166
Strain-Engineered MOSFETs
S ID (1 Hz; σ)/S ID (1 Hz; 0), is shown as a function of stress in Figure  6.9(c).
When the PSD follows 1/f γ dependence over a wide frequency range, the
global and local LSF both show good agreement for two gate biases.
Figures 6.10 and 6.11 show the extracted average drain current noise PSD,
S ID (f; σ), at specific frequencies for n-MOSFETs as a function of applied tensile and compressive stress, and the normalised change in PSD, ΔS ID (f; σ)/
S ID (f; 0), is shown as a function of frequency for a specific stress.
Both 1/f noise magnitude and exponent are functions of applied mechanical stress. Therefore, the strain-induced relative change in 1/f noise PSD, referenced at zero stress, can also be expressed from Equation (6.38) as
S f
S f
S
Hz
S
Hz
f
ln 1
( ; )
( ;0)
ln 1
(1 ; )
(1 ;0)
( )ln[ ]
I
I
I
I
D
D
D
D
+
σ

 

  =
+
σ

 

  − γ σ
(6.40)
where S f
( ; )
ID
σ = S f
( ; )
ID
σ – S f
( ;0)
ID
and Δγ(σ) = γ(σ) – γ(0). Linear relationships of S f
( ; )
ID
σ and γ(σ) can be assumed since the applied stresses are
small (<250 MPa). The main focus of the study of strain effects on noise PSD
f = 50 Hz
4.8
×10
–20
4.4
S
ID (σ) (A
2
/Hz)
4.0
3.6
0
50
100
Stress (MPa)
(a)
150
250
200
f = 200 Hz
σ = 200 MPa
1.39
×10
–20
1.26
S
ID (σ) (A
2
/Hz)
1.13
1.00
0
50
100
Stress (MPa)
(b)
150
250
200
f = 1.2 kHz
3.35
×10
–21
3.10
S
ID (σ) (A
2
/Hz)
2.85
2.60
0
50
100
Stress (MPa)
(c)
150
250
200
20
16
∆S
ID (σ)/S
ID (0) (%)
12
8
10
1
10
2
Stress (MPa)
(d)
10
3
10
4
FIGURE 6.10
n-MOSFET noise PSD under tensile stress: (a–c) Changes in noise PSD vs. applied stress at
different frequencies. (d) Relative change in noise PSD vs. frequency at a stress of 200 MPa.
(After Lim, J.-S., Strain Effects on Silicon CMOS Transistors: Threshold Voltage, Gate Tunneling
Current, and 1/f Noise Characteristics, PhD thesis, University of Florida, 2007.)