1. Active Device Channel SPICE Thermal Modeling and Parameter Extraction
Fujiang Lin （林福江）

2. Outline Introduction Classification of semiconductors’ models
Self-heating in semiconductor devices
Impact of self-heating on the semiconductor properties
Schottky Diode Thermal Model
Temperature Estimation Methods
Extraction methods of Schottky Diode parameters
Conclusion

3. About the Speaker: Fujiang Lin
A special China “1000-Talents Program” USTC full Professor
Educated from USTC with BSC and MSEE in uWave
Received Dr.-Ing. (PhD in Engineering) in uE+uWave from Germany
Over 28 years hand-on experience in RF modeling cum IC validation
Singapore pioneer MMIC/RFIC/mmWIC designer and manager
Proactive IEEE SM, RFIT founder and ExCom vice Chair
Current research interests:
GaN, SiC, … modeling cum PA design
Black Phosphorus (Phosphorene) FET research
Quantum chip and brain-computing chip research
MESIC is a platform for R&D and bridge to industries

4. Device Modelling as a Foundation for IC Design
1- the demands for high capacity of wireless communication system is growing up
: Internet of things (IoT), cloud computing, social media, low-cost mobile devices and so o
mentioned technologies have been standardized in currently available 5G , the question about their realization remains open

5. Utilization Failure of the New Nano- devices
The main reasons prolonging the utilization of the new devices are:
Low reproducibility
Deficiency of accurate modelling technique
Poor integrability
However, several devices based on latest achievements of Micro/Nano technology end up with several publication in high impact factors scientific journals and did not find practical implementation in both RF and high-power industry. This is due to several reasons:1) Low reproducibility 2) deficiency of accurate modelling technique and 3) poor integrability. For some types of electronic devices, the problems of reproducibility and integrability have been successfully solved. Nevertheless, the modelling issue remains to be the crucial obstacle for the most of modern devices, as it’s the primary bridge connecting so-called band-gap engineering and the practical (or industrial) IC design.

6. Modelling Technique as bridge between IC design and bandgap Engineering
For that end, this presentation will go through some of modelling issues starting by their classification, simulation methodology and finally thermal modeling issue.

7. Classification of semiconductors’ models
Models of micro/nano electronic components can be divided into two categories: 1) Physical and 2) Empirical. Physical models based on numerical simulation or TCAD packages have very high accuracy and explain the physical process flow within the devices, however they are computationally costly and cannot be used for design purposes. Currently, the most used in the industry are the empirical and semi-empirical models due to computational efficiency and high agreement with experimental data. At the same time, these models (like Angelov) have enormous numbers of fitting parameters that have no physical meaning and cannot be used for circuit and devices optimization purpose (no feedback to bandgap engineers). Appealing approach is the physics-based modelling, which describes the current flow in the devices using a closed-form physical equations. Utilizing such modeling technique may lead us to overcome shortcomings that typical for TCAD or empirical models. This approach (ASM) however still at the development stage and several issues should be addressed. One of the most obstacles in circuit-physics-based modelling is the calculation of active region temperature.

8. Classification of semiconductors’ models
Advantages
Disadvantages
2D/3D TCAD models
High accuracy
Physics-based
Explain quantum and self-heating effects
Scalable
High computation cost
Useless for IC design
Time consuming
High complexity
Applicable mainly to active region of devices
Closed-form Physical models
Low computation cost
Compatible with Spice program
Numerous fitting parameters
Do not explain self-heating and quantum effects
Empirical Models
High agreement with experimental data
No physical base for models
Not scalable

9. Self-heating in semiconductor devices

10. Impact of self-heating on the semiconductor properties
𝜈 𝑠𝑎𝑡 = 𝜈 𝑠𝑎𝑡, 𝑇 −𝐴 +𝐴 𝑇 𝐿 𝑇 0
𝐸 𝑔 = 𝐸 𝑔, 𝑇 0 − 𝛼 𝑇 𝐿 2 𝛽+ 𝑇 𝐿
𝜏 𝜖 = 3 𝑘 𝐵 2𝑞 𝑓 𝑇 𝐿 − 𝑇 𝐿 𝜐 𝑛 𝑇 𝐿 𝐸
Measured temperature-dependent current–voltage characteristics for 9- µm single-anode varactor diode. Temperature points from 283 to 333 K with 10 K steps are used.
𝜇 𝐿 = 𝜇 𝐿 𝑇 𝐿 𝑇 0 𝛽
𝑁 𝑐 =2 𝑀 𝑐 𝛾 𝑚 𝑛 𝑇 𝐿 ℎ
𝑚 𝑛 = 𝑚 0,𝑛 + 𝑚 1,𝑛 ∙ 𝑇 𝐿 𝑇 0
Slice of the diode for temperature distribution in XZ plane with 5 mW input power.

11. Schottky Diode Thermal Model
An accurate thermal model necessary to:
Predict the device reliability;
Predict the Series (or negative) resistance.
𝐼 𝑉,𝑇 = 𝐼 𝑠𝑎𝑡 (𝑇)𝑒𝑥𝑝 𝑞 𝑉−𝐼(𝑉,𝑇) 𝑅 𝑠 𝜂(𝑇)𝑘𝑇 ; (1)
𝐼 𝑠𝑎𝑡 𝑇 =𝑆𝐴 𝑇 2 exp −𝑞 𝜙 𝑏 𝜂(𝑇)𝑘𝑇 , (2)
where
𝐼 𝑠𝑎𝑡 (𝑇) is the saturation current,
𝜂 is the ideality factor,
𝑅 𝑠 is the series resistance of the diode,
V is the applied voltage,
𝑆 is the junction area,
𝐴 is the Richardson constant,
𝑘 is Boltzmann’s constant,
𝜙 𝑏 is the barrier height,
𝑞 is the elementary charge
𝑇 is the junction temperature.

12. Temperature Estimation Methods

13. Temperature Estimation Methods
Advantages
Disadvantages
Physical methods
Temperature map
Potentially high spatial resolution
Need surface view
Contact may disturb temperature
Electrical and optimization methods
Packaged devices
No contact
Potentially subsurface
Averages
May require special device operation
Optical methods
Good spatial resolution
Potentially expensive
Electrical simulator
Accurate
high spatial resolution
Nonlinear
Theoretical
High computational cost
Closed-Form 1D equation
Simple electrical measurement
Linear
Time independent
Thermal simulator
3D Temperature map
Need data for heat source

14. Extraction method of Schottky Diode parameters with allowance for temperature
Extraction method based on the combination of I-V and S- parameters measurement; (The temperature-sensitive parameters here is voltage)
Transient-current based method. (The temperature-sensitive parameters here is transient current)

15. Extraction method based on the combination of I-V and S- parameters measurement
𝐼 𝑉,𝑇 = 𝐼 𝑠𝑎𝑡 𝑇 𝑒𝑥𝑝 𝑞 𝑉−𝐼 𝑉,𝑇 𝑅 𝑠 𝜂𝑘𝑇 ; (1)
𝑞 is the elementary charge,
𝑇 is the junction temperature,
𝐸 0 is a constant,
𝑅 𝑠 is the series resistance,
Δ 𝑉 𝑒𝑟𝑟 +∆𝑉is the difference between current model and experimental data,
𝑇 0 is the ambient temperature,
𝑃 𝑇 is the dissipated power,
𝑅 𝑇 is the thermal resistance,
𝑟 𝑡𝑜𝑡 is the total diode resistance.
𝐼 𝑠𝑎𝑡 𝑇 =𝑆𝐴 𝑇 2 exp −𝑞 𝜙 𝑏 𝜂𝑘𝑇 ; (2)
𝜂= 𝑞 𝑘𝑇 𝐸 0 coth 𝑞 𝐸 0 𝑘𝑇 ; (3)
𝑅 𝑠 = Δ 𝑉 𝑒𝑟𝑟 +∆𝑉 𝐼 = 𝑉 𝐼 − 𝜂𝑘𝑇 𝑞𝐼 𝑙𝑛 𝐼 𝐼 𝑠𝑎𝑡 𝑇 ; (4)
𝑇= 𝑇 0 + 𝑃 𝑇 𝑅 𝑇 ; (5)
𝑃 𝑇 =𝑉𝐼= 𝜙 𝑏 𝐼+ 𝑅 𝑠 𝐼 2 , (6)
𝑟 𝑡𝑜𝑡 = 𝜂𝑘𝑇 𝑞𝐼 + 𝑅 𝑠 , (7)
𝐼 is the total current of the diode under test,
𝐼 𝑠𝑎𝑡 (𝑇) is the saturation current,
𝜂 is the ideality factor,
𝑅 𝑠 is the series resistance of the diode,
V is the applied voltage,
𝑆 is the junction area,
𝐴 is the Richardson constant,
𝑘 is Boltzmann’s constant,
𝜙 𝑏 is the barrier height,

16. Extraction method based on the combination of I-V and S- parameters measurement
Measured I–V characteristics and calculated I–V characteristics using traditional two-step approach and least squares curve fitting algorithms.
Series resistance values calculated using (4) and traditional extraction methods for an diode, including the lower and upper error limits showing the effect of a 30% error in the extracted value of the thermal resistance.

17. Transient-current based method
Advantages:
Using Current as temperature sensitive parameters;
Avoiding pulse heating;
Possibility to perform measurement at different terminals.
Time-dependent of heat transport can be described using:
𝑇 𝑡 = 𝑇 0 + 𝑖=1 𝑖=𝑛 𝑇 𝑖 𝑒𝑥𝑝 −𝑡 𝜏 𝑖 , (8)
where 𝜏 𝑖 = 𝑅 𝜃,𝑖 𝐶 𝜃,𝑖 is the thermal time constant.

18. Transient-current based method