOSFET.
Introduction
The investigation and the monitoring of electrophysical characteristics are the most important parts in modern CMOS technology. To successfully resolve this task of sub-micron technology, it is necessary to use the most informative techniques of investigation, such as charge pumping, investigation of gate-induced drain leakage, multi-level current stress technique [1], etc. Hardware implementation of these techniques requires high sensitivity and accuracy of measurement equipment, what is not a trivial technical task.
Among the investigation techniques above, the charge pumping technique is highlighted by the following advantages:
• high resolution (as low as 109 states/cm2 or better), single trap capability,
• ability to determine separate shifts in threshold and flat-band voltages from interface trap generation,
• ability to determine the energy distribution of interface states,
• information on spatial position of interface states in the source-drain direction and/or in the depth direction,
• ability to measure inversion charge density.
Thus, the charge pumping technique is well known for its outstanding resolution and accuracy of measuring the interface state density at the Si-SiO2 interface and extracting the localized trapped charge profile in the gate oxide.
Mathematical Framework
As an excellent measurement technique, CP (charge pumping) technique is well known for the study of interface states in MOS transistors. By extending CP frequency to a low frequency range, CP technique can also detect and even profile in-depth of oxide traps near the Si-SiO2 interface, i.e., border traps [5, 12, 13]. Hence, by applying a pulse train of various frequencies f) to the gate and measuring the CP current (Icp), the contributions due to interface traps and border traps may be obtained. If we only con-
© Drach V.E., 2015
FEFU: SCHOOL OF ENGINEERING BULLETIN. 2015. N 2 /23 / ВЕСТНИК ИНЖЕНЕРНОЙ ШКОЛЫ ДВФУ. 2015. № 2 (23)
sider the recombination current to solely be contributed by the interface traps, Icp is proportional to f or the charge recombined per cycle, Qcp=Icpf is almost independent off.
This holds true at least in the high frequency range, as the frequency is too high for border traps to respond. Considering the effects of border traps on CP current, an additional component of Icp due to border traps appears at a low frequency range, as explicitly shown in Fig. 1.
The component of Icp due to border traps is attributed to the quantum mechanical (QM) tunnelling of carriers from the substrate. Based on this idea, two different models have been proposed based on interface trap-border trap tunnelling [12, 13], and on channel-border trap tunnelling [2, 11].
Cr - Charge Recombined per Cycle (C/Cycle)
f - Frequency (Hz) S - Slow States F - Fast States
The model based on interface trap-border trap tunnelling assumes that the carriers are first captured in the interface traps from where they tunnel into the border traps [12, 13]. Based on the above assumption and Shockley-Read-Hall (SRH) statistics and tunnelling theory, a pair of coupled differential equations, which governs the rate of emission of electron occupying interface traps and border traps. These coupled differential equations can be de-coupled by assuming the rise time and fall time of pulses to be small enough, so that the tunnelling during the rising and falling edges can be ignored. The resulting uncoupled differential equations are [12, 13]:
j-t[Dit(E,t)] = -en0(E)Dft(E,t),
dtLfot\ >> J J TT(E,x) '
Fig. 1. The frequency characteristics of charge pumping current of
a radiation soft device after irradiation (after [13]). The Iq, component due to border trap (slow states) is apparently shown in low frequency range, while in high frequency range, Icp is almost constant, which is mainly due to the interface traps (fast states).
(1)
(2)
where D-t(E, t) and p-t(E,x, t) are the areal density of occupied interface traps and thevolume density of occupied near-interface oxide traps (i.e. border traps), respectively; eno(E) is the equilibrium emission coefficient; TT(E,x) is the trap-to trap tunnelling time constant. Since the two processes are uncoupled, the total CP current may be written as the sum of the interface trap contribution, Icpit and the border trap contribution, Icpot-Icpit can be obtained by solving Equation (1), utilizing nonsteady state charge dynamics [12, 13]:
Icpit = 2qDltfAkTln
IVfb-Vthl
Wgl
^ (Jn dp tr tf
(3)
where q is the electronic charge, Dlt is the mean areal density of interface states, f is the frequency, A is the gate area, k is the Boltzmann's constant, T is the absolute temperature, vth is the thermal velocity, ni is the thermal velocity, A is the gate area, Vfb, and Vth are the flat-band voltage and threshold voltage, respectively, AVg is the amplitude of the gate pulse, on, and op are the capture cross sections of electrons and holes, respectively, tr and tf are the rise and fall time respectively. From Equation (3), the charge recombined per cycle due to interface traps, Qcpit can be obtained as Qcpit=Icpit f which is, to the first order, independent of CP frequency, f. By solving Equation (2), the border trap pumped per cycle Qcpot can be ob-
tained by assuming a mono-energetic trap level, pot(E,x) = NT(x)S(E-ET), and averaging over the period of the applied pulse [12, 13]:
CcP0t = qA dxNT(x) {1 - exp (- (4)
3.
where Nt(x) (cm-) is the volume density of traps in the oxide, tox is the oxide thickness, xmin is the minimum distance a border trap is located from interface to be distinguished from an interface trap, ET is the border trap energy level. The in-depth profile of border traps can be obtained by differentiating Equation (4):
(5)
дlog(/) аг
where NT(xm) is the density of traps located at the maximum tunnelling distance appropriate for the frequency of measurement, and xm is the maximum tunneling distance.
Similar results are obtained by using the model based on channel-border trap tunnelling [2, 11]. It seems both models applicable in contributing to the CP current due to border traps.
Methodology and Equipment
The charge pumping (CP) technique was firstly introduced by Brugler and Jes-pers in 1969 [4]. After many decades of development, CP technique demonstrates itself to be one of the most powerful techniques in measuring and investigating the interface states by directly employing MOS transistor as a test vehicle [7]. Until now, CP technique is still under extensive study and fast development [10, 14, 15].
The basic experiment setup of CP is shown in Fig. 2. from which the basic principle of CP technique can be understood [4, 7]. The source and drain are connected with a reverse bias applied to the source and the drain diodes. A train of usually trapezoidal pulses is applied to the gate, causing the MOSFET to be pulsed repetitively between accumulation and inversion. Take an n-channel MOS transistor as an example. When this transistor is pulsed into inversion, electrons will flow into the channel
from source and drain, with a fraction of them trapped by the interface traps.
When the free electrons in the channel are driven back to the source and the dram, as the transistor is pulsed into accumulation, most of the interface trapped electrons will stay until they are recombined by holes from the substrate. These "pumped" holes flow from substrate to the source and the drain via interface traps in each cycle of the pulse and constitute the charge pumping current (Icp). This current can be obtained by measuring the substrate current or the current flows through the source and drain [7, 8, 9]. In a simplified model given by Brugler and Jespers, is given as [4, 7]:
Fig. 2. The Basic experimental setup of charge pumping measurement (after ref. [7])
Icp = fQcp = A Dit (E) dE = fqAG Dit AE,
(6)
where q is the electron charge, f is the frequency, AG is the channel area, Dit(E) is the interface trap density at energy level E, EKimv and EFacc are the Fermi level in inversion and accumulation, respectively, Dit is the mean interface trap density over the energy range AE = Ep inv -Ep acc.
This is a simple first-order theory which omits the possibility of emitting trapped charges from the interface traps during the transition from accumulation to inversion and vice versa. When emission processes have to be taken into account, e.g., for not too small transition times or for not too low temperature, a more sophisticated model is required [4]. Groeseneken el al. suggested that only those interface traps that are not able to emit charges during the rise and fall edges can contribute to CP current [7]. Hence, in a revised model, Groeseneken et al. restricted the energy range AE in (6) to [8]:
' i—V-f—]
''V a"a" AV vf r , (7)
AE = 2kT ln
no-
where k is the Boltzmann constant, T is the absolute temperature, vth is the thermal velocity of the carriers, mi is the intrinsic carrier concentration, om and op are the capture cross-section of the traps for electrons and holes, respectively, Vfh and Vth are the flat-band voltage and threshold voltage, respectively, AVa is the amplitude of the gate pulse, tf and tr are the fall and rise times of the gate pulse, respectively. Improved results can be obtained by substituting Eqn (7) into Eqn (6).
Fig. 3.The principle of constant pulse amplitude CP technique. The base level of the train pulses changes from below Vfb, to above Vth while the amplitude keeps constant. The CP curve reveals five regions. The interface trap density can be obtained from the flat plant of CP curve. Vfb, and Vth can be obtained from the half value of the fall edge and the rise edge of CP curve, respectively (after ref. [4, 7, 14]).
Fig. 4. The principle of constant pulse-base level CP technique. The top level of the train pulses charge from below Vfb to above Vth with the base level keeps constant. The CP curve reveals three regions. The interface trap density can be obtained from the flat plant of CP curve. (after ref. [6, 14])
Fig. 5. The principle of constant pulse-top level CP technique. The base level of the train pulses charge from above Vth to below Vfb with the top level keeps constant. The CP curve reveals three regions. The interface trap density can be obtained from the flat plant of CP curve (after ref [8, 14]).
By using a different pulse train, CP measurement can be performed in many different ways, e.g., the constant pulse amplitude method (Fig. 3), the constant pulse base-level method (Fig. 4), and constant pulse top-level method (Fig. 5).
891...
The integral version of CP technique has the sensitivity as low as 10 cm- eV- , which is considered as the most sensitive techniques among existing techniques [14]. This high sensitivity is primarily due to the amplification effect of pulse frequency on CP signal [7].
Hardware implementation
Due to the aggressive shrinkage of MOSFET devices and their elements, the thickness of gate dielectric is being dramatically reduced and now occurs within a range of nanometers. Hence, the above equations (1)-(7) will operate the values of absolutely different orders: very low and very high. In order to measure charge pumping current and calculate oxide charge characteristics, one must build laboratory set up of extremely sensitive equipment.
In contrast to other optical measuring procedures, for the charge pumping technique, there is no principal limitations for amount of detected states, and both the measurement equipment sensitivity and the gate voltage frequency become critical.
In real life measurements, the investigation of nanoscale gate oxide MOSFET is dramatically complicated due to heavy requirements to equipment sensitivity, accuracy, gate voltage range, measured current value.
In order to develop the experimental set up, it is necessary to satisfy the following requirements:
1) DC current sensitivity of 10-15A,
2) measurement of charge pumping current of 1014A, under frequency up to 1 MHz,
3) low-frequency noise amplitude of 1015A (max.),
4) absolute error of the current measurement of 2x1014A (max.).
To meet the above requirements, the previously used laboratory equipment [2] was supplemented and updated. Pico ammeter of B2981A model from Agilent Technologies Inc. was used as a core. Agilent stabilized power supplies were used to feed the system. Agilent pulse generators were used to form influence pulses.
It is necessary to emphasize that special events are needed to extend dynamic range and to avoid leakage, specifically, fluoropolymer insulation and the use of shielded connection cables. Also, a special commutation module is required for interconnections of devices.
The described laboratory equipment could be referred to a low-cost segment.
Conclusion
Charge pumping is a powerful technique for MOSFET interface characterization, it allows to measure the interface state density at the substrate-dielectric interface and, furthermore, to determine the energy distributions over a large part of the semiconductor energy gap. Charge pumping allows to characterize both uniform and non-uniform degradation damage in short-channel MOSFET with nanoscale gate oxide. The integral version of charge pumping technique has the outstanding sensitivity and resolution.
Based on a thorough insight in the electrophysical mechanisms that are governing the charge pumping current, the interpretation of the results has been recently improved, leading to a widespread use of the technique.
For the charge pumping technique, both the measurement equipment sensitivity and the applied frequency become critical. Taking into account the mathematical framework, a new experimental set up had been described. The described experimental set up meets the requirements of sensitivity and allows to investigate MOSFET oxides of nanoscale thickness.
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Электротехника
В.Е. Драч
ДРАЧ ВЛАДИМИР ЕВГЕНЬЕВИЧ - кандидат технических наук, доцент кафедры конструирования и производства электронной аппаратуры (Московский государственный технический университет имени Н.Э. Баумана (Калужский филиал)). Баженова, 2, Калуга, ЭИУ1-КФ. 248000. E-mail: drach@kaluga.org
Метод накачки заряда для исследования наноразмерного оксида полевого транзистора: физическая база и оборудование (обзор)
Приводится обзор метода зарядовой накачки, применяемого для исследования электрофизических характеристик подзатворного диэлектрика полевого транзистора со структурой МДП. Широкая распространенность метода обусловливается улучшенной в последнее время интерпретацией полученных результатов. Обсуждается аппаратная реализация метода зарядовой накачки, которая позволяет внедрить его в цикл измерений подзатворного диэлектрика полевого транзистора со структурой МДП. Показано, что в настоящее время этот метод обладает достаточной точностью для оценки зарядовых состояний подзатворного диэлектрика наноразмерной толщины.
Ключевые слова: зарядовая накачка, зарядовое состояние, приграничные ловушки, подза-творный диэлектрик, полевой транзистор.
Примечание: список литературы см. в английском тексте статьи.
