Please show all steps. A silicon bipolar transistor has diffusion constants in b

Question

Please show all steps.

A silicon bipolar transistor has diffusion constants in base and emitter Ds = 6 cm^2/s and DE = 2 cm^2/s. The widths of base and emitter are W_B = 100 nm and W_E = 300 nm. The doping concentrations in base is N_B = 10^18 cm^-3. For this transistor a) determine common emitter current gain, common base current gain and emitter efficiency for the doping concentrations in emitter N_E = 10^19 cm^-3 and N_E = 10^20 cm^-3 beta_F = D_B W_E/D_E W_B times N_E n^2 _i/N_B n^2_iE n^2 _iE = n^2 _i e^delta E_gE/kT At N_E = 10^19 cm^-3, delta E_gE = 50 meV At N_E = 10^20 cm^-3, delta E_gE = 95 meV beta_F = D_B W_E/D_E W_B times N_E n^2 _i/N_B n^2_iE = 9 middot 10^19 middot n^2 _i/10^18 middot 6.8n^2 _i = 13 beta_F = D_B W_E/D_E W_B times N_E n^2 _i/N_B n^2_iE = 9 middot 10^20 middot n^2 _i/10^18 middot 38n^2 _i = 24 beta_F = I_C/I_B beta_F = alpha_F/1 - alpha_F gamma_E = I_E - I_B/I_E = I_C/I_C + I_B b) what happens to the gain values if the base would be made of SiGe with a band narrowing of E_gB = 60 mev? N^2_iB = n^2 _i e^delta gB/kT = n^2 _i e^60/26 meV = 10n_i^2 beta_F = D_B W_E/D_E W_B times N_E n^2 _iB/N_B n^2_iE = 9 middot 10^20 middot 10n^2 _iB/10^18 middot 39n^2 _i = 237 c) estimate the base transit time and the amount of charge accumulated in the base if the collector current is 100 mA. Q_HB/I_C = tau_FB = W^2_B/2D_B d) find density of collector current transistor for V_EB = 0.3V jc = q D_B/W_B n^2 _iB/N_B (e^qV_BE/kT - 1)

Explanation / Answer

Solution:

A) 1. Common emitter current gain =  Be

The formulae are already given in the above question,

Be = ( 9 x 1020 x ni2 ) / 1018 x 38 ni2 = 24

here, niE2 = ni2 x exp (Eg / KT) = 38 ni2 .......... here Eg = 95 meV

  

2. Common base current gain

  Bb = ( 9 x 1019 x ni2 ) / 1018 x 6.8 ni2 = 13

here, niB2 = ni2 x exp (Eg / KT) = 6.8 ni2 ........... Eg = 50 meV

3. Emitter injection efficiency (y)

y = Ic / Ic + Ib = a / a +1 where, a is base transport factor

4. Now   niB2 = ni2 x exp (Eg / KT) = 10ni2    ........... here, Eg = 60 meV

  Bb = ( 9 x 1020 x10 niiB2 ) / 1018 x 39ni2

Bb = ( 9 x 1020 x10 x 10ni2 ) / 1018 x 39ni2 = 237

5.

Transit time in base

tFB = WB2 / 2WD = 1002 / 2 x 6 = 833.3 sec

  

  

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