Non linear equation containing integral

I am bit new with matlab programming. I want to solve the above equation for phi0 but getting problem using solve function. Please help me. I expect a solution like this: different phi0 for different Nt

clc;clear;close all;
warning('off')

% number of data points for r, R and Et-Ef
N = 100;

% define the parameters
Nd = 1e24;
e  = 12*1e-12;
r  = 40*1e-9
R  = 40*1e-9;
Et_Ef = 0.21*1.6*1e-19;
K  = 1.3807e-23;
T  = 600;
Nt = 1e11;
q  = 1.6e-19;
for j = 1:length(Nt)
% initializing
LHS_vals = [];
RHS_vals = [];
P = [];

% loop to solve LHS - RHS = 0 N times
for i = 1:N
    
    syms phi0
    
    Ld = sqrt(e*K*T/(q^2*Nd));
    integrand = @(r)Nd-(Nd.*exp(-1.*(phi0+(1./6).*(r(i)/Ld).^2)));
    LHS = integral (integrand,0,40*10^-9);
    RHS = 4.*pi.*R.^2.*Nt./(1+2.*exp(Et_Ef + K.*T .*(phi0 + (1/6).*(r(i)./Ld).^2)));
    eq =  LHS - RHS==0;
    
    phi0 = solve(eq,phi0)
    
    if ~isempty(phi0)
        
    LHS_vals(end+1) = eval(LHS);
    RHS_vals(end+1) = eval(RHS);
    P(end+1) = phi0;
    
    fprintf('LHS - RHS = %1.2e\n',eval(LHS) - eval(RHS))
    end
    
end

%Plotting the Figure

if ~isempty(P)
    
figure()
hold on
plot(P,RHS_vals,'r--')
plot(P,LHS_vals,'b--')
hold off
xlabel('\phi_0')
ylabel('LHS,RHS')
ax = gca;
ax.YScale = 'log';
legend('RHS','LHS')

end
end
%plot (r,phi0)

[Matt J]

Do the values you are getting solve the equations?

[Anil Kumar]

No Sir, After execution of this code; i am getting error:

Error using integralCalc/finalInputChecks (line 522)

Input function must return 'double' or 'single' values. Found 'sym'.

Error in integralCalc/iterateScalarValued (line 315)

finalInputChecks(x,fx);

Error in integralCalc/vadapt (line 132)

[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)

[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 88)

Q = integralCalc(fun,a,b,opstruct);

Error in final03062019 (line 30)

LHS = integral(integrand,0,40*10^-9);

[Anil Kumar]

I want to know whether it is the right approach for the solution? phi0 value will be given by the intersection of LHS solution and RHS solution for a particular value of Nt!

[Anil Kumar]

It has been a long time I am stuck in this problem! Please help me.

[SACHIN VERMA]

sir, i also got stuck in simlar problem, please help if anyone knows how to solve it for complicated functions like above...