Royal Military College of Canada

Concordia University Department of Electrical and Computer Engineering COEN 451, Midterm Exam Date: 17th Feb. 2009 Time: 1hour, Attempt all 3 Questions

Question 1 (2 marks) With respect to nMOS transistor, define the following parameters: 1) Channel Pinch-Off 2) Hot Carrier Injection 3) Lateral Diffusion 4) Velocity Saturation

Question 2. (5marks) Determine the resistance of the following structure shown in Fig. 1 Assume polysilicon=10Ω /, Contacts =1Ω/ contact. NOTE: Accuracy of calculation of the resistance of the constricted area shown with an X is important for this question.

60µ 40 µ

Metal Polysilicon Metal

Fig. 1 structure of Question 2

of 4 Midterm Winter 2008 Question 3. (8 marks) An experimental results of a set up shown in Fig. 2 is shown in Table 1 The nMOS transistor has the following parameters: 2 -1 Cox= 1 fF /µm , = 0.0V , |2F| = 0.64V , Determine: a) Electron mobility µ n b) Threshold Voltage Vt0 c) Body coefficient γ

W/L=1 MI V SB V V gs ds

Fig. 2 (Question 3)

Table 1 (Question 3)

Vgs (V) Vds (V) VSB (V) ID (µA) 4 4 0.0 256 5 5 0.0 441 4 4 2.6 144

of 4 Midterm Winter 2008 Some Useful Equations

Current Equations PMOS: NMOS:   W  V V V V   n, p  n, p  GS tn - Cut-off GS tp - Cut-off,   tOX  Ln, p  V  V  V GS tn DS - Saturation

V  V  V 1 W 2 GS tp DS - Saturation I  K' V  V  1  V  DS 2 n L GS tn DS 1 W 2 I DS  K'P VGS  Vtp  1   VDS  2 L V  V  V GS tn DS - Linear

W  1 2  V  V  V - Linear I DS  K'n VGS  Vtn VDS  VDS GS tp DS L  2  W  1 2  I DS  K'P VGS  Vtp .VDS  VDS L  2 

Transistor resistance: Delay and Power:  L  1  R =   : Linear region    CL CL W  K' VGS Vt  tr  k , t f  k , k ≈3.3  pVDD  nVDD 2 L  1      t C t R =    2 : Saturation r L f CL   tdr   AP , t   A ,  K' W  VGS Vt   df n 2  p 2  n t  t Body effect equation: t  dr df , Delay of line Td = 0.5 rcl2 d 2 Vtn, p  Vton, p    VSB  or more accurately, below Power: (1) Static: i pVDD

Vtn, p  Vton, p    2 f  VSB  2 f  2 (2) Dynamic: (a) switching: Pd  CLVDD f p

 3 tr, f (b) Short circuit: Psc  VDD  2Vt  12 t p Delay with Input slope: V ti / p _ fall tp ti / p _ rise Vtn tdr  tdr _ step  1  2 p , p = tdf  tdf _ step  1  2n, n = 6 VDD 6 VDD

Cload 2Vt, p 4(VDD  Vt, p ) 1 DD [ + ln ( ) ] Kp(V  Vt, p ) VDD  Vt, p VDD

Cload 2Vt,n 4(VDD  Vt,n ) 1 DD [ + ln ( ) ] Kn(V  Vt,n ) VDD  Vt,n VDD

Noise Margins: NML = VILmax – VOLmax , NMH = VOHmin -VIhmin

of 4 Midterm Winter 2008 Values of some useful constants

Boltzman constant k 1.38 * 10 –23 J/K Electron charge q 1.6 * 10 –19 C

Thermal voltage T 26 mv (at 300 K) –14 Electrical permittivity (vacuum) o 8.85 * 10 F/cm –13 Permittivity of Si si 3.5 * 10 F/cm –12 Permittivity of SiO2 ox 1.05 * 10 F/cm –7 Magnetic permeability o 12.6 * 10 Wb/Am Room Temperature T 300 (=27 0C) K

Appendix B: SPICE Parameters

.MODEL CMOSN mos3 type=n

+PHI=0.700000 TOX=9.6000E-09 XJ=0.200000U TPG=1 +VTO=0.6566 DELTA=6.9100E-01 LD=4.7290E-08 KP=1.9647E –04 +UO=546.2 THETA=2.6840E-01 RSH=3.5120E+01 GAMMA=0.5976 +NSUB=1.3920E+17 NFS=5.9090E+11 VMAX=2.0080E+05 ETA=3.7180E-02 +KAPPA=2.8980E-02 CGDO=3.0515E-10 CGSO=3.0515E-10 +CGBO=4.0239E-10 CJ=5.62E-04 MJ=0.559 CJSW=5.00E-11 +MJSW=0.521 PB=0.99 +XW=4.108E-07 +CAPMOD=bsim XQC=0.5 XPART=0.5 *Weff = Wdrawn - Delta_W *The suggested Delta_W is 4.1080E-07

.MODEL CMOSP mos3 type=p

+PHI=0.700000 TOX=9.6000E-09 XJ=0.200000U TPG=-1 +VTO=-0.9213 DELTA=2.8750E-01 LD=3.5070E-08 KP=4.8740E-5 +UO=135.5 THETA=1.8070E-01 RSH=1.1000E-01 GAMMA=0.4673 +NSUB=8.5120E+16 NFS=6.5000E+11 VMAX=2.5420E+05 ETA=2.4500E-02 +KAPPA=7.9580E+00 CGDO=2.3933E-10 CGSO=2.3922E-10 +CGBO=3.7579E-10 CJ=9.35E-04 MJ=0.468 CJSW=2.89E-10 MJSW=0.505 PB=0.99 +XW=3.622E-07 +CAPMOD=bsim XQC=0.5 XPART=0.5 *Weff = Wdrawn –Delta_W

of 4 Midterm Winter 2008