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<header>
<h1 class="title">Module <code>dopes.data_analysis.diode</code></h1>
</header>
<section id="section-intro">
</section>
<section>
</section>
<section>
</section>
<section>
<h2 class="section-title" id="header-functions">Functions</h2>
<dl>
<dt id="dopes.data_analysis.diode.depletion_length"><code class="name flex">
<span>def <span class="ident">depletion_length</span></span>(<span>doping_in, doping_out, Vbias=0, temp=300)</span>
</code></dt>
<dd>
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">def depletion_length(doping_in, doping_out, Vbias=0,temp=300):
    &#34;&#34;&#34; Function to calculate the depletion length in a pn junction
        
        args:
            - doping_in (scalar): the doping in the region for which the depletion length has to be calculated
            - doping_out (scalar): the doping in the adjacent region for which the depletion length has to be calculated
            - Vbias (scalar): the bias voltage of the pn junction
            - temp (scalar): the temperature
                
        return:
            - a scalar with the depletion length calculated in one region
    &#34;&#34;&#34; 
    
    kB = 1.38e-23 # J/K
    q = 1.602e-19 # C
    epsilon_0 = 8.8542e-12 # F/m
    epsilon_si = 11.7
    
    phi_0 = kB * temp / q * np.log(doping_in * doping_out / sc.intrinsic_concentration(temp)**2 )
    return np.sqrt(2 * epsilon_si * epsilon_0 / q * doping_out / doping_in / (doping_in + doping_out) * (phi_0 - Vbias))</code></pre>
</details>
<div class="desc"><p>Function to calculate the depletion length in a pn junction</p>
<p>args:
- doping_in (scalar): the doping in the region for which the depletion length has to be calculated
- doping_out (scalar): the doping in the adjacent region for which the depletion length has to be calculated
- Vbias (scalar): the bias voltage of the pn junction
- temp (scalar): the temperature</p>
<p>return:
- a scalar with the depletion length calculated in one region</p></div>
</dd>
<dt id="dopes.data_analysis.diode.ideal_diode"><code class="name flex">
<span>def <span class="ident">ideal_diode</span></span>(<span>Vbias, Is, n=1, temp=300)</span>
</code></dt>
<dd>
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">def ideal_diode(Vbias,Is,n=1, temp=300):
  
    &#34;&#34;&#34; Function to calculate the current in an ideal diode 
        
        args:
            - Vbias (scalar or sequence): the bias voltage of the diode
            - Is (scalar): the saturation current of the diode
            - n (scalar): the ideality factor of the diode, 1 for radiative recombination, 2 for SRH recombination
            - temp (scalar): the temperature
                
        return:
            - a scalar or sequence with same dimension as Vbias
    &#34;&#34;&#34; 
    
    kB = 1.38e-23 # J/K
    q = 1.602e-19 # C

    return Is * (np.exp(q * Vbias / (n * kB * temp)) -1 )</code></pre>
</details>
<div class="desc"><p>Function to calculate the current in an ideal diode </p>
<p>args:
- Vbias (scalar or sequence): the bias voltage of the diode
- Is (scalar): the saturation current of the diode
- n (scalar): the ideality factor of the diode, 1 for radiative recombination, 2 for SRH recombination
- temp (scalar): the temperature</p>
<p>return:
- a scalar or sequence with same dimension as Vbias</p></div>
</dd>
<dt id="dopes.data_analysis.diode.j_radiative"><code class="name flex">
<span>def <span class="ident">j_radiative</span></span>(<span>Vbias, mu_n, mu_p, tau_n, tau_p, ND, NA, ln, lp, temp=300)</span>
</code></dt>
<dd>
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">def j_radiative(Vbias,mu_n,mu_p,tau_n,tau_p,ND,NA,ln,lp,temp=300):
    &#34;&#34;&#34; Function to calculate the radial contribution to the current density in a silicon pn junction
        
        args:
            - Vbias (scalar): the bias voltage of the pn junction
            - mu_n (scalar): the mobility of the electrons
            - mu_p (scalar): the mobility of the holes
            - tau_n (scalar): the lifetime of the electrons
            - tau_p (scalar): the lifetime of the holes
            - ND (scalar): the donor doping concentration in the n region 
            - NA (scalar): the acceptor doping concentraion in the p region 
            - ln (scalar): the length of the cathode (n-doped region)
            - lp (scalar): the length of the anode (p-doped region)
            - temp (scalar): the temperature

        return:
            - a scalar with the radiative current density calculated 
    &#34;&#34;&#34;  
    b_rad = 4.76e-15 # cm3/s - low-impurity value entre 1 et 10

    kB = 1.38e-23 # J/K
    q = 1.602e-19 # C

    Dn = kB * temp / q * mu_n
    Dp = kB * temp / q * mu_p
    
    Ln = np.sqrt( Dn * tau_n )
    Lp = np.sqrt( Dp * tau_p )
    
    ld_n = depletion_length(ND, NA, Vbias)
    ld_p = depletion_length(NA, ND, Vbias)
    
    ni = sc.intrinsic_concentration(temp)
    n_p0=ni**2/NA
    p_n0=ni**2/ND
        
    coeff_radial = Dn * n_p0 / Ln / np.tanh( (lp-ld_p) / Ln ) + Dp * p_n0 / Lp / np.tanh( (ln-ld_n) / Lp ) + ni**2 *b_rad* (ld_p + ld_n)
    
    
    return q * ( coeff_radial * (np.exp(q * Vbias/ ( kB * temp)) - 1 ) )</code></pre>
</details>
<div class="desc"><p>Function to calculate the radial contribution to the current density in a silicon pn junction</p>
<p>args:
- Vbias (scalar): the bias voltage of the pn junction
- mu_n (scalar): the mobility of the electrons
- mu_p (scalar): the mobility of the holes
- tau_n (scalar): the lifetime of the electrons
- tau_p (scalar): the lifetime of the holes
- ND (scalar): the donor doping concentration in the n region
- NA (scalar): the acceptor doping concentraion in the p region
- ln (scalar): the length of the cathode (n-doped region)
- lp (scalar): the length of the anode (p-doped region)
- temp (scalar): the temperature</p>
<p>return:
- a scalar with the radiative current density calculated</p></div>
</dd>
<dt id="dopes.data_analysis.diode.j_srh"><code class="name flex">
<span>def <span class="ident">j_srh</span></span>(<span>Vbias, ND, NA, tau=1e-07, temp=300)</span>
</code></dt>
<dd>
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">def j_srh(Vbias,ND,NA,tau=1e-7,temp=300):
    &#34;&#34;&#34; Function to calculate the Shockley-Read-Hall contribution to the current density in a pn junction
        
        args:
            - Vbias (scalar): the bias voltage of the pn junction
            - ND (scalar): the donor doping concentration in the n region 
            - NA (scalar): the acceptor doping concentraion in the p region 
            - tau (scalar): the global lifetime associated to the SRH mechanism
            - temp (scalar): the temperature

        return:
            - a scalar with the SRH current density calculated 
    &#34;&#34;&#34;  
    kB = 1.38e-23 # J/K
    q = 1.602e-19 # C

    ld_n = depletion_length(ND, NA, Vbias)
    ld_p = depletion_length(NA, ND, Vbias)
    ni = sc.intrinsic_concentration(temp)
    x=(ld_p + ld_n) # approximation by considering only the depletion region without diffusion mechanism, gives an upper limit as the effective length is always below
    
    coeff_SRH = q * ni * x / (2 * tau)
    
    return ( coeff_SRH * (np.exp(q * Vbias/ (2 * kB * temp)) - 1 ) )</code></pre>
</details>
<div class="desc"><p>Function to calculate the Shockley-Read-Hall contribution to the current density in a pn junction</p>
<p>args:
- Vbias (scalar): the bias voltage of the pn junction
- ND (scalar): the donor doping concentration in the n region
- NA (scalar): the acceptor doping concentraion in the p region
- tau (scalar): the global lifetime associated to the SRH mechanism
- temp (scalar): the temperature</p>
<p>return:
- a scalar with the SRH current density calculated</p></div>
</dd>
<dt id="dopes.data_analysis.diode.two_diodes"><code class="name flex">
<span>def <span class="ident">two_diodes</span></span>(<span>Vbias, Is1, Is2, n1=1, n2=2, temp=300)</span>
</code></dt>
<dd>
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">def two_diodes(Vbias,Is1,Is2,n1=1,n2=2, temp=300):
    &#34;&#34;&#34; Function to calculate the current for a two diodes model 
        
        args:
            - Vbias (scalar or sequence): the bias voltage of the diode
            - Is1 (scalar): the saturation current of the first diode
            - Is2 (scalar): the saturation current of the second diode
            - n1 (scalar): the ideality factor of the first diode, 1 for radiative recombination, 2 for SRH recombination
            - n1 (scalar): the ideality factor of the second diode, 1 for radiative recombination, 2 for SRH recombination
            - temp (scalar): the temperature
                
        return:
            - a scalar or sequence with same dimension as Vbias
    &#34;&#34;&#34; 
    kB = 1.38e-23 # J/K
    q = 1.602e-19 # C

    return Is1 * (np.exp( q * Vbias / (n1 * kB * temp)) -1 ) + Is2 * (np.exp( q * Vbias / (n2 * kB * temp)) -1 )</code></pre>
</details>
<div class="desc"><p>Function to calculate the current for a two diodes model </p>
<p>args:
- Vbias (scalar or sequence): the bias voltage of the diode
- Is1 (scalar): the saturation current of the first diode
- Is2 (scalar): the saturation current of the second diode
- n1 (scalar): the ideality factor of the first diode, 1 for radiative recombination, 2 for SRH recombination
- n1 (scalar): the ideality factor of the second diode, 1 for radiative recombination, 2 for SRH recombination
- temp (scalar): the temperature</p>
<p>return:
- a scalar or sequence with same dimension as Vbias</p></div>
</dd>
<dt id="dopes.data_analysis.diode.two_diodes_with_resistances"><code class="name flex">
<span>def <span class="ident">two_diodes_with_resistances</span></span>(<span>Vbias, Is1, Is2, n1=1, n2=2, temp=300, Rs=0, Rsh=inf)</span>
</code></dt>
<dd>
<details class="source">
<summary>
<span>Expand source code</span>
</summary>
<pre><code class="python">def two_diodes_with_resistances(Vbias,Is1,Is2,n1=1,n2=2, temp=300, Rs=0, Rsh=float(&#34;inf&#34;)):
    &#34;&#34;&#34; Function to calculate the current for a two diodes model by taking into account the series and shunt resistances
        
        args:
            - Vbias (scalar or sequence): the bias voltage of the diode
            - Is1 (scalar): the saturation current of the first diode
            - Is2 (scalar): the saturation current of the second diode
            - n1 (scalar): the ideality factor of the first diode, 1 for radiative recombination, 2 for SRH recombination
            - n1 (scalar): the ideality factor of the second diode, 1 for radiative recombination, 2 for SRH recombination
            - temp (scalar): the temperature
            - Rs (scalar): the serie resistance 
            - Rsh (scalar): the shunt resistance 
                
        return:
            - a scalar or sequence with same dimension as Vbias
    &#34;&#34;&#34; 
    
    kB = 1.38e-23 # J/K
    q = 1.602e-19 # C
    

    if isinstance(Vbias, (int,float)):
        # x0=np.min((two_diodes(Vbias,Is1,Is2,n1,n2, temp),Vbias/Rs))
        I = fsolve(lambda x:Is1 * (np.exp( q * (Vbias - Rs * x) / (n1 * kB * temp)) -1 ) + Is2 * (np.exp( q * (Vbias - Rs * x) / (n2 * kB * temp)) -1 ) + (Vbias - Rs * x ) / Rsh - x,x0=0)
    else:
        I=np.zeros(len(Vbias))
        i=0
        i=0
        for v in Vbias:
            # x0=np.min((two_diodes(v,Is1,Is2,n1,n2, temp),v/Rs))
            I[i] = fsolve(lambda x : Is1 * (np.exp( q * (v - Rs * x) / (n1 * kB * temp)) -1 ) + Is2 * (np.exp( q * (v - Rs * x) / (n2 * kB * temp)) -1 ) + (v - Rs * x ) / Rsh - x,x0=0)
            i+=1
    return I</code></pre>
</details>
<div class="desc"><p>Function to calculate the current for a two diodes model by taking into account the series and shunt resistances</p>
<p>args:
- Vbias (scalar or sequence): the bias voltage of the diode
- Is1 (scalar): the saturation current of the first diode
- Is2 (scalar): the saturation current of the second diode
- n1 (scalar): the ideality factor of the first diode, 1 for radiative recombination, 2 for SRH recombination
- n1 (scalar): the ideality factor of the second diode, 1 for radiative recombination, 2 for SRH recombination
- temp (scalar): the temperature
- Rs (scalar): the serie resistance
- Rsh (scalar): the shunt resistance </p>
<p>return:
- a scalar or sequence with same dimension as Vbias</p></div>
</dd>
</dl>
</section>
<section>
</section>
</article>
<nav id="sidebar">
<div class="toc">
<ul></ul>
</div>
<ul id="index">
<li><h3>Super-module</h3>
<ul>
<li><code><a title="dopes.data_analysis" href="index.html">dopes.data_analysis</a></code></li>
</ul>
</li>
<li><h3><a href="#header-functions">Functions</a></h3>
<ul class="">
<li><code><a title="dopes.data_analysis.diode.depletion_length" href="#dopes.data_analysis.diode.depletion_length">depletion_length</a></code></li>
<li><code><a title="dopes.data_analysis.diode.ideal_diode" href="#dopes.data_analysis.diode.ideal_diode">ideal_diode</a></code></li>
<li><code><a title="dopes.data_analysis.diode.j_radiative" href="#dopes.data_analysis.diode.j_radiative">j_radiative</a></code></li>
<li><code><a title="dopes.data_analysis.diode.j_srh" href="#dopes.data_analysis.diode.j_srh">j_srh</a></code></li>
<li><code><a title="dopes.data_analysis.diode.two_diodes" href="#dopes.data_analysis.diode.two_diodes">two_diodes</a></code></li>
<li><code><a title="dopes.data_analysis.diode.two_diodes_with_resistances" href="#dopes.data_analysis.diode.two_diodes_with_resistances">two_diodes_with_resistances</a></code></li>
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