Hello,
I am trying to solve the following code for x. According to the attached plot, x should be ~1.3
however, using the solve command gives me this error:
Warning: The solutions are parameterized by the symbols: k, z1. To include parameters and conditions in the solution, specify the 'ReturnConditions' option. > In solve>warnIfParams (line 500) In solve (line 356) In HW5 (line 27) Warning: The solutions are valid under the following conditions: exp(log(z1) + k*pi*2i) ~=-661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256/2969614242875447& in(k, 'integer') & (z1 == root(z^3 +(661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256*z^2)/2969614242875447-(7389015366435323967908908022371910771811603653921098701335406985236788968973433234508946305610994222893417207445031565100274626525888048356861860564629277155285935890388881077320961676529455407039532535682776566997321416812576672328618134497918976*z)/8552739147866811329799841636241-5572448313541411075572754442691595320934361841848741683192517222247028915535681815974691113703119944719040419346258432307987094672556923829465808318357201252183187273097626875632198907520424901383961794447304103842444201755391556919461542396321333248/8552739147866811329799841636241,z, 1) | z1 == root(z^3 +(661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256*z^2)/2969614242875447-(7389015366435323967908908022371910771811603653921098701335406985236788968973433234508946305610994222893417207445031565100274626525888048356861860564629277155285935890388881077320961676529455407039532535682776566997321416812576672328618134497918976*z)/8552739147866811329799841636241-5572448313541411075572754442691595320934361841848741683192517222247028915535681815974691113703119944719040419346258432307987094672556923829465808318357201252183187273097626875632198907520424901383961794447304103842444201755391556919461542396321333248/8552739147866811329799841636241,z, 2) | z1 == root(z^3 +(661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256*z^2)/2969614242875447-(7389015366435323967908908022371910771811603653921098701335406985236788968973433234508946305610994222893417207445031565100274626525888048356861860564629277155285935890388881077320961676529455407039532535682776566997321416812576672328618134497918976*z)/8552739147866811329799841636241-5572448313541411075572754442691595320934361841848741683192517222247028915535681815974691113703119944719040419346258432307987094672556923829465808318357201252183187273097626875632198907520424901383961794447304103842444201755391556919461542396321333248/8552739147866811329799841636241,z, 3)). To include parameters and conditions in the solution, specify the 'ReturnConditions' option. > In solve>warnIfParams (line 507) In solve (line 356) In HW5 (line 27)
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Here is the code:
syms xEconv=1.60218*10^-19; %%J/eV
Eg=1.11 %%Bandgap energy in eV
k=(1.38064852*10^-23)/Econv; %%Bolzmann Constant in eV/K
m0=9.109*10^-31; %%Mass of electron
mn=1.1*m0; %%Mass of e carrier
mp=0.58*m0; %%Mass of e hole
Eion=0.045;hbar=1.054571800*10^-34; %Planck's constant in Js
T=50; %Temperature range in K
Nd=((10^15)*(100)^3); %%#Donors/m^3
Nc=2.*(mn*Econv*k.*T./(2*pi*hbar^2)).^(3/2);Nv=2.*(mp*Econv*k.*T./(2*pi*hbar^2)).^(3/2);Eiv=Eg/2+(3/4)*k.*T.*log(mp/mn);ni=((Nc.*Nv).^(1/2)).*exp(-Eg./(2*k.*T));p=ni.*exp(-x./(k.*T)).*(exp(Eiv./(k.*T)));Ndion=Nd./(1+exp(x./(k.*T)).*exp((Eion-Eg)./(k.*T)));LHS=p.*(p+Ndion);Efv=solve(LHS==(ni.^2),x);
Best Answer