EE 105 Midterm 1 Formula

no = po = ni^2 , where no = e- concentration at thermal equilibrim, po = hole concentration at thermal equilibrim, ni=10^10 cm^-3 (27)intrinsic concentration at 300k (26)

n-type

no^2 �C Nd*no �C ni^2 =0

no = (Nd +- sqrt(Nd^2 + 4* ni^2))/2

no = Nd/2 + Nd/2*sqrt(1+4ni/(Nd^2)) ~=  Nd (29)

po = ni^2/no ~= ni^2/Nd (29)

p-type

po ~= Na (31)

no = ni^2/po ~= ni^2/Na (31)

n = ((Nd-Na)/2 + (Nd-Na)/2*sqrt(1+4ni/((Nd-Na)^2)) ~=  Nd (Brian Review)

ni = 3.9*10^16 T(3/2)e^(-0.605eV/kT) cm^-3, Equilibrium Intrinsic Concentration,where T is in K, k is Boltzman��s constant = 8.62^10^-5 eV/K

p = q(po �C no + Nd �C Na)=0, where p is charge neutrality, no = e- concentration at thermal equilibrim, po = hole concentration at thermal equilibrium, Nd = donor concentration, Na=acceptor concentration (HW3)

vdn = -un*E, where vdn is e- drift velocity, un is mobility of e-, E is electrical field (37)

vdp = up*E, where vdp is hole drift velocity, up is mobility of hole, E is electrical field (V/m)

if E >> Esat, -vdn=vdp=10^7 cm/s (37)

Net charge (delta Q) = -q*n*A*vdn*(delta t), where q = e- density, n = e- concentration (HW3), t=thickness

Jn,drift = -q*n*vn , where J(A/cm^2), current density, where vn is �Cve, vn=e- drift velocity(40)

Jp, drift = q*p*vp (HW3)

Jdrift = Jn,drift + Jp, drift

R(sheet) = (q*un*Nd*t)^-1, where q is charge of electron, un is mobility of e-, Nd is donor density, t is thickness, unit is ohm/square (61)

N(sheet) = L/W

Rtotal = N(sheet) * R(sheet) (HW3)

pn ~= 1/(q*Nd*un) = (q*Nd*un + (q*ni^2*up)/Nd)^-1, pn is the n-type resistivity, q = charge of e-, Nd=donor concentration, un=mobility of e-. [m ohm-cm] (59)

pp ~= 1/(q*Na*up) = (q*Na*up + (q*ni^2*un)/Na)^-1, pp is the p-type resistivity, q = charge of e-, Na=donor concentration, up=mobility of hole. [m ohm-cm](59)

Qn,avg = 1/2*(Qn(y=0) +Qn(y=L)) = 1/2*[-Cox(Vgs �C Vtn) �C Cox(Vgs �C Vds �C Vtn)], Average Channel Charge, where L position from source (same as the position for drain), C is coulomb, 1e- = 1.6x10^-19 C, [pC/um^2] (202)

# of e- = (Qn,avg)(W)(L)/(-q), where Qn is charge density, q is charge of e-, W and L is width and length of the MOSFET,(HW3)

MOSFET

Id = (W/L) un * Cox [Vgs �C Vtn- (Vds/2)]Vds, where Vgs-Vds>Vtn (Triode), un is mobility, Cox is capacitance of the oxide (203)

Rds = Vds/Id = (L/W) [1/ (un * Cox (Vgs �C Vtn- (Vds/2))] = (L/W) Rsheet, (HW3)

Rsheet = 1/ (un * Cox (Vgs �C Vtn- (Vds/2)), (HW3)

R,sheet = p/t, where p=resistivity, t= thickness, [ohm/square]

R = (p/t)*(L/W)= p*L/A, where p=resistivity(u ohm cm), t=thickness, A = area (cm^2) (HW3)

Vo = Vi * (1-e^-(t/RC)), Voltage of Capacitor as time (t) >0(HW3)

Vth = Vth + gamma [ sqrt(-2 phi,p �C Vbs) �C sqrt(-2 phi,p) ], where gamma = (V^(1/2)), (Boser Review)

Lamda = lamda,o *(Lo/L) (Boser Review)

Units: Yotta=1E24, Zetta=1E21, Exa=1E18, Peta, 1E15, Tera=1E12, Giga=1E9, Mega-1E6, Kilo=1E3, milli=1E03, u(micro)=1E-6, nano=1E-9, pico=1E-12, femto=1E-15

Group III Doper: B, Al, Ga

Group IV Doper: C, Si, Ge

Group V Doper: N, P, As

EE 105 Midterm 2 Formula

Id = un*Cox*(W/2L)(Vgs �C Vth)^2 (1+lamda*Vds)(HW6)

gm = 2(Id)/Vdsat  = 2(Id)/(Vgs - Vth)= d(Id)/d(Vgs) |q point= un*Cox(W/L)(Vgsq-Vth) = 2* sqrt[un*Cox(W/2L) *Idq] = sqrt[2*un*Cox(W/L) *Idq]= sqrt(2un*Cox)*sqrt(W/L)*sqrt(Idq), where Vgs is Large signal, Vgsq is Vgs at the q point , Idq = Id at the q point, dy/dx = partial y/partial x (HW6)

ro = 1/(lamda*Id) = d(Id)/d(Vds) |q point (HW6)

Id = (W/L) (un*Cox) (Vgs �CVtn)^2 (HW6)

In Triode

Id = un*Cox(W/L)(Vgs - Vtn - Vds/2) Vds

gds = Ids*(lamda,n)

ro = 1/ gds = 1/(lamda,n*Vds)

ids = d(Ids)/d(Vgs)*vgs + d(Ids)/d(Vds)*vds + d(Ids)/d(Vbs)*vbs

ids = gm*vgs + gds*vds + gmb*vbs

diode-connected transistors = transistor that bulk and source tied together = resistance of 1/(gm + gmb) // ro

Large Signal Shortcut

Rdrain = Ro + Rsource +(gm + gmb)*Ro*Rsource

Rsource = (Ro + Rdrain) / (gm + gmb)Ro

GM                             Rin                 Rout

CS   gm                               Inf                   ro//roc

CG   -1                                 1/(gm+gmb)  [ro+gm*ro*Rs]//roc

CD   gm/(gm+gmb)          Inf                   1/(gm+gmb)

Iout = (W/L)_2 / (W/L)_1 * Iref

Two Port Model

-----Rin------Rout

high Vin       Iout

low  Iin       Vout

Find Gm or Av

1. Calculate Rout

2. Calculate Gm

3. Av = -Gm*Rout

Find Ai or Rm

1. Calculate Rout

2. Calculate Ai

3. Rm = -Ai*Rout

Vb and Vg has to be small signal ground