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.