Ballistic mobility model

1. BALLISTIC MOBILITY MODEL
By
Avishek Sarkar
Kaustubh Kamalanand Tiple
Krishnajith S S
Rudrampalli Naresh
Sura Shivani
Suraja K S

2. Introduction
BALLISTIC EFFECTs in short channel devices
HEMTs
Short channel => Submicron (<1um)
Reduced mobility in short channel compared to long
channel structures
Mesoscopic Structure
Ballistic Transport
Ballistic Effects
Mathematical Model
Ballistic Devices
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3. Mesoscopic Devices
Smaller than one electron
scattering
100nm – 1000nm
Used in nanofabrication
Ballistic Transport
Electrons travel from one
electric lead to another without
encountering scattering effect
Electrons are scattered only at
device boundaries
Observed when mean free path
of electron is longer than the
dimension of the medium
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4. Ballistic Effect
The effective electron mobility in short channel (submicron) HEMTs must be much smaller
than the electron mobility in long channel devices.
Reason - They have only a limited time to accelerate in the electric field and acquire a drift
velocity
𝝁 𝒃𝒂𝒍𝒍𝒊𝒔𝒕𝒊𝒄 =
𝟐𝒒𝑳
𝝅𝒎𝒗 𝒕𝒉
𝑞 = 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑖𝑐 𝑐ℎ𝑎𝑟𝑔𝑒
𝐿 = 𝐷𝑒𝑣𝑖𝑐𝑒 𝑙𝑒𝑛𝑔𝑡ℎ
𝑚 = 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑚𝑎𝑠𝑠
𝑣 𝑡ℎ = 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑘 = 𝐵𝑜𝑙𝑡𝑧𝑚𝑎𝑛𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑇 = 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒
𝑣𝑡ℎ =
8𝑘𝑇
π𝑚
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[1]

5. Ballistic Mobility vs Device Length
Ballistic mobility for GaAs as a function of device length at T = 77K
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6. Effective Mobility
Ballistic mobility not a real mobility
Ballistic mobility & collision dominated electron mobility independent of each other
The effective mobility can be defined using Mathiessen’s rule, i. e.,
𝟏
𝝁 𝒆𝒇𝒇
=
𝟏
𝝁 𝒃𝒂𝒍𝒍𝒊𝒔𝒕𝒊𝒄
+
𝟏
𝝁 𝒐
μ 𝑜 = 𝐶𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛 𝑑𝑜𝑚𝑖𝑛𝑎𝑡𝑒𝑑 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑚𝑜𝑏𝑖𝑙𝑖𝑡𝑦
μ 𝑒𝑓𝑓 = 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑚𝑜𝑏𝑖𝑙𝑖𝑡𝑦
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[1]

7. Effective Mobility vs Device Length
Effective mobility for GaAs as a function of device length at T = 77K 7/11

8. Mobility is a concept where scattering dominates
In ballistic regime, mobility loses its physical meaning
LONG
CHANNEL
DEVICES
HIGH
BALLISTIC
MOBILITY
(than physical mobility)
Effective Mobility ≈
Physical Mobility
SHORT
CHANNEL
DEVICES
LOW
BALLISTIC
MOBILITY
(than physical mobility)
Effective Mobility ≈
Ballistic Mobility
 Silicon devices Low mobility Ballistic effect not significant
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9. Conclusion
• Ballistic effects in short channel devices greatly reduce the effective values of the field
effect mobility compared to those in long gate devices.
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10. References
[1] M. S. Shur, “Low ballistic mobility in submicron HEMT’s,” IEEE Electron Device
Lett., vol. 23, pp. 511–513, Sept. 2002.
[2] J. Wang and M. Lundstrom, “Ballistic transport in high electron mobility transistors,”
IEEE Trans. Electron Devices, vol. 50, no. 7, pp. 1604–1609, 2003.
[3] Vikram Jagannathan, “Ballistic devices”, Graduate student, University of Rochester.
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