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 Capacitance of High-K HfO 2 MIM Capacitors: A 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, 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.

 Among various high-k dielectrics, HfO 2 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 model The Physical Model S. Blonkowski, M. Regache, and A. Halimaou, Journal of Applied Physics, Vol. 90, No. 3, pp , 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 HfO 2 MIM capacitor. Inset shows its J-V curve The Physical Model

Measured and calculated normalized capacitance as a function of voltage. n 0 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

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 HfO 2 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 HfO 2 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 HfO 2 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 HfO 2 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 HfO 2 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.

Outline  Introduction  The Physical Model  Results and Discussions  Thickness Dependence  Frequency Dependence  Stress Induced VCC  Temperature Dependence  Prediction of VCC  Conclusions

Prediction of VCC Quadratic VCC as a function of thickness with different carrier concentration pre-factor and different carrier mobility in HfO 2 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.