Introduction MIM capacitors have received more and more attention due to its advantageous - Low parasitic capacitance - Low voltage coefficients of capacitance - High Q factor Conventionally, SiO 2 and Si 3 N 4 are widely used in MIM capacitors, but it could only provide the capacitance density of ~1 fF/μm 2. High-κ dielectrics needs to be used for future MIM application for higher capacitance density.
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Chunxiang Zhu 1 , Hang Hu 1 , Xiongfei Yu 1 , SJ Kim 1 , Albert Chin 2 , M. F. Li 1,4 , Byung Jin Cho 1 , and D. L. Kwong 3 1 SNDL, Dept. of ECE, National Univ. of Singapore, Singapore 2 Dept. of Electronics Eng., National Chiao Tung Univ., Taiwan 3 Dept. of ECE., Univ. of Texas, Austin, TX 78712, USA 4 Institute of Microelectronics, Singapore Voltage and Temperature Dependence of Voltage and Temperature Dependence of Capacitance of High-K HfO Capacitance of High-K HfO 2 MIM MIM Capacitors: Capacitors: A Unified Understanding and Prediction A Unified Understanding and Prediction
Transcript
Chunxiang Zhu1, Hang Hu1, Xiongfei Yu1, SJ Kim1, Albert Chin2, M. F. Li1,4,
Byung Jin Cho1, and D. L. Kwong3
1SNDL, Dept. of ECE, National Univ. of Singapore, Singapore2Dept. of Electronics Eng., National Chiao Tung Univ., Taiwan
3Dept. of ECE., Univ. of Texas, Austin, TX 78712, USA4Institute of Microelectronics, Singapore
Voltage and Temperature Dependence of Voltage and Temperature Dependence of Capacitance of High-K HfOCapacitance of High-K HfO22 MIM Capacitors: MIM Capacitors:
A Unified Understanding and PredictionA Unified Understanding and Prediction
Outline Introduction The Physical Model Results and Discussions
Thickness Dependence Frequency Dependence Stress Induced VCC Temperature Dependence Prediction of VCC
Conclusions
Introduction MIM capacitors have received more and more attention
due to its advantageous- Low parasitic capacitance
- Low voltage coefficients of capacitance
- High Q factor
Conventionally, SiO2 and Si3N4 are widely used in MIM capacitors, but it could only provide the capacitance density of ~1 fF/μm2.
High-κ dielectrics needs to be used for future MIM application for higher capacitance density.
Among various high-k dielectrics, HfO2 was demonstrated to be a good high-k material for MOSFET and MIM capacitor.
One of most important parameters in MIM C is voltage coefficients of capacitance (VCC)
Experimental results reported that VCC is highly related to dielectric thickness, measurement frequency, etc.
However, no clear understanding of VCC so far.
Introduction
Outline Introduction The Physical Model Results and Discussions
Thickness Dependence Frequency Dependence Stress Induced VCC Temperature Dependence Prediction of VCC
Conclusions
Free carrier injection modelFree carrier injection model
The Physical Model
S. Blonkowski, M. Regache, and A. Halimaou, Journal of Applied Physics, Vol. 90, No. 3, pp. 1501-1508, 2001.
- Capacitance variation is attributed to injected carriers.
- Excess charges will follow ac signal with a relation time which is depends on carrier mobility, carrier density, dielectric constant, etc.
- Carriers concentration is assumed to follow Schottky emission
Schottky plot of 30 nm HfO2 MIM capacitor. Inset shows its J-V curve
The Physical Model
The Physical Model
Measured and calculated normalized capacitance as a function of voltage. n0 and are extracted by fitting the measured data.
- Good agreement of simulation result with experiment data confirms the model.
Outline Introduction The Physical Model Results and Discussions
Thickness Dependence Frequency Dependence Stress Induced VCC Temperature Dependence Prediction of VCC
Conclusions
Dependence of carrier concentration pre-factor on thickness.
Thickness Dependence
Thickness Dependence
Simulated normalized capacitance as a function of voltage for different thickness of 20, 30, 40, 50, and 60 nm.
- Normalized capacitance bends more with decreasing the dielectric thickness.
Thickness Dependence
Quadratic VCC as a function thickness.
- Quadratic VCC () decrease with dielectric thikcnesses.
- A relationship of =ct-n (n~2) is expected.- The relationship between
and t were reported with different high-k materials.
- This implies that the is mainly due to the enhancement of electrical field with scaled dielectric thickness
Outline Introduction The Physical Model Results and Discussions
Thickness Dependence Frequency Dependence Stress Induced VCC Temperature Dependence Prediction of VCC
Conclusions
Frequency Dependence
Measured quadratic VCC and fitted carrier mobility as a function of frequency.
- From the model itself, there is no frequency dependence of VCC
- To fit the frequency dependence of VCC, the change of mobility at different frequencies need to be considered.
Frequency Dependence
Simulated normalized capacitance as a function of voltage e of 30 nm HfO2 MIM capacitors at for different frequencies of 10K, 100K, 500K, and 1MHz.
- It is believed that the carrier mobility becomes smaller with increasing frequency, which leads to a higher relaxation time and a smaller capacitance variation
Outline Introduction The Physical Model Results and Discussions
Thickness Dependence Frequency Dependence Stress Induced VCC Temperature Dependence Prediction of VCC
Conclusions
Stress Induced VCC
Stress induced leakage current and stress induced quadratic VCC of thick HfO2 MIM capacitor.
- The results imply that both SILC and the variation of quadratic VCC are correlated to each other.
Stress Induced VCC
Stress induced leakage current and stress induced quadratic VCC of thin HfO2 MIM capacitor.
With the increase of stress time More traps generated Carrier mobility could be modulated to be smaller Leads to a higher relaxation time A smaller capacitance variation
Outline Introduction The Physical Model Results and Discussions
Thickness Dependence Frequency Dependence Stress Induced VCC Temperature Dependence Prediction of VCC
Conclusions
Temperature Dependence
Dependence of carrier concentration pre-factor on temperature for 30 nm HfO2 MIM capacitor.
- We assume that carrier concentration pre-factor has a dependence with temperature T
Temperature Dependence
Measured normalized capacitance and fitted carrier mobility as a function of temperature for 30nm HfO2 MIM capacitor.
-Higher temperature generates more traps, which modulate the carrier mobility to be smaller
-On the other hand, higher temperature results in a much higher carrier concentration pre-factor (n0).
-Overall, a smaller relaxation time is achieved, which leads to a larger capacitance variation.
Prediction of VCC
Quadratic VCC as a function of thickness with different carrier concentration pre-factor and different carrier mobility in HfO2 dielectric film.
- Both the carrier conc. pre-factor and carrier mobility should be small enough to meet requirement of ITRS roadmap
Conclusions In summary, a unified understanding of voltage
and temperature dependence of capacitance is achieved for the first time.
Based on the free carrier injection model, it is found that: (1) The thickness (t) dependence of VCC (), which exhibits
a relation of, is an intrinsic property due to E-field polarization,
(2) The frequency dependence of VCC, the stress induced VCC, and temperature dependences of capacitance are all due to change of relaxation time with different carrier mobility in insulator
(3) This model is also applied to predict the VCC for future applications.
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